Managerial Economics: Applications, Strategy, and Tactics, 8th Edition
by
McGuigan, Moyer, & Harris
prepared by
Richard D. Marcus
University of Wisconsin - Milwaukee
Ó1999 South-Western College Publishing
Chapter 1
Introduction to Managerial Economics
Structure of Decision Models
Profit’s Role
Agency Problems & Solutions
Not-for-Profit Organizations
Why Corporations Have Succeeded Over Other Organizational Forms
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Managerial Economics:
An Applied Course
Integrates the use of economics, math, and financial analysis to make good business decisions
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TOPICS
Demand and Supply Analysis
and how to estimated elasticities
Production and Cost Analysis
and how to estimate relationships
Monopoly, Competition, and Oligopolies
and good pricing decisions
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Economic Decisions
Constraints -- limitations of time, energy, money, productive capacity, regulatory climate, etc.
Information -- forecasting, relationships, expectations, possible retaliation by rivals, etc.
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CONSTRAINTS
INFORMATION
GOALS & OBJECTIVES
Objectives of the Firm
Profit maximization
Shareholder wealth
The value of the firm, V, is the present value of expected future profits (p) or cash flows, discounted at the shareholders required rate of return, ke, ignoring taxes. ¥
V = S p t /(1+ke) t
t=1
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Goals or Objectives
Maximize Present Value of Profits =
N
S (Revenuet - Costst) / (1+ke)t
t=1
Decision Model Language:
Objective Function = sets up the goals & the constraints
Decision Rule = shows what is optimal
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EXAMPLE: MAX P { A, B }
simple objective function, simple decision rule
Pick A if profit {A} > profit {B}, otherwise pick B.
Max Profit { Q} for a competitive firm
produce where P = MC
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MC
P
Q
Profit = TR - TC =
P•Q - TC
Q-
Q+
To make good economic decisions, managers need to be able to forecast & estimate relationships
Will forecast demand
applies to for-profit corporations
non-profit organizations
Hospital Administrators -- # patients
University Administrator -- enrollment
Will use regression analysis, time series methods, and qualitative forecasting methods
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The Role of Profits
Economic Cost (or opportunity cost) is the highest valued benefit that must be sacrificed as a result of choosing an alternative.
Economic profit is the difference between revenues and total economic cost (including the economic or opportunity cost of owner supplied resources such as time and capital.
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Theories of Why Profit Varies Across Industries
RISK-BEARING THEORY OF PROFIT
DYNAMIC EQUILIBRIUM (OR FRICTIONAL) THEORY OF PROFIT
MONOPOLY THEORY OF PROFIT
INNOVATION THEORY OF PROFIT
MANAGERIAL EFFICIENCY THEORY OF PROFIT
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Agency Problems
Modern corporations allow managers to have no, or limited, ownership participation in the profitability of the firm.
Shareholders may want profits, but managers may wish to relax.
The shareholders are principals, whereas the managers are agents.
Conflicting motivations between these groups are called agency problems.
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The Principal-Agent Problem
Shareholders (principals) want profit
Managers (agents) want leisure & security
Examples
The LBO by . Scott from ITT improved Scott’s performance
KKR’s takeover of RJR Nabisco to refocus on wealth-maximization
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Solutions to Agency Problems
Compensation as incentive
Extending to all workers stock options, bonuses, and grants of stock
Help make workers act as owners of firm
Incentives to help the company, because that improves the value of stock options and bonuses.
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Shareholder Wealth Maximization: Conditions
COMPLETE MARKETS - liquid markets for firm's inputs and by-products (including polluting by-products).
NO SIGNIFICANT ASYMMETRIC INFORMATION - buyers and sellers all know the same things.
KNOWN RECONTRACTING COSTS future input costs are part of the present value of expected cash flows.
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Goals in the Public Sector and the
Not-For-Profit (NFP) Enterprise
Instead of profit, NFP organizations may have as their goals:
a. Maximization of the quantity of output, subject to a breakeven constraint.
b. Maximization of the utility (happiness) of NFP administrators.
c. Maximization of cash flows.
d. Maximization of the utility of contributors to the NFP organization.
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Which goal a NFP manager selects affects the types of decisions made.
A manager of a food shelter may decide to maximize the utility of contributors by selecting only "healthy foods"
Public sector managers are frequently monitored with regard to how they perform their jobs.
If a . hospital administrator is rewarded by reducing the cost per bed over a year, then the administrator may become quite efficient with respect to costs.
However, the "friendliness" of the hospital staff is harder to measure, so friendliness will tend not be a high priority of the public sector manager.
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Firms vs. Household Production
Business classes presume production in firms
We can & do produce things at home
Suppose all goods produced in households
Limited by size of household
Suppose there exist some economies of scale in organizational size
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Two households merge
if more productive, other households emulate
Four households merge
if true for 2, why not true for 2 million households merging?
problems arise as the size of the collective grows
Less Personal Incentives
Who is in Charge?
Disagreements & Conflict Resolution Issues
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Entrepreneurship
Synonym is CONTRACTOR
contractor monitors production
hires labor at fixed rates
purchases materials
receives the residual
This is a firm —contractor - entrepreneur
87% of all production by corporations
remaining 13% in proprietorships & other
The Corporation has demonstrated its resiliency over time.
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Fundamental Economic Concepts
Chapter 2
Total, Average, and Marginal
Equations and Finding the Optimum Point
Present Value, Discounting & NPV
Risk-Return & Probability
Use of a z-value
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How to Maximize Profits
Decision Making Isn’t Free
Max Profit { A, B}, but suppose that we don’t know Profit {A} or the Profit {B}
Should we hire a consultant for $1,000?
Should we market an Amoretto Flavored chewing gum for adults?
complex combination of marketing, production, and financial issues
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Break Decisions Into Smaller Units: How Much to Produce ?
Graph of output and profit
Possible Rule:
Expand output until profits turn down
But problem of local maxima vs. global maximum
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quantity B
MAX
GLOBAL
MAX
profit
A
Average Profit = Profit / Q
Slope of ray from the origin
Rise / Run
Profit / Q = average profit
Maximizing average profit doesn’t maximize total profit
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MAX
C
B
profits
Q
PROFITS
quantity
Marginal Profits = DP/DQ
profits of the last unit produced
maximum marginal profits occur at the inflection point (A)
Decision Rule: produce where marginal profits = 0.
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profits
max
A
marginal
profits
Q
Q
average
profits
B
C
Using Equations
profit = f(quantity) or
P = f(Q)
dependent variable & independent variable(s)
average profit = P/Q
marginal profit = DP / DQ
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Optimal Decision (one period)
example of using marginals
The scale of a project should expand until
MB = MC
Example: screening for prostate or breast cancer
How often?
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MB
MC
frequency per decade
Present Value
Present value recognizes that a dollar received in the future is worth less than a dollar in hand today.
To compare monies in the future with today, the future dollars must be discounted by a present value interest factor, PVIF= 1/(1+i), where i is the interest compensation for postponing receiving cash one period.
For dollars received in n periods, the discount factor is PVIFn =[1/(1+i)]n
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Net Present Value, NPV = Present value of future returns minus Initial outlay. This is for the simple example of a single cost today yielding a benefit or stream of benefits in the future.
For the more general case, NPV = Present value of all cash flows (both positive and negative ones).
NPV Rule: Do all projects that have positive net present values. By doing this, the manager maximizes shareholder wealth.
Some investments may increase NPV, but at the same time, they may increase risk.
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Net Present Value (NPV)
Most business decisions are long term
capital budgeting, product assortment, etc.
Objective: max the present value of profits
NPV = PV of future returns - Initial Outlay
NPV = St=0 NCFt / ( 1 + rt )t
where NCFt is the net cash flow in period t
Good projects have
High NCF’s
Low rates of discount
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Sources of Positive NPVs
Brand identify and loyalty
Control over distribution
Patents or legal barriers to entry
Superior materials
Difficulty for others to acquire factors of production
Superior financial resources
Economies of large scale or size
Superior management
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Most decisions involve a gamble
Probabilities can be known or unknown, and outcomes can be known or unknown
Risk -- exists when:
Possible outcomes and probabilities are known
., roulette wheel or dice
Uncertainty -- exists when:
Possible outcomes or probabilities are unknown
., drilling for oil in an unknown field
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Risk and Uncertainty
Concepts of Risk
When probabilities are known, we can analyze risk using probability distributions
Assign a probability to each state of nature, and be exhaustive, so that S pi = 1
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States of Nature
Strategy Recession Economic Boom
p = .30 p = .70
Expand Plant - 40 100
Don’t Expand - 10 50
Payoff Matrix
Payoff Matrix shows payoffs for each state of nature, for each strategy
Expected Value = r = S pi ri .
r = S piri = .30(-40) + .70(100) = 58 if Expand
r = S piri = .30(-10) + .70(50) = 32 if Don’t Expand
Standard Deviation = s = Ö S pi (ri - r ) 2.
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^
^
^
^
Example of
Finding Standard Deviations
sexpand = SQRT{ .3(-40 - 58)2 + .7(100 - 58)2 } = SQRT{ .3(-98)2 + .7(42)2 } = SQRT{ 4116} =
sdon’t = SQRT{ .3(-10 - 32)2 + .7(50 - 32)2 } = SQRT{ .3(-42)2 + .7(18)2 } =SQRT { 756} =
Expanding has a greater standard deviation, but higher expected return.
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Coefficients of Variation
or Relative Risk
Coefficient of Variation (.) = s / r
. is a measure of risk per dollar of expected return.
The discount rate for present values depends on the risk class of the investment.
Look at similar investments
Corporate Bonds, or Treasury Bonds
Common Domestic Stocks, or Foreign Stocks
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^
Projects of Different Sizes:
If double the size, the . is not changed!!!
Coefficient of Variation is good for comparing projects of different sizes
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Example of Two Gambles
A: Prob X } R = 15
.5 10 } s = SQRT{.5(10-15)2 +(20-15)2(.5)}
.5 20 } = SQRT{25} = 5
. = 5 / 15 = .333
B: Prob X } R = 30
.5 20 } s = SQRT{.5(20-30)2 +(40-30)2(.5)}
.5 40 } = SQRT{100} = 10
. = 10 / 30 = .333
Continuous Probability Distributions (vs. Discrete)
Expected valued is the mode for symmetric distributions
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RA
RB
A
B
A is riskier, but
it has a higher
expected value
^
^
z-Values
z is the number of standard deviations away from the mean
z = (r - r )/ s
68% of the time within 1 standard deviation
95% of the time within 2 standard deviations
99% of the time within 3 standard deviations
Problem: income has mean $1,000 and a standard deviation of $500.
What’s the chance of losing money?
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^
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STOCK RETURNS 1970-1995
in US Dollars
Annual% Std Dev%
Australia
Canada
France
Germany
Hong Kong
Italy
Japan
Mexico
Netherlands
Singapore
U. Kingdom
U. States
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Australia Belgium Canada France Germany
return % % % % %
std dev % % % % %
Netherlands New Zealand Ireland Italy Japan
return % % % % %
std dev % % % % %
South Africa Sweden Swiss England USA
return % % % % %
std dev % % % % %
BOND RETURNS: 1967 - 1995
in US Dollars
Chapter 3
Optimization Techniques
Overview
Unconstrained & Constrained Optimization
Calculus of one variable
Partial Differentiation in Economic Problems
Appendix 3A: Lagrangians and Constrained Optimization
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Optimum Can Be Highest or Lowest
Finding the maximum flying range for the Stealth Bomber is an optimization problem.
Calculus teaches that when the first derivative is zero, the solution is at an optimum.
The original Stealth Bomber study showed that a controversial flying V-wing design optimized the bomber's range, but the original researchers failed to find that their solution in fact minimized the range.
It is critical that managers make decision that maximize, not minimize, profit potential!
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Unconstrained Optimization
Unconstrained Optimization is a relatively simple calculus problem that can be solved using differentiation, such as finding the quantity that maximizes profit in the function:
p(Q) = 16·Q - Q2
The answer is Q = 8, as we will see.
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Constrained Optimization
Constrained Optimization involves one or more constraints of money, time, capacity, or energy.
When there are inequality constraints (as when you must spend less than or equal to your total income), linear programming can be used.
Most often, managers know that some constraints are binding, which means that they are equality constraints. Lagrangian multipliers are used to solve these problems. (see Appendix 3A).
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Optimization Format
Economic problems require tradeoffs forced on
us by the limits of our money, time, and energy.
Optimization involves an objective function
and one or more constraints, b.
Maximize y = f(x1 , x2 , ..., xn )
Subject to g(x1 , x2 , ..., xn ) < b
or: Minimize y = f(x1 , x2 , ..., xn )
Subject to g(x1 , x2 , ..., xn ) > b
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Using Equations
profit = f(quantity) or P = f(Q)
dependent variable & independent variable(s)
average profit = P/Q
marginal profit = DP / DQ
Calculus uses derivatives
dP/dQ = lim DP / DQ DQ 0
SLOPE = MARGINAL = DERIVATIVE
NEW DECISION RULE: To maximize profits, find where dP/dQ = 0 -- first order condition
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Quick Differentiation Review
Constant Y = c dY/dX = 0 Y = 5
dY/dX = 0
Line Y = c•X dY/dX = c Y = 5•X
dY/dX = 5
Power Y = cXb dY/dX = b•c•X b-1 Y = 5•X2 dY/dX = 10•X
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Name Function Derivative Example
Quick Differentiation Review
Sum Rule Y = G(X) + H(X) dY/dX = dG/dX + dH/dX
example Y = 5•X + 5•X2 dY/dX = 5 + 10•X
Product Rule Y = G(X)•H(X)
dY/dX = (dG/dX)H + (dH/dX)G
example Y = (5•X)(5•X2 )
dY/dX = 5(5•X2 ) + (10•X)(5•X) = 75•X2
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Quick Differentiation Review
Quotient Rule Y = G(X) / H(X)
dY/dX = (dG/dX)•H - (dH/dX)•G H2
Y = (5•X) / (5•X2) dY/dX = 5(5•X2) -(10•X)(5•X) (5•X2)2
= -25X2 / 25•X4 = - X-2
Chain Rule Y = G [ H(X) ]
dY/dX = (dG/dH)•(dH/dX) Y = (5 + 5•X)2
dY/dX = 2(5 + 5•X)1(5) = 50 + 50•X
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Applications of Calculus in Managerial Economics
maximization problem: A profit function might look like an arch, rising to a peak and then declining at even larger outputs. A firm might sell huge amounts at very low prices, but discover that profits are low or negative.
At the maximum, the slope of the profit function is zero. The first order condition for a maximum is that the derivative at that point is zero. If p = 50·Q - Q2, then dp/dQ = 50 - 2·Q, using the rules of differentiation.
Hence, Q = 25 will maximize profits.
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More Applications of Calculus
minimization problem: Cost minimization supposes that there is a least cost point to produce. An average cost curve might have a
U-shape. At the least cost point, the slope of the cost function is zero.
The first order condition for a minimum is that the derivative at that point is zero. If C = 5·Q2 - 60·Q, then dC/dQ = 10·Q - 60.
Hence, Q = 6 will minimize cost.
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More Examples
Competitive Firm: Maximize Profits
where P = TR - TC = P•Q - TC(Q)
Use our first order condition: dP/dQ = P - dTC/dQ = 0
Decision Rule: P = MC
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a function of Q
Max P = 100•Q - Q2
100 -2•Q = 0 implies Q = 50 and P = 2,500
Max P = 50 + 5•X2
So, 10•X = 0 implies Q = 0 and P = 50
Second Order Condition:
One Variable
If the second derivative is negative, then it’s a maximum
If the second derivative is positive, then it’s a minimum
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Max P = 100•Q - Q2
100 -2•Q = 0
second derivative is: -2 implies Q =50 is a MAX
Max P = 50 + 5•X2
10•X = 0
second derivative is: 10 implies Q = 0 is a MIN
Partial Differentiation
Economic relationships usually involve several independent variables.
A partial derivative is like a controlled experiment -- it holds the “other” variables constant
., suppose price is increased, holding the disposable income of the economy constant Q = f (P, I ) ¶Q/¶P holds income constant
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Problem:
Sales are a function of advertising in newspapers and magazines ( X, Y)
Max S = 200X + 100Y -10X2 -20Y2 +20XY
Differentiate with respect to X and Y and set equal to zero.
¶S/¶X = 200 - 20X + 20Y= 0
¶S/¶Y = 100 - 40Y + 20X = 0
solve for X & Y and Sales
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Solution: 2 equations & 2 unknowns
200 - 20X + 20Y= 0
100 - 40Y + 20X = 0
Adding them, the -20X and +20X cancel, so we get 300 - 20Y = 0, or Y =15
Plug into one of them: 200 - 20X + 300 = 0, hence X = 25
To find Sales, plug into equation: S = 200X + 100Y -10X2 -20Y2 +20XY = 3,250
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International Import Restraints
Import quotas of Japanese automobiles are inequality constraints. The added constraint will affect decisions.
A Japanese manufacturer will shift more production to . assembly facilities and increase the price of cars exported to the .
We may also expect that the exported cars will be "top of the line" models, and we expect . manufacturers to raise domestic car prices.
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Appendix 3A: Lagrangians
Objective functions are often constrained by one or more “constraints” (time, capacity, or money)
Max L = (objective fct.) - l{constraint set to zero}
Min L = (objective fct.) +l{constraint set to zero}
An artificial variable is created for each constraint in the Lagrangian multiplier technique. This artificial variable is traditionally called lambda, l.
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Maximize Utility Example
example: Max Utility subject to a money constraint
Max U = X•Y2 subject to a $12 total budget with the prices of X as $1, the price of Y as $4 (suppose X represents soda and Y, movie tickets).
Max L = X•Y2 - l { X + 4Y - 12}
differentiate X, Y and lambda, l.
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¶L/¶X = Y2 - l = 0 Y2 = l
¶L/¶Y = 2XY - 4l = 0 2XY = 4l
¶L/¶l = X + 4Y- 12 = 0
Three equations and three unknowns
Solve: Ratio of first two equations is:
Y/2X = 1/4 or Y = .5 X. Substitute into the third equation: We get:
X = 4; Y = 2; and l = 4
Lambda is the marginal (objective function) of the (constraint).
Here, l = the marginal utility of money.
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Problem
Minimize Crime in your town
Police, P, costs $15,000 each.
Jail, J, costs $10,000 each.
Budget is $900,000.
Crime function is estimated: C = 5600 - 4PJ
Set up the problem as a Lagrangian
Solve for optimal P and J, and C
What is economic meaning of lambda?
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Answer
Min L= 5600 - 4PJ + l{15,000•P + 10,000•J -900,000 }
To Solve, differentiate
1. ¶L/¶P: - 4•J +15,000•l = 0
2. ¶L/¶J: - 4•P +10,000•l = 0
3. ¶L/¶l : 15,000•P +10,000•J -900,000 =0
J/P = so J = •P & substitute into (3.)
15,000•P +10,000•[•P] - 900,000 = 0
solution: P = 30, J = 45, C = 200 and l =
Lambda is the marginal crime (reduction) for a dollar of additional budget spent
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DEMAND ANALYSIS
Chapter 4
OVERVIEW
Demand Relationships
Demand Elasticities
Income Elasticities
Cross Elasticities of Demand
Appendix 4A: Indifference Curves
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Demand Analysis
An important contributor to firm risk arises from sudden shifts in demand for the product or service.
Demand analysis serves two managerial objectives:
(1) it provides the insights necessary for effective management of demand, and
(2) it aids in forecasting sales and revenues.
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Demand Curves
Individual Demand Curve - the greatest quantity of a good demanded at each price the consumers are willing to buy, ceteris paribus.
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Willing to
Buy
Unwilling to
Buy
$/Q
Q/time unit
The Market Demand Curve is the horizontal sum of the individual demand curves.
The Demand Function includes all variables that influence the quantity demanded
4 3 7
Sam Diane Market
Q = f( P, Ps, Pc, I, W, E)
+ + - ? ? +
Supply Curves
Firm Supply Curve - the greatest quantity of a good supplied at each price the firm is profitably able to supply, ceteris paribus.
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$/Q
Q/time unit
Able to
Produce
Unable to
Produce
The Market Supply Curve is the horizontal sum of the firm supply curves.
The Supply Function includes all variables that influence the quantity supplied
4 3 7
Acme Universal Market
Q = g( P, W, R, TC)
+ - - +
Equilibrium: No Tendency to Change
Superimpose demand and supply
If No Excess Demand
and No Excess Supply
No tendency to change
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D
S
Pe
willing
& able
Q
P
Downward Slope
Price and quantity are negatively related Some reasons include:
income effect--as the price of a good declines, the consumer can purchase more of all goods since his or
her real income increased.
substitution effect--as the price declines, the good becomes relatively cheaper. A rational consumer maximizes satisfaction by reorganizing consumption until the marginal utility in each good per dollar is equal:
Optimality Condition is MUA/PA = MUB/PB = MUC/PC = ...
If MU per dollar in A and B differ, the consumer can improve utility by purchasing more of the one with higher MU per dollar.
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Comparative Statics
& the Supply-Demand Model
Suppose a shift in Income, and the good is a “normal” good
Does demand or supply shift?
Suppose wages rose, what then?
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D
S
e1
P
Q
Elasticity as Sensitivity
Elasticity is measure of responsiveness or sensitivity
Beware of using slopes
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bushels hundred tons
price price
per per
bu. bu
Slopes
change
with a
change in
units of
measure
Price Elasticity
E P = % change in Q / % change in P
Shortcut notation: E P = %DQ / %DP
A percentage change from 100 to 150
A percentage change from 150 to 100
Arc Price Elasticity -- averages over the two points
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D
arc price
elasticity
Arc Price Elasticity Example
Q = 1000 at a price of $10
Then Q= 1200 when the price was cut to $6
Find the price elasticity
Solution: E P = %DQ/ %DP = +200/1100 - 4 / 8
or . The answer is a number. A 1% increase in price reduces quantity by .36 percent.
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Point Price Elasticity Example
Need a demand curve or demand function to find the price elasticity at a point.
E P = %DQ/ %DP =( ¶Q/¶P)(P/Q)
If Q = 500 - 5•P, find the point price elasticity at P = 30; P = 50; and P = 80
E Q•P = ( ¶Q/¶P)(P/Q) = - 5(30/350) = - .43
E Q•P = ( ¶Q/¶P)(P/Q) = - 5(50/250) = -
E Q•P = ( ¶Q/¶P)(P/Q) = - 5(80/100) = -
Price Elasticity (both point price and arc elasticity )
If E P = -1, unit elastic
If E P > -1, inelastic, ., -
If E P < -1, elastic, .,
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price
elastic region
unit elastic
inelastic region
Straight line
demand curve
TR and Price Elasticities
If you raise price, does TR rise?
Suppose demand is elastic, and raise price. TR = P•Q, so, %DTR = %DP+ %DQ
If elastic, P , but Q a lot
Hence TR FALLS !!!
Suppose demand is inelastic, and we decide to raise price. What happens to TR and TC and profit?
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Another Way to Remember
Linear demand curve
TR on other curve
Look at arrows to see movement in TR
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Elastic
Unit Elastic
Inelastic
TR
Q
Q
1979 Deregulation of Airfares
Prices declined
Passengers increased
Total Revenue Increased
What does this imply about the price elasticity of air travel ?
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Determinants of the Price Elasticity
The number of close substitutes
more substitutes, more elastic
The proportion of the budget
larger proportion, more elastic
The longer the time period permitted
more time, generally, more elastic
consider examples of business travel versus vacation travel for all three above.
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Income Elasticity
E I = %DQ/ %DI =( ¶Q/¶ I)( I / Q)
arc income elasticity:
suppose dollar quantity of food expenditures of families of $20,000 is $5,200; and food expenditures rises to $6,760 for families earning $30,000.
Find the income elasticity of food
%DQ/ %DI = (1560/5980)•(10,000/25,000) = .652
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Definitions
If E I is positive, then a normal good
some goods are Luxuries: E I > 1
some goods are Necessities: E I < 1
If E Q•I is negative, then an inferior good
consider:
Expenditures on automobiles
Expenditures on Chevrolets
Expenditures on 1991 Chevy Cavalier
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Point Income Elasticity Problem
Suppose the demand function is:
Q = 10 - 2•P + 3•I
find the income and price elasticities at a price of P = 2, and income I = 10
So: Q = 10 -2(2) + 3(10) = 36
E I = ( ¶Q/¶ I)( I/Q) = 3( 10/ 36) = .833
E P = ( ¶Q/¶ P)(P/Q) = -2(2/ 36) =
Characterize this demand curve !
Ó1999 South-Western College Publishing
Cross Price Elasticities
E X = %DQx / %DPy = ( ¶Qx/¶ Py)(Py / Qx)
Substitutes have positive cross price elasticities: Butter & Margarine
Complements have negative cross price elasticities: VCR machines and the rental price of tapes
When the cross price elasticity is zero or insignificant, the products are not related
Ó1999 South-Western College Publishing
HOMEWORK PROBLEM:
Find the point price elasticity, the point income elasticity, and the point cross-price elasticity at P=10, I=20, and Ps=9, if the demand function were estimated to be: Qd = 90 - 8·P + 2·I + 2·Ps
Is the demand for this product elastic or inelastic? Is it a luxury or a necessity? Does this product have a close substitute or complement? Find the point elasticities of demand.
Ó1999 South-Western College Publishing
Indifference Curve Analysis
Appendix 4A
Consumers attempt to max happiness, or utility: U(X, Y)
Subject to an income constraint:
I = Px•X + Py•Y
Graph in 3-dimensions
Ó1999 South-Western College Publishing
Y
X
U
Uo
Uo
Consumer Choice - assume consumers can rank preferences, that more is better than less (nonsatiation), that preferences are transitive, and that individuals have diminishing marginal rates of substitution.
Then indifference curves slope down, never intersect, and are convex to the origin.
Ó1999 South-Western College Publishing
X
Y
5 6 7
9
7
6
convex
Uo
U1
U2
give up 2X for a Y
Ó1999 South-Western College Publishing
X
Y
Y
Uo U1
a
c
demand
b
Indifference Curves
• We can "derive" a demand curve graphically from maximization of utility subject to a budget constraint. As price falls, we tend to buy more due to (i) the Income Effect and (ii) the Substitution Effect.
Py
Consumer Choice & Lagrangians
The consumer choice problem can be made into a Lagrangian
Max L = U(X, Y) - l {Px•X + Py•Y - I }
i) ¶L / ¶X = ¶U/¶X - l Px = 0 MUx = Px
ii) ¶L / ¶Y = ¶U/¶Y - l Py = 0 MUy = Py
iii) Px•X + Py•Y - I = 0
Equations i) and ii) are rearranged on the right-hand side after the bracket to show that the ratio of MUs equals the ratio of prices. This is the equi-marginal principle for optimal consumption.
Ó1999 South-Western College Publishing
}
Optimal Consumption Point
Rearranging we get the Decision Rule:
MUx / Px = MUy / Py = MUz / Pz
“the marginal utility per dollar in each use is equal”
Lambda is the marginal utility of money
Suppose MU1 = 20, and MU2 = 50
and P1 = 5, and P2 = 25
are you maximizing utility?
Ó1999 South-Western College Publishing
Problem
Max L = 2X + 2Y +XY - .6Y2 - l {48 - 4X - 6Y }
1. Lx: 2 - X + Y = 4 l
2. Ly: 2 + X - = 6 l
3. Ll: 48 - 4X - 6Y = 0
(1) and (2) yields: X = •Y + .4
(3) can be reduced to X = 12
Together we get: X = , Y =
Substitute X and Y into (1) we find l = .31
Ó1999 South-Western College Publishing
X = •Y + .4
Estimation of Demand
Chapter 5
Objective: Learn how to estimate a demand function using regression analysis, and interpret the results
A chief uncertainty for managers -- what will happen to their product.
forecasting, prediction & estimation
need for data: Frank Knight: “If you think you can’t measure something, measure it anyway.”
Ó1999 South-Western College Publishing
Sources of information on demand
Consumer Surveys
ask a sample of consumers their attitudes
Consumer Clinics
experimental groups try to emulate a market (Hawthorne effect)
Market Experiments
get demand information by trying different prices
Historical Data
what happened in the past is guide to the future
Plot Historical Data
Look at the relationship of price and quantity over time
Plot it
Is it a demand curve or a supply curve?
Problem -- not held other things equal
Ó1999 South-Western College Publishing
quantity
Price
92
97
94
93
96
98
95
D? or S?
Identification Problem
Q = a + b P can appear upward or downward sloping.
Suppose supply varies and demand is FIXED.
All points lie on the demand curve
Ó1999 South-Western College Publishing
|____________________________Quantity
quantity
P
S1
S2
S3
Demand
Suppose SUPPLY is Fixed
Let DEMAND shift and supply be FIXED.
All points are on the SUPPLY curve.
We say that the SUPPLY curve
is identified.
Ó1999 South-Western College Publishing
quantity
P
D1
D2
D3
Supply
When both Supply
and Demand Vary
Often both supply and demand vary.
Equilibrium points are in shaded region.
A regression of Q = a + b P will be neither a demand nor a supply curve.
Ó1999 South-Western College Publishing
quantity
P
D1
D2
S1
S2
Statistical Estimation of the a Demand Function
Steps to take:
Specify the variables -- formulate the demand model, select a Functional Form
linear Q = a + b•P + c•I
double log ln Q = a + b•ln P + c•ln I
quadratic Q = a + b•P + c•I+ d•P2
Estimate the parameters --
determine which are statistically significant
try other variables & other functional forms
Develop forecasts from the model
Specifying the Variables
Dependent Variable -- quantity in units, quantity in dollar value (as in sales revenues)
Independent Variables -- variables thought to influence the quantity demanded
Instrumental Variables -- proxy variables for the item wanted which tends to have a relatively high correlation with the desired variable: ., Tastes Time Trend
Ó1999 South-Western College Publishing
Functional Forms
Linear Q = a + b•P + c•I
The effect of each variable is constant
The effect of each variable is independent of other variables
Price elasticity is: E P = b•P/Q
Income elasticity is: E I = c•I/Q
Ó1999 South-Western College Publishing
Functional Forms
Multiplicative Q = A • P b • I c
The effect of each variable depends on all the other variables and is not constant
It is log linear Ln Q = a + b•Ln P + c•Ln I
the price elasticity is b
the income elasticity is c
Ó1999 South-Western College Publishing
Simple Linear Regression
Qt = a + b Pt + e t
time subscripts & error term
Find “best fitting” line
et = Qt - a - b Pt
et 2= [Qt - a - b Pt] 2
min S et 2= S [Qt - a - b Pt] 2
Solution: b = Cov(Q,P)/Var(P) and a = mean(Q) - b•mean(P)
Ó1999 South-Western College Publishing
_
P
Q
_
Q
OLS --
ordinary
least
squares
Ordinary Least Squares:
Assumptions & Solution Methods
error term has a mean of zero and a finite variance
dependent variable is random
the independent variables are indeed independent
Spreadsheets -
Statistical calculators
Minitab, SAS, SPSS
ForeProfit
Excel, Lotus, Quatro Pro, Joe Spreadsheet
tools/data analysis in Excel
/Data/Regression in Lotus
Ó1999 South-Western College Publishing
Demand Estimation Case (p. 181)
Riders = 785 •Price +.110•Pop +.0015•Income + .995•Parking
Predictor Coef t-ratio p
Constant .083
Price .4890 .002
Pop .1096 .2114 .520 .618
Income .0015 .03534 .040 .966
Parking .9947 .5715 .120
R-sq = % R-sq(adj) = %
Ó1999 South-Western College Publishing
Coefficients of Determination: R2
R-square -- % of variation in dependent variable that is explained ^
Ratio of S [Qt -Qt] 2 to S [Qt - Qt] 2
As more variables are included, R-square rises
Adjusted R-square, however, can decline
Ó1999 South-Western College Publishing
_
P
Q
_
Q
Qt
T-tests
Different samples would yield different coefficients
Test the hypothesis that coefficient equals zero
Ho: b = 0
Ha: b ¹ 0
RULE: If absolute value of the estimated t > Critical-t, then REJECT Ho.
It’s significant.
estimated t = (b - 0) / s b
critical t
Large Samples, critical t @ 2
N > 30
Small Samples, critical t is on Student’s t-table
. = # observations, minus number of independent variables, minus one.
N < 30
Ó1999 South-Western College Publishing
Double Log or Log Linear
With the double log form, the coefficients are elasticities !!!
Q = A • P b • I c • Ps d
multiplicative fct form
So: Ln Q = a + b•Ln P + c•Ln I + d•Ln Ps
Transform all variables into natural logs
Ó1999 South-Western College Publishing
Econometric Problems
Simultaneity Problem -- Indentification Problem:
some independent variables may be endogenous
Multicollinearity
independent variables may be highly related
Serial Correlation -- Autocorrelation
error terms may have a pattern
Heteroscedasticity
error terms may have non-constant variance
Ó1999 South-Western College Publishing
Identification Problem
Problem:
Coefficients are biased
Symptom:
Independent variables are known to be part of a system of equations
Solution:
Use as many independent variables as possible or
Use 2SLS
Ó1999 South-Western College Publishing
Multicollinearity
Sometimes independent variables aren’t independent.
EXAMPLE: Q =Eggs
Q = a + b Pd + c Pg
where Pd is for a dozen
and Pg is for a gross.
Coefficients are UNBIASED, but t-values are small.
Symptoms of Multicollinearity -- high R-sqr, but low t-values.
Q = 22 - Pd Pg
() ()
R-square = .87
t-values in parentheses
Solutions:
Drop a variable.
Do nothing if forecasting
Ó1999 South-Western College Publishing
PROBLEM
Serial Correlation
Problem:
Coefficients are unbiased
but t-values are unreliable
Symptoms:
look at a scatter of the error terms to see if there is a pattern, or
see if Durbin Watson statistic is far from 2.
Solution:
Find more data
Take first differences of data: DQ = a + b•DP
Ó1999 South-Western College Publishing
Scatter of Error Terms
Serial Correlation
Ó1999 South-Western College Publishing
Q
P
Heteroscedasticity
Problem:
Coefficients are unbiased
t-values are unreliable
Symptoms:
different variances for different sub-samples
scatter of error terms shows increasing or decreasing dispersion
Solution:
Transform data, ., logs
Take averages of each subsample: weighted least squares
Scatter of Error Terms
Heteroscedasticity
Ó1999 South-Western College Publishing
Height
AGE
1 2 5 8
alternative
log Ht = a + b•AGE
Nonlinear Forms
Appendix 5A
Semi-logarithmic transformations. Sometimes taking the logarithm of the dependent variable or an independent variable improves the R2. Examples are:
log Y = a + ß·X.
Here, Y grows
exponentially at rate
ß in X; that is, ß percent growth per period.
Y = a + ß·log X. Here, Y doubles each time X increases by the square of X.
X
Y
Ln Y = .01 + .05X
Reciprocal Transformations
The relationship between variables may be inverse. Sometimes taking the reciprocal of a variable improves the fit of the regression as in the example:
Y = a + ß·(1/X)
shapes can be:
declining slowly
if beta positive
rising slowly
if beta negative
X
Y
., Y = 500 + 2 ( 1/X)
Polynomial Transformations
Quadratic, cubic, and higher degree polynomial relationships are common in business and economics.
Profit and revenue are cubic functions of output.
Average cost is a quadratic function, as it is U-shaped
Total cost is a cubic function, as it is S-shaped
TC = a·Q + ß·Q2 + g·Q3 is a cubic total cost function.
If higher order polynomials improve the R-square, then the added complexity may be worth it.
Business and Economic Forecasting
Chapter 6
Ó1999 South-Western College Publishing
Demand Forecasting:
critical managerial activity which comes in two forms:
Qualitative Forecasting
Gives the Expected Direction
Quantitative Forecasting
Gives the precise Amount
%
Why Forecast Demand?
Both public and private enterprises operate under conditions of uncertainty.
Management wishes to limit this uncertainty by predicting changes in cost, price, sales, and interest rates.
Accurate forecasting can help develop strategies to promote profitable trends and to avoid unprofitable ones.
A forecast is a prediction concerning the future. Good forecasting will reduce, but not eliminate, the uncertainty that all managers feel.
Ó1999 South-Western College Publishing
Hierarchy of Forecasting
The selection of forecasting techniques depends in part on the level of economic aggregation involved. The hierarchy of forecasting is:
National Economy (GDP, interest rates, inflation, etc.)
sectors of the economy (durable goods)
industry forecasts (automobile manufacturers)
firm forecasts ( Ford Motor Company )
Forecasting Criteria
The choice of a particular forecasting method depends on several criteria:
costs of the forecasting method compared with its gains
complexity of the relationships among variables
time period involved
accuracy needed in forecast
lead time between receiving information and the decision to be made
Significance of Forecasting
The accuracy of a forecasting model is measured by how close the actual variable, Y, ends up to the forecasting variable, Y.
Forecast error is the difference. (Y - Y)
Models differ in accuracy, often based on the square root of the average squared forecast error over a series of N forecasts and actual figures
Called a root mean square error, RMSE.
RMSE = S (Y - Y)2 / N
Ó1999 South-Western College Publishing
^
^
^
Ó1999 South-Western College Publishing
Qualitative Forecasting
Flexibility --
easily altered as economy changes
Early Signals --
can catch changes and anomalies in data
Complex --
hard to keep track of interactions in the primary variables
Lack of Tests for Accuracy --
can’t easily test the accuracy in prior periods.
Ó1999 South-Western College Publishing
ADVANTAGES
LIMITATIONS
Quantitative Forecasting and the Use of Models
Advantages
Organize relationships
Behavioral relationships
Tests of reliability
Limitations
Economy changes
Data mining of same information
Only a crude approximation
Ó1999 South-Western College Publishing
“Economic forecasting is really the art of identifying tensions or imbalances in the economic process and understanding in what manner they will be resolved.”
Ó1999 South-Western College Publishing
I see Trouble
ahead.
Alan Greenspan --
Chairman of the Board of
Governors of the Federal
Reserve
Qualitative Forecasting
1. Comparative
Statics
Shifts in Demand
Shifts in Supply
Forecast Changes in Prices and Quantities
Suppose Income Shifts
Price Rises
Quantity Rises
quantity
P
supply
D1
D2
A
B
2. Expert Opinion
The average forecast from several experts is a Consensus Forecast.
Mean
Median
Mode
Truncated Mean
Proportion positive or negative
Ó1999 South-Western College Publishing
EXAMPLES:
IBES and Zacks Investment -- earnings forecasts of stock analysts
Conference Board -- macroeconomic predictions
Livingston Surveys--macroeconomic forecasts of 50-60 economists
Delphi Technique--panel of diverse experts.
1. Write out forecasts
2. Show them to other panelists
3. meet to arrive at consensus
Note: problems of expense and intransigence
Chicago Daily News Sportswriters
NFL predictions of 16 forecasters
Ó1999 South-Western College Publishing
The consensus predicted better over time than any 1 writer.
Year 1 Year 2 Year 3
3. Surveys
Sample bias--
telephone, magazine
Biased questions--
advocacy surveys
Ambiguous questions
Respondents may lie on questionnaires
Ó1999 South-Western College Publishing
New Products have no
historical data -- Surveys
can assess interest in new
ideas.
Survey Research Center
of U. of Mich. does repeat
surveys of households on
Big Ticket items (Autos)
Common Survey Problems
4. Economic Indicators (Barometric Forecasting)
Direction of sales can be indicated by other variables.
TIME
Index of Capital Goods
peak
PEAK
Motor Control Sales
4 Months
Example: Index of Capital Goods is a “leading indicator”
There are also lagging indicators and coincident indicators
LEADING INDICATORS*
M2 money supply ()
S&P 500 stock prices ()
New housing permits()
Initial unemployment claims ()
Orders for plant and equipment ()
COINCIDENT INDICATORS
Nonagricultural employment (+.9)
Index of industrial production ()
Personal income less transfer payment ()
LAGGING INDICATORS
Prime rate (+)
Duration of unemployment (+)
*Handbook of Cyclical Indicators, 1984
Time given in months from change
Questions
Why are contracts and orders for plant and equipment appropriate leading indicators?
Why is the index of industrial production an appropriate coincident indicator?
Why is the prime rate an appropriate lagging indicator?
Examples of Indicators
Composite Example: One indicator rises 4% and another rises 6%, the composite is a 5% increase.
Diffusion Example: Louis Rukeyser’s Eleven Elves, where 4 are negative about stocks and 7 are positive:
index is 7/11, or %
Interpreting and Using Indices
composite index - weighted average index of individual indicators
index interpreted in terms of % change
composite index of leading economic indicators: sustained increase indicates economic growth
diffusion index - measure of the proportion of individual time series that increase
for diffusion index of leading economic indicators, if index > 50%, improved conditions are expected
Ó1999 South-Western College Publishing
Quantitative Forecasting
Time Series
Looks For Patterns
Ordered by Time
No Underlying Structure
Econometric Models
Explains relationships
Supply & Demand
Regression Models
Ó1999 South-Western College Publishing
Like technical
security analysis
Like fundamental
security analysis
Ó1999 South-Western College Publishing
Time Series Examine Patterns in the Past
TIME
To
X
X
X
Dependent Variable
Time Series
is a quantitative forecasting method
Uses past data to project the future
looks for highest ACCURACY possible
Accuracy (MSE & MAD)
Mean Squared Error & Mean Absolute Deviation
Ft+1 = f(At, At-1, At-2, ...)
Let F = forecast and
Let A = actual data
MSE = SNt=1 [Ft - At ]2 /N
The LOWER the MSE or MAD, the greater the accuracy
MAD = SNt=1 |(Ft - At)| /N
Ó1999 South-Western College Publishing
Methods of Time Series Analysis for Economic Forecasting
1. Naive Forecast
Ft+1 = At
Method best when there is no trend, only random error
Graphs of sales over time with and without trends
Ó1999 South-Western College Publishing
NO Trend
Trend
F
F
F
F
F
s
s
s
s
s
s
2. Moving Average
A smoothing forecast method for data that jumps around
Best when there is no trend
3-Period Moving Av.
Ft+1 = [At + At-1 + At-2]/3
Ó1999 South-Western College Publishing
*
*
*
*
*
Forecast
Line
TIME
Dependent Variable
3. Exponential Smoothing
A hybrid of the Naive and Moving Average methods
Ft+1 = a .•At +(1-a)Ft
A weighted average of past actual and past forecast.
Each forecast is a function of all past observations
Can show that forecast is based on geometrically declining weights.
Ft+1 = a .•At +(1-a)•a•At-1 +
(1-a)2•a•At-1 + …
Find lowest MSE to pick the best alpha.
Ó1999 South-Western College Publishing
4. Linear & 5. Semi-log
Used when trend has a constant AMOUNT of change
A t = a + b•T, where
A t are the actual observations and
T is a numerical time variable
Used when trend is a constant PERCENTAGE rate
Log At = a + b•T,
where b is the continuously compounded growth rate
Ó1999 South-Western College Publishing
Linear Trend Regression Semi-log Regression
More on Semi-log Form-
A proof
Suppose: Salest = Sales0( 1 + G) t where G is the annual growth rate
Take the natural log of both sides:
Ln St = Ln S0 + t • Ln (1 + G)
but Ln ( 1 + G ) = g, the equivalent continuously compounded growth rate
SO: Ln St = Ln S0 + t • g
Ln St = Ln S0 + g • t
Ó1999 South-Western College Publishing
Numerical Examples: 6 observations
MTB > Print c1-c3
Sales Time Ln-sales
1
2
3
4
5
6
Ó1999 South-Western College Publishing
Using this sales
data, estimate
sales in period 7
using a linear and
a semi-log
functional
form
Ó1999 South-Western College Publishing
The regression equation is
Sales = + Time
Predictor Coef Stdev t-ratio p
Constant
Time
s = R-sq = % R-sq(adj) = %
The regression equation is
Ln-sales = + Time
Predictor Coef t-ratio p
Constant
Time
s = R-sq = % R-sq(adj) = %
Forecasted Sales @ Time = 7
Linear Model
Sales = + Time
Sales = + ( 7)
Sales =
Semi-Log Model
Ln-sales = + Time
Ln-sales = + ( 7 )
Ln-sales =
To anti-log:
=
Ó1999 South-Western College Publishing
85
linear
7
Sales Time Ln-sales
1
2
3
4
5
6
7 semi-log
7 linear
Ó1999 South-Western College Publishing
Which prediction
do you prefer?
Semi-log is
exponential
7
6. Procedures for Seasonal Adjustments
Take ratios of A/F for past years. Find the average ratio. Adjust by this percentage
If average ratio is , adjust forecast upward 2%
Use Dummy Variables in a regression: D = 1 if 4th quarter; 0 otherwise
Ó1999 South-Western College Publishing
12 -quarters of data
I II III IV I II III IV I II III IV
t
t
t
§
t
t
t
§
t
t
t
§
Quarters designated with roman numerals.
Dummy Variables for Seasonal Adjustments
Let D = 1, if 4th quarter and 0 otherwise
Run a new regression:
A t = a + b•T + c•D
the “c” coefficient gives the amount of the adjustment for the fourth quarter. It is an
Intercept Shifter.
EXAMPLE: Sales = 300 + 10•T + 18•D
12 Observations, 93 I - 95IV, Forecast ‘97
Sales(97 I) = 430; Sales(97 II) = 440; Sales(97 III) = 450; Sales(97 IV) = 478
Ó1999 South-Western College Publishing
Dummy Variable Interactions
Can introduce a slope shifter by “interacting” two variables
A t = a + b•T + c•D + d•D•T
c is the intercept shifter
d is the slope shifter
., Sales = 300 + 10•T + 18•D - 3•D•T
implies that the Intercept is 318, when D = 1
implies that the slope is 7, when D = 1
Ó1999 South-Western College Publishing
Econometric Models
Specify the variables in the model
Estimate the parameters
single equation or perhaps several stage methods
Qd = a + b•P + c•I + d•Ps + e•Pc
But forecasts require estimates for future prices, future income, etc.
Often combine econometric models with time series estimates of the independent variable.
Garbage in Garbage out
Ó1999 South-Western College Publishing
example
Qd = 400 - .5•P + 2•Y + .2•Ps
anticipate pricing the good at P = $20
Income is growing over time, the estimate is: Ln Yt = + .03•T, and next period is T = 17.
The prices of substitutes are likely to be P = $18.
Find Qd
Y = =
Hence Qd =
Ó1999 South-Western College Publishing
AWARD
for Excellence in
Economic Forecasting
Exchange Rates and
Managing Exports
Chapter 7
Import-Export Sales & Exchange Rates
Market for US Dollars
Risk Management
Purchasing Power Parity
Comparative Advantage & Trade
Ó1999 South-Western College Publishing
Exchange Rates and International Trade
OVERVIEW: More and more firm are becoming multinational enterprises.
Exporting and importing can be impacted by changes in international exchange rates.
Differences in long run inflation rates (according to the theory of purchasing power parity) help explain long-term exchange rate movements.
We also look at regional trading blocs in Europe, North American, and the Far East.
Ó1999 South-Western College Publishing
Import & Export Sales and Exchange Rates
The international competitiveness of products can be affected by exchange rates.
If the DM-price of a BMW stays the same in Germany, the export revenue in received by BMW changes as the $/DM price changes.
If the price of the mark falls, BMW receives less revenue from US dealerships, when the dollar price of cars stays the same.
Cummins Engine, a US exporter, faces a problem when the dollar strengthens in value.
Their engines become more expensive to foreign purchasers, if they keep the dollar price of engines constant.
Ó1999 South-Western College Publishing
Language used to discuss exchange rate changes depends on whether under floating or fixed exchange rates
Appreciates or Depreciates -- Under Flexible FX Rate Regimes
Revalues or Devalues -- Under Fixed FX Rates
Spot Price for FX -- current price (2 day delivery) can appear in different terms
Forward FX Price -- price of a foreign currency for delivery at a future date agreed by contract today
Ó1999 South-Western College Publishing
Exchange Rates (1998)
DM Spot and Forward Rates
Ó1999 South-Western College Publishing
Country US $ equivalent Per US $
Thurs. Wed. Thurs. Wed. Germany (DM) .5562 .5576
30 day forward .5571 .5585
90 day forward .5589 .5604
180 day forward .5616 .5631
Supply & Demand Model of Exchange Rates
FX is used for trade and investment. Use a supply & demand
model to explore FX rates
Demand for Marks: Demand is associated with US demand for imports from Germany and purchase of German securities
D
$/DM
DM
DM
We expect that as the price of German products to . customers goes down, there will be greater demand for DM.
As the dollar has more purchasing power in Germany (at point B), Americans will want more Marks.
DM
$/DM
A
B
Supply of DM &
Market Clearing in FX
Supply of DM -- Supply is associated with German demand for US exports and US investments.
Market Clears-- no excess demand or excess supply of DM
In Flexible Markets, buying & selling through international banks
D
$/DM
DM
S1
SUPPOSE: There is a rise in the Inflation Rate in the US
Both Supply & Demand of DM Shift
German products appear cheaper
US exports appear more expensive
The Mark appreciates, and the dollar depreciates
D
$1/DM
DM
S
D'
S'
$2/DM
Ó1999 South-Western College Publishing
Exchange Rates: One Year Changes in ‘97
52 Wk High 52 WK Low Close %Change 52 Wks
British Pound in US$
$ $ $ +%
Canadian Dollar in US$
$ $ $ %
Swiss Franc Per US$
%
or $ $ $.69 (it was at $.81)
Japanese Yen Per US$
%
or $.0079 $.0096 $.0077 (it was at $.0094)
German Mark Per US$
%
or $ $. $ (it was at $)
Cross Rates: Dow Jones Telerate
Interbank for $1 million or more (1998)
US Dollar Pound Yen D-Mark
Canada .01103 .79873
France .04633
Germany .01381 ---------
Italy
Japan ---------
Mexico .06505
Netherlands .01555
Switzerland .01145 .82849
. .60060 --------- .00461 .33402
. --------- .00768 .55614
Upper triangle(above dashed lines) are in home country as in 130 yen for a dollar, ¥/$. Lower BOLD triangle are in foreign currency as in less than a penny a yen, $/¥
Bid - Ask Spreads
Market makers earn their profit on the spread
Ó1999 South-Western College Publishing
ASK price
price willing to sell
Bid price
price willing to buy
.66627
.66539
Key Currencies & Cross Rates
Markets develop in each pair of currencies
If there are N=4 countries, there are as many as N•(N-1)/2 = 6 different possible FX rates
With the US as a Key currency, can reduce the number to only 3
For hundreds of countries, chief or key currencies is natural
Ó1999 South-Western College Publishing
B
A C
D
Economic Exposure (or Risk) involves the impact of exchange rates on a firm’s cash flows
Economic decisions should incorporate expectations about future exchange rates.
Firms may self insure by accepting these risks
or they may buy foreign exchange insurance via entering into contracts such as forward contracts.
Ó1999 South-Western College Publishing
Exchange Rates, Cash Flows, & Risk
Types of Hedges
Internal hedges – multinational firms buy and sell within the firm in any currency that they select.
Hedges using forward contracts – firms can offset exposure in foreign currency by buying or selling that amount of currency in a forward contract.
Hedges using future contracts – firm may offset risk with a futures contract in that currency.
Hedges using currency swaps – firms may agree to exchange (swap) streams of payments in different currencies, with adjustments at each settlement date.
Ó1999 South-Western College Publishing
Asset - Liability
Management for Exchange Risk
One simple approach to reduce exchange rate exposure is to structure parent and subsidiaries such that exchange rate changes affect assets and liabilities in tandem.
Method: Suppose that a percent of the business exported to country X, the firm could borrow the a percentage in the currency of country X.
Hence, financing is a convenient way to arrange forms of hedging “revenue” assets.
Ó1999 South-Western College Publishing
Exchange Risk & Stockholders
Eliminating all exchange risk may not be in the interest of shareholders.
If shareholders are well diversified, they may not be particularly sensitive to unsystematic variations due to changes in exchange rates and "exchange risk", especially if reducing that risk sacrifices profits.
Ó1999 South-Western College Publishing
Long-Run Exchange Rate Determinants
tend to have declining value of their currency when they run trade deficits, and tend to have rising currency values if they run trade surpluses.
-run trends in exchange rates are affected by differences in inflation-adjusted interest rates. High relative interest rates attract investors, tending to raise the value of the currency.
with high inflation tend to depreciate; countries with low relative inflation appreciate.
Ó1999 South-Western College Publishing
Purchasing Power Parity (PPP)
Purchasing power parity says that the price of traded goods tends to be equal around the world. The law of one price.
if exchange rates are flexible and there are no significant costs or barriers to trade.
S1 1 + (ph )
S0 ( 1 + pf )
S1/ S0 shows the expected change in the direct quote of a currency. The right side of the equation is the ratio of home and foreign inflation rates. If the foreign inflation rises (pf), then the domestic expected future spot rates S1declines.
Ó1999 South-Western College Publishing
=
Problems (or qualifications) with relative PPP:
PPP is sensitive to the starting point, S0. The base time period may not in equilibrium
Differences in the traded goods, or cross-cultural differences, may make prevent the law of one price to equilibrate price differences.
The inflation rate may include non-traded goods.
PPP tends to work better in the long run than in short run changes in inflationary expectations.
Ó1999 South-Western College Publishing
International Trade and Trading Blocs
Countries restrict trade through tariffs, quotas, and currency restrictions.
Several regions have reduced trade restrictions
MERCOSUR (in South America)
NAFTA (in North America)
EU (the European Union, or often the European Community)
looser arrangements in Southeast Asia (ASEAN)
APEC throughout the Pacific area including the US, Mexico, and Canada.
Ó1999 South-Western College Publishing
Comparative Advantage
Countries or firms should produce more of those goods for which they have lower relative cost.
Ó1999 South-Western College Publishing
Relative Cost in US Relative Cost in Japan
Automotive carburetors .4 Chips Chips
Computer Chips Carburetors .8 Carburetors
It costs $120 in the US to make a carburetor and $300 to make chips, the “cost” of a carburetor is the .4 chips foregone (take the ratio $120/$300 to find .4 chips).
The US relative cost of carburetors is much lower than that of the Japanese ( Chips), whereas the Japanese relative cost of chips (.8 Carburetors) is much lower than that of the US. Japan should make chips and US should make carburetors.
Trade Deficits
and the Balance of Payments
Current account = goods and service trade flows, receipts and payments US assets abroad and foreign assets in the US, and unilateral governmental and private transfers
Capital account = capital inflows and outflows of foreign assets.
The current account (deficit or surplus) comes from a capital account (surplus or deficit) to balance payments. This is the idea behind the accounting identity of the balance of payments.
Ó1999 South-Western College Publishing
Exchange Rates and International Trade
Market for . dollars
Comparative advantage
Free trade
. balance of payments
Import & Export Sales and Exchange Rates
The international competitiveness of products can be affected by exchange rates.
Cummins Engine, a US exporter, faces a problem when the dollar strengthens in value.
Their engines become more expensive to foreign purchasers, if they keep the dollar price of engines constant.
1999 South-Western College Publishing
Foreign Exchange Terminology
Language used depends on exchange rate regime: floating or fixed
Appreciates or Depreciates -- Under Flexible FX Rate Regimes
Revalues or Devalues -- Under Fixed FX Rates
Spot Price for FX -- current price (2 day delivery)
Forward FX Price -- currency price for future delivery
1999 South-Western College Publishing
Exchange Rates (1998)
DM Spot and Forward Rates
1999 South-Western College Publishing
Country US $ equivalent Per US $
Thurs. Wed. Thurs. Wed. Germany (DM) .5562 .5576
30 day forward .5571 .5585
90 day forward .5589 .5604
180 day forward .5616 .5631
Supply & Demand Model of Exchange Rates
FX is used for trade and investment. Use a supply & demand
model to explore FX rates
Demand for Marks: Demand is associated with US demand for imports from Germany and purchase of German securities
D
$/DM
DM
DM
We expect that as the price of German products to . customers goes down, there will be greater demand for DM.
As the dollar has more purchasing power in Germany (at point B), Americans will want more Marks.
DM
$/DM
A
B
Supply of DM &
Market Clearing in FX
Supply of DM -- Supply is associated with German demand for US exports and US investments.
Market Clears-- no excess demand or excess supply of DM
In Flexible Markets, buying & selling through international banks
D
$/DM
DM
S1
SUPPOSE: There is a rise in the Inflation Rate in the US
Both Supply & Demand of DM Shift
German products appear cheaper
US exports appear more expensive
The Mark appreciates, and the dollar depreciates
D
$1/DM
DM
S
D'
S'
$2/DM
1999 South-Western College Publishing
Exchange Rates: One Year Changes in ‘97
52 Wk High 52 WK Low Close %Change 52 Wks
British Pound in US$
$ $ $ +%
Canadian Dollar in US$
$ $ $ %
Swiss Franc Per US$
%
or $ $ $.69 (it was at $.81)
Japanese Yen Per US$
%
or $.0079 $.0096 $.0077 (it was at $.0094)
German Mark Per US$
%
or $ $. $ (it was at $)
Cross Rates: Dow Jones Telerate
Interbank for $1 million or more (1998)
US Dollar Pound Yen D-Mark
Canada .01103 .79873
France .04633
Germany .01381 ---------
Italy
Japan ---------
Mexico .06505
Netherlands .01555
Switzerland .01145 .82849
. .60060 --------- .00461 .33402
. --------- .00768 .55614
Upper triangle(above dashed lines) are in home country as in 130 yen for a dollar, ¥/$. Lower BOLD triangle are in foreign currency as in less than a penny a yen, $/¥
Bid - Ask Spreads
Market makers earn their profit on the spread
1999 South-Western College Publishing
ASK price
price willing to sell
Bid price
price willing to buy
.66627
.66539
Key Currencies & Cross Rates
Markets develop in each pair of currencies
If there are N=4 countries, there are as many as N•(N-1)/2 = 6 different possible FX rates
With the US as a Key currency, can reduce the number to only 3
For hundreds of countries, chief or key currencies is natural
1999 South-Western College Publishing
B
A C
D
Economic Exposure (or Risk) involves the impact of exchange rates on a firm’s cash flows
Economic decisions should incorporate expectations about future exchange rates.
Firms may self insure by accepting these risks
or they may buy foreign exchange insurance via entering into contracts such as forward contracts.
1999 South-Western College Publishing
Exchange Rates, Cash Flows, & Risk
Types of Hedges
Internal hedges – multinational firms buy and sell within the firm in any currency that they select.
Hedges using forward contracts – firms can offset exposure in foreign currency by buying or selling that amount of currency in a forward contract.
Hedges using future contracts – firm may offset risk with a futures contract in that currency.
Hedges using currency swaps – firms may agree to exchange (swap) streams of payments in different currencies, with adjustments at each settlement date.
1999 South-Western College Publishing
Asset - Liability
Management for Exchange Risk
One simple approach to reduce exchange rate exposure is to structure parent and subsidiaries such that exchange rate changes affect assets and liabilities in tandem.
Method: Suppose that percent of the business exported to country X, the firm could borrow the percentage in the currency of country X.
Hence, financing is a convenient way to arrange forms of hedging “revenue” assets.
1999 South-Western College Publishing
Exchange Risk & Stockholders
Eliminating all exchange risk may not be in the interest of shareholders.
If shareholders are well diversified, they may not be particularly sensitive to unsystematic variations due to changes in exchange rates and "exchange risk", especially if reducing that risk sacrifices profits.
1999 South-Western College Publishing
Long-Run Exchange Rate Determinants
tend to have declining value of their currency when they run trade deficits, and tend to have rising currency values if they run trade surpluses.
-run trends in exchange rates are affected by differences in inflation-adjusted interest rates. High relative interest rates attract investors, tending to raise the value of the currency.
with high inflation tend to depreciate; countries with low relative inflation appreciate.
1999 South-Western College Publishing
Purchasing Power Parity (PPP)
Purchasing power parity says that the price of traded goods tends to be equal around the world. The law of one price.
if exchange rates are flexible and there are no significant costs or barriers to trade.
S1 1 + (h )
S0 ( 1 + f )
S1/ S0 shows the expected change in the direct quote of a currency. The right side of the equation is the ratio of home and foreign inflation rates. If the foreign inflation rises (f), then the domestic expected future spot rates S1declines.
1999 South-Western College Publishing
=
Problems (or qualifications) with relative PPP:
PPP is sensitive to the starting point, S0. The base time period may not in equilibrium
Differences in the traded goods, or cross-cultural differences, may make prevent the law of one price to equilibrate price differences.
The inflation rate may include non-traded goods.
PPP tends to work better in the long run than in short run changes in inflationary expectations.
1999 South-Western College Publishing
International Trade and Trading Blocs
Countries restrict trade through tariffs, quotas, and currency restrictions.
Several regions have reduced trade restrictions
MERCOSUR (in South America)
NAFTA (in North America)
EU (the European Union, or often the European Community)
looser arrangements in Southeast Asia (ASEAN)
APEC throughout the Pacific area including the US, Mexico, and Canada.
1999 South-Western College Publishing
Comparative Advantage
Countries or firms should produce more of those goods for which they have lower opportunity cost.
1999 South-Western College Publishing
Relative Cost in US Relative Cost in Japan
Automotive carburetors .4 Chips Chips
Computer Chips Carburetors .8 Carburetors
It costs $120 in the US to make a carburetor and $300 to make chips, the “cost” of a carburetor is the .4 chips foregone (take the ratio $120/$300 to find .4 chips).
The US relative cost of carburetors is much lower than that of the Japanese ( Chips), whereas the Japanese relative cost of chips (.8 Carburetors) is much lower than that of the US. Japan should make chips and US should make carburetors.
Trade Deficits
and the Balance of Payments
Current account = goods and service trade flows, receipts and payments US assets abroad and foreign assets in the US, and unilateral governmental and private transfers
Capital account = capital inflows and outflows of foreign assets.
The current account (deficit or surplus) comes from a capital account (surplus or deficit) to balance payments. This is the idea behind the accounting identity of the balance of payments.
1999 South-Western College Publishing
Production Economics
Chapter 8
Managers must decide not only what to produce for the market, but also how to produce it in the most efficient or least cost manner.
We develop a widely accepted tool for judging whether or not production choices are least cost.
A production function relates the most that can be produced from a given set of inputs. This allows the manager to measure the marginal product of each input.
Ó1999 South-Western College Publishing
1. Production Economics:
In the Short Run
Short Run Production Functions:
Max output, from a n y set of inputs
Q = f ( X1, X2, X3, X4, ... )
FIXED IN SR VARIABLE IN SR
_
Ó1999 South-Western College Publishing
Q = f ( K, L) for two input case, where K as Fixed
Average Product = Q / L
output per labor
Marginal Product = ¶ Q / ¶ L = dQ / dL
output attributable to last unit of labor applied
Similar to profit functions, the Peak of MP occurs before the Peak of average product
When MP = AP, we’re at the peak of the AP curve
Ó1999 South-Western College Publishing
Production Elasticities
The production elasticity for any input, X, EX = MPX / APX = (¶Q/¶X) / (Q/X) = (¶Q/¶X)·(X/Q), which is identical in form to other elasticities.
When MPL > APL, then the labor elasticity,
EL > 1. A 1 percent increase in labor will increase output by more than 1 percent.
When MPL < APL, then the labor elasticity,
EL < 1. A 1 percent increase in labor will increase output by less than 1 percent.
Ó1999 South-Western College Publishing
Short Run Production Function
Numerical Example
Ó1999 South-Western College Publishing
Marginal Product
L
1 2 3 4 5
Average
Product
Labor Elasticity is greater then one,
for labor use up through L = 3 units
When MP > AP, then AP is RISING
IF YOUR MARGINAL GRADE IN THIS CLASS
IS HIGHER THAN YOUR AVERAGE GRADE POINT AVERAGE, THEN YOUR . IS RISING
When MP < AP, then AP is FALLING
IF THE MARGINAL WEIGHT ADDED TO A TEAM IS LESS THAN THE AVERAGE WEIGHT, THEN AVERAGE TEAM WEIGHT DECLINES
When MP = AP, then AP is at its MAX
IF THE NEW HIRE IS JUST AS EFFICIENT AS THE AVERAGE EMPLOYEE, THEN AVERAGE PRODUCTIVITY DOESN’T CHANGE
Ó1999 South-Western College Publishing
Law of Diminishing Returns
Ó1999 South-Western College Publishing
INCREASES IN ONE FACTOR OF PRODUCTION,
HOLDING ONE OR OTHER FACTORS FIXED,
AFTER SOME POINT,
MARGINAL PRODUCT DIMINISHES.
A SHORT
RUN LAW
point of
diminishing
returns
MP
Three stages of production:
Stage 1: average product rising.
Stage 2: average product declining (but marginal product positive).
Stage 3: marginal product is negative, or total product is declining.
Ó1999 South-Western College Publishing
L
Total Output
Stage 1
Stage 2
Stage 3
Optimal Employment of a Factor
HIRE IF GET MORE REVENUE THAN COST
HIRE IF
D TR/D L > D TC/D L
HIRE IF MRP L > MFC L
AT OPTIMUM,
MRP L = W
MRP L º MP L • P Q = W
Ó1999 South-Western College Publishing
optimal labor
MP L
MRP L
W
W
L
wage
•
MRP L is the Demand for Labor
If Labor is MORE productive, demand for labor increases
If Labor is LESS productive, demand for labor decreases
Suppose an EARTHQUAKE destroys capital ®
MP L declines with less capital, wages and labor are HURT
Ó1999 South-Western College Publishing
D L
D' L
S L
W¯
L' L
2. Long Run Production Functions
All inputs are variable
greatest output from any set of inputs
Q = f( K, L ) is two input example
MP of capital and MP of labor are the derivatives of the production function
MPL = ¶ Q / ¶ L
MP of labor declines as more labor is applied. Also MP of capital declines as more capital is applied.
Ó1999 South-Western College Publishing
Homogeneous Functions of Degree n
A function is homogeneous of degree-n
if multiplying all inputs by l, increases the dependent variable by l n
Q = f ( K, L)
So, f( l K, l L) = l n • Q
Homogenous of degree 1 is CRS.
Cobb-Douglas Production Functions are homogeneous of degree a + b
Ó1999 South-Western College Publishing
Cobb-Douglas Production Functions:
Q = A • K a • L b is a Cobb-Douglas Production Function
IMPLIES:
Can be IRS, DRS or CRS:
if a + b = 1, then CRS
if a + b < 1, then DRS
if a + b > 1, then IRS
Coefficients are elasticities
a is the capital elasticity of output
b is the labor elasticity of output,
which are EK and E L
Ó1999 South-Western College Publishing
Problem
Suppose: Q = L .70 K .35
Is the function homogeneous?
Is the production function constant returns to scale?
What is the labor elasticity of output?
What is the capital elasticity of output?
What happens to Q, if L increases 3% and capital is cut 10%?
Ó1999 South-Western College Publishing
Answers
Increases in all inputs by l, increase output by
Increasing Returns to Scale
.70
.35
%DQ= EQL• %DL+ EQK • %DK = .7(+3%) + .35(-10%) = % % = %
Ó1999 South-Western College Publishing
Isoquants & LR Production Functions
In the LONG RUN, ALL factors are variable
Q = f ( K, L )
ISOQUANTS -- locus of input combinations which produces the same output
SLOPE of ISOQUANT is ratio of Marginal Products
ISOQUANT MAP
Ó1999 South-Western College Publishing
B
A
C
Q1
Q2
Q3
K
L
Optimal Input Combinations
in the Long Run
The Objective is to Minimize Cost for a given Output
ISOCOST lines are the combination of inputs for a given cost
C0 = CX·X + CY·Y
Y = C0/CY - (CX/CY)·X
Equimarginal Criterion Produce where MPX/CX = MPY/CY where marginal products per dollar are equal
Ó1999 South-Western College Publishing
Q1
E
X
Y
at E, slope of
isocost = slope
of isoquant
Use of the Efficiency Criterion
Is the following firm EFFICIENT?
Suppose that:
MP L = 30
MP K = 50
W = 10 (cost of labor)
R = 25 (cost of capital)
Labor: 30/10 = 3
Capital: 50/25 = 2
A dollar spent on labor produces 3, and a dollar spent on capital produces 2.
USE RELATIVELY MORE LABOR
If spend $1 less in capital, output falls 2 units, but rises 3 units when spent on labor
Ó1999 South-Western College Publishing
Economies of Scale
CONSTANT RETURNS TO SCALE (CRS)
doubling of all inputs doubles output
INCREASING RETURNS TO SCALE (IRS)
doubling of all inputs MORE than doubles output
DECREASING RETURNS TO SCALE (DRS)
doubling of all inputs DOESN’T QUITE double output
Ó1999 South-Western College Publishing
Increasing Returns to Scale
Specialization in the use of capital and labor. Labor becomes more skilled at tasks, or the equipment is more specialized, less "a jack of all trades," as scale increases.
Other advantages include: avoid inherent lumpiness in the size of equipment, quantity discounts, technical efficiencies in building larger volume equipment.
Ó1999 South-Western College Publishing
REASONS FOR
DECREASING RETURNS TO SCALE
Problems of coordination and control as it is hard to send and receive information as the scale rises.
Other disadvantages of large size:
slow decision ladder
inflexibility
capacity limitations on entrepreneurial skills (there are diminishing returns to the . which cannot be completely delegated).
Ó1999 South-Western College Publishing
REASONS FOR
Economies of Scope
FOR MULTI-PRODUCT FIRMS, COMPLEMENTARY IN PRODUCTION MAY CREATE SYNERGIES
especially common in Vertical Integration of firms
TC( Q 1 + Q 2) < TC (Q 1 ) + TC (Q 2 )
Ó1999 South-Western College Publishing
+
=
Cost
Efficiencies
Chemical firm
Petroleum firm
Statistical Estimation of
LR Production Functions
Choice of data sets
cross section
output and input measures from a group of firms
output and input measures from a group of plants
time series
output and input data for a firm over time
Ó1999 South-Western College Publishing
Estimation Complexities
Industries vary -- hence, the appropriate variables for estimation are industry-specific
single product firms vs. multi-product firms
multi-plant firms
services vs. manufacturing
measurable output (goods) vs unmeasurable output (customer satisfaction)
Ó1999 South-Western College Publishing
Choice of Functional Form
Linear ? Q = a • K + b • L
is CRS
marginal product of labor is constant, MPL = b
can produce with zero labor or zero capital
isoquants are straight lines --
perfect substitutes
in production
Ó1999 South-Western College Publishing
K
L
Q3
Q2
Multiplicative -- Cobb Douglas Production Function
Q = A • K a • L b
IMPLIES
Can be CRS, IRS, or DRS
MPL = b • Q/L
MPK = a • Q/K
Cannot produce with zero L or zero K
Log linear -- double log
Ln Q = a + a • Ln K + b • Ln L
coefficients are elasticities
Ó1999 South-Western College Publishing
Data on 15 plants that produce fertilizer
what sort of data set is this?
what functional form should we try?
Determine if IRS, DRS, or CRS
Test if coefficients are statistically significant
Determine labor and capital production elasticities and give an economic interpretation of each value
Ó1999 South-Western College Publishing
CASE: Wilson Company
Ó1999 South-Western College Publishing
Output Capital Labor
1 18891
2 19201
3 20655
4 15082
5 20300
6 16079
7 24194
8 11504
9 25970
10 10127
11 25622
12 12477
13 24002
14 8042
15 23972
LnOutput Ln-Cap Ln-labor
Data Set: 15 plants
Ó1999 South-Western College Publishing
The linear regression equation is
Output = - 351 + Capital + Labor
Predictor Coef Stdev t-ratio p
Constant
Capital .012725 .007646
Labor
s = R-sq = % R-sq(adj) = %
Ó1999 South-Western College Publishing
The log-linear regression equation is
LnOutput =
- + LnCapital + Ln-labor
Predictor Coef Stdev t-ratio p
Constant
LnCapital
Ln-labor
s = R-sq = % R-sq(adj) = %
More Problems
Ó1999 South-Western College Publishing
Suppose the following production function is estimated to be:
ln Q = + .19 ln K + .87 ln L
R 2 = .97
Q U E S T I O N S:
1. Is this CRS?
2. If L increases by 2%, what
happens to output?
3. What’s the MPL at L = 50, K = 100, & Q = 741?
Answers
Ó1999 South-Western College Publishing
1.) Take the sum of the coefficients
.19 + .87 = , which shows
that this production function is Increasing Returns to Scale
2.) Use the Labor Elasticity of Ouptut.
%DQ = E L • %DL
%DQ = (.87)•(+2%) = +%
3). MPL = b Q/L = .87•(741 / 50) =
Electrical Generating Capacity
A cross section of 20 electrical utilities (standard errors in parentheses):
Ln Q = + .53 Ln K + .65 Ln L (.65) (.12) (.14) R 2 = .966
Does this appear to be constant returns to scale?
If increase labor 10%, what happens to electrical output?
Ó1999 South-Western College Publishing
Answers
No, constant returns to scale. Of course, its increasing returns to scale as sum of coefficients exceeds one.
.53 + .65 =
If %DL = 10%, then %DQ = E L • %DL = .65(10%) = %
Ó1999 South-Western College Publishing
Lagrangians and Output Maximization: Appendix 8A
Max output to a cost objective. Let r be the cost of capital and w the cost of labor
Max L = A • K a • L b - l { w•L + r•K - C}
LK: a•A• K a-1•Lb - r •l = 0 MPK = r
LL: b•A• K a•Lb-1 - w •l = 0 MPL = w
Ll: C - w•L - r•K = 0
Solution a Q/K/ b Q/L = w / r
or MPK / r = MPL /w
Ó1999 South-Western College Publishing
}
Production and Linear Programming: Appendix 8B
Manufacturers have alternative production processes, some involving mostly labor, others using machinery more intensively.
The objective is to maximize output from these production processes, given constraints on the inputs available, such as plant capacity or union labor contract constraints.
The linear programming techniques are discussed in Chapter 11.
Cost Analysis
Chapter 9
The meaning and measurement of cost
Short-run Cost Functions
Long-run Cost Functions
Scale Economies and Cost
Appendix 9A: Cobb-Douglas & LR COST
Ó1999 South-Western College Publishing
The Object of Cost Analysis
Managers seek to produce the highest quality products at the lowest possible cost.
Firms that are satisfied with the status quo find that competitors arise that can produce at lower costs.
The advantages once assigned to being large firms (economies of scale and scope) have not provided the advantages of flexibility and agility found in some smaller companies.
Cost analysis is helpful in the task of finding lower cost methods to produce goods and services.
Ó1999 South-Western College Publishing
Meaning of Cost
There are Many Economic Cost Concepts
Opportunity Cost -- value of next best alternative use.
Explicit vs. Implicit Cost -- actual prices paid vs. opportunity cost of owner supplied resources.
Ó1999 South-Western College Publishing
Examples of Relevant Cost Concepts
Depreciation Cost Measurement. Accounting depreciation (., straight-line depreciation) tends to have little relationship to the actual loss of value
To an economist, the actual loss of value is the true cost of using machinery.
Inventory Valuation. Accounting valuation depends on its acquisition cost
Economists view the cost of inventory as the cost of replacement.
Ó1999 South-Western College Publishing
Unutilized Facilities. Empty space may appear to have "no cost”
Economists view its alternative use (., rental value) as its opportunity cost.
Measures of Profitability. Accountants and economists view profit differently.
Accounting profit, at its simplest, is revenues minus explicit costs.
Economists include other implicit costs (such as a normal profit on invested capital).
Economic Profit = Total Revenues - Explicit Costs - Implicit Costs
Ó1999 South-Western College Publishing
Ó1999 South-Western College Publishing
Sunk Costs -- already paid for, or there is already a contractual obligation to pay
Incremental Cost - - extra cost of implementing a decision = D TC of a decision
Marginal Cost -- cost of last unit produced = ¶ TC/ ¶ Q
SHORT RUN COST FUNCTIONS
1. TC = FC + VC fixed & variable costs
2. ATC = AFC + AVC = FC/Q + VC/Q
Short Run Cost Graphs
Ó1999 South-Western College Publishing
AFC
Q
Q
1.
2.
AVC
3.
Q
AFC
AVC
ATC
MC
MC intersects lowest point
of AVC and lowest point of
ATC.
When MC < AVC, AVC declines
When MC > AVC, AVC rises
Relation of Cost & Production Functions in SR
AP & AVC are inversely related. (ex: one input)
AVC = WL /Q = W/ (Q/L) = W/ APL
As APL rises, AVC falls
MP and MC are inversely related
MC = dTC/dQ = W dL/dQ = W / (dQ/dL) = W / MPL
As MPL declines, MC rises
prod. fcts.
cost fcts.
MPL
MC
AP
AVC
Problem
Let there be a cubic VC function:
VC = .5 Q3 - 10 Q2 + 150 Q
find AVC from VC function
find minimum variable cost output
and find MC from VC function
Minimum AVC, where dAVC/dQ = 0
AVC = .5 Q 2 -10 Q + 150
dAVC / dQ = Q - 10 = 0
Q = 10, so AVC = 100 @ Q = 10
MC= dVC/dQ= Q2 - 20 Q + 150
Ó1999 South-Western College Publishing
Long Run Costs
In long run, ALL inputs are variable
LRAC
long run average cost
ENVELOPE of SRAC curves
LRMC is FLATTER than SRMC curves
Ó1999 South-Western College Publishing
Q
LRAC
LRMC
SRAC1
SRMC1
Long Run Cost Functions:
Envelope of SRAC curves
Ó1999 South-Western College Publishing
Q
SRAC-small capital
SRAC-med. capital
SRAC-big capital
LRAC--Envelope
of SRAC curves
Ave Cost
Economists think that the LRAC is U-shaped
Downward section due to:
Product-specific economies which include specialization and learning curve effects.
Plant-specific economies, such as economies in overhead, required reserves, investment, or interactions among products (economies of scope).
Firm-specific economies which are economies in distribution and transportation of a geographically dispersed firm, or economies in marketing, sales promotion, or R&D of multi-product firms.
Ó1999 South-Western College Publishing
Flat section
Constant returns to scale
Upward rising section of LRAC is due to:
diseconomies of scale. These include transportation costs, imperfections in the labor market, and problems of coordination and control by management.
The minimum efficient scale (MES) is the smallest scale at which minimum per unit costs are attained.
Modern business management offers techniques to avoid diseconomies of scale through profit centers, transfer pricing, and tying incentives to performance.
Ó1999 South-Western College Publishing
Equi-marginal Principle in LR
Since LR costs are least cost, they must be efficient; they must obey the equi-marginal principle:
MPX/CX = MPY/CY
That is, the marginal product per dollar in each use is equal.
Ó1999 South-Western College Publishing
Cost Functions and Production Functions:
LR Relationships and the Importance of Factor Costs
A. CRS & Constant Factor Prices
TC
AC
Q 2Q
B. IRS & Constant Factor Prices
Q 2Q
TC
AC
C. DRS & Constant Factor Prices
Q 2Q
AC
D. CRS & Rising Factor
Prices -- looks like “C”
Problem: Let TC & MC be:
TC = 200 + 5Q - .4Q2 + .001Q3
MC = 5 - .8Q + .003 Q2
a. FIND fixed cost
FIND AVC function
b. FIND minimum average variable cost point
c. If FC rises $500, what happens to minimum average variable cost?
TC = 200 + 5Q - .4Q2 + .001Q3
MC = 5 - .8Q + .003 Q2
a. FIND fixed cost
FIND AVC function
Answer: FC = 200 and AVC = 5 - .4Q + .001Q2.
b. FIND minimum average variable cost point
Answer: First find dAC/dQ = 0: From (a) that is:
+ .002Q = 0, so Q = 2,000
c. If FC rises $500, what happens to minimum average variable cost?
Answer: No change, since AVC doesn’t change.
Cobb-Douglas Production Function
and the Long-Run Cost Function: Appendix 9A
Long Run Costs & Production Functions: 1 Input
In the long run, total cost is: TC = w·L, where w is the wage rate.
production function is Cobb-Douglas: Q = Lß.
Solving for L in the Cobb-Douglas production function, we find: L = Q1/ß.
Substituting this into the total cost function, we get:
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One Input Case
TC = w·Q1/ß.
This also demonstrates that if the production function were constant returns to scale (ß=1), then TC rises linearly with output and average cost is constant.
If the production function is increasing returns to scale (ß>1), then TC rises at a decreasing rate in output and average cost is declining.
If the production function is decreasing returns to scale (ß<1), then TC rises at an increasing rate in output and average cost rises.
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TWO Input Case
With two inputs, long run cost is: TC = w·L + r·K,
where w is the wage rate
and r is the cost of capital, K.
Cobb-Douglas: Q = Ka·Lß.
The manager attempts to minimize cost, subject to an output constraint. This is a Lagrangian Multiplier problem.
Min L = w·L + r·K + l·[ Ka·Lß - Q ]
Taking derivatives and solving yields a total cost:
TC = w·L* + r·K* =
C=w·Q(1/(a+ß))·(a·w/ß·r)(ß/(a+ß))+ r·Q(1/(a+ß))·(a·w/ß·r)(a/(a+ß))
If (a+ß>1), then 1/(a+ß) less than 1, and total cost rises at a decreasing rate in output. That means that average cost declines.
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Applications of Cost Theory
Chapter 10
Industries vary -- hence, the appropriate variables for estimation are industry-specific
single product firms vs. multi-product firms
multi-plant firms
services vs. manufacturing
measurable output (goods) vs unmeasurable output (customer satisfaction)
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Estimating Costs in the SR
Typically use TIME SERIES data for a plant or firm.
Typically use a functional form that “fits” the presumed shape.
For TC, often CUBIC
For AC, often
QUADRATIC
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quadratic is U-shaped or arch shaped
cubic is S-shaped
or backward S-shaped
Estimating Short Run Cost Functions
Example: TIME SERIES data of total cost
Quadratic Total Cost (to the power of two)
TC = C0 + C1 Q + C2 Q2
TC Q Q 2
900 20 400
800 15 225
834 19 361
ß ß ß
REGR c1 1 c2 c3
Time
Series
Data
Predictor Coeff StdErr T-value
Constant 1000 300
Q -50 20
Q-squared 10
R-square = .91
Adj R-square = .90
N = 35
Regression Output:
®
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PROBLEMS: 1. Write the cost regression as an equation. 2. Find the AC and MC functions.
1. TC = 1000 - 50 Q + 10 Q 2
() () (4)
2. AC = 1000/Q - 50 + 10 Q
MC = - 50 + 20 Q
t-values in the
parentheses
NOTE: We can estimate TC either as quadratic or as CUBIC:
TC = C1 Q + C2 Q2 + C3 Q3
If TC is CUBIC, then AC will be quadratic:
AC = C1 + C2 Q + C3 Q2
Estimating LR Cost Relationships
Use a CROSS SECTION of firms
SR costs usually uses a time series
Assume that firms are near their lowest average cost for each output
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Q
AC
LRAC
Log Linear LR Cost Curves
One functional form is Log Linear
Log TC = a + b• Log Q + c•Log W + d•Log R
Coefficients are elasticities.
“b” is the output elasticity of TC
IF b = 1, then CRS long run cost function
IF b < 1, then IRS long run cost function
IF b > 1, then DRS long run cost function
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Example: Electrical
Utilities
Sample of 20 Utilities
Q = megawatt hours
R = cost of capital on rate base, W = wage rate
Electrical Utility Example
Regression Results:
Log TC = +.83 Log Q + Log(W/R)
() (.03) (.21)
R-sqr = .9745
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Std-errors are in
the parentheses
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QUESTIONS:
1. Are utilities CRS, IRS, or DRS?
2. Are coefficients statistically significant?
3. Test the hypothesis:
Ho: b = 1
A n s w e r s
coefficient on Log Q is less than one. A 1% increase in output lead only to a .83% increase in TC -- It’s IRS !
t-values are coeff / std-errors:
t = .83/.03 = is Significant and
t = = which is Significant.
t-value is (.83 - 1)/.03 =
= - which is Significantly different than CRS.
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Cement Mix
Processing Plants
13 cement mix processing plants provided data for the following cost function. Test the hypothesis that cement mixing plants have constant returns to scale?
Ln TC = .03 + .35 Ln W + .65 Ln R + Ln Q
(.01) (.24) (.33) (.08)
R2 = .563
parentheses contain standard errors
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Discussion
Cement plants are CRS if the coefficient on Ln Q were 1
is more than 1, which appears to be DRS
TEST: t = ( -1 ) /.08 =
Small Sample, . = 13 - 3 -1 = 9
critical t =
We reject constant returns to scale.
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Engineering Cost Approach
Engineering Cost Techniques offer an alternative to fitting lines through historical data points using regression analysis.
It uses knowledge about the efficiency of machinery.
Some processes have pronounced economies of scale, whereas other processes (including the costs of raw materials) do not have economies of scale.
Size and volume are mathematically related, leading to engineering relationships. Large warehouses tend to be cheaper than small ones per cubic foot of space.
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Survivor Technique
The Survivor Technique examines what size of firms are tending to succeed over time, and what sizes are declining.
This is a sort of Darwinian survival test for firm size.
Presently many banks are merging, leading one to conclude that small size offers disadvantages at this time.
Dry cleaners are not particularly growing in average size, however.
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Break-even Analysis &
Can have multiple B/E points
If linear total cost and total revenue:
TR = P•Q
TC = F + v•Q
where v is Average Variable Cost
F is Fixed Cost
Q is Output
cost-volume-profit analysis
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Total
Cost
Total
Revenue
B/E B/E
Q
The Break-even Quantity: Q B/E
At break-even: TR = TC
So, P•Q = F + v•Q
Q B/E = F / ( P - v) = F/CM
where contribution margin is: CM = ( P - v)
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TR
TC
B/E
Q
PROBLEM: As a garage
contractor, find Q B/E
if: P = $9,000 per garage
v = $7,000 per garage
& F = $40,000 per year
Amount of sales revenues that breaks even
P•Q B/E = P•[F/(P-v)]
= F / [ 1 - v/P ]
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Break-even Sales Volume
Variable Cost Ratio
Ex: At Q = 20,
B/E Sales Volume is $9,000•20 =
$180,000 Sales Volume
Answer: Q = 40,000/(2,000)= 40/2 = 20 garages at the break-even point.
Target Profit Output
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Quantity needed to attain a target profit
If p is the target profit,
Q target p = [ F + p] / (P-v)
Suppose want to attain $50,000 profit, then,
Q target p = ($40,000 + $50,000)/$2,000
= $90,000/$2,000 = 45 garages
Degree of Operating Leverage
or Operating Profit Elasticity
DOL = E p
sensitivity of operating profit (EBIT) to changes in output
Operating p = TR-TC = (P-v)•Q - F
Hence, DOL = ¶ p/¶ Q•(Q/p) =
(P-v)•(Q/p) = (P-v)•Q / [(P-v)•Q - F]
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A measure of the importance of Fixed Cost
or Business Risk to fluctuations in output
Suppose Contractor Builds 45 Garages,
What is the ?
DOL = (9000-7000) • 45
{(9000-7000)•45 - 40000}
= 90,000 / 50,000 =
A 1% INCREASE in Q ® % INCREASE in operating profit.
At the break-even point, DOL is INFINITE.
A small change in Q increase EBIT by astronomically large percentage rates
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DOL as
Operating Profit Elasticity
DOL = [ (P - v)Q ] / { [ (P - v)Q ] - F }
We can use empirical estimation methods to find operating leverage
Elastiticities can be estimated with double log functional forms
Use a time series of data on operating profit and output
Ln EBIT = a + b• Ln Q, where b is the DOL
then a 1% increase in output increases EBIT by b%
b tends to be greater than or equal to 1
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Regression Output
Dependent Variable: Ln EBIT uses 20 quarterly observations N = 20
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The log-linear regression equation is
LnEBIT = - .75 + Ln Q
Predictor Coef Stdev t-ratio p
Constant
Ln Q
s = R-sq = % R-sq(adj) = %
The DOL for this firm, . So, a 1% increase in output leads to a % increase in operating profit
Operating Profit and the Business Cycle
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Output
recession
TIME
EBIT =
operating
profit
Trough
peak
1. EBIT is more volatile
that output over cycle
2. EBIT tends to
collapse late in
recessions
Appendix 10A: Learning Curve
”Learning by doing" has wide application in production processes.
Workers and management become more efficient with experience.
the cost of production declines as the accumulated past production, Q = Sqt, increases, where qt is the amount produced in the tth period.
Airline manufacturing, ship building, and appliance manufacturing have demonstrated the learning curve effect.
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Functionally, the learning curve relationship can be written C = a·Qb, where C is the input cost of the Qth unit:
Taking the (natural) logarithm of both sides, we get: log C = log a + b·log Q
The coefficient b tells us the extent of the learning curve effect.
If the b=0, then costs are at a constant level.
If b > 0, then costs rise in output, which is exactly opposite of the learning curve effect.
If b < 0, then costs decline in output, as predicted by the learning curve effect.
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Linear Programming Applications
Chapter 11
Constrained Optimization problems occur frequently in economics:
maximizing output from a given budget;
or minimizing cost of a set of required outputs.
Lagrangian multiplier problems required binding constraints.
A number of business problems have inequality constraints.
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Profit Maximization Problem Using Linear Programming
Constraints of production capacity, time, money, raw materials, budget, space, and other restrictions on choices. These constraints can be viewed as inequality constraints
A "linear" programming problem assumes a linear objective function, and a series of linear inequality constraints
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Linearity implies:
1. constant prices for outputs (as in a perfectly competitive market).
2. constant returns to scale for production processes.
3. typically, each decision variable also has a non-negativity constraint. For example, the time spent using a machine cannot be negative.
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Solution Methods
Linear programming problems can be solved using graphical techniques, SIMPLEX algorithms using matrices, or using software, such as ForeProfit software.
In the graphical technique, each inequality constraint is graphed as an equality constraint. The Feasible Solution Space is the area which satisfies all of the inequality constraints.
The Optimal Feasible Solution occurs along the boundary of the Feasible Solution Space, at the extreme points or corner points.
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The corner point that maximize the objective function is the Optimal Feasible Solution.
There may be several optimal solutions. Examination of the slope of the objective function and the slopes of the constraints is useful in determining which is the optimal corner point.
One or more of the constraints may be slack, which means it is not binding.
Each constraint has an implicit price, the shadow price of the constraint. If a constraint is slack, its shadow price is zero.
Each shadow price has much the same meaning as a Lagrangian multiplier.
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GRAPHICAL
X1
X2
A
B
C
CONSTRAINT # 1
CONSTRAINT
# 2
Corner Points
A, B, and C
Feasible
Region OABC
O
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GRAPHICAL
X1
X2
A
B
C
CONSTRAINT # 1
CONSTRAINT
# 2
Optimal Feasible
Solution at
Point B
Highest
Profit
Line
O
The Dual Problem
Each linear programming problem (the primal problem) has an associated dual problem.
EXAMPLE: A maximization of profit objective function, subject to resource constraints has an associated dual problem
The dual is a minimization of the total costs of the resources subject to constraints that the value of the resources used in producing one unit of each output be at least as great as the profit received from the sale of that output.
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Duality Theorem
THEOREM: the maximum value of the primal (profit max problem) equals the minimum value of the dual (cost minimization) problem.
The resource constraints of the primal problem appear in the objective function of the dual problem
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Primal:
Maximize p = P1·Q1 + P2·Q2 subject to:
c·Q1 + d·Q2 < R1 The budget constraint, for example.
e·Q1 + f·Q2 < R2 The machine scheduling time constraint.
where Q1 and Q2 > 0 Non-negativity constraint.
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Dual:
Minimize C = R1·w1 + R2·w2 subject to:
c·W1 + e·W2 > P1 Profit Contribution of Product 1
d·W1 + f·W2 > P2 Profit Contribution of Product 2
where W1 and W2 > 0 Non-negativity constraint.
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Complexity and the
Method of Solution
The solutions to primal and dual problems may be solved graphically, so long as this involves two dimensions.
With many products, the solution involves the SIMPLEX algorithm, or software available in ForeProfit
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Cost Minimization Problem Using Linear Programming
Multi-plant firms want to produce with the lowest cost across their disparate facilities. Sometimes, the relative efficiencies of the different plants can be exploited to reduce costs.
A firm may have two mines that produces different qualities of ore. The firm has output requirements in each ore quality.
Scheduling of hours per week in each mine has the objective of minimizing cost, but achieving the required outputs.
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If one mine is more efficient in all categories of ore, and is less costly to operate, the optimal solution may involve shutting one mine down.
The dual of this problem involves the shadow prices of the ore constraints. It tells the implicit value of each quality of ore.
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Capital Rationing Problem
Financial decisions sometimes may be viewed as a linear programming problem.
EXAMPLE: A financial officer may want to maximize the return on investments available, given a limited amount of money to invest.
The usual problem in finance is to accept all projects with positive net present values, but sometimes the capital budgets are fixed or limited to create "capital rationing" among projects.
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The solution involves determining what fraction of money allotted should be invested in each of the possible projects or investments.
In some problems, projects cannot be broken into small parts.
When this is the case, integer programming can be added to the problem.
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Price, Output, and Strategy: Pure and Monopolistic Competition
Chapter 12
Pure competition is a standard against which other market structures are compared. The product is perfectly undifferentiated.
When there are many firms, but the product is differentiated, the market is monopolistically competitive.
This brand competition often involves advertising campaigns and promotional expenditures to stress sometimes minor distinctions among products
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The Market Concept
A market is a group of economic agents that interact in a buyer-seller relationship. The nature of that relationship is affected by the number and size of the buyers and sellers.
A popular measure of seller concentration is the percentage of an industry comprised of the top 4 firms.
Similarly, the top 4 buyers is a popular measure of buyer concentration.
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Individual Firm Demand Conditions & the Market
a. the number of firms and their relative sizes.
b. whether the product is differentiated or standardized.
c. whether decisions by firms are independent or coordinated (collusion).
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4 Market Structures
a. pure competition
b. monopolistic competition
c. oligopoly
d. monopoly
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A Brief Overview of the Four Market Structures
Pure Competition
1. a very large number of buyers and sellers
2. homogeneous product (standardized)
3. free entry and exit (no barriers)
4. no collusion among the firms
5. complete knowledge of all market information
Each firm views its demand curve as perfectly elastic. We say that pure competition makes firms price takers.
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Monopolistic Competition
1. many buyers and sellers
2. differentiated product
3. free entry and exit
4. no collusion among the firms
Each firm will view its demand curve as declining in its own price. A monopolistically competitive firm will have to have a pricing strategy, unlike a purely competitive firm.
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Oligopoly
1. few firms
2. the products may be differentiated or standardized
3. there is a noticeable degree of interdependence among the firms
Many outcomes are possible in oligopolies, ranging from acting nearly competitively to acting like a monopoly.
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Monopoly
1. one firm
2. a perfectly differentiated product (low cross price elasticities with other products.
3. substantial barriers to entry, such as absolute cost advantages, consumer loyalty, scale economies, large capital requirements, or legal barriers to entry.
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Forces of Competition
Michael Porter, in his Competitive Advantage, lists 5 forces that determine competitive advantage:
Substitutes (threat of substitutes can be offset by brands and special functions served by the product).
Potential Entrants (threat of entrants can be reduced by high fixed costs, scale economies, restriction of access to distribution channels, or product differentiation).
Buyer Power (threat of concentration of buyers).
Supplier Power (threats from concentrated suppliers of key inputs affect profitability).
Intensity of Rivalry (market concentration, price competition tactics, exit barriers, amount of fixed costs, and industry growth rates impact profitability).
Price-cost margin percentage (PCM) = ( P – MC)/P
A price cut may help or hurt profitability depending on price elasticities and price cost margins.
See how much quantity must change after a price cut to breakeven If the price cut were 10%, to breakeven the percentage change in quantity (DQ/Q) must be large enough to satisfy the equation:
PCM / (PCM – .10) > (1 + DQ/Q ).
The larger the price-cost margin percentage, the smaller the necessary quantity response to justify cutting price.
Price and Output Under Pure Competition
Competitive firms attempt to maximize profits.
Competitive firms cannot charge more than the market price of others, since their product is identical to all others.
Hence, competitive firms are price takers.
Total revenue, TR, is P·Q, where price is given. Therefore, marginal revenue, MR, is price, P.
Profit is total revenue minus total cost
(p = TR - TC)
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Profit maximization implies that each firm produces an output where Price = Marginal Cost (P = MC).
To produce more than this quantity implies that P < MC, which is not the most profitable decision.
To produce less than where P=MC, implies that P > MC, and the firm could increase profits by expanding output.
In short run, a competitive firm may earn economic profits.
In long run, entry pushes price down to the minimum point of the average cost curve, so that economic profits are zero.
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Welcome Properties
of Pure Competition
1. Firms are Price Takers
Assume the opposite
P1 > P2
But everyone knows this
The products are homogeneous.
So, no one buy from firm 2.
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Q
firm’s demand curve
d d
MC
P
2. A firm’s demand curve is perfectly elastic at the competitive price
Diagram of firm demand
in pure competition
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3. Profit Maximization implies each firm
produces at a quantity where P = MC
Max P = P•Q - TC(Q)
¶P/¶Q = 0 implies that: P = MC
decision rule
4. The firm’s MC curve is the firm’s
SUPPLY CURVE
prices
quantities
{
As price changes, the optimal
amount SUPPLIED changes
MC
Equilibrium Price in a Competitive Market
Equilibrium for each firm if P = MC. Each firm is “happy”
Equilibrium for the industry if: Demand equals Supply at the going price
When both occur, the market is in a Competitive Equilibrium
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a firm the industry
MC
D
S MC
AC
CAN EARN ECON PROFITS
IN THE SHORT RUN
A Competitive Equilibrium Implies:
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NOTICE:
1. Competitive firm can earn economic profits in SR
2. If Price < AVC, firm will shut down
so-called “shut down price” is AVC
3. In LR, entry forces price down to the
minimum of the AC curve
AC
MC
AVC
P
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NORMATIVE PROPERTIES of Competitive Markets:
1. The Division of Output Among Firms is EFFICIENT
Suppose 2 firms with different MC
If firm 2 expands and firm 1contracts production, TC rises.
firm 1
firm 2
MC
MC
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2. The total output of the Industry is CORRECT, .,
Maximizes the Sum of Consumer & Producer Surplus
demand
supply
CS
PS
correct output
Consumer surplus is
area Below demand
and Above price
Producer surplus is
area Below price and
Above supply
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3. In the LR, each firm produces at the lowest
point of their AC curves
AC
MC
Q (at least cost point)
PLR
4. Political Decentralization
5. Price signals the true cost to society
6. Economic profits are zero in the LR
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For the industry:
QS = 3000 + 200 P and
QD = 13500 - 500 P
For the firm:
FC = 50
MC = 15 - 4 Q + 3 Q2 / 10
AVC = 15 - 2 Q + Q 2 / 10
FIND OPTIMAL output for this firm.
PROBLEM - The following is given:
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Answer: Find equilibrium price. Set D = S
we see 3000 + 200 P = 13500 - 500 P. This implies:
10500 / 700 = P = $15.
At this price, the firm produces where P = MC, so
$15 = 15 - 4 Q + 3 Q2 / 10
4Q = .3 Q 2
so Q =
PROFIT = TR - TC at this output.
Profit = (15)() - 50 - = $
= TR - FC - VC
Two Theories on Competition & Price
The MORE firms there are, the greater the competition and the lower the price.
Contestable Markets--Potential Entry as well as actual number of firms, so the number of actual firms may not matter empirically
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N = number of firms
PRICE of Air Travel
no effect after
a certain number
of firms
MES
Monopolistic Competition
Monopolistic Competition
MARKET STRUCTURE
Many Firms and Many Buyers
Easy Entry & Exit
PRODUCT DIFFERENTIATION ! ! !
Historical Background
Joan Robinson “Economics of Imperfect Competition, 1933
Edward Chamberlin, “Theory of Monopolistic Competition, 1933
Small Groups & Large Groups
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Product
Differentiation
Among Gas
Stations
Product Differentiation
Differentiation occurs when consumers perceive that a product differs from its competition on any physical or nonphysical characteristic, including price.
Examples: restaurants, dealer-owned gas stations, Video rental stores, book & convenience stores, etc.
Assumptions of the Model:
Large number of firms
Differentiated Product
Conditions of Cost and Demand are Similar
Easy Entry & Exit
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Basic Model of
Monopolistic Competition
In the Short Run
produce where MR= MC
price on the demand curve
NOTICE:
P > MC
economic profits exist
P > AC
there exists incentives for entry into this industry
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AC
MC
D
MR
PM
QM
SHORT RUN DIAGRAM
Profits in the SR Induces Entry
Entry in this industry “steals” customers.
Demand curve shifts inward
RESULTS
MR = MC (like monopoly)
P = AC (like competition)
Profits in LR are zero (like competition)
not at Least Cost Point of AC curve (like monopoly)
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AC
D’
D
LONG RUN DIAGRAM
P
Q
MC
MR
Properties of Monopolistic Competition
Dead Weight Social Loss continues to exist
Inefficient Production
EXCESS CAPACITY
not at least cost point of AC curve
Could Avoid Excess Capacity by JOINTLY PRODUCING at the same plant
Kroger Salt & Morton Salt OR Sears’ Kenmore and Whirlpool
Location -- hard to jointly produce
Does the decline in profits stifle innovation?
Is there too much product differentiation?
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Optimal Advertising Intensity
Suppose the price-cost margin percentage is constant, (P-MC)/P.
Advertising more if the profit contribution margin (PCM) times the advertising elasticity, Ea , is greater than the per unit cost of an advertising message, k, times the advertising to total sales ratio, A/PQ.
[(P-MC)/P] Ea > k A/PQ
If the contribution margin percentage were 50%, and the advertising elasticity were 2.
The left-hand side is 1.
Let the advertising to sales ratio
be 20%. The decision to expand advertising depends on k, the per unit cost of an advertising message.
If it costs less than $5 per unit,
in this example, it pays to
increase advertising efforts
Competitive Markets Under Asymmetric Information
Chapter 13
An assumption of pure competition was complete knowledge of all market information. But knowledge can be unevenly distributed among firms and consumers.
The concept of a "lemon" in the car market and adverse selection problem are only two of the interesting market phenomena when information is unevenly distributed (asymmetric) among the market participants
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Asymmetric Information
Used car: who knows what about it?
Incomplete Information -- uncertain knowledge of payoffs, choices, or types of opponents a market player faces.
Asymmetric Information -- unequal or dissimilar knowledge among market participants.
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Incomplete Contracting and Incomplete Markets
Insurance works when we can pool a group of possible events (like injuries at work) to reduce the risk of loss to any one party.
But some risks are catastrophic, like a nuclear accident. It is difficult to assess the likelihood or the damage; hence, insurance in this case is often unavailable.
Contracts can specify duties under several states of the world, but sometimes the outcomes are too numerous or unknowable for years. This creates incomplete contracts.
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Types
Full contingent claims contract -- specifies all possible future events.
Incomplete contingent claims contract -- not all possible future events are specified.
Due to incomplete contracts, some people may take advantage of spirit of the contract.
Accident insurance may permit people to succumb to a moral hazard by acting recklessly.
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Asymmetric Information
in a Lemon's Market
Search goods are products or services whose quality is best detected through a market search.
Experience goods are products and services whose quality is undetected when purchased.
To protect consumers, warranties and firm reputations are used to assure quality.
But if someone is selling his or her car, isn't it likely that the car is no good: a lemon?
If one firm defrauds customers, how do the reputable firms signal that they are NOT like the fraudulent firm?
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Adverse Selection and the Notorious Firm
Game: A firm may decide to produce a High Quality or Low Quality product, and the buyer may decide to offer a High Price or a Low Price.
Since the firm fears that if it offers a High Quality product but that buyers only offer a Low Price, they only produce Low Quality products and receive Low Prices.
This is the problem of adverse selection
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Notorious Firm Game Analysis
Simultaneous decisions
Maximin decision by firm is Low Quality product
Best for the buyer is a low price, but a high quality good. Worst is a High price but a Low quality good.
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BUYER
SELLER
Hi Price Lo Price
Hi
Lo
130 70
150 90
Payoffs are for
the Seller only
Solutions to the Problem of Adverse Selection
Regulation
Long term relationships, or reliance relationships
Brand names
Nonredeployable assets are assets that have little value in another other use
Example: the egg-shaped carton for L'eggs hosiery
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Cost Revelation in Joint Ventures and Partnerships
Potential partners have different information upon beginning a venture together
The Clarke tax mechanism
The mechanism is to assign probabilities to the revelation of costs of the partner.
After the other partner's expected costs are covered, they receive the residual or net profit.
Then each has an incentive to reveal their true cost.
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Optimal Incentives Contract
is an agreement about the payoffs and penalties that creates appropriate incentives
If the contract creates a stream of profits, then a breach is a costly penalty
example: an employee who steals is fired! If the employee felt the employment at that firm was rewarding, the penalty of firing is severe.
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Principal-Agent Problem
in Managerial Labor Markets
Stockholders (principals) hire managers (agents) with different incentives.
Alternative labor contracts
Pay based on profits
Paying a bonus on top of a salary when goals are exceeded
Have manager own stock
Benchmarking involves a comparison of similar firms, plants, or divisions
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Signaling and Sorting of Managerial Talent
Applicants to positions know more about themselves than they reveal, which is the problem of asymmetric information.
For example, is the applicant highly risk averse or a risk taker?
How can we sort between risk-takers and risk averse candidates?
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One Sorting Method
A Linear Incentive Contract provides a combination of salary and (plus or minus!) a profit sharing rate.
An offer that dominates all other offers will not help distinguish among applicants. This is a pooling equilibrium.
An offer that distinguishes between behaviors is a separating equilibrium.
For example, a risk averse person would tend to select an offer which primarily paid a base salary
Whereas the risk-loving individual would tend to select an offer with more profit sharing.
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STRATEGIC MOVES
Strategic Moves
scorched earth tactic or pledge as “strategic moves”
require (1) a planned course of actions & (2) credible commitment to this path
Ex: R&D efforts by Japan & US. If US commits first to high effort in R&D, Japan will likely take low effort, whereas
If Japan commits first to high effort, US will likely take the low effort.
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Threats and Promises
Threats -- a known response after a specific action or course of actions
often threats hurt everyone in the process
excessive threats though ‘won’t be believed’ as attacking Japan if they don’t reduce trade barriers.
Promises -- a known reward for specific action or course of actions
sharing a ‘trade secret’ or leaving a particular market
offering amnesty for a criminal who provides evidence
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Credible Commitments
In the cartoon Peanuts, Lucy’s promise to
Charlie Brown is not to be believed
But “selling English bonds” by Baron v. Rothschild appeared to be based on knowledge of Napoleon’s victory. Yet he made money on state-of-the art carrier pigeons by changing strategy after prices fell. The opposite of a commitment.
How to Build Commitment?
invest in reputation, use contracts, build on small steps to build trust.
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Unpredictability? Or Mixed Strategies
Most ‘games’ lend themselves to known preferences and actions, but sometimes a reputation for fast change can be useful.
Ex: IRS audits of Schedule A “gifts in kind” to charity were < $1,000, then what?
Suppose a baseball batter is known for always “looking at” the first pitch, then what?
Can be an “optimal amount” of randomness (Example: Tennis serves, fore- and back-hand)
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Increasing attention in business is being given to other tactics and strategies to achieve competitive advantages.
We’ll discuss rival firm behavior as if they were games.
Sometimes being the first-mover offers advantages.
Sometimes credible threats affect opponents' behavior.
In oligopolistic industries, the interdependence among firms is most keenly felt.
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Business Decisions as Simultaneous Games
An advertising campaign which kicks off during the Final Four basketball tournament is also a simultaneous game:
What will the rival firms do?
Sometimes it is useful to hide one's strategy by randomly changing strategies.
Not announcing when a price cut will occur.
Randomizing when reduced financing plans for autos will appear.
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Business Strategy Games
When oligopolistic rivals alter their products or pricing, our firm must react or adapt.
Best would be proactive behavior that could anticipate actions.
A sequential game is one in which there is an explicit order of play.
A sequential example is when one firm has announced a price cut, your decision to respond or not is sequential.
In simultaneous game occurs when all players must chose their actions at the same time. More in Chapter 16.
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Price and Output
Determination:MONOPLY
Chapter 14
"Monopoly" conjures images of firm with huge profits, great wealth, and indiscriminate power, labeled as robber barons.
There are also exist monopolies that are not very profitable, and those regulated by State Public Service or Utility Commissions. Some have had very low rates of return on invested capital.
We look at unregulated monopolies and regulated monopolies (known as utilities).
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Sources of Market Power
Legal restrictions -- copyrights & patents.
Control of critical resources creates market power.
Government-authorized franchises, such
as provided to cable TV companies.
Economies of size allow larger firms to produce at lower cost than smaller firms.
Brand loyalty and extensive advertising makes entry highly expensive.
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Monopoly: Single Seller; Entry is Prohibited; No Close Substitutes
1. FIRM = INDUSTRY
2. MR < P
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Q
D
P = 100 - Q
60
59
40 41
TR1 = 60•40 = 2400
TR2 = 59•41 = 2419
So, MR = 19
where MR < P
19
An Unregulated Monopoly
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D
MR
3. At output where MR = MC, profit
is maximized
MC
PM
QM
dP/dQ = dTR/dQ - dTC/dQ
Proof: Max P = TR - TC
Set dP/dQ = 0
equal to zero
0 = MR - MC
MR = MC
4. Charge highest price that the market will bear, PM
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MARGINAL REVENUE is twice as steep as a linear demand curve
If P = a - b•Q, then
TR = aQ - bQ2
so
MR = a - 2b•Q
If we use a linear demand curve:
Numerical Example
P = 100 - Q, where MC = 20.
Find where MR = MC
TR = P•Q = 100•Q - Q2
MR = 100 - 2•Q = 20
80 = 2•Q
QM = 40
Find Monopoly Price:
PM = 100 - 40 = 60
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The highest price
that the market will
bear.
Elasticity Form for Monopoly
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P [ 1 + 1/ EP ] = MC
Marginal Revenue
As EP goes to
negative infinity,
MR approaches
P
MONOPOLY has MR = MC
TR = Q•P(Q)
MR = P + (dP/dQ)Q = P [ 1 + (dP/dQ)(Q/P) ] =
P[ 1 + 1/ E P ]
Example: If EP is infinite, then
MR = P = MC
MR = MC implies
P[ 1 + 1/( - 3) ] = 100
P[ 2/3 ] = 100
So, P = $150.
If EP = -5, then optimal monopoly price falls to $125.
The more elastic is the demand, the closer is price to MC.
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If EP = - 3
& MC = 100
What’s PM ?
ANSWER
EVALUATION OF MONOPOLY
Wealth transfers from CONSUMERS to PRODUCERS: CS falls & PS rises in monopoly
Economic Profits are positive even in the Long Run
P > MC, price doesn’t signal cost
Output is RESTRICTED
Monopolists MUST restrict quantity
Licenses restrict entry into occupations
Dead Weight Social Loss (DWSL)
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D
MC
QM
PM
DWSL
PS
C S
Additional Problems with Monopoly
Technical Inefficiency
monopolists may be lax on costs
Rent-seeking Behavior
firms may spend great sums to preserve monopoly power.
Higher Incidence of Discrimination
textiles & agriculture vs plumbing & electrical work
Less Technologically progressive
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Q
MC
MC’
added costs
monopolists as less than
modern or efficient
Monopoly Pricing
Regression results for Land’s End Sportswear:
Log Q = - .4 Log P + Log Y
( 3 . 2) ( 4. 5)
Let MC of imported sports jacket be $, find the Monopoly Price for a Land’s End jacket.
ANSWER: P( 1 + 1/E ) = MC
P ( 1 + 1/() ) =
P = $
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NATURAL MONOPOLY
Declining Cost Industries
distributional economies
economies of scale
Without Regulation they face Cyclical Competition
railroad history
frequent bankruptcies
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AC
MC
DEMAND
MR
QM
P M
PR = AC
PC = MC
QR QC
Solutions to the
Problem of Natural Monopolies
PREVENT ENTRY, set P = MC and subsidize.
subsidies require some form of taxation, which will tend to distort work effort.
subsidies to AMTRAK
NATIONALIZE, prevent entry, set price typically low
governments find changing price a highly political event
once popular solution in Europe
REGULATE, prevent entry, & set P = AC
common in US for local telephone, electricity, water
FRANCHISE through a bidding war, likely P = AC
Cable .
concessions at various stadiums
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The Regulatory Process
Each state has Public Utility Commissions or Public Service Commissions who determine entry into the industry, jurisdictional disputes, and set a fair rate of return on the rate base.
If a company wants higher rates, it petitions the Commission for a specific amount of money. A quasi-judicial "rate case" hearing occurs before an administrative law judge. Evidence from the firm, the staff, and others determines if rate relief is justified or not.
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The revenue (R) must cover all operating costs (C) plus a permissible rate of return (k) on the rate base (V-D), where D is the accumulated depreciation and V is the value of the firm's assets.
R = C + (V - D)·k
The price for each class of customer, residential, commercial, or industrial, must cover the costs.
Utilities are permitted to price discriminate across classes of customers.
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Price Discrimination
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Price Discrimination - Goods which are NOT priced in proportion to their marginal cost, even though technically similar
Discussed in detail in Chapter 17
Block Pricing
Price declines as the quantity purchased increases
Examples:
Electrical rates (at one time)
TJ Maxx, second pair at half price
telephone charges
foreign film festivals
Price declines, similar to the demand curve
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Q
P
D
Peak Load Pricing
Examples: Long Distance Calls, Electrical Prices, Seasonally Pricing at Amusement Parks
Conditions
Not Storable
Same Facilities
Demand Variation
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Peak and Off-Peak Demand
What price should we charge for peak and off-peak users?
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Off Peak
Demand
Peak Load Demand
price
Pp
Po
General Solution
P(peak) = variable costs + capital costs
P(off-peak) = variable costs only
Some argue that off-peak users benefit from capacity
Electrical Case: Less chance of a brown out
Amusement Park: Off peak users enjoy more space
Then, off-peak users should pay for some part of the capacity
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Monopoly in Cable TV
Ó1999 South-Western College Publishing
CABLE
TELEVISION
Naturally Monopolist -- Distributional advantages for one firm.
AC
subscribers
Expect that price is a function of
P = f( Competition, Density, Age,
Total # of Major Channels in Basic
Service)
Easy to compare
Cable rates in US
Log Linear Regression Results
R-squared = .255
LPRICE = * COMP + .0377 LDENSITY
LAGE + .2712* LMAJCHANNELS
where asterisks ( * ) designate statistically significant
Do the signs make economic sense? Are they significant?
Are the results consistent with competition influencing the prices of Cable .?
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dummy variable
1 if other cable firm
in the city, 0 if not
Some cities have only one Cable firm,
whereas others have several
Cable . and the Future
Competition enhanced if there are more MODES for transmission
Telephone wires, fiber-optic, & microwave as good alternatives to Cable wires for transmission of “signals”
Ó1999 South-Western College Publishing
Get out from under the thumb of the Cable companies
Oligopoly
Chapter 15
Market Structure
Few Firms
Consequently, must consider the reaction of rivals to decisions
Interrelated reactions
Heterogeneous or Homogeneous Products
Models: Cournot, Kinked Oligopoly Demand, Price Leadership, Collusion, and the Prisoner’s Dilemma
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Cournot Oligopoly
Oligopoly -- just a few firms
Models vary depending on assumptions of actions of rivals to pricing and output decisions.
Augustin Cournot (1838) created a model that is the basis of Anti-trust Policy in the .
Simple Model
Calculus is Easy
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A Model Between Monopoly & Competition
IN COMPETITION
P = MC, so 950 - Q = 50
PC = $50 and QM = 900
IN MONOPOLY
MR = MC, so 950 -2Q = 50
QM = 450 so
PM = 950 - 450 = $500
IN DUOPOLY
Let Q = q1 + q2
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D
PM
Pcournot
PC
QM QCournot QC
EXAMPLE:
450 600 900
$500
$350
$50
P = 950 - Q and MC =50
Cournot Solution:
Case of 2 Firms (Duopoly)
Assume each firm maximizes profit
Assume each firm believes the other will NOT change output as they change output.
The so-called Cournot Assumption
Find where each firm sets MR = MC
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Let Q = q1 + q2
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P = 950 - Q = 950 - q1- q2 and MC = 50
substitute for Q
Let Q = q1 + q2
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P = 950 - Q = 950 - q1- q2 and MC = 50
TR1 = Pq1= (950- q1-q2)q1 =950q1 - q12 - q1q2 and
TR2 = Pq2= (950- q1-q2)q2 =950q2 - q2q1 - q22
Find TR for each firm
Let Q = q1 + q2
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P = 950 - Q = 950 - q1- q2 and MC = 50
TR1 = Pq1= (950- q1-q2)q1 =950q1 - q12 - q1q2 and
TR2 = Pq2= (950- q1-q2)q2 =950q2 - q2q1 - q22
Set MR1= MC & MR2= MC
950 -2q1 - q2 = 50
950 - q1 - 2q2 = 50
2 equations &
2 unknowns
With 2 Equations & 2 Unknowns: Solve for Output
950 -2q1 - q2 = 950 - q1 - 2q2
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With 2 Equations & 2 Unknowns: Solve for Output
950 -2q1 - q2 = 950 - q1 - 2q2
So, q2 = q1 Plug this into the demand equation we find:
950 - 2q1 - q1 = 950 - 3q1 = 50
Therefore q1 = 300 and Q = 600
The price is: P = 950 - 600 = $350
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P Q
Competition 50 900
Cournot 350 600
Monopoly 500 450
N-Firm Cournot Model
For 3 firms with linear demand and cost functions:
Q = q 1 + q 2 + q 3
the solution is higher output and lower price
QCournot = { N / (N+1) }QCompetition
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QC
N
N
PC
THEREFORE, increasing the Number of Firms increases Competition. This is the historical basis for Anti-trust Policies
Example: Cournot as N Increases
If N = 3 Triopoly
P = 950 - Q & MC=50
Then, Q = (3/4)(900)
Q = 675
P =$275
If N = 5
P = 950 - Q and MC = 50
Then Q = (5/6)(900)
Q = 750
P = $200
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N = 3 N = 5
Oligopolies & Incentives to Collude
When there are just a few firms, profits are enhanced if all reduce output
But each firm has incentives to “cheat” by selling more
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MC
S MC
P
q
D
QM
incentive
to cut
price
MR
Collusion vs Competition
Sometimes collusion will succeed
Sometimes forces of competition win out over collective action
When will Collusion tend to succeed?
Determinants of successful collusion, for industries with only a few firms
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Factors Likely to Affect Collusion
1. Number and Size Distribution of Sellers. Collusion is more successful with few firms or if there exists a dominant firm.
2. Product Heterogeneity. Collusion is more successful with products that are standardized or homogeneous
3. Cost Structures. Collusion is more successful when the costs are similar for all of the firms in the oligopoly.
4. Size and Frequency of Orders. Collusion is more successful with small, frequent orders.
5. Secrecy and Retaliation. Collusion is more successful when it is difficult to give secret price concessions.
6. Social Structure of the Industry. Collusion is more successful when industry executives often meet together.
Kinked Oligopoly Demand Curve
Belief in price rigidity founded on experience of the great depression
Price cuts lead to everyone following
highly inelastic
Price increases, no one follows
highly elastic
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everyone
follows
price cuts
no one follows
a price increase
a kink at the price
P
A Kink Leads to Breaks in the MR Curve
Although MC rises, the optimal price remains constant
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P
D
D
MR
MC1
A Kink Leads to Breaks in the MR Curve
Although MC rises, the optimal price remains constant
Expect to find price rigidity in markets with kinked demand
QUESTION:
Where would we more likely find KINKS and where NOT?
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P
D
D
MR
MC2
MC1
Which industries are likely to have kinks and which have no kinks?
The GREATER the number of firms, likely more kinked
Prices Likely More Rigid
The more HOMOGENEOUS, likely more kinked
Prices More Rigid
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N = 10
N = 2
homogeneous
heterogeneous
Which industries are likely to have kinks and which have no kinks?
The more EQUAL SIZED are the firms, likely more kinked
Prices Likely More Rigid
The existence of a Dominant Firm creates a price leader
With a price leader, there is no need to imagine a kink in the demand
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Equal
Sized
Firms
DOMINANT
Firm Exists
Empirical Evidence vs.
Predictions of the Model
Oligopolies with few firms were more rigid in FACT
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s 2
N
prediction
FACT
Empirical Evidence vs.
Predictions of the Model
Oligopolies with few firms were more rigid in FACT
Oligopolies with homogeneous products were MORE rigid in FACT
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s 2
s 2
N
prediction
FACT
heterogeneous homogeneous
prediction
FACT
Empirical Evidence vs.
Predictions of the Model
Oligopolies with Dominant Firms were actually more rigid in FACT
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s 2
Dom. Firm Equal Sized
prediction
FACT
Are these Empirical Findings Surprising?
A Kink is a barrier to profitability
Firms are in business to make profits
Simple Alternative Explanations Exist:
More Firms are More competitive
More Homogenous Products are more competitive
More equal-sized are more Competitive
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Price Rigidities and
Employment Impacts
Price rigidity will make business downturns worse
Employment will be more volatile over the business cycle if there are price rigidities
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D BOOMS
D BUSTS
A rigid price
OUTPUT
if price changes
with shifts in demand
Q3 Q2 Q1
PRICE LEADERSHIP
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Barometric Price Leadership
PRICE LEADERSHIP
Barometric: One (or a few firms) sets the price
One firm is unusually aware of changes in cost or demand conditions
The barometer firm senses changes first, or is the first to ANNOUNCE changes in its price list
Find barometric . where the conditions unsuitable to collusion, & have good forecasting abilities or good management
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Barometric Price Leader Example: Citibank & Prime Rate Announcements
Banking: 8,000 banks and falling, but still a lot.
New York, center of Open Market activities of the Fed Reserve
Citibank’s announcement represents changes in interest rate conditions to other banks tolerably well.
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Dominant Firm Price Leadership
Dominant Firm: 40% share of market or more.
No price or quantity collusion
Dominant Firm (L) expects the other firms (F) to follow its price
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D
S MC F
Dominant Firm Price Leadership
Dominant Firm: 40% share of market or more.
No price or quantity collusion
Dominant Firm (L) expects the other firms (F) to follow its price and produce where S MC F = PL
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D
S MC F
DL
Net Demand Curve: DL = D - S MC F
leader’s
demand
Find leader’s demand curve, DL = (D - S MC F)
Find where MRL = MCL
At QL, find the leader’s price, PL
Followers will supply the remainder of Demand: (QT - QL) = QF
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D
S MC F
DL
MRL
Find leader’s demand curve, DL = (D - S MC F)
Find where MRL = MCL
At QL, find the leader’s price, PL
Followers will supply the remainder of Demand: (QT - QL) = QF
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D
S MC F
DL
MRL
MCL
PL
QL
Find leader’s demand curve, DL = (D - S MC F)
Find where MRL = MCL
At QL, find the leader’s price, PL
Followers will supply the remainder of Demand: (QT - QL) = QF
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D
S MC F
DL
MRL
MCL
PL
QL
QT
Implications of a Dominant Firm .
Market Share of the Dominant Firm Declines Over Time
Entry expands S MC F, and Shrinks DL and MRL
Profitability of the Dominant Firm Declines Over Time
Market Share of the Dominant Firm is PROCYCLICAL
rises in booms, declines in recessions
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TIME
profits
. Steel (USX)
Judge Gary
Industrial “Cocktail Parties” to discuss pricing
1901 steel mergers led by
66% market share
46% market share by 1920
42% share by 1925
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profits in a
dominant firm
model
normal
profits
profits when using a lower price
Oligopolistic Rivalry & Game Theory
John Von Neuman & Oskar Morgenstern--
Game Theory used to describe situations where individuals or organizations have conflicting objectives
Examples: Pricing of a few firms, Strategic Arms Race, Advertising plans for a few firms, Output decisions of an oligopoly
Strategy--is a course of action
The PAYOFF is the outcome of the strategy.
Listing of PAYOFFS appear in a payoff matrix.
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Two Person, Zero Sum Game
Each player knows his and opponent’s alternatives
Preferences of all players are known
Single period game
Sum of payoffs are zero
Like a Poker Game
An Equilibrium--none of the participants can improve their payoff
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ASSUMPTIONS
PLAYER 2
PLAYER 1
a
b
c d
1, -1 3, -3
-2, 2 0, 0
Player 1 is the first number in
each pair. We will get to {a,c}
which is an Equilibrium
Dominant Strategies & Maximin Strategy
For Player 1, strategy (a) is a dominant strategy
best regardless of what others do
Maximin Strategy
the choice that MAXIMIZES across the set of MINIMUM possible payoffs.
Best of the Worst
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PLAYER 2
PLAYER 1
a
b
c d
1, -1 3, -3
-2, 2 0, 0
Player 1 looks for the Max { Min}
as Max {1, -2} so picks Strategy-a
Player 2 looks for Max { Min } as
as Max {-1, -3} so picks Strategy-c
Find Maximin Strategies for Bob & Alice
Alice’s payoffs appears in upper triangle and Bob’s appear in the bottom
Find Maximin Solution
Is it an Equilibrium?
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Bob
Alice
a
b
c d e
5 1 -1
-5 -1 1
3 7 -8
-3 -7 8
Worst for Alice with a-strategy is -1
Worst for Alice with b-strategy is -8
Worst for Bob with c-strategy is -5
Worst for Bob with d-strategy is -7
Worst for Bob with e-strategy is 1
best
best
?
Unstable Games: No Equilibrium Is Found
In the Alice-Bob Game here, Maximin Strategies lead to solution {b, c}
But Alice has an incentive to switch to strategy-a
Then Bob has an incentive to switch to strategy-d, etc., etc.
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Bob
c d
Alice
a
b
3, - 3 1, - 1
2, - 2 4, - 4
There is no, single stable equilibrium
Each player may elect a random
strategy
Two-Person, Non-Zero Sum Games
Often the payoffs vary depending on the strategy choices
Famous Example: The Prisoner’s Dilemma
Two spies are caught & held separately
Confess or Not Confess:
1period game
Noncooperative Solution
both confess: {C, C}
Cooperative Solution
both do not confess {NC,NC}
Off-diagonal represent a Double Cross
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spy 2
spy 1
NC
C
NC C
1 yr 15 yrs
0 yrs 5 yrs
1 yr 0 yrs
15 yrs 5 yrs
Duopoly as a Prisoner’s Dilemma
Even if both spies meet to agree on a cooperative solution, one may double cross.
Two firms: Decision is the amount of output [ S = small, or L = large ]
{L,L} represents normal profits
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FIRM 2
FIRM 1
S L
S
L
100, 100 10, 150
150, 10 20, 20
MAXIMIN SOLUTION {L, L }
Is it an Equilibrium?
Duopoly as a Multiperiod Game
The single period game predicts that there will be competition
But duopolists are likely to have many periods in which to compete
Multiple periods allow for “Punishment” or retribution not found in single period games.
We would expect that collusion is More Likely to Succeed, the greater chance for more periods
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N - Person Games
Can extend also to more than 2 players
Chief new complication:
Coalitions of players
Issues of cooperation & duplicity
Solutions for N-person games can be difficult
It gives mangers a way to gain an insight into the nature of conflict, posturing, and resolution
Ó1999 South-Western College Publishing
Game-Theoretic Rivalry:
Best Practice Tactics
Chapter 16
Increasing attention in business is being given to tactics and strategy to achieve competitive advantages.
This chapter predicts rival firm behavior as if they were games.
Sometimes being the first-mover offers advantages. Sometimes credible threats affect opponent’s behavior.
In oligopolistic industries, the interdependence among firms is most keenly felt.
Ó1999 South-Western College Publishing
Business Strategy Games
When oligopolistic rivals alter their products or pricing, our firm must react or adapt.
Best would be proactive behavior that could anticipate actions.
A sequential game is one in which there is an explicit order of play.
A sequential example is when one firm has announced a price cut, your decision to respond or not is sequential.
A simultaneous game occurs when all players must chose their actions at the same time.
Ó1999 South-Western College Publishing
Business Rivalry
as a Sequential Game
The first to introduce a product, lower price, etc., often achieves recognition and an advantage, called a first-mover advantage.
When games last several periods, the actions by firms in one period can be punished or rewarded in future period.
If a new firm enters a market, the threat is that the incumbent firm may drop prices down to levels that are unprofitable.
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First Mover Games
A. Carnegie: The first person gets the oyster, the second person gets the shell.
Some markets are too small for multiple firms.
Game with Military and Civilian markets for “water-land vehicles” (DUCKS)
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B
civilian military
A
civilian
military
-10, -10 30, 15
15, 30 -10, - 10
In a simultaneous game, both
would want the civilian market. But
in a sequential game, the first to get
the civilian market preempts it. The
other firm takes the military market.
Game Tree
Way to Illustrate Sequential Games
A game tree is like a decision tree.
It is a schematic diagram of decision nodes
(or focal outcomes).
Solutions to games parallels board games like chess.
One way to solve a decision problem is to use end-game reasoning, where we start with the final decision and use backward induction to find the best starting decision on the game tree.
If I lower price, the end may be a price war!!!
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A “credible threat”
A credible threat is an action that is perceived as a possible penalty in a noncooperative game.
Its existence sometimes induces cooperative behavior.
A credible commitment is a mechanism for establishing trust
such as a reward for good behavior in a noncooperative game.
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Mechanisms for credible threats
and commitments
contractual side payments, but these may violate antitrust laws.
use of nonredeployable assets such as reputation.
entering alliance relationships which would fall apart if any party violated their commitments.
using a "hostage mechanism" that is irreversible and irrevocable can deter breaking commitments.
Examples are "double your money back guarantees," and "most favored nation" clauses.
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Hostage Mechanisms in Oligopoly
Best Buy’s offer: If you find a lower advertised price, you’ll get that money back
This makes Best Buy cut prices whenever local TV stores cuts prices
Local stores realize they won’t undercut
Best Buy
Customers realize it is unlikely to find lower prices
If potential entrants ( Silo, Freddy’s, etc.) think they can get a foothold in area, they know that Best Buy’s pricing is a credible commitment.
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Size Barriers
Sometimes entrants must leap to a large scale if they wish to enter a market
incumbent firms may accommodate the entrant, allowing a niche.
incumbent firms may take entry deterring actions, such as cutting their prices at any threat of entry.
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Excess Capacity, Scale of Entry, and Entry Deterrence
Building excess capacity can deter entry. Potential entrants know that the price can
be driven down to near zero if they entered, and the incumbent firm began a price war.
The building of extra capacity is an action in a sequential game, often with the intent of forestalling entry. This is called a precommitment game.
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Sorting Rules
Brand loyalty to incumbents
Efficient rationing
Random rationing
Inverse intensity rationing
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Theory of
Contestable Markets
The theory of contestable markets holds that, with no barriers to entry, even a monopolist must
be aware that charging higher prices will encourage entry.
Hence, a contestable market will tend to have zero economic profits and competitive prices.
Potential entry, rather than number of firms matters most
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Simultaneous Games
A sealed bid auction is a simultaneous game.
A dominant strategy is the best decision, no matter what anyone else does. It is an action (strategy) that is better in each "state of the world."
When no Nash equilibrium exists, it is useful to hide one's strategy by randomly changing strategies. This is a mixed Nash equilibrium strategy.
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Nash Equilibrium
When all players make their best reply responses (so changing their choices cannot improve their position) then the game is in a Nash Equilibrium.
Since game trees have several branches, we can examine the concept of equilibrium in each part of the tree, called a subgame
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Escape From Prisoner's Dilemma: Repeated Games
If the games are repeated, there is greater expectation that firms will achieve the cooperative solution.
Each firm "shows" by its behavior each period that it wants to cooperate.
Firms that expand production "show" that they do not want to cooperate.
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Examples of
Repeated Game Strategies
a grim trigger strategy which has an infinitely long punishment.
alternatively, the punishment can last for a period.
For multi-period games, there usually is some period of punishment that can induce cooperation.
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trembling hand trigger
For non-infinite lived games, if you are
one period before the end, the best strategy is
to act noncooperatively.
Yet this logic works for two periods before the end,
and tends to unravel a cooperative, multi-period game.
Some game theorists have wondered if the slight defections could go unpunished, called a trembling hand trigger strategy.
If the rival acts noncooperatively once, perhaps you can forgive. But fool me twice, and then watch out!
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Optimal Mechanism Design
Appendix 16A
Contracts between players are binding that specifies actions by both parties. Contracts must assign penalties for not living up to the agreement. These payments are part of a several step sequential game.
A vertical requirements contract is one in which the firms in successive stages of production agree to payments and/or penalties for taking an action.
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Choice of Organizational Form
A reliant asset is a non-redeployable durable asset. Specialized equipment or specialized knowledge cannot be transferred to other uses.
Markets with reliant assets one party could “hold-up” the other party. The choice of organization will require explicit contracts. The likely outcome is franchise contracts.
Relational contracts are promissory agreements of coordinated performance. A jet charter company is a good example.
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Filling customer orders from those waiting
in line is the service queue problem
First-come, first-served ¾ The people with the lowest cost of time get the tickets.
Last-come, first-served ¾ removes the incentive to wait in line. The best strategy is to show up anytime, whenever the ticket window is open.
Stratified lotteries ¾ advanced reservation tickets are assigned different prices than last minute walk-ups.
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Auction Design
Simultaneous bidding ¾ open outcry at estate auctions. Information about other bidders valuation is revealed
Sequential bidding ¾ such as private placement for newly issued securities.
Bid prices can be discrete or continuous ¾ by agreed increments, as in 1/8 or 1/16 for stocks or any price.
Bids can be sealed or posted ¾ sealed bids make them anonymous and secret to other bidders
Bids can be one-time-only or multiple rounds.
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Types of Auctions
In English auctions, the prices rise as more bids arrive.
In Dutch auctions, a high price is announced, and if no one agrees, the auctioneer lowers the price until the first bid arrives.
If mineral rights to 1,000 acres of land were auctioned, the winning bid may elect to purchase less than 1,000 acres or rights.
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Winner’s Curse
If the true value of an item is not known, but
bidders have a distribution of values that they are willing to pay, the winning bid is very likely to be higher than the true value.
The regret for the bidder is that he or she paid too much: the winner’s curse.
If everyone is aware of the winner’s curse, then all would bid less than what they think is its true value. This problem has led some auctions to award the highest bidder with the second-best price in a sealed bid auction. Even though you won, the price was a bit lower than what you paid.
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Pricing Techniques and Analysis Chapter 17
Value-based over cost-based pricing often helps build profits.
Firms charge different customers different prices, which is known as price discrimination.
This chapter also looks at pricing within a firm called transfer pricing.
Pricing techniques that are used by many multi-product firms, such as full-cost pricing and target return pricing.
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Proactive Value-based Pricing
If the price doesn’t fit what customers are willing to pay, then the product may not be profitable to produce, even if price is above cost.
Customer value is the focus for pricing, not just the costs associated with the product. Apple Computer lost market share by ignoring this.
It’s profitable to refuse some orders and accept others by differentially pricing products.
Pricing peak demand above off-peak demand, is a simple form of differential pricing.
Toll bridges could charge more at rush hour.
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Price Discrimination
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Price Discrimination -- Goods which are NOT priced in proportion to their marginal cost, even though technically similar
Some Necessary Conditions:
1. Some Monopoly Power
In Perfect Competition, P = MC
2. Ability to Arbitrage
Separate Customers and Prevent Reselling
Arbitrage - Buy Low to Sell Higher
Arbitrage of Goods is Very Easy
Hard to be effective with price discrimination
Arbitrage of Services is Very Difficult
Easy to price discriminate
Little price discrimination by age at grocery stores, but found at restaurants
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Many Ways to Separate Customers for Price Discrimination
1. Geography
2. Income
3. Gender
4. Age
5. Time
6. Race
7. Language
8. Transient/ Resident
9. Ability to Haggle
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Why Practice Price Discrimination?
In Simple Monopoly, there is only one price
Consumers receive a consumer surplus
In Price Discrimination, monopolists can SCOOP OUT all consumer surplus
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Q
D
MC
PSM
QSM
CS
Simple
Monopoly
First Degree Price Discrimination
Charge the MOST that a person is willing to pay for each good
Zero .
Produce MORE than in Simple Monopoly
Output the same as in Competition
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Q
D
MC
Price Discriminating
Monopoly
Q1st
Car Sales as First Degree Price Discrimination
“How much do you plan to pay a month?”
you inadvertently reply:
“Only $200 per month, but I have $1,000 down payment!”
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Ahh, that’s
$9,887 for 60 months at our % financing,
plus $1,000!
Here’s one for only
$10,887. It’s swell.
Notice: Incentives to Understate One’s True Willingness to Pay
The conditions for First Degree . are seldom met
Hence, some close approximations exist
There are are a variety of ways to group units to attempt to scoop out consumer surplus
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Second Degree Price
Discrimination:
Units are Grouped
Second Degree Price Discrimination Methods
All or nothing offers
Two part pricing
Bundling methods
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All or Nothing Price Discrimination
Buy a group of items, but CANNOT buy them individually
Four light bulbs, but not individual bulbs
Candy bars in movie theaters -- large size
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Second Degree Price Discrimination:
Not permitted to bring FOOD
into a movie theater: Why?
Demand for Ounces of Chocolate
Willing to pay $ for a 4-ounce chocolate bar
At 50¢ per ounce, would buy only 2 bars
All or Nothing gets one off his or her demand curve at, say, $ for a 4-ounce bar
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90¢ 60¢ 40¢ 30¢
50¢
1 2 3 4 Oz.
all or nothing
Two-Part Pricing:
Another 2nd Degree Form
A price for the privilege of buying items
And a price per item
Examples:
Country club dues and greens fees
Cover charge to
enter and a price
per drink
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Cover
Charge
MC
Q
If P = - Q and MC = .50
Find Optimal Cover Charge
At P = $.50, you buy 4 mugs beer
Biggest cover charge is the area of a triangle
Height is 4
Base is 4
(1/2)Height•Base
Max cover charge is $
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Cover
Charge $8
$.50
Q
4
$
Monopoly: QM = 2 & PM =
QM
PM=$
Cover
Charge
$
Bundling (or Block Booking)
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Often the pricing arrangement includes purchasing groups of dissimilar products. The products are bundled or sold as a block, as in theatrical or sporting tickets.
Preferences are uncorrelated Preferences are correlated
1
2
A B A B
150 100
80 190
250
270
160 200 = 360 simple
monopoly
500
80 100
165 175
180
340
165 200 = 365
simple monopoly
360
Third Degree Price Discrimination
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East West Market
MC
MR
PM
Example with a Simple Monopoly
Price in both markets
Third Degree Price Discrimination
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East West Market
MC
MR
PM
Example with Different Prices in Each Market
PE
PW
MR
MR
Pricing In Segmented Markets
Segment markets by price sensitivity
Charge higher prices in the markets that are the most inelastic
Then P1 = $150 and
P2 = $120
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P ( 1 + 1/ EQ•P ) = MC
Suppose MC = $100 in 2 markets
and E1 = - 3 and E2 = - 6
Why are
haircuts for
kids cheaper
than for
adults?
Products are INDEPENDENT when changes in price and quantity of one product do not alter revenues or cost in the others
Products are INTERDEPENDENT, when changes DO affect other products
Ex: Procter & Gamble makes both Luvs and Pampers
TR = TRA + TRB
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Pricing in Multiple Product Firms
Substitutes & Complements
Look for interdependencies in marginal revenues:
MRA = ¶TRA / ¶QA + ¶TRB / ¶QA
MRB = ¶TRA / ¶QB + ¶TRB / ¶QB
Substitutes when cross terms are negative
Erosion or Cannibalism are terms used
Complements when cross terms are positive
BASE sells tapes and tape head cleaners
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Decision Rule for Multiple Product Firms
Do NOT use the rule to produce where
MR=MC, as in MRA = MCA
INSTEAD:
Produce where the FULL MR = FULL MC
For a Two Product Firm of A & B
Produce where:
¶TRA /¶QA + ¶TRB /¶QA = ¶TCA /¶QA + ¶TCB /¶QA
Include all relevant revenue and cost effects
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Curious Pricing Example
Turkey prices fall during Thanksgiving
Yet we would expect DEMAND to be greatest?!
Loss Leader Pricing
Consider T as turkey
and A as all other food
TRstore = TRT + TRA
MRstore for turkey = ¶TRT /¶QT + ¶TRA /¶QT
Complementarity with other food explains the apparent conundrum
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Pricing of Joint Products
Interdependencies in costs occur in products that are produced simultaneously
., Beef & Hides; Wool & Mutton; Natural Gas & Crude Oil
Suppose FIXED PROPORTIONS in production: 500 lbs of Beef + 10 sq. yards of Hide for 1 steer.
Two cases: No Excess of Hides, and Excess Hides case
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Steers: No Excess Case
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steers (T)
DH
DB
MRH
MRB
Two Demand Curves:
Hides & Beef
Two MR Curves:
Hides & Beef
Steers: No Excess Case 2
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steers (T)
DH
DB
MCT
MRH
MRT
Find where
MRT = MCT
to find the
optimal of
steers.
Steers: No Excess Case 3
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steers (T)
DH
DB
MCT
MRH
MRT
At the optimal number of
steers, find
the prices of beef & hides on their
respective
demand curves
T
PB
PH
If demand for beef
rises, the price
of hides will
fall !
Excess of One of the Joint Products
Excess means the price would be ZERO
Solution: hold back some of the excess to reach the Unit Elastic Point on the Demand Curve
This Maximizes TR
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Multi-Divisional Firms
and the Economics of
Transfer Pricing
Transfer Pricing serves two functions:
1. Measure of the marginal value of the resource
2. Provides a performance measures of resources used
Create Transfer Prices Similar to Competitive Market Prices
Disagreements across divisions are common
“Selling” Division wants a HIGH transfer price
“Buying” Division wants a LOW transfer price
When External Markets exists, use those prices for transfer (a market-based competitive price)
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motor assembly
final car
assembly
sell to others @ “P”
purchase motors from others @ “P”
Transfer Pricing
With No External Markets
When no external markets exist, use the MC of the transferred good.
Often, however, the MC is a function of output.
Marketing and Production steps (M & P)
Transfer price is PT = MC P on following figure
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Find Where MCM+P = MR
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D
MCM
MCP
MCM+P
MR
P
PT
Pricing in Practice
Managers report wide use of cost-plus pricing methods
Streamline pricing of multiple products
Streamline pricing of retail prices
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Cost-Plus and Full Cost Pricing
P = ACn + Markup
or
P = ACn(1+ m)
where ACn is average cost at a normal output and m is a percentage markup
Notice: Little reliance on MC pricing or use of elasticities, as in: P( 1 + 1/Ep ) = MC
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Cost-Plus Pricing: Illustrated
Manufacturing pricing illustrated: One Good
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AFC
AVC
Qn
Qcapacity
ACn
} markup
P
ATC
Cost-Plus Pricing: Illustrated
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AFC
AVC
Qn
Qcapacity
ACn
} markup
P
D1 D2
quantity
varies as
demand
varies
Cost-Plus Pricing: Illustrated
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AFC
AVC
Qn
Qcapacity
ACn
} markup
P
D1 D2
quantity
varies as
demand
varies
Q1
Q2
Full Cost Pricing
Full Cost--
Covers all Costs at the standard or normal output
Plus a return on the investment
P = AFCn + AVCn + X / Qn
where X is the target amount of profit
Example: Low Tech Security
FC = 200,000, Qn = 3000, VC = 90,000
X = 100,000, Find Full Cost Price!
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Full Cost Pricing
Answer
P = AVC + AFC + X/Q
P = 30 + +
= $130
Suppose a 35% markup
P = [ AC] ()
P = [ 30 + ]()
P = $
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Reconcile Cost-Plus Pricing and
Economic Theory
Theory says: P= MC in Competition, and in Monopoly P(1 + 1/EP) =MC
Practice says: Cost-Plus pricing
In Retail, MC = AVC
So, P(1 + 1/Ep) = MC = AVC
Rearranging: P ( (E+1)/E ) = AVC
P = AVC[ E /(E+1)] =AVC[(E+1-1)/(E+1)]=
AVC[ 1 + (-1/(E + 1)) ] = AVC( 1 + m)
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The Optimal Markup in Theory
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P = AVC [ 1 + m ]
m = -1 / (E+1)
If E = - 3, then
the markup is 50%
if E = - 5, then
the markup is 25%
if E = - 11, then
the markup is 10%
The Optimal Markup
Depends on the
Price Elasticity
Problem: Koss CD Players
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Double-log regression: Log Q = 4 + Log I - log P
R-square = .4548
1. Koss production department estimates MC = $100. Find the Optimal Monopoly Price.
2. Average total cost is expected to be $103 at an
output approximately at 85% of capacity. With an
investment of $2 million, and a target of 20% rate
of return, and a normal output of 10,000 units,
Find the Full Cost Price .
ANSWER
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1. Optimal markup is [ -1/( + 1)] =
.8333 or %. The Optimal Monopoly
Price is 100() = $
2. The full cost price is:
P = ATC + (p • Investment) / Q
P = 103 + (.20 • 2,000,000)/10,000
P = 103 + 40 = $
Advantages & Disadvantages of Cost-Plus Pricing
Cost-Plus is simple
Easy to Delegate to Others
Easy to Apply to Thousands of Items
Can Use Categories of Markups for Different Classes of Products
But Cost-Plus Ignores Demand Changes
May be Based on Poor Cost Data
Output Varies in Business Cycle
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Hybrid Method: Variable
Cost-Plus Pricing -- the
markup can vary over the
season, or business cycle
Optimal Markups in Practice
Grocery stores have low markups
Many close substitutes -- at other grocery stores (bread varieties and qualities are standardized)
Frequent purchase, so customers are knowledgeable about prices & quality
Demand is therefore highly elastic
Optimal markup would consequently be small
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Markups on Jewelry
Jewelry Markups are known to be large
Difficult to make comparisons across jewelry stores
Little repeat purchases, so knowledge about prices is low
Consequently, lower price elasticity for jewelry
The optimal markup is larger
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Skimming
Price declines over time
Those in the avant garde wish to get it first, others are willing to wait
Examples:
Hardcover & Paperback Books
Electrical & Computer Products
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TIME
P
D
Yield Management: Appendix 17A
Yield Management is the problem of the disappearing inventory.
Managers must be flexible to change their predicted sales by market segment as information arrives.
Airlines price discriminates between business and non-business travelers. If too few business travelers have booked tickets compared to the amount expected, then more non-business tickets should be released.
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Optimal Overbooking - Managers may authorize reservation clerks to sell more seats (rooms) than are available.
The greater the overbooking, the lower are the costs of spoilage. Spoilage is an inventory NOT sold. If capacity is large, an airline or hotel will have high spoilage.
The greater the overbooking, the greater are the costs of spillage, making customers unhappy by finding that they have no seat or “room in the inn."
Spillage is the excess demand that cannot be met. If the service industry has low capacity, the spillage will be great, as customers leave the hotel or airline unable to get a room or an airplane seat.
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Government Regulations
Chapter 18
Corporations are legal entities which exist because governments allow them.
Governments impose many restrictions on firms: mergers, patents, licensing, or subsidies.
The stated intention of governments is set restrictions that promote social welfare, but they sometimes benefit particular groups or individuals.
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Market Performance, Market Conduct, and Market Structure
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Market basic supply and demand conditions
MARKET STRUCTURE
MARKET CONDUCT
MARKET PERFORMANCE
Feedback
Effects
Good Market Performance Depends on:
Efficient resource allocation
Technologically progressive.
Promote full employment
Equitable distribution of income
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Market Conduct
Pricing behavior.
Product policy.
Sales promotion and advertising.
R&D and innovation strategies.
Legal tactics with regard to entry.
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Market Structure
Seller and buyer concentration in a market. With one buyer we get to monopsony.
Product differentiation. A market structure of highly differentiated products may be monopolistically competitive.
Conditions surrounding entry conditions. The ease of entry and exit are market structure determinants.
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Contestable Markets
Economists have thought that structure influences conduct and performance in an industry.
This is the central paradigm in the economic field known as industrial organization.
The idea of contestable markets is applied in markets with scale economies.
A perfectly contestable market has many "potential entrants" with the same cost functions as the incumbent firms.
They enter or not depending on the incumbent's price, which causes the incumbent firms to set prices equal to marginal costs
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Condition of Entry
1. Demand conditions.
2. Control over input supplies.
3. Legal barriers.
4. Scale Economies.
5. Large capital requirements
6. Technological barriers.
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Market Concentration
1. Concentration ratio sum the market shares of the largest 4, 8, 20, 50 firms.
A four-firm concentration ratio (4CR) of 80 says that the top for firms comprise 80% of the sales in the industry.
2. Herfindahl-Hirschman Index (HHI) is: HHI = S Si2, which is the sum of the squares of the market shares of all firms in the industry.
It is near zero when there are countless tiny firms. When an industry approaches monopoly, the HHI gets close to one.
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Antitrust: Government Regulation of Market Conduct and Structure
In trusts, the voting rights to the several firms are conveyed to a legal trust to manage the group of firms as if it were one firm. This tends to create monopolization of an industry.
The Sherman Antitrust Act (1890) outlawed monopolies per se and attempted monopolization.
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The Clayton Act
The Clayton Act (1914) extended the list of conduct that was anti-competitive:
a. price discrimination.
b. tying contracts force customers to buy added products with one product.
c. purchasing shares of competing firms.
d. corporate directorship interlocks occur when the same people are in directorships of competing firms.
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The Federal Trade Commission was established in 1914 to prohibit unfair methods of competition.
The Wheeler-Lea Act of 1938 made deceptive practices illegal.
The Celler-Kefauver Antimerger Act (1950) restricted mergers through asset acquisition when the acquisition "may be substantially to lessen competition."
The Hart-Scott-Rodino Antitrust Improvement Act (1976) requires notification by large firms to the Justice Department of impending mergers.
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Regulatory Constraints
Operating controls appear in environmental pollution and product quality and safety issues.
The government, mandates that automobile manufacturers must sell cars with seat-belts and must attain certain emissions standards for their fleet.
EXAMPLE: The Palladium Metal-Casting
Adding an additional fixed cost (to reduce smoke) lowers profit without changing the price.
If the operating controls raise variable costs, the output and price changes in the directions you would expect: higher prices and lower output.
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The Deregulation Movement
Airline and trucking has been deregulated.
They are no longer "infant industries."
Deregulation of long-distance occurred due in large part to technological changes in transmitting phone messages by microwave.
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Government Support to Business
Governments historically have "helped" some companies, by restricting or eliminating competition.
Examples
Licensing of professions (or businesses)
Patents of ideas or processes restricts use of the idea
Restrictions on price competition
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Coase Theorem
The Coase Theorem argues that if the transaction costs for private contracting between parties are very low, the problems of externalities will be resolved without governmental intervention.
Even if governments and the courts can assign property rights or duties however they wish, the solution is unaffected if transaction costs are low.
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Robinson-Patman Act of 1936
Section 2(a) prohibits price discrimination which "substantially lessen competition".
Section (2b) provides a cost justification for price discrimination.
Section (2c) prohibits some kinds of brokerage commissions.
Sections (2d-2e) prohibits discounts to buyers not afforded to other customers.
These sections are the basic laws against price discrimination.
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Other Governmental Regulations
Import Quotas and Import Tariffs
Government Subsidies
Government Promotion occurs when the government spends money on research & development or on the benefits of particular life styles or practices.
Tax as a Regulatory Tool
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Economic Externalities and Market Failure Appendix 18A
Types of Externalities
Production Externalities:
External Production Economies ¾ expansion generates benefits to other firms.
External Production Diseconomies ¾ expansion generates uncompensated costs on other firms.
Consumption Externalities:
External Consumption Economies ¾ an increase in use of this product increases the utility of others.
External Consumption Diseconomies ¾ an increase in use results in uncompensated costs on others.
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Solutions to Externalities
Solution by Prohibition
Solution by Directive
Solution by Voluntary Payment
Solution by Merger
Solution by Taxes and Subsidies
Solution by Sale of Pollution Rights
Solution by Regulation
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Long Term Investment Analysis
Chapter 19
Budgeting is a form of planning
Operational Budgeting -- revenues & expenses
Capital Budgeting -- assets that generate returns more than a year
even more significant, since projects will impact the firm for many years to come
Problem of Limits:
Every manager wants more equipment, more supplies, more buildings, more employees
The issue is to accept good projects, and forego others
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Categories of Capital Projects
Projects to reduce costs
Projects to expand output
New products or new markets
Projects to meet governmental regulations
Most capital projects require
good information
sales and cost projections
advertising
financing, etc.
Ó1999 South-Western College Publishing
Objective Function: Top Management
Objective is to maximize the value, V, of the firm
Ó1999 South-Western College Publishing
Max V = S {(Rt - Ct) / (1 + r ) t }
objective function is:
the decision rule is:
Invest until IRR = MCC
internal rate or return = marginal cost of capital
IRR
MCC
Optimal Investment
ROR
If IRR = 20% & MCC =10%
then do it to increase V
Process of Capital Budgeting
Estimate initial costs
Bids, “request for proposals” (RFPs), Estimates, Guesses
Estimates net cash flows (NCFs) for the future depends of life of asset
often spreadsheets, Excel, Lotus, are helpful
NCF = ( DR - DC - DD)·( 1 - t ) + DD
after tax cash flows, plus the depreciation tax shield, because
NCFt = (DRt - DEt)( 1 - t ) + t • DDt
Ó1999 South-Western College Publishing
Include All Relevant NCFs
Include:
only incremental cash flows
all changes in working capital
salvage value
tax effects
positive and negative externalities on other products
Don’t Include:
sunk costs
overhead
financial flows, such as interest or dividends
Rule for Inflation:
If using nominal cash flows, discount with a nominal discount rate
If real NCF, real discount rates
Ó1999 South-Western College Publishing
Evaluation of Capital Projects
Four Criteria:
1. Consider all relevant NCFs
2. Discount at Firm’s Opportunity Cost of Capital
3. If mutually exclusive projects, pick the best one
4. If independent projects, pick the ones that maximize firm value
Ó1999 South-Western College Publishing
Selecting the Best Project
Payback Method
amount of time it take for S NCFt = C0
if mutually exclusive, pick shortest time
if independent, only arbitrary cut-off time periods
Internal Rate of Return, IRR
if mutually exclusive, pick the highest IRR
if independent, pick all projects with IRR > MCC
Net Present Value, NPV = S NCFt/( 1 + r) t
if mutual exclusive, pick highest NPV
if independent, pick all projects with positive NPVs
Ó1999 South-Western College Publishing
Conflicts Between IRR & NPV
Can have multiple IRRs
For mutually exclusive projects, IRR can say one thing and NPV another
Can have a tiny project with a Huge IRR
If there is a restriction on the amount to invest
List projects by descending profitability ratios (PR)
Select top PR and next, until amount used up
If PR < 1, don’t do it, it has a negative NPV
Ó1999 South-Western College Publishing
Therefore, NPV is always
useful. Most financial
economists advocate NPVs
Capital Rationing
PR = S NCFt/( 1 + r) t
C0
Opportunity Cost of Capital
Cost of Debt: ki = kd ( 1 - t ) after-tax interest
If kd = 9%, and t = .40 tax rate, ki = %
Cost of Equity: ke = rf + risk premium 6%
If bought own shares ke = D0/P + g div. yield + growth rate
If using the CAPM
ke = rf + b ( km - rf )
Weighted Average Cost of Capital (WACC)
ka = wi•ki + we•ke
there may be some optimal debt-equity structure
Ó1999 South-Western College Publishing
Optimal Debt-Equity
Structure Argument
Cost of Debt Financing is higher than equity financing, and rises with percentage debt
Cost of Equity Financing rises with percentage debt
Ó1999 South-Western College Publishing
% Debt
ke
ki
optimal
ka
Rates of Return: Various Methods
One period ROR:
r = A1/C0 - 1
Ex: $1,000 investment = C0, receive A1 =$1,200 20%, or r = 1200/1000 -1
Multiperiod ROR: IRR
Find r, such that:
S { At / (1 + r ) t = C0
where At are the net cash flows
Problem: Find IRR if the NCF’s are as follows:
Ó1999 South-Western College Publishing
Net Cash Flows
There are several methods
IRR Methods
Trial and Error
Try 10%, 20%
as the answer lies between, narrow to 17%
Financial Calculator
Enter the CF’s: -1000; 1000; 200
Push the IRR key
Analytical: Solve the equation explicitly
Find r, such that:
1000/(1+r) + 200/(1+r)2 = 1000
or,
1000(1+r)+200 = 1000(1+r)2
0 = -200 +1000 r + 1000 r 2
0 = 5•r 2 + 5•r -1
Quadratic Rule:
r = [-5 ± SQRT{52 -4(5)(-1)}]/2(5)
r = [-5 ± SQRT{45}]/10
r = ± .67 or +.17 or 17%
Ó1999 South-Western College Publishing
Constraints on cost-benefit
analysis include:
Physical constraints. Limited by technology.
Legal constraints. Laws on property rights.
Administrative constraints. Hire qualified administrators.
Distributional constraints. Must not harm.
Political constraints. What is possible vs best.
Financial or budget constraints.
Social and religious constraints. Cultural and religious considerations.
Ó1999 South-Western College Publishing
Cost Effectiveness Analysis
In cost-effectiveness analysis looks at we ask what are the costs of alternative means for reaching goal.
We know we must fight crime, but what is the cheapest way to do it?
Constant-cost studies specify the output for a given cost from alternative programs.
Least-cost studies alternative programs to achieve a given goal are examined in terms of cost.
Objective-level studies estimate the cost of achieving several performance levels of the same objective.
Ó1999 South-Western College Publishing
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Purchasing, production, marketing operations on several continents.
Exchange rate volatility can make or break a transaction.
Differences in long run inflation rates (according to the theory of purchasing power parity) help explain long-term exchange rate movements.
Regional trading blocs: EU and NAFTA
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If the DM-price of a BMW stays the same in Germany, the export revenue in received by BMW changes as the $/DM price changes.
If the price of the mark falls, BMW receives less revenue from US dealerships, when the dollar price of cars stays the same.
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Role of growth rates
Role of interest rates
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Big Mac index
Why Big Macs? 2 all beef patties, special sauce, pickles, cheese, lettuce, onions on a sesame seed bun.
In 1996 Big Mac sold for in Munich and $ in Atlanta. Ratio of = should be exchange rate.
Market value of implied that the . dollar was undervalued. In 1997 the value of the dollar rose to validating burger economics.
Not a perfect application: 1) VAT in Germany different from sales tax in . 2) downtown land rents were different, 3) degree of competition varied, 4) no ability to arbitrage.
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