CHAPTER 11
MONETARY AND FISCAL POLICY
Solutions to the Problems in the Textbook :
Conceptual Problems:
. An open market operation is an exchange of bonds for money or vice versa by the Fed. In an open market purchase, the Fed buys bonds from the public (generally via government bond dealers) in exchange for money. This action increases the monetary base and therefore the supply of money. In an open market sale, the Fed sells bonds in exchange for money, decreasing the monetary base and therefore the supply of money.
. When the Fed undertakes open market sales, it exchanges bonds for money. This decreases the monetary base and the resulting decrease in money supply creates a portfolio disequilibrium. The public adjusts by selling other assets, so asset prices decrease and yields (interest rates) increase. This increase in interest rates has a negative effect on aggregate demand (investment spending) and output contracts. A lower level of national income reduces money demand and therefore interest rates decline again. But if the price level is assumed to be fixed (as in the IS-LM model), then interest rates still settle at a level higher than the original one. Overall, in an IS-LM diagram, the LM-curve shifts to the left, leading to a higher level of interest rates and a lower level of income.
2. The IS-curve is vertical, if investment spending is totally interest insensitive. This is called investment insufficiency; in this case the monetary multiplier is zero. Since the parameter b in the investment equation equals zero, the equation changes from
I = I o - bi to I = I o .
A horizontal LM-curve will also render monetary policy ineffective. This is called the liquidity trap. In this case, money demand is totally interest elastic, and the parameter h in the money demand equation is assumed to be infinitely large.
The fiscal policy multiplier is zero if the LM-curve is vertical. This case is called the classical case, and money demand (and money supply) is assumed to be totally interest insensitive. Since the parameter h in the money demand equation equals zero, the equation changes from
L = kY - hi to L = kY.
None of these three cases is very likely to occur. However, some economists assert that Japan in the late 1990 ’ s and the . in the Great Depression were in, or close to, the liquidity trap.
3. A liquidity trap is a situation in which the public is willing to hold, at a given interest rate, however much money the Fed is willing to supply. In this case, the LM-curve is horizontal and monetary policy is totally ineffective. Fiscal policy (which will shift the IS-curve) is clearly the better choice to stimulate the economy in such a situation, since no crowding out will occur. This means that fiscal policy will have its maximum effect.
4. Crowding out occurs when an increase in government spending raises interest rates, which reduces private spending (especially investment). For example, an increase in government purchases (G) will increase income (Y) and therefore consumption (C); but because the interest rate (i) will increase, the level of investment spending (I), and most likely also net exports (NX), will decrease, changing the composition of GDP. Some degree of crowding out will always occur as long as the LM-curve is upward sloping, that is, in all cases except the liquidity trap. The steeper the LM-curve is, the greater the degree of crowding out. This implies that if the LM-curve is steep monetary policy will be more effective than fiscal policy in stimulating national income.
5. In the classical case, the LM-curve is vertical at the full-employment level of output. In this case, money demand (and money supply) would be completely interest inelastic. After any type of disturbance, a return to an equilibrium in the money sector could only be accomplished through changes in the level of output. In this situation, fiscal policy would be completely ineffective, since it would be totally crowded out. On the other hand, monetary policy would achieve its maximum effect.
6. Assume the government finances an increase in government spending by borrowing from the public (the Treasury sells government bonds to finance the increase in the budget deficit). The increase in the demand for credit by the government will lead to an increase in interest rates. If the Fed is worried about high interest rates, it may monetize the budget deficit, that is, buy the government bonds that the public now holds. This will inject money into the economy, and interest rates will drop again, so no crowding out of private spending may occur, at least in the short run.
In an IS-LM model, the expansionary fiscal policy will shift the IS-curve to the right, while the Fed ’ s action will shift the LM-curve to the right. This means that the AD-curve will shift further to the right than would have been the case if the Fed had not accommodated the expansionary fiscal policy. But this causes more upward pressure on the price level. In a recession, when there is little inflationary pressure, such a fiscal/monetary policy mix may be beneficial and cause only a small increase in the price level. However, if the economy is close to full employment, then we can expect a significant increase in the price level. In the long run, when the AS-curve is vertical, there will be total crowding out, whether the Fed monetizes the increase in the budget deficit or not.
7. A combination of restrictive fiscal policy and expansionary monetary policy will not significantly affect aggregate demand or income, and neither will expansionary fiscal policy combined with restrictive monetary policy. However, the first policy mix will decrease interest rates, while the latter will increase interest rates. Therefore the composition of output will be different in each case.
The first combination will shift the IS-curve to the left and the LM-curve to the right, in which case income will remain roughly the same while interest rates will be reduced. A tax increase will lower consumption while increasing investment spending due to lower interest rates. The second combination will shift the IS-curve to the right and the LM-curve to the left, leaving income roughly the same, while increasing interest rates. This will decrease the level of investment spending, while either government spending or consumption (through a tax cut) will increase.
Other considerations may involve the effect of a given policy mix on the budget surplus and the value of the dollar (and therefore net exports). The first policy mix will increase the budget surplus. Lower interest rates may also lead to an outflow of funds, which will lower the value of the dollar, leading to an increase in net exports. The second policy mix will decrease the budget surplus. Higher interest rates may lead to an inflow of funds, which will increase the value of the dollar, leading to a decrease in net exports.
Technical Problems:
1. If the government wants to change the composition of GDP towards investment and away from consumption without changing the level of aggregate demand, it needs to implement a combination of restrictive fiscal policy and expansionary monetary policy. An increase in personal income taxes or a decrease in transfer payments will reduce consumption and thus aggregate demand. The IS-curve will shift to the left, leading to a decrease in the level of output and the interest rate. To increase output to its original level, the Fed can undertake expansionary monetary policy. This will shift the LM-curve to the right, leading to a further decrease in the interest rate, thus stimulating investment, and, in turn, aggregate demand. If the intersection of the new IS- and LM-curves is at the same income level as previously, then the decrease in the interest rate will have stimulated investment spending sufficiently to exactly offset the decrease in consumption. (Note: The tax increase can be combined with an investment subsidy. In this case, the IS-curve will not shift as far to the left as before.)
The following diagram shows the effect of a decrease in transfer payments (TR) that is combined with an increase in money supply (M/P). The adjustment process is as follows:
1-->2: TR ¯ ==> C ¯ ==> Y ¯ == m d ¯ ==> i ¯ ==> I ==> Y . Effect: Y ¯ and i ¯ .
2-->3: (M/P) up ==> i ¯ ==> I ==> Y ==> m d ==> i Effect: Y and i ¯ .
Combined effect: Y about the same and i ¯ .
i IS 1 LM 1
IS 2 LM 2
1
i 1
2
i 2
3
i 3
0
Y 2 Y 1 Y
2. A cut in the income tax rate will flatten the IS-curve and shift it to the right. Both the level of income and the interest rate will increase. If the Fed increases money supply to keep the interest rate constant, then the LM-curve will also shift to the right, maximizing the multiplier effect, since no crowding out will take place. However, if money supply is held constant, then the LM-curve will not shift and the overall effect of this fiscal expansion on income will be weakened, since the increase in the interest rate will crowd out investment.
i IS 2
IS 1 LM 1
LM 2
2
i 2
1 3
i 1
0
Y 1 Y 2 Y 3 Y
The adjustment process is as follows:
1-->2: t ¯ ==> C ==> Y == md ==> i up ==> I ¯ ==> Y down. Effect: Y and i .
2-->3: (M/P) ==> i ¯ ==> I ==> Y ==> md ==> i Effect: Y and i ¯ .
Combined effect: Y and i about the same.
3. Either a removal of an investment subsidy or an increase in the income tax rate will shift the IS-curve to the left. This will lead to a decrease in the level of income and the interest rate. A rise in the income tax rate will reduce consumption, but investment will increase due to the decrease in the interest rate. Removing an investment subsidy will reduce investment, but the effect will be partially offset by the decrease in the interest rate. The decrease in income will lead to a decrease in consumption.
i IS 1 i I 1
IS 2 LM I 2
i 1 i 1
i 2 i 2
0 0
Y 2 Y 1 Y I 2 I 1 I
Note: An increase in the income tax rate will decrease the multiplier. The IS-curve will not only shift to the left but will also become steeper. The removal of an investment subsidy, as shown in the textbook, will lead to a parallel shift of the IS-curve to the left. Here, only a parallel shift is shown.
4. Monetary expansion will lead to lower interest rates, which will stimulate investment and thus output. The LM-curve will shift to the right, and a new equilibrium will be reached at point E 2 in Figure 11-8.
Fiscal expansion will lead to a higher level of output and higher interest rates. The IS-curve will shift to the right and a new equilibrium can be reached at point E 1 in Figure 11-8.
Fiscal expansion through an increase in government purchases will allow public spending as a share of GDP to increase, while private spending (especially investment) as a share of GDP will decline. A reduction in income taxes will increase the level of consumption, while decreasing the level of investment because of higher interest rates. Monetary expansion will increase the level of investment spending (due to lower interest rates) and consumption (due to higher income).
A more balanced growth can be achieved through an investment subsidy. This will shift the IS-curve to the right and a new equilibrium will be reached at E 1 . But even though interest rates will rise, the impact of the investment subsidy will not be totally lost. Here we have an example in which both consumption, induced by higher income, and investment, induced by the subsidy, will rise.
Full employment can also be achieved through a combination of expansionary monetary and expansionary fiscal policy. This will shift both the LM- and IS-curves to the right and we will end up somewhere between points E 1 and E 2 in Figure 11-8.
Additional Problems :
1. True or false? Why?
"Fiscal policy is more effective when the interest sensitivity of money demand is lower."
False. If money demand is totally independent of interest rates, the LM-curve is vertical. This is the classical case. A change in government spending has no effect on output, since there is complete crowding out. Clearly, in the case of a normal (upward-sloping) LM-curve, less crowding out will occur and income will go up as government spending increases. But the more interest insensitive money demand is, that is, the steeper the LM-curve is, the smaller the increase in income will be, due to a larger crowding out effect.
2. Comment on the following statement:
"Crowding out is complete when money demand is perfectly interest inelastic."
Crowding out refers to the fact that an increase in public spending may lead to a decrease in private spending, thus dampening the output expansion. An increase in government spending raises interest rates, which leads to a reduction in investment spending. When money demand is perfectly interest inelastic, the LM-curve is vertical at the level of real output that clears the money market. An increase in government spending will stimulate income and encourage people to hold more money balances. The excess demand for money will cause interest rates to rise to the level at which equilibrium in the money market is restored. If money demand is perfectly interest inelastic, the rise in interest rates will not lower the quantity of money demanded. Instead, income will have to go back to its original level before the money market is back in equilibrium. This means that interest rates will have to increase until the level of investment spending has been reduced by the same amount as government spending has been increased. Therefore the level of output demanded is unchanged and crowding out is complete.
3. True or false? Why?
"Expansionary monetary policies reduce bond prices in the liquidity trap."
False. Expansionary monetary policies generally reduce interest rates and thus increase bond prices. In the liquidity trap, however, interest rates do not change, since the LM-curve is horizontal. If the Fed increases the money supply through an open market purchase, the public is willing to hold all the money the Fed supplies at the prevailing interest rate. Nobody wants to shift into bonds and thus bond prices do not change.
4. True or false? Explain your answer.
"Expansionary fiscal policy is more effective when it is financed by borrowing from the public than when it is monetized."
False. If the government finances an increase in its spending by selling bonds to the public, no change in the supply of money will occur, and the IS-curve will shift without a corresponding shift in the LM-curve. On the other hand, if an increase in the budget deficit is monetized, then money supply will increase, as the central bank buys government bonds from the public. Therefore, the LM-curve will also shift to the right, leading to lower interest rates than in the first case. Less crowding out will occur and the overall effect on income will be greater--at least in the IS-LM model, that is, the short run. In the long run, when prices are allowed to be flexible, then crowding out cannot be avoided by monetizing the debt, since an increase in the price level will lead to lower real money balances and therefore higher interest rates.
5. True or false? Why?
"Crowding out is complete in the liquidity trap."
False. In the liquidity trap the public is prepared to hold whatever money is supplied at any given interest rate. This implies that the LM-curve is horizontal. If government spending rises, the IS-curve will shift to the right. Income will rise but interest rates will not increase. This means that there will be no crowding out.
i IS 1 IS 2
i 1 LM
0
Y 1 Y 2 Y
6. Assume the government wants to increase output without changing interest rates. What kind of policy mix would you recommend and how would your policy mix affect the composition of GDP? Explain your answer and the adjustment processes that take place with the help of an IS-LM diagram.
A combination of expansionary fiscal and monetary policy will increase output without affecting interest rates. Expansionary fiscal policy will shift the IS-curve to the right and income and interest rates will both increase. Expansionary monetary policy will shift the LM-curve to the right and interest rates will decrease while income increases. Thus we will have an increase in income without a change in interest rates.
Since income will increase, consumption will also increase, but since interest rates will not change, induced investment will not be affected (Note: In a more advanced model, an increase in sales expectations may actually increase the overall investment level. See Chapter 14). Therefore the level of investment as a fraction of GDP will decrease, while consumption and government purchases will have a greater share. (A more balanced growth can be achieved if investment subsidies are given.)
1-->2: G up ==> Y up ==> money demand up ==> i up ==> I down ==> Y up
Effect : Y up and i up
2-->3: (M/P) up ==> i down ==> I up ==> Y up ==> money demand up ==> i up.
Effect : i down and Y up Overall effect: Y up and i constant .
i IS 2 LM 1
IS 1 LM 2
2
i 2
i 1 1 3
0
Y 1 Y 2 Y 3 Y
7. Discuss the effect of an investment subsidy on consumption. In your answer, indicate whether the effect on consumption would differ if money demand were more interest sensitive.
An investment subsidy will stimulate investment spending and therefore income, which will lead to an increase in consumption. If money demand were more interest sensitive, then the LM-curve would be flatter and the shift of the IS-curve to the right would have a larger effect on income (and thus consumption). As income increases, so does money demand, but if money demand were more interest sensitive, then a smaller increase in the interest rate would be required to bring the money sector back to equilibrium. Thus, less crowding out would occur and the overall increase in income or consumption would be greater.
i IS 1 IS 2 LM 1
i 3 LM 2
i 2
i 1
0
Y 1 Y 3 Y 2 Y
8. "Monetary policy cannot change real output as long as investment is independent of interest rates." Comment on this statement.
When investment spending is not affected by changes in the interest rate but is determined solely by changes in business expectations, then monetary policy is ineffective. In this case, the transmission mechanism breaks down and monetary policy will not bring about changes in real output. Expansionary monetary policy may reduce interest rates, but this will not increase the level of investment spending and the economy will not be stimulated. In the IS-LM framework, we would have a vertical IS-curve. Thus, when the LM-curve shifts, we simply see a change in the interest rate, while the output level remains constant.
9. Assume investment is very interest inelastic and money demand is very interest elastic. With the help of an IS ‑ LM diagram, explain the effect of a cut in the income tax rate (t) on investment (I), money demand (md), and the budget surplus (BuS) and briefly explain the adjustment process.
Investment is interest inelastic so the IS-curve is steep; money demand is interest elastic so the LM-curve is flat. An income tax cut will shift the IS-curve to the right and make it flatter. Income and the interest rate will increase. Since the LM-curve is flat, the interest rate will not increase by much, so investment will decrease only a little. The budget deficit will increase due to the tax cut. Higher income will lead to more money demand but a higher interest rate will lead to lower money demand. Overall, money demand will remain constant, since money supply hasn't changed. The adjustment process can be described a follows:
t ¯ C Y md i I ¯ Y ¯ effect: Y and i
i
LM
i 2
i 1
IS 1 IS 2
0
Y 1 Y 2 Y
10 . Assume money demand is very interest inelastic and investment is very interest elastic. Explain how the level of savings (S), money demand (md) and investment (I) would be affected if the government increased welfare spending.
If money demand is very interest inelastic, the LM ‑ curve is very steep, and if investment is very interest elastic, the IS ‑ curve is very flat. With a steep LM ‑ curve and a flat IS ‑ curve, fiscal policy is not very effective, since most of it is crowded out. An increase in government transfer payments (TR) shifts the IS-curve to the right and income and the interest rate increase. Since income has increased, saving has increased and since the interest rate has increased, investment has decreased. In the end, money demand cannot be affected since money supply has not changed. The increase in income increases money demand, but the increase in the interest rate brings it back to its original level, that is, in equilibrium with money supply. The adjustment process that takes place is as follows:
TR Y md i I ¯ Y ¯ Effect: Y i
Since i increases a lot a lot, the effect on I is large, as is the offsetting effect (the crowding out effect) on output (Y). This means that the overall effect on Y is small.
i LM
i 1
i o
IS 1
IS o
0
Y o Y 1 Y
11. Use the formal IS-LM model derived in Chapter 10 to show algebraically how the degree of crowding out that is associated with an increase in government spending (G) is determined by the different parameters in the fiscal policy multiplier (b, k, h and a ).
The equilibrium interest rate for the IS-LM model was derived in Equation (9) of Chapter 10 as
i = (k/h) g A o - [1/(h + kb a )](M/P).
If we substitute this equation into the equation for investment, we get
I = I o - bi = I o - b { (k/h) g A o - [1/(h + kb a )](M/P) } ,
and therefore we get
D I = - (bk/h) g ( D Ao) = - (bk/h) { a /[1 + k a (b/h)] } ( D A o ) = - [(bk a )/(h + k a b)]( D G o ).
From this we can see the following:
· If the interest sensitivity of investment (b) goes up, then we have more crowding out.
· If the interest sensitivity of money demand (h) goes up, then we have less crowding out.
· If the income elasticity of money demand (k) goes up, then we have more crowding out.
· If the multiplier ( a ) goes up, then we have more crowding out.
Note: Since b, k, and a are in both the numerator and the denominator of the factor preceding ( D G) in the equation above, some students may have difficulty deciding whether this factor goes up or down as these parameters increase. An easy way to find out is to calculate the inverse of this factor, which is
(h + k a b)/(k a b) = h/(k a b) + 1.
As either k, a , or b increases, then this inverse decreases and the factor will increase.
12. If the government increased the income tax rate (t) and the Fed responded by increasing the money supply, how would investment (I), savings (S) and money demand (md) be affected?
1.->2. A higher income tax rate decreases the expenditure multiplier. The IS ‑ curve becomes steeper and shift to the left, so both income and the interest rate increase.
2.->3. An increase in money supply shifts the LM ‑ curve to the right. The interest rate decreases, leading to an increase in investment and thus income.
Overall, the interest rate will decrease, but it is unclear what will happen to income. A lower interest rate means an increase in investment. Since income has not changed much, savings hasn't been affected much, although it will change in the same direction as income. Since the tax rate is lower, most likely savings will increase. Money demand has increased, since money supply has been increased (the money sector has to be in equilibrium).
The adjustment processes that take place can be described as follows:
1.->2. t C ¯ Y ¯ md ¯ i ¯ I Y effect: Y ¯ i ¯
2.->3. ms i ¯ I Y md i effect: Y i ¯
Overall effect: Y ? i
i IS 1 LM 1 LM 2
IS 2
1
i 1
2
i 2
i 3 3
0
Y 1 Y o Y
13. "Combining income tax cuts with restrictive monetary policy is counterproductive, since it will lead to a higher budget deficit and higher interest rates. What we need instead is a tax increase in combination with expansionary monetary policy, since the tax increase will lower the budget deficit while the money expansion stimulates the economy." Comment on this statement.
Neither policy mix described above is likely to significantly affect the level of output. A combination of expansionary fiscal policy and restrictive monetary policy will lead to an increase in interest rates but it will not significantly affect output. The IS-curve will become flatter and shift to the right, and the LM-curve will shift to the left. The budget deficit will increase due to the tax cut.
Restrictive fiscal policy that is combined with expansionary monetary policy will also not significantly affect output, but it will reduce interest rates. (The IS-curve will become steeper and shift to the left, and the LM-curve will shift to the right.) The tax increase will lead to a decrease in consumption, but the decrease in interest rates will lead to an increase in investment and a higher potential for future economic growth. The budget deficit will decrease due to the higher tax rates. Lower interest rates will also help to finance the existing national debt and may stimulate net exports, since a capital outflow may occur that will reduce the value of the dollar.
14. “ If investment is very interest inelastic, then most of an income tax rate cut will be crowded out; therefore the Fed should always supplement a tax cut with an increase in money supply. ” Comment on this statement with the help of an IS-LM diagram and explain the adjustment process.
If investment is very interest inelastic, then the IS-curve is very steep. An income tax cut will shift the IS-curve to the right and make it flatter. Therefore income and the interest rate increase. The increase in the interest rate will crowd out only a small part of investment, since investment is very inelastic. If the Fed increases money supply, the LM-curve will shift to the right and income will increase, while interest rates will go down. Overall, we have an increase in income, but interest rates will be largely unaffected. Therefore, we do not have to worry about the crowding out of investment. The adjustment processes that take place can be described as follows:
1.->2. t ¯ C Y md i I ¯ Y ¯ effect: Y and i
2.->3. ms i ¯ I Y md i effect: Y and i ¯
Overall Effect: Y and i unchanged
i
LM 1
i 2 2 LM 2
1
i 1 3
IS 1 IS 2
0
Y 1 Y 2 Y 3 Y
15. "A cut in the income tax rate is not an effective way to stimulate the economy if money demand is very interest elastic, since most of the tax cut will be crowded out." Comment on this statement.
A situation in which money demand is extremely interest elastic comes very close to the so-called liquidity trap (the LM-curve will be almost horizontal). A decrease in the income tax rate (t) will stimulate consumption and increase national income. The size of the expenditure multiplier ( a ) will increase and the IS-curve will become flatter and shift to the right. The increase in income will initially induce people to hold more money balances and thus provide upward pressure on interest rates. But since money demand is extremely interest sensitive, it will take only a very small increase in interest rates to bring the money sector back to equilibrium. Therefore, the crowding out effect on investment will be minimal and the tax cut will prove to be very effective in stimulating national income.
16. "Expansionary monetary policy becomes more effective as the interest sensitivity of investment increases." Comment on this statement.
One of the ways monetary policy affects the level of output demanded is by changing interest rates and thereby the level of investment spending. The adjustment can be described as follows: An increase in money supply lowers the interest rate. If investment is very interest elastic, a large increase in investment spending will follow. This means that, given a certain size of the expenditure multiplier, income will change by more than in the case when investment does not respond much to a change in interest rates. In other words, if investment is very interest sensitive, then we have a flat IS-curve. For the same change in money supply, the flatter the IS-curve is, the larger the change in real output will be.
The formal analysis of Chapter 10 shows that, if investment becomes more interest sensitive, then the value of b increases. This leads to an increase in the monetary policy multiplier, which is defined as
( D Y)/( D M/P) = (b/h) g .
Note: b is also in the denominator of the equation for g , and therefore an increase in b will lower the value of g . But the change in g is proportionally less than the change in b and thus the value of the monetary policy multiplier will actually increase as b gets larger.
17. Assume that the marginal propensity to save increases. If the Fed wants to keep the level of output from fluctuating, should it undertake open market purchases or sales? In your answer discuss the combined effect of these changes on the composition of GDP.
An increase in the marginal propensity to save (s = 1 - c) will decrease the size of the expenditure multiplier ( a ) and therefore the IS-curve will shift to the left and become steeper. If people save more and spend less, then firms will experience an increase in unintended inventories. Firms will respond to this by decreasing production and national income will decrease. Therefore, the Fed will have to stimulate the economy by increasing the supply of money via open market purchases (which will shift the LM-curve to the right). As a result of these two shifts we will have lower interest rates. This means that investment as a fraction of GDP will increase, while consumption's share of GDP will decrease. (Lower interest rates may also cause an outflow of capital, which will lower the value of the domestic currency, leading to an increase in net exports.)
18. "In 1991, the transmission mechanism broke down, since banks were still suffering from having made bad real estate loans and were unwilling to increase their lending in response to the Fed's expansionary monetary policy." Comment on this statement.
It is true that many banks had made bad loans in the late 1980s and were therefore extremely cautious in their lending in 1991. They preferred to buy virtually risk-free government bonds. Thus, even though the Fed's money expansion led to lower interest rates, private firms had little access to bank loans and the economy was not significantly stimulated. But it would be an exaggeration to say that the transmission mechanism had broken down, since bank lending finally picked up in 1992 after the Fed increased its expansionary monetary policy effort. One can argue that, given the economic situation at the time, the Fed's initial policy measure simply was not sufficient to achieve the desired result.
19. "If investment is very interest elastic and money demand is very interest inelastic, then fiscal policy is less effective than monetary policy." Comment on this statement.
The more interest elastic investment is, the flatter the IS-curve will be. Expansionary fiscal policy (a shift of the IS-curve to the right) becomes less effective, since the crowding-out effect becomes larger. Expansionary monetary policy (a shift of the LM-curve to the right) becomes more effective, since the decrease in the interest rate will now stimulate investment to a larger degree.
The more interest inelastic money demand is, the steeper the LM-curve will be, since any increase in money demand due to an increase in income now has to be offset by a larger increase in the interest rate. Expansionary fiscal policy becomes less effective, since any increase in income will increase money demand and this will have to be offset by a larger increase in the interest rate, leading to a larger crowding-out effect. Expansionary monetary policy becomes more effective, since the increase in money demand needed to bring the money sector back into equilibrium must be achieved primarily through an increase in income.
The formal analysis in Chapter 10 introduces the fiscal and monetary policy multipliers as
( D Y)/( D G) = g = a /[1 + k a (b/h)] and ( D Y)/( D M/P) = (b/h) g
respectively. Therefore, if investment becomes more interest elastic, the value of b increases and the value of the fiscal policy multiplier decreases, while the value of the monetary policy multiplier increases. But if money demand becomes less interest elastic, then the value of h and the fiscal policy multiplier become smaller, while the monetary policy multiplier becomes larger.
Chapter 13 Solutions to the Problems in the Textbook :
Conceptual Problems:
. According to the life-cycle theory of consumption, people try to maintain a fairly stable consumption path over their lifetime. Individuals save during their working years so they can keep up the same consumption stream after they retire. This implies that wealth increases steadily until retirement while consumption remains stable. We should therefore expect the ratio of consumption to accumulated saving (wealth) to decrease over time up to retirement.
. After retirement, wealth is used up to finance consumption during the remaining years. Therefore the ratio of consumption to accumulated saving (wealth) increases again after retirement, eventually approaching 1.
. Suppose that you and your neighbor both work the same number of years until retirement and you both have the same annual income. If your neighbor is in bad health and does not expect to live as long as you do, she will expect to have fewer retirement years in which to use accumulated wealth to finance a steady consumption stream. Your neighbor's goal for retirement saving will not be as high as yours, and compared to you, she will have a higher level of consumption over her working years.
Since planned annual consumption (C) is determined by the number of working years (WL), the number of years to live (NL), and income from labor (YL), we get the equation:
C = [(WL)/(NL)](YL).
WL and YL are the same for you and your neighbor, but NL is smaller for your neighbor. Therefore you will have a lower level of consumption (C).
(Note: Students may come up with a variety of different answers. For one, your neighbor, who is in bad health, currently has much larger medical bills than you do. Therefore she may not be able to save as much for retirement, even if she might expect to live as long as you. On the other hand, she may not have large medical bills now, but expects them later, as she gets older. This may induce her to save more now. While such arguments are valid, instructors should point out that the answer should be related to the life-cycle theory.)
. If we assume for simplicity that the rate of return on Social Security is the same as the rate of return on private saving, then the introduction of a Social Security system based on a trust fund should not have any effect on your level of consumption. Social Security may be considered a form of "forced saving," since you are forced to pay Social Security taxes during your working years and will, in return, receive benefits during your retirement years. However, most likely you would have voluntarily saved as much as the government is now “ forcing ” you to save with levying a Social Security tax. Therefore your consumption behavior will not change. Still, the levying of a Social Security tax reduces disposable income during your working years, increasing the ratio of consumption to disposable income (the average propensity to consume). If private saving were simply replaced with government saving, national saving would not be affected.
In reality, however, the Social Security system is not strictly financed through a trust fund, but largely on a pay-as-you-go basis. The size of the Social Security trust fund was fairly insignificant until the system was amended in 1983. Now the trust fund is increasing and, in effect, contributing to the federal budget surplus. But because of our aging population, predictions are that the Social Security system will experience severe financial difficulties within the next 20-30 years. If the credibility of the system becomes an issue, people may intensify their saving efforts, since they no longer feel they can rely on the public system to provide for them during retirement. In the past, most of the Social Security taxes were not "saved" but immediately used by the government to finance the benefits of the current retirees. This is why most economists claim that the Social Security system has led to a decrease in the national savings rate and a decrease in the rate of capital accumulation. The magnitude of this decrease, however, has not been clearly established.
. If you get a yearly Christmas bonus, you immediately treat it as part of your permanent income and spend it accordingly, that is, D C = c( D Y). In other words, your current consumption will change significantly.
. If you get a Christmas bonus for only this year, you will consider it as transitory income. Since your permanent income is hardly affected, you will consume only a small fraction of it and save the rest. In other words, your current consumption will not be significantly affected.
4. Gamblers (or thieves) seldom have a very stable income. However, their consumption is determined by their permanent income, that is, their expected average lifetime income. Whether they have a large or small income during any given period, their consumption pattern remains relatively stable, since their permanent income is not significantly affected by temporary changes in earnings.
5. Both theories, in their own way, try to explain why the short-run mpc is smaller than the long-run mpc. The life-cycle theory attributes the difference to the fact that people prefer a smooth consumption stream over their lifetime. Therefore the average expected lifetime income is the true determinant of current consumption. The permanent income theory suggests that the difference is due to measurement errors. Measured income has two components, that is, permanent and transitory income. But only permanent income is a true determinant of current consumption.
. One possible explanation could be that the “ baby boomers ” were still in their dissaving phase. In other words, if households of the baby boom generation still had to buy houses or pay for expenses related to childcare in their late twenties, they may not have been able to save for retirement yet.
. If the above explanation is correct, one can expect an increase in saving as these “ baby boomers ” age, become more financially solvent, and begin to prepare for retirement.
7. The ranking from highest to lowest value should be first (a), then (d), and then (b). Clearly, (c) should be lower than (a), but where exactly it ranks after that depends largely on the severeness of the liquidity constraint.
8. A series follows a random walk when future changes cannot be predicted from past behavior. In other words, it does not have a mean or clear long-run value. Any major change comes about because of random shocks. Hall asserted that changes in current consumption largely come from unanticipated changes in income. According to the life-cycle theory or permanent-income theory, people try to smoothen out their consumption stream in such a way that its expected value is always the same in each period. Therefore, we can express future consumption as the expected value plus some error term, that is, some random value that is unpredictable. This error term is a shock to future income that is spread over the remaining lifetime. Hall supported the permanent-income hypothesis by showing that lagged consumption is the most significant determinant of future consumption.
9. The problem of excess sensitivity means that consumption responds more strongly to predictable changes in current income than the life-cycle theory and permanent-income theories predict. The problem of excess smoothness means that consumption does not respond as strongly to unpredictable changes in current income as these theories predict. However, the existence of these problems does not invalidate the theories. It simply means that the theories can explain consumption behavior only to a certain degree.
10. Precautionary (or buffer stock) saving can be explained by uncertainty. It could be uncertainty in regard to one ’ s life expectancy or one ’ s time of retirement (affecting the accumulated saving needed to finance retirement), or uncertainty about future spending needs (which may be caused by a change in family composition or health). Clearly, if we account for such uncertainties, we bring the model much closer to reality. For example, many elderly still continue to save after retirement in anticipation of predicted high medical costs not covered by Medicare.
. It is unclear whether an increase in the interest rate leads to an increase or a decrease in saving. On the one hand, as the interest rate increases, the return on saving increases and people may therefore increase their savings effort (due to the substitution effect). On the other hand, a higher return on saving implies that a given future savings goal can now be reached with a smaller savings effort in each year (due to the income effect).
. The income effect and the substitution effect generally tend to go in different directions, and the overall outcome depends on the relative magnitude of these two effects. Until now, empirical evidence has not established a significant sensitivity of saving to changes in the interest rate. This would imply that the income and the substitution effects have about the same magnitude.
. According to the Barro-Ricardo hypothesis, it does not matter whether an increase in government spending is financed by taxation or by issuing debt.
. The Barro-Ricardo hypothesis states that people realize that government debt financing by issuing bonds simply postpones taxation. In other words, people know that the government will have to raise taxes in the future to pay back what they have borrowed now. Therefore, expansionary fiscal policy that results in an increase in the budget deficit will no stimulate the economy since it will lead to an increase in saving rather than consumption. People want to be prepared to pay future taxes.
. There are two main objections to the Barro-Ricardo hypothesis. One is based on liquidity constraints, that is, people may want to consume more but may not be able to borrow as much as they like. Therefore, if there is a tax cut, they will consume more, rather than save the tax cut. The other argument is that those people who benefit from a tax cut or an increase in government spending are not the same as those who will have to pay the higher taxes to pay off the debt. This argument assumes that people are not concerned about the welfare of their descendants.
Technical Problems:
. If income remains constant over time, permanent income equals current income. Your permanent income this year is YP 0 = (1/5)(5*20,000) = 20,000.
. Your permanent income next year is YP 1 = (1/5)(15,000 + 4*20,000) = 19,000.
. Since C = , your consumption this year is C 0 = *20,000 = 18,000.
Your consumption next year is C 1 = *19,000 = 17,100.
. In the short run, the mpc = ()(1/5) = ; but in the long run, the mpc = .
. We have already calculated this and next year's permanent income. In each of the coming years you add $30,000 and subtract $20,000, and therefore your permanent income (which is your average over a five year period) will increase by $2,000 each year until it reaches $30,000 after 5 years.
YP o = (1/5)(5*20,000) = 20,000
YP 1 = (1/5)(1*30,000 + 4*20,000) = 22,000
YP 2 = (1/5)(2*30,000 + 3*20,000) = 24,000
YP 3 = (1/5)(3*30,000 + 2*20,000) = 26,000
YP 4 = (1/5)(4*30,000 + 1*20,000) = 28,000
YP 5 = (1/5)(5*30,000) = 30,000
Y
30,000
28,000
26,000
24,000
22,000
20,000
0 1 2 3 4 5 time
. The person lives for NL = 4 periods and earns a lifetime income of
YL = 30 + 60 + 90 + 0 = 180 .
Therefore consumption in each period will be C i = (1/4)180 = 45, i = 1, 2, 3, 4.
This implies that saving in each period is:
S 1 = 30 - 45 = - 15 ; S 2 = 60 - 45 = + 15 ; S 3 = 90 - 45 = + 45 ; S 4 = 0 - 45 = - 45 .
. If liquidity constraints exist and the person cannot borrow in the first period, then she will consume all of her income, that is, Y 1 = C 1 = 30 .
For the remaining three periods the person wants a stable consumption stream. Thus she will consume C(i) = (1/3)(60 + 90 + 0) = 50 in each of the remaining three periods i = 2, 3, 4.
. An increase in wealth of only $13 is not enough to offset the difference in consumption patterns between period 1 and the other periods. Therefore all of the increase in wealth will be consumed in period 1, such that C 1 = 43 . In the remaining three periods, consumption will be the same as in .
An increase in wealth of $23 will be enough to offset the difference in consumption patterns. Lifetime consumption in each period will now be C i = (1/4)(180 + 23) = . This means that (or almost all of the additional wealth) will be used up in the first period; the remaining will be distributed over the next three years.
. According to the life-cycle theory and permanent income hypothesis (LC-PIH), the change in consumption equals the surprise element, that is, D C LC-PIH = e . According to the traditional theory, the change in consumption equals D C tr = c( D YD). Therefore if a fraction l of the population behaves according to the traditional theory and the other fraction behaves according to LC-PIH, then the total change in consumption is
D C = l ( D C tr ) + (1 - l )( D C LC-PIH ) = l c( D YD)+ (1 - l )c e = (.7)(.8)10 + (.3) e = + (.3) e
. D C = (.3)(.8)10 + (.7) e = + (.7) e
. D C = (0)(.8)10 + 1 e = e
. If the real interest rate increases, the opportunity cost of consuming should increase. Therefore, the average propensity to save, that is, the fraction of total income that is saved, should increase.
. If you only save for retirement and your savings goal is fixed, then you actually will save less. With a higher interest rate it will take less saving each year to achieve your goal.
. The first case (.) describes the substitution effect, whereas the second case (.) describes the income effect. Unless the magnitude of each of these effects is known, we cannot predict the overall effect of this interest rate increase on saving.
5. One way to increase saving would be to either privatize or eliminate the Social Security system, so people would have to save for retirement on their own. (Eliminating Social Security is not a very popular measure, but the privatization of Social Security is often discussed.) This would do away with the negative effect on saving that comes from the pay-as-you-go nature of financing Social Security. Another way might be to make it more difficult to borrow. The . tax system encourages people (and firms) to borrow rather than save.
Additional Problems:
1. As a share of GDP, how large is consumption compared to the other three main components. Would you expect consumption's share to increase or decrease in a recession?
Consumption expenditures are roughly two thirds of total GDP, which is higher than the other three components (investment, government purchases, and net exports) taken together. The ratio of consumption to GDP, however, does not always remain constant. In a recession, for example, when income is below trend, we should expect the consumption-to-GDP ratio to increase, while in a boom, when income is above trend, we should expect the ratio to decrease. The reason is that current consumption is based on permanent rather than current income and when current income is greater than permanent income, the ratio of consumption to income (the apc) goes down. This argument is reinforced by the concept of automatic stability. When GDP falls, personal disposable income falls by less and thus consumption does not fall dramatically.
2. True or false? Why?
"The marginal propensity to consume out of transitory income is greater than the marginal propensity to consume out of permanent income."
False. The permanent-income hypothesis argues that consumption is related to permanent disposable income. Individuals will only revise their consumption behavior significantly if they perceive a change in income as permanent. Very often people are uncertain as to whether a rise in income is permanent or transitory, so they do not significantly revise their consumption patterns immediately. This suggests a lower marginal propensity to consume out of transitory income than out of permanent income.
3. Do you think that the marginal propensity to consume out of current income would differ between tenured professors who have a high degree of job security and professional gamblers who never know when luck will strike?
Tenured professors have a high degree of job security and their income does not vary a great deal. They can therefore relatively accurately estimate their permanent income. This means that their current consumption is largely based on current income, implying that their short-run mpc is fairly high. Gamblers, on the other hand, never know what their income in any given year is going to be. Therefore, they base their consumption decisions on their average expected lifetime income (permanent income) rather than on current income. This implies that their short-run mpc is fairly low.
4. Is the short-run marginal propensity to save different between farmers and government employees? Why or why not?
Government employees generally have very stable incomes and high job security. Therefore they base their consumption decision to a large extent on current income so their short-run mpc is high, while their short-run mps is low. Farmers, on the other hand, have highly variable incomes, depending on weather conditions. Therefore they tend to base their consumption decisions on their permanent income. Their short-run mpc is low, while their short-run mps is high.
5. "If most people base their consumption decisions on their current rather than their permanent income, then the short-run multiplier is greater than the long-run multiplier." Comment on this statement.
If most people follow the traditional theory and base their consumption decisions mostly on current income, then their mpc out of current income is high, making the value of the short-run multiplier high. But if most people follow the permanent-income theory and base their consumption decisions primarily on permanent income, then the short-run mpc is low, making the value of the short-run multiplier low. In either case, as long as some people follow the permanent-income theory, then the short-run multiplier should always be smaller than the long-run multiplier.
6. Assume you define your permanent income as the average of this and the past four years ’ incomes and you always consume 4/5 of your permanent income. Your earnings record over these years has been: Y t = 40,000, Y t-1 = 38,000, Y t-2 = 34,000, Y t-3 = 32,000, Y t-4 = 31,000.
If next year your income increases to Y t+1 = 46,000, by how much will your consumption change between year t and year t+1?
YP t = (1/5)(40,000 + 38,000 + 34,000 + 32,000 + 31,000) = (1/5)175,000 = 35,000
C t = (4/5)YP t = (4/5)35,000 = 28,000
YP t+1 = (1/5)(46,000 + 40,000 + 38,000 + 34,000 + 32,000) = (1/5)190,000 = 38,000
C t+1 = (4/5)YP t+1 = (4/5)38,000 = 30,400
Therefore your consumption will change by D C = 2,400.
7. Assume a distant aunt gives you several thousand dollars and you use the money to pay back part of your student loan. Does your behavior correspond to the prediction of the permanent-income theory? Why or why not?
Paying back your debts actually can be seen as an act of "saving." Therefore, since you use some unexpected income to save (rather than consume), your behavior fits the permanent income theory nicely.
8. "Early retirement raises aggregate consumption." Comment on this statement.
Early retirement reduces lifetime income and increases the length of retirement. The life ‑ cycle model states that individuals consume on the basis of their average lifetime income to maintain a stable consumption path throughout their lives. In an economy with a constant population and no technological progress, aggregate consumption will fall if retirement age drops because people who retire earlier have to accumulate funds for more retirement years over fewer working years. As this can only be accomplished with greater saving, consumption has to be reduced.
However, if the population is growing and retirement benefits are financed through taxes levied on workers currently employed, then aggregate consumption may actually rise. In this case, the working population will be paying for the reduction in lifetime earnings experienced by those who have retired early, and there is less need for retirement saving.
9. The simple life-cycle hypothesis predicts that people save over their working years but dissave during their retirement years. Do we actually observe such behavior? If not, can you explain why not?
Most elderly actually do not dissave, but they do save less than they did during their working years. One of the reasons that the elderly still save may be the fact that they anticipate large medical bills as they grow older and therefore prefer to keep a certain buffer stock of saving. The elderly may also hope to leave some of their savings as bequests to their children or grandchildren.
10. On October 19, 1987, the Dow Jones industrial average dropped about 500 points, or a little more than 23%. What effect should a decline in stock values of this magnitude have had on aggregate demand according to the life-cycle theory of consumption?
According to the life-cycle theory, any change in wealth should affect consumption behavior. The decline in stock values constituted roughly a $500 billion decline in wealth. However, we did not see a huge decrease in consumption in 1987, since the wealth effect tends to be fairly small. In addition, the Fed reacted promptly, announcing that liquidity would be provided if needed.
11. Does the random walk model of consumption disprove the permanent income hypothesis? Why or why not?
Robert Hall tried to disprove the permanent income theory by applying the concept of rational expectations to the theory of consumption. He asserted that consumption patterns may follow a random walk, that is, changes in consumption may come from unanticipated changes in income. However, by concluding that lagged consumption is the most significant determinant of future consumption, Hall actually supported the predictions of the permanent-income hypothesis.
12. How is Hall ’ s random walk model of consumption related to the permanent-income hypothesis and what are the implications of these theories for fiscal policy?
Hall asserted that changes in current consumption largely come from unanticipated changes in income. Any major change in consumption comes about because of random shocks. According to the permanent-income theory, people try to smoothen out their consumption stream in such a way that its expected value is always the same in each period. Therefore, we can express future consumption as the expected value plus some error term, that is, some random value that is unpredictable. This error term is a shock to future income that is spread over the remaining lifetime. Hall supported the permanent-income hypothesis by showing that lagged consumption is the most significant determinant of future consumption. The implication for fiscal policy is that a temporary tax change will not significantly affect current consumption, unless there are liquidity constraints.
13. True or false? Why?
"A temporary tax surcharge never has a significant effect on current consumption."
False. If individuals know that the tax surcharge is temporary they will not alter their spending patterns as the tax change has little impact on their permanent income. However, when liquidity constraints exist, individuals may be forced to adjust their consumption behavior immediately. If individuals barely earn enough to finance their current consumption, for example, they may be forced to cut their current consumption if a temporary tax surcharge is levied.
14. "As a response to a temporary increase in personal and corporate income taxes consumers will reduce their spending and firms will cut production and increase prices. Therefore all we will get is stagflation, that is, an increase in both unemployment and inflation, and tax revenues won't increase." Comment on this statement.
The life-cycle/permanent-income theory of consumption predicts that temporary changes in income will not significantly affect the level of consumption. Thus a temporary tax surcharge should not significantly affect aggregate demand. A similar argument can be made about firms, since changes in production are often costly and therefore a temporary surcharge on corporate income taxes should not affect the level of output and prices. The levels of national income and prices should not be affected significantly but we should see a (temporary) increase in tax revenues due to the surcharge. (Note, however, that if consumers and firms face liquidity constraints, they may react to a temporary surcharge in the way described in the statement.)
15. "Any tax cut that results in an increase in the budget deficit will fail to stimulate aggregate demand." Comment on this statement. In your answer explain the effect of such a tax cut on interest rates, money supply, and private domestic saving.
The Barro-Ricardo proposition states that a tax cut that results in a budget deficit increase leads to higher saving. Since people will anticipate a future tax increase to finance the higher deficit, permanent income will not be affected. Thus consumption will not be affected; instead people will save the tax cut. Since this is purely a fiscal policy measure, money supply is not affected. The increase in the budget deficit will lead to higher interest rates due to the increased demand for credit. (Note that evidence from the 1980s does not support this hypothesis. The Reagan tax cuts in 1981 resulted in a large increase in the budget deficit but there was no subsequent increase in saving.)
16. Assume the government announces plans for fiscal expansion that are likely to result in increased government borrowing. What effect should this have on aggregate consumption , money supply, the income velocity of money, the trade deficit, and savings?
The Barro-Ricardo proposition states that if fiscal expansion results in a budget deficit, the public will anticipate a future tax increase to finance the deficit. They believe that their permanent income will not be affected and choose to save rather than consume more. Therefore, we should expect an increase in private saving but no significant change in consumption. Thus there is no significant change in national income and, since this is solely a fiscal policy, money supply is also not affected. Therefore there is no change in the income velocity. The trade deficit may also not be significantly affected, since domestic saving supports the budget deficit. However, evidence from the 1980s does not lend support for this hypothesis. Saving did not increase after the Reagan tax cuts that resulted in a huge increase in the budget deficit. Instead, we saw an increase in consumption and the trade deficit, since higher interest rates caused an inflow of funds, leading to an appreciation of the . dollar. The income velocity also increased, due to the increase in economic activity.
Chapter 14 Solutions to the Problems in the Textbook :
Conceptual Problems:
1. Even if the economy has achieved the desired capital stock some (gross) investment still must take place to keep the capital stock at this level. The level of investment has to be sufficient to cover depreciation (due to wear and tear or because capital becomes obsolete).
2. High-tech capital (such as computers) becomes obsolete at a very fast rate and therefore needs to be replaced much earlier if firms want to stay competitive. Therefore the rate of depreciation will increase if more is invested in high-tech machines.
Human capital also depreciates since knowledge tends to become outdated (new theories are advanced and new discoveries are made continuously). Thus knowledge needs to be updated. Who for example, wants to be treated by a physician who hasn't kept up with new advances in medical technology? Similarly, since one can also think of health as human capital, we can see that, as we grow older, our stock of health tends to depreciate. But the more we invest in health, that is, the healthier we live and the more preventive measures we take, the slower this stock of human capital will depreciate.
3. The interest rate cannot simply be considered as the rental cost of capital but is also an opportunity cost. Retained earnings can be used to invest in new machinery but also to make a loan to someone else. In other words, at any time retained earnings can be "financially invested," that is, given to someone in need of funds (the government, for example), in which case these funds would earn interest. For example, if the yield on a government bond or a commercial paper is much higher than the expected rate of return on an investment in real capital, a firm may not want to undertake this investment and "invest" in a government bond.
4. The price of a share of stock in a company should, in an efficient stock market, be equal to the price of a claim on the capital in the company. Tobin ’ s q is an estimate of the value the stock market places on a firm ’ s assets relative to the cost of producing those assets. In other words, it can be thought of as the ratio of the market value of a firm to the replacement cost of capital. The replacement cost of capital is a measure for the marginal cost of capital. If q is greater than 1, then a firm should add physical capital, since for each dollar ’ s worth of new machinery the firm can sell stock for q > 1 dollars. But this means that the marginal product of capital exceeds its marginal costs.
5. A sudden increase in the demand for a firm's product will increase expectations of future sales and induce a firm to increase its desired capital stock. This will require an increase in net investment. The speed with which the capital stock is increased to its new desired level depends on whether the firm believes that the increase in sales is permanent or temporary and on the cost to the firm of adjusting the capital stock to its new desired level quickly.
6. Large firms have easier access to credit than small firms, since large firms tend to have an established and good credit rating. Therefore, small firms are often limited in their investment opportunities by their retained earnings. But if we have many more small firms than large firms, we may observe larger output fluctuations over the business cycle. This is due to the fact that small firms will invest less in a recession than they otherwise might have because credit is not available to them and profits are down. On the other hand, in a boom these small firms are likely to invest more than they would otherwise, since profits are high and they want to compensate for the lack of investment during the past downturn.
. When profits are high, more internal funds are available for firms. Firms generally will use these funds for financing new capital investments, even at times when outside funding is not easily obtainable. Higher profits may come from increased sales. This may make entrepreneurs more optimistic about future sales and encourage them to increase investment spending. Higher profits also mean higher dividends and thus higher stock values. But if stock values are high, firms are more inclined to raise new funds for additional investment. It should be noted, however, that higher profits and the availability of internal funds should not distract from the fact that the cost of capital still is an important factor in investment decisions. Any interest that could be earned on such funds has to be seen as an opportunity cost.
. Credit rationing by banks occurs since banks realize that while a cautious entrepreneur may be deterred from investing when interest rates are high, a more reckless entrepreneur may still invest in spite of high rates. Entrepreneurs who are more reckless are also more likely to fail and default on their loans. Therefore in times of tight funds, rationing credit may be a more effective way for banks to ensure profits than increasing the interest rate on loans. Credit rationing may also occur for other reasons. For example, the Federal Reserve can impose credit limits on financial institutions.
. Mortgage interest payments are an important consideration in buying a house. Even a small change in mortgage interest rates can significantly affect homebuyers' monthly mortgage payments. Therefore most people will wait to buy a home until interest rates are fairly low. The purchase of a home is different from the purchase of a consumption good, since most people can delay purchasing a home for some time if market conditions are unfavorable. If interest rates are very low, many more prospective homebuyers will qualify for a mortgage. On the supply side, housing developers with large financing needs are more likely to undertake new construction if the cost of credit declines. But as the supply of new housing increases, the price for houses may drop, inducing more people to buy.
. A state usury law prohibits banks or thrifts from charging mortgage rates above a certain maximum. This in effect provides a price ceiling on mortgage rates. But when market interest rates go above this interest rate ceiling, the mortgage market cannot adjust to an equilibrium and there will be excess demand for mortgage funds. At such high interest rates banks may channel their funds away from mortgages and into other, higher yielding ventures. Thus the supply of mortgage credit may decrease. If the inflation rate is high, the real interest rate that homebuyers actually pay may be quite low. Therefore homebuyers may demand more mortgage funds, creating excess demand for mortgages while there is no opportunity for the market to clear due to the price ceiling. This explains why a low level of housing investment may exist even at low real interest rates.
9. The flexible accelerator model tries to explain the speed at which firms adjust their capital stock over time. The larger the gap between the desired and actual capital stock is, the higher the level of the firm ’ s investment spending on machinery. Much, but not all, inventory investment can be explained with the help of this accelerator model. The level of inventory investment is based on changes in output and therefore sales expectations.
10. Unanticipated inventory accumulation occurs when the demand for a product is lower than was expected. Firms generally respond by decreasing their level of production and a recession may be imminent. However, a planned inventory increase generally occurs when firms expect an economic upturn and want to be ready for the anticipated increase in the demand for their product.
11. The inventory-to-sales ratio did not increase in the 1990-91 recession, probably because of new and better methods of management and firms keeping much tighter control over their inventories. Advanced computer technology and the synchronization of shipments of material allow firms to operate with leaner, less costly inventories. Therefore the inventory-to-sales ratio is not only less likely to increase due to an undesired inventory increase at the beginning of a recession, but it is also less likely to increase due to a desired inventory increase at the beginning of a new boom. It appears that the role of inventory spending in a business cycle may have changed.
12. The level of net investment is the addition to the capital stock, that is, I N = D K. A low level of net investment implies slow growth in the capital stock and hence future productive capacity. A low rate of capital accumulation generally implies lower future living standards.
13. In the long run (when the AS-curve is vertical), monetary policy will not affect the real interest rate. However, it will affect inflation and therefore the nominal interest rate. The nominal interest rate (i n ) is determined by the real interest rate (i r ) plus the inflation rate ( p ), that is,
i n = i r + p
But if the nominal interest rate increases, the nominal cost of borrowing funds for investments rises and some borrowers may no longer qualify for loans because of perceived cash flow problems. Banks may actually limit credit when nominal interest rates increase, because they feel that borrowers still interested in loans may be high credit risks. This is particularly true for residential investment, since housing is very sensitive to real and nominal interest rates. One reason is that in the . tax system nominal interest payments are tax-deductible, while nominal capital gains due to inflation remain untaxed. A higher rate of inflation may also have a negative impact on stock market values due to increased uncertainty about the future. But a decrease in stock values may make it more difficult for firms that want to raise funds for investment projects through issuing new stocks. Expectations about inflation also may affect the timing of investments. As a result, the level of investment may be affected by monetary policy despite the fact that real interest rates have not changed.
Technical Problems:
1. The rental cost of capital (r c ) is equal to the real interest rate (r) plus the rate of depreciation (d), with the real interest rate defined as the nominal interest rate (i) minus the expected inflation rate ( p e ):
r c = = r + d = i - p e + d.
A car rental firm would want to know how fast its cars will depreciate (or what is needed to keep the stock of cars at the original level) and what the costs are of having funds tied up in owning the cars. In order to make a profit, a car rental firm would charge more per car than the interest it could get (or has to pay) on the funds tied up plus the depreciation rate times the value of the car. Since the rental firm charges a nominal price and is charged a nominal interest rate by a bank for any funds that are borrowed, the charge would be
P > (i + d)V, with V = the value of the car.
For example, if the current market interest rate is 10%, the rate of depreciation is 20%, and the value of the car is $10,000, then the car rental company would charge at least
( + )(10,000) = ()(10,000) = 3,000
per year or roughly $ dollars per day. If we further assume that the car is rented only half of the time, then the costs would go up to $ per day. Since the $ charge does not include any other costs to the firm or any profits, we should expect the actual price for a car rental to be higher.
. If the net present discounted value (NPV) of a project is positive, the project is profitable. Assuming that Year 1 is the present year, the net present value of the project can be calculated in the following way:
NPV = R 1 + R 2 /(1 + r) + R 3 /(1 + r) 2
At an interest rate of r = 5% we get
NPV = - 200 + 100/() + 120/() = - 200 + + = > 0 .
This means that the project is profitable and should be undertaken.
. Using the same equation as in . but with an interest rate of r = 10%, we get
NPV = - 200 + 100/() + 120/() = - 200 + + = - < 0.
This means that the project is unprofitable and should not be undertaken.
. A temporary investment tax credit should have a positive effect on investment for the period to which it applies. In the long run, however, we should not see a significant effect on investment arising from a temporary investment tax credit. The desired capital stock depends mainly on a firm's estimate of future or permanent output and a temporary investment tax credit should not affect the firm's desired long-run capital stock.
. A temporary investment tax credit will increase the number of current projects, since firms will invest in projects that they otherwise might have delayed. Firms may also initiate some marginal projects that were unprofitable under previous conditions. Therefore the level of investment in the year that the tax credit is imposed will increase. Since so many projects are undertaken during the current year, fewer projects will be undertaken the following year, when the tax credit is no longer in effect. Thus the level of investment in the second year will be lower than it would have been otherwise.
. While a permanent tax credit does not induce firms to accelerate investment projects, it may encourage them to undertake marginal investment projects that might not previously have been profitable. We should therefore see an overall increase in the level of investment, both in the first year of the tax credit and beyond. The effect of a permanent tax credit on investment in the long run will be greater than that of a temporary tax credit.
. The difference between output and final sales is a result of inventory adjustments. Before a recession, actual sales may go down, while output (which is based on expected sales) is slow to respond. Therefore we have an unanticipated inventory accumulation. This will cause firms to cut back their production, lowering output even more. On the other hand, if firms expect an increase in sales they will raise production to increase their inventories. This can increase output before sales pick up.
. In 1981, GDP exceeded final sales, which meant that inventories increased. The initial inventory increase may have been intentional as industries prepared for an upswing after the recession of 1980. However, later in the year, as the economy headed into the recession of 1981/82, sales and GDP both decreased. Since GDP exceeded sales, an undesired inventory accumulation occurred. While output declined sharply, firms cut inventories. In the first quarter of 1982 there was a desired inventory decrease as sales exceeded output. In mid-1982, sales and GDP were almost equal, but by the fourth quarter sales started to increase faster than GDP. This meant that aggregate demand had picked up, a clear sign that the economy was recovering. This led to an undesired inventory decrease.
. In a period of slow and steady growth, firms anticipate an increase in sales and want to be prepared by holding a large stock of inventory. However, since the growth is slow and steady, we should expect output to exceed sales only slightly and both should grow at about the same rate. Therefore we may see a fairly constant inventory-to-sales ratio.
$ output
sales
0 time
. The total value of the outstanding shares is $25 million. Therefore Tobin ’ s q has the following value:
q = (value of all shares)/(replacement cost of capital) = 25/18 > 1.
But a value of q that is greater than 1 implies that the value of the marginal product of capital is greater than its marginal cost. Therefore the firm should invest.
. With a replacement cost of $25 million, q = 1. Therefore net investment should be zero. But there should still be some gross investment to replace the capital stock that depreciates.
With a replacement cost of $28 million, q < 1. In this case, the firm should “ disinvest, ” that is, let its capital stock depreciate but not replace it.
. From K * = ( q Y)/r c ==> K * = [()(5)]/() =
==> the desired capital stock is valued at $ trillion.
. From K * = [()(6)]/() = 15
==> the desired capital stock is now valued at $15 trillion.
. From I 1 = l (K * - K) ==> I 1 = ()(15 - ) = ()() = 1
==> in the first year, net investment will be I 1 = $1 trillion, and the new capital stock will be
K 1 = $ trillion.
From I 2 = (K * - K) ==> I 2 = ()(15 - ) =
==> in the second year, net investment will be I 2 =$ trillion and the new capital stock will be
K 2 = $ trillion.
. As indicated above, the answers in . refer to net investment, that is, an addition to the capital stock. Gross investment would include replacement of worn out capital.
7. The q-theory of investment predicts that high stock values will induce corporate managers to invest more in real capital. In an efficient stock market, the price of a share of stock in a company should be equal to the price of a claim on the capital in the company. Tobin ’ s q can be thought of as the ratio of the market value of a firm to the replacement cost of capital, since it is an estimate of the value the stock market places on a firm ’ s assets relative to the cost of producing those assets. If the value of q is high, a firm wants to add physical capital and the level of investment rises. But this means that in periods in which stock prices rise rapidly, corporations will increase their investment spending.
Additional Problems :
1. Explain why the stock of existing housing would decline if no more new houses were built.
There will always be some depreciation, as existing houses burn or are torn down. If no new houses are built (gross investment is zero), the housing stock will decline (net investment will be negative).
2. Low interest rates should encourage firms to invest. So why did the . have a low level of investment spending during the 1930s when interest rates were very low?
During the 1930s the economy was in a deep recession. Therefore, in spite of low interest rates, businesses were reluctant to invest. The level of investment depends not only on the interest rate but also on changes in income, that is, the sales expectations of businesses. In the 1930s, most businesses did not expect sales to increase.
3. "Firms will undertake investments as long as the value of the marginal product of capital is below the rental cost of capital." Comment on this statement.
If this were true, then the last unit of capital employed would cost more than the value of the increase in output. Competitive firms minimize costs when the rental cost of capital is equal to the value of additional output produced as one more unit of capital is added. Otherwise it would pay the firm to use more (if the value of the marginal product of capital exceeded the rental rate) or less (if the value of the marginal product of capital were less than the rental rate) capital in the production process.
4. "Investment is pro-cyclical in the flexible accelerator model." Comment on this statement.
Assuming away depreciation and the real time required to make adjustments to the capital stock, the desired capital stock (K * ) is proportional to real output, where a is the capital ‑ output ratio, that is,
K * t = aY t .
If investment makes up part of the difference between the actual and the desired capital stock, then
I t = l [K * t - K t-1 ] ==> I t = l a[Y t ‑ Y t-1 ].
Therefore, we can see that if output is growing, the level of investment is positive. But if output is falling, investment is negative. This means that investment in the accelerator model is pro-cyclical, that is, it follows output. Note, however, that as long as output is increasing at an increasing rate, investment will increase. On the other hand, if the increases in output become smaller, the level of investment will decline.
5. Why is the level of investment inversely related to the level of the interest rate? Can you think of any consumer spending that may also depend on the interest rate? Explain your answer.
When calculating the present discounted value of an investment, the interest rate is in the denominator. Thus a decrease in the interest rate increases the net present value of an investment. As more investment projects become profitable, the level of investment rises. Also, the neoclassical theory predicts that the desired capital stock increases as the interest rate, and therefore the rental cost of capital decreases, that is,
K * = q Y/r c .
Durable consumption goods, such as cars and appliances, are often purchased on credit. Therefore, spending on durable goods is influenced by interest rate changes, which affect the overall costs of purchasing these goods. But, as we have seen in the previous chapter, one can interpret the purchase of a durable good as an “ investment. ”
6. "Restrictive monetary policy has a negative effect on investment." Comment on this statement.
If inflationary expectations are held constant, monetary restriction will raise both real and nominal interest rates, at least in the short run. Since the level of investment is inversely related to the real interest rate, investment will fall. Business fixed investment and housing investment will fall as the returns generated by projects have to compete with the much higher costs of funds. Inventory investment will also fall as firms find it more expensive to warehouse raw materials and finished goods.
In the long run, restrictive monetary policy will not have any effect on real interest rates, but will lower nominal interest rates due to a lower inflation rate. When nominal interest rates are lower, more people may qualify for mortgage loans and therefore housing investment will increases. A lower inflation rate may also have a positive impact on stock values. But higher stock values may enable more corporations to issue new stocks to finance more investment projects. Thus monetary policy may affect investment even if it does not affect the real interest rate.
7. Which of the following two policy measures would affect GDP more and why: a temporary investment tax credit for businesses or a temporary income tax cut for individuals? Explain your answer.
A temporary investment tax credit should have a positive effect on investment for the period in which it applies. Firms may decide to accelerate projects that they would have undertaken later. They also may initiate some marginal projects that would otherwise not have been profitable. But in the long run, we should not see a significant effect on investment from a temporary investment tax credit. On the other hand, if the government temporarily decreases income taxes, consumption will not be significantly affected according to the permanent income hypothesis (unless liquidity constraints exist). Therefore the economy will not be stimulated at all by a temporary income tax cut.
8. Which would stimulate the economy more: a $50 billion tax cut financed by a $50 billion spending cut, or a temporary tax credit of 15% on each productive investment undertaken next year? Explain your answer.
According to the balanced budget theorem, a decrease in taxes and government spending by $50 billion would actually decrease national income. A temporary investment tax credit, which has a positive effect on the economy, is therefore much more beneficial. A temporary tax credit would make marginal investment projects profitable. Some firms would also undertake projects earlier to take advantage of the tax credit. Temporary investment tax credits can be used successfully to stimulate economic activity.
9. “ Firms are more likely to invest if current GDP increases. ” Comment on this statement.
The level of desired capital stock generally depends on the level of expected future (or permanent) output. But if the desired capital stock is above the actual capital stock, firms will invest. Entrepreneurs will invest more if they feel optimistic about the future and expect their sales to increase. If they are pessimistic about the future and have low sales expectations, they will invest relatively little. Current output affects capital demand only to the extent that it affects expectations about future output.
10. For a given nominal interest rate, how does an increase in the expected rate of inflation affect the level of investment?
The rental cost of capital is defined as r c = i - p e + d. This means that an increase in the expected rate of inflation ( p e ) decreases the rental cost of capital (r c ). But a decrease in the rental cost of capital increases the level of investment, as more investment projects become profitable. A decrease in r c also increases the desired capital stock K * = ( q Y)/r c and therefore encourages investment.
11. Comment on the following statement:
“ The discounted cash flow analysis is inconsistent with the neoclassical theory of investment. ”
The neoclassical theory of investment states that the level of desired capital stock increases with an increase in expected output (sales) and a decrease in the rental cost of capital. In practice, firms base their investment decisions on the discounted cash flow analysis. An investment project is evaluated by calculating its net present discounted value. If a firm expects an increase in sales, the cash flow associated with any investment project will be larger and the net present discounted value of the investment will rise. At the same time, if the rental cost of capital decreases, then the net present discounted value of the project increases and the firm is more likely to undertake the investment. The decision making of firms using this discounted cash flow analysis is therefore consistent with the neoclassical theory of investment.
12. Assume your firm buys a new computer system at a cost of $12,600 that will save you $5,600 after one year, $4,840 more after the second year and another $4,000 after the third year. Then the computer will become outdated and no further saving will accrue. Is this a worthwhile investment if we assume that there is no inflation and that the market rate of interest remains at i = 10% over these three years?
The net present discounted value of your investment is
NPV = - 12,600 + 6,600/(1+ ) 1 + 4,840/(1+ ) 2 + 4,000/(1+ ) 3
= - 12,600 + 6,000 + 4,000 + 3,000 = + 400 > 0.
Since the net present discounted value of your investment is positive, it is profitable and you should undertake this investment.
13. Evaluate the following project, assuming that the market interest rate remains at i = 10%.
Year 0 Year 1 Year 2 Year 3
costs $3,700 $605 $363 $0
revenues $0 $2,640 $2,420 $400
The investment should be undertaken, since the net present discounted value of this investment is positive. It can be calculated as follows:
NPV = -3,700 + (2,640 – 605)/(1 + .1) 1 + (2,420 - 363)/(1 + .1) 2 + 400/(1 + .1) 3
= - 3,700 + 1,850 + 1,700 + 300 = 150 > 0
Since NPV > 0, this investment is profitable and should be undertaken.
14. Would you undertake the following investment project? Why or why not?
Year 0 Year 1 Year 2 Year 3
costs $3,993 $4,840 $3,630 $0
revenues $0 $3,630 $4,840 $3,993
This problem does not list an interest rate so, under normal circumstances, we cannot solve the problem. But if we simply add up the costs and the benefits, we can see that both sums are equal. Since the costs occur earlier than the benefits, we can conclude that the project is unprofitable, since we could have invested the funds we spent at any positive interest rate. For example, if the market interest rate was i = 10%, then the net present value would be:
NPV = - 3,993 + (3,630 - 4,840)/ + (4,840 - 3,630)/ + 3,993/
= - 3,993 - 1,100 + 1,000 + 3,000 = - 1,093
Since NPV < 0, this investment is not profitable and should not be undertaken.
The investment project is unprofitable at any positive real interest rate. But it is conceivable that the real interest rate is actually negative, if the rate of inflation is greater than the nominal interest rate. In this case, the project would be profitable. At high rates of inflation it makes sense to borrow money and pay it back later with money that has lost some of its purchasing power.
15. "Credit rationing reinforces monetary policies." Comment on this statement.
Credit is rationed when lending institutions limit the amount that firms or consumers can borrow. Tight money policy raises the cost of borrowing and banks may be concerned that irresponsible borrowers will continue to borrow at the higher rates while more conservative borrowers will be deterred. To avoid the higher risks incurred with irresponsible customers, banks often limit the amount of credit given to any one customer. As fewer funds are made available, less investment takes place. Thus the rationing of credit reinforces restrictive monetary policy.
However, in the early 1990s the Fed tried to stimulate the . economy by repeatedly lowering the discount rate. Banks nonetheless chose to increase their holdings of Treasury bills rather than to expand their lending, since they were still recovering from huge losses encountered in the real estate market. In this case, the banks, in effect, rationed credit and worked against the expansionary monetary policy of the Fed.
16. Is inventory investment pro-cyclical? Why or why not?
During periods of economic expansion, firms increase production to meet sales and add to inventories, since the desired stock of inventories increases with output. But when the boom reaches its peak and economic growth and sales slow, inventories rise involuntarily until firms cut back production. This may actually contrib ute to the upcoming recession. Before growth resumes after the recession, firms may want to increase their inventories to be ready for the increase in demand for their product. When demand picks up, inventories serve to fill the demand until sales can be met through increased production. Inventory investment is usually not pro-cyclical but more counter-cyclical, that is, during recessions it rises and during booms it falls.
17. Briefly how explain inventory cycles relate to the multiplier ‑ accelerator model that states that the level of investment is positively related to the change in income.
According to the multiplier ‑ accelerator principle, any economic disturbance will lead to business cycles. A change in investment will bring about a larger change in national income, but the level of investment is proportional to the change in income. This can be expressed as follows:
I t = l [K * t - K t-1 ] ==> I t = l a[Y t ‑ Y t-1 ]. ==> I = k( D Y), with k = l a.
The multiplier principle states that the change in investment will cause a larger change in national income, or D Y = a ( D I). (Note that a is the expenditure multiplier and different from the a mentioned above.) As long as the economy is growing at an increasing rate, the level of investment will go up, stimulating growth even further. As the economy peaks, however, a reduction in the growth rate of income will reduce the level of investment, which will lead the economy into a recession. If, for example, firms expect an economic upswing, they will increase inventories since they expect future sales to increase. They will step up production, which will stimulate the economy. When the economy approaches its full potential, bottlenecks will occur, so prices and interest rates will increase. While actual sales may still increase (since the economy is still growing), they may fall below expected sales, so there may be an unwanted increase in inventories. Firms will then cut production, which may eventually cause layoffs and possibly a recession.
18. "Even though the economy may still be growing, a decrease in the growth rate of income may in itself be sufficient to lead the economy into a recession." Comment on this statement.
The multiplier ‑ accelerator principle implies that any economic disturbance can lead to economic cycles. A change in investment will bring about a larger change in national income, but the level of investment is proportional to the change in income. As long as the economy grows at an increasing rate, the level of investment will also increase which will further stimulate the economy. However, a reduction in the growth rate of income will reduce the level of investment. If the level of investment decreases, the change of investment becomes negative. This will be multiplied to produce an even larger negative change in output and the economy will go into a recession. For example, we can explain inventory cycles in the following way: If firms expect an economic upswing, they will let inventories grow since they expect future sales to increase also. To increase inventories they will have to step up production, which will stimulate the economy. When the economy approaches its full potential, then bottlenecks will occur, and prices and interest rates will increase. While actual sales may still increase (since the economy is still growing), they may fall below expectations, so there will be an unwanted increase in inventories. Firms will then cut their production level which may eventually cause some layoffs and a reduction in spending, that is, the economy enters a recession.
19. Explain why a lending institution may prefer a variable mortgage rate, while the homebuyer may prefer a fixed mortgage rate. Relate your answer to the situation of many S&Ls in the late 1970s and early 1980s.
A variable mortgage rate shifts the risk of a change in interest rates from the lending institution onto the homebuyer. If interest rates go up, then mortgage interest payments go up as well. Many homebuyers, especially those who barely qualify for mortgage loans, will not want to take this risk and will therefore prefer a fixed mortgage rate that will guarantee a fixed payment each month.
A fixed mortgage rate leaves the risk of changing interest rates with the lending institution, which may incur losses if interest rates go up substantially. As interest rates rose substantially in the late 1970s, S&Ls were faced with low returns on assets and high costs of obtaining new funds. As a result, they incurred huge losses. S&Ls held a large part of their assets in mortgages that had been negotiated in the 1960s when interest rates were low. At the same time consumers shifted their funds from S&Ls into primary securities that paid higher yields. The S&Ls therefore were faced with a liquidity problem.
20. Comment on the following statement:
"Continued high budget deficits will adversely affect the construction industry."
If the government finances an increase in spending by borrowing from the public, the budget deficit increases. As the demand for credit increases, interest rates increase as well. This negatively affects the housing sector, which is highly interest sensitive. Higher mortgage interest rates not only lead to a decrease in the demand for new houses, but may also deter some housing developers from financing new projects.
CHAPTER 15
THE DEMAND FOR MONEY
Solutions to the Problems in the Textbook :
Conceptual Problems:
1. Money is any asset that is widely used as a medium of exchange. People want to hold money since it simplifies their current or future transactions. Since the nominal value of money is always known with certainty, it is a very safe and liquid asset, unless there is a very high rate of inflation. Therefore holding money protects asset holders against potential capital losses on riskier assets.
2. In a society in which there was no money, all trade would be completely based on barter. But barter is fairly inefficient, since suppliers of goods and services can't always find people who are both in need of the goods and services being offered and willing to trade something of value to the suppliers. Therefore, sooner or later, some form of money has to be invented to facilitate trade. A good example of a money substitute is . cigarettes, which were used as medium of exchange during the hyperinflation in Germany in 1922/23, in . camps after World War II, and in some Eastern European countries during the transition from command economies to more market-based economies when people lost confidence in their own currencies.
It is easier to imagine a society in which there is no currency but everyone has a credit or debit card. The cashless purchase of goods via credit or debit cards (or via e-commerce) is not only convenient for customers but can also provide valuable information to sellers about the buying habits of consumers (which is one reason grocery stores now willingly accept credit or debit cards). In a cashless society all transactions would require electronic fund transfers through bank computers. At the end of the month, all accounts would have to be settled with the company that issued the credit or debit card, again through electronic fund transfers. This requires investment in computer technology, not only for banks but also for merchants. Such a system may seem highly efficient, but it may not work well for very small purchases, such as a magazine at a newspaper stand, a can of soda from a vending machine, or a local phone call. However, financial institutions have already developed pre-paid cash cards or phone cards that allow the purchase of smaller items or phone calls, with the amount of the purchase automatically deducted from the card.
It should be noted, however, that a cashless society still requires money, that is, funds that can be stored in accounts, whether these are traditional bank accounts used to settle outstanding bills or accounts that exist simply for e-commerce. However, if pre-paid cash cards, debit and credit cards, or e-commerce funds are used increasingly, monetary aggregates may have to be redefined.
3. One could certainly make an argument for including credit card limits as part of money stock, since people substitute credit cards for cash as a means of payment. They may also use unused credit lines for precautionary purposes. But if we include this form of credit in the money stock, it becomes difficult to justify excluding others. Therefore it may be better not to include credit card limits in the definition of money.
4. In deciding how many traveler's checks to take on a vacation, an individual has to weigh the cost of obtaining the checks against the probability of cash being stolen and the possibility that personal checks or credit cards might not be honored. The lower the cost of traveler's checks and the higher the probability that cash may be stolen, the larger the sum that is likely to be carried in traveler's checks. On the other hand, holding cash or traveler's checks involves an opportunity cost, since no interest can be earned on cash or traveler's checks. Therefore, if credit cards are accepted at the vacation spot, vacationers may rely primarily on credit cards as a means of payments, since they can earn interest on their money holdings until they have to pay their credit card bill. Many travelers now actually prefer to rely on ATM cards to obtain cash in foreign countries. This not only allows them to carry less cash or traveler's checks, but also eliminates the fee for exchanging currency. Some ATM cards also serve as debit cards and can be used for the purchase of goods or services. Possible drawbacks of relying on ATM cards include the possibility of a strike among bank employees in the foreign country or the absence of ATM machines in remote areas.
5. The opportunity cost measures the benefit or revenue foregone from using a resource in one way rather than another. Individuals who hold money give up the return they could have earned had the money been invested in a bond (or any other interest-earning asset not included in the definition of money). To guarantee lenders a positive rate of return, bonds pay nominal interest rates that include an inflation premium to cover the expected loss in purchasing power over the period that the bond is held. Therefore it is the nominal and not the real interest rate that is the opportunity cost of holding money. However, when the rate of inflation is very high, nominal interest rates do not adequately reflect the rate of inflation. In this case, the inflation rate (if it is higher than the interest rate) should be used as the appropriate opportunity cost.
6. The more inflation increases, the more individuals fear a loss of purchasing power from their money holdings. People are therefore not as likely to hold much money in periods of high inflation. An increase in inflation will increase the nominal interest rate, which is the opportunity cost of holding money. This will reduce the demand for money. From the equilibrium condition in the money sector (m d = L(i,Y) = M/P = m s ), we can see that if prices (P) increase more than nominal money supply (M), then real money balances (M/P) will decrease and the demand for real money balances (m d ) will also decrease to get the money sector back into equilibrium. In periods of high inflation, nominal money supply tends to increase rapidly, so nominal money holdings become larger.
7. During periods of deflation, the cost of holding cash decreases and people tend to carry more cash. Therefore muggers can expect a much higher return from their activity.
Technical Problems:
. Cash machines that allow withdrawals from saving accounts reduce the need to hold precautionary funds in cash or checking accounts. Therefore the demand for M1 would decrease, but the demand for M2 would not be affected since M1 is included in M2.
. If more tellers worked at your bank, then your waiting time would be reduced, so you might be willing to go to the bank more often to make withdrawals. The demand for M1 would decrease, but the demand for M2 would not be affected since M1 is included in M2.
. An increase in inflationary expectations would reduce the demand for money, since people would be afraid of losing purchasing power. In times of low inflation, people may switch from low interest accounts to higher interest accounts. The demand for M1 decreases, while the demand for M2 is not affected. However, if inflation is very high, people may hold less money in any form and spend more on durable goods. In this case the demand for both M1 and M2 might decrease.
. Increased use of credit cards would reduce the need to hold money for transactions, even though people would still need to settle their monthly credit card charges in a convenient way. They would most likely shift funds from demand deposits into time deposits, that is, away from M1 and into M2. The demand for M1 would decrease, but the demand for M2 would not be affected.
. If the fear of a collapse of the government led to the fear that money would lose its value, people would try to spend as much money as possible to buy durable or tradable goods before the government collapses. Thus the demand for both M1 and M2 would decrease.
. With an increase in the interest rate on time deposits, people would shift more funds from demand deposits into time deposits. The demand for M1 would decrease while the demand for M2 would remain unaffected. However, if interest rates on M2 components increased much more than the yield on other assets, the demand for other assets could also decrease. In such a case, the demand for M2 would increase.
. With the rise in e-commerce, more cashless transactions take place. Therefore people would most likely shift funds from demand deposits into high-interest earning accounts until their accounts had to be settled. Most e-commerce transactions involve the use of credit cards, so the answer here is the same as in . Funds are shifted away from M1 and into M2, and the demand for M1 decreases, but the demand for M2 is not affected. However, some banks have already established e-cash accounts exclusively for e-commerce; increased use of e-cash requires a re-definition of monetary aggregates.
. As the economy goes into a recession, income and interest rates are both likely to decline. Since velocity decreases as income and interest rates decrease, we should expect the velocity to decline in a recession. Also, since velocity is defined as nominal GDP over nominal money supply, it is easy to see that velocity should decrease, since nominal income declines while nominal money supply is not affected.
. The Fed can influence velocity by injecting or withdrawing money through its open market operations. If money supply increases more than nominal GDP, velocity decreases.
3. This problem is just a reversal of the inventory approach used by Baumol and Tobin, since now only one withdrawal has to be made at the end of the month, while many deposits can be made during the month. The firm would have to calculate the benefits from interest earned and compare them to the cost of making the deposits. It would therefore calculate its cash holdings in the same way as in the inventory approach.
. The person tries to minimize the cost of managing the portfolio. This cost is: C = nt c + (iY/2n)
n = 1 ==> C = 1*1 + ()(1,600)/(2*1) = 1 + 4 = 5
n = 2 ==> C = 2*1 + ()(1,600)/(2*2) = 2 + 2 = 4
n = 3 ==> C = 3*1 + ()(1,600)/(2*3) = 3 + 4/3 =
n = 4 ==> C = 4*1 + ()(1,600)/(2*4) = 4 + 1 = 5
Therefore 2 transactions are optimal.
. With two transactions, the optimal cash holding is: m d = Y/(2n) = 1,600/(2*2) = $400.
. n = 1 ==> C = 1*1 + ()(1,800)/(2*1) = 1 + =
n = 2 ==> C = 2*1 + ()(1,800)/(2*2) = 2 + =
n = 3 ==> C = 3*1 + ()(1,800)/(2*3) = 3 + =
n = 4 ==> C = 4*1 + ()(1,800)/(2*4) = 4 + =
Therefore it is still optimal to make two transactions, but the optimal cash holding is now
m d = 1,800/(2*2) = $450.
This is a % increase, since (450 - 400)/400 = .125.
Additional Problems :
1. Do people use credit cards more often when interest rates are high or low?
Many credit card companies charge a high but fixed interest rate on all balances that are not immediately paid off. Therefore, in periods of high interest rates, the interest charge becomes relatively smaller and thus we should expect the use of credit cards to go up. Also, since it may take up to a month from the time of purchase to get the credit card bill and people generally have an additional month to pay the balance, card holders get, in effect, an interest-free loan for up to two months. In times of high interest rates people have a greater incentive to keep their funds in an interest-earning account for these two months. Therefore they have a greater incentive to use their credit cards in times of high interest rates.
2. “ The opportunity cost of holding a bond is the return from holding money." Comment.
The opportunity cost is the benefit foregone when using a resource one way instead of another. People who hold bonds receive a rate of return but they are giving up the utility that holding money provides to them through its role as a medium of exchange. Since different individuals value such utility differently, the opportunity cost of holding a bond varies from one individual to another. Money is also held to protect against capital losses that may occur from a decrease in bond values arising from an increase in interest rates. The avoidance of such a capital loss can be seen as part of the return of holding money.
3. "The real interest rate is the opportunity cost of holding money." Comment on this statement.
The opportunity cost measures the benefit or the revenue foregone when using a resource in one way rather than another. If individuals hold money, they give up the return they would have earned had they used the money to purchase a bond. Bonds pay nominal interest rates to guarantee the lender a real return plus a premium to cover the expected loss in the purchasing power of the principal over the period of the "loan." Therefore it is the nominal and not the real interest rate that is the opportunity cost of holding money. If the rate of inflation is higher than the prevailing nominal interest rate, then the rate of inflation should be used as the opportunity cost.
4. "Money market deposit accounts are offered by banks, are FDIC insured, and have check-writing privileges. Therefore they should be included in M1 rather than M2." Comment on this statement.
Even though money market deposit accounts (MMDAs) limit the number of checks that can be written per month, they do provide a very cheap and convenient way of making immediate payments. Therefore it can be argued that they should be included as part of M1. However, once the check limit is reached, such accounts are much less liquid than normal checking accounts. Therefore it makes sense to include MMDAs as part of M2 rather than M1.
5. How did the introduction of so-called NOW-accounts affect the money demand of M1 and M2? How did it affect the income velocity of M1 and M2?
With the introduction of NOW-accounts, many people transferred funds from their saving accounts to these interest-earning checking accounts. This meant that more money balances were held in M1 assets and the income velocity for M1 decreased. Since M1 is part of M2, such transfers did not affect money balances held in M2 or the income velocity of M2.
6. Derive the square-root formula of the Baumol-Tobin transactions demand model. Then explain how this formula can be used to explain that high-income individuals on average hold a smaller proportion of their income in money assets than low-income people.
The square-root formula can easily be derived by minimizing the total cost of holding money with respect to the number of transactions n. This total cost is the sum of the transaction cost (nt c ) and the interest cost im d , with m d being the average cash balance, that is,
m d = Y/(2n).
Therefore from C = nt c + (iY)/(2n) ==>
D C/ D n = t c - (iY)/(2n 2 ) = 0 ==> t c = (iY)/(2n 2 ) ==> (t c Y)/(2i) = [Y/(2n)] 2 = m d 2
==> m d = [(t c Y)/(2i)] 1/2 .
According to this formula, money holdings increase proportionally less than income. This implies that individuals in higher income brackets can hold proportionally less money than people in lower income brackets. Most likely this is due to the fact that high-income individuals tend to have better access to financial markets than low-income individuals, which means that they have a lower probability of becoming illiquid.
7. Use the Baumol-Tobin transactions demand approach to calculate the interest elasticity of money demand for transaction.
From the Baumol-Tobin approach we can derive the square-root formula, that is,
m d * = [(t c Y)/(2i)] 1/2 .
This equation shows that money demand (m d ) is positively related to income (Y) but inversely related to the interest rate (i). From this square-root formula, the interest elasticity of money demand can be derived as follows:
D m d / D i = - [(1/2)[(t c Y)/(2i)] -1/2 (t c Y/2i 2 ) = - (1/2)(1/i)m d
==> [( D m d /m d )]/[( D i/i)] = ( D m d / D i)(i/m d ) = - 1/2
8. "According to the classical quantity theory of money, any decrease in nominal money supply will lead to a decrease in the unemployment rate." Comment on this statement.
The classical quantity theory of money suggests that velocity is constant and that output stays at its full-employment level. Any change in nominal money supply will therefore lead to a proportional change in the price level. According to the classical quantity theory, a decrease in nominal money supply will lead to a decrease in the price level and not the unemployment rate.
9. Which is greater: the transaction velocity of money or the income velocity of money?
The income velocity of money only includes transactions involving final goods and services, whereas the transaction velocity of money includes all transactions, including intermediate goods and wealth transfers. Therefore the transaction velocity of money is greater than the income velocity of money.
10. "Financial innovation raises the velocity of money." Comment on this statement.
The money demand function can be expressed as a function of interest rates, income, and financial innovation (e), where a positive value of e reduces the demand for money, that is,
m d = L(i, Y, e).
Velocity is defined as V = (PY)/M = Y/(M/P).
If we assume that the money sector is in equilibrium, then money demand can be substituted for money supply, and we get
m d = L(i,Y,e)= M/P = m s ==> V = Y/L(i, Y, e) ==> V = f(Y,i,e),
that is, velocity is a function of income, the interest rate and financial innovation. Therefore, if there are financial innovations (and the value of e goes up), the demand for money declines. This raises the number of times a dollar bill circulates in the economy during a given period of time. In other words, it increases the income velocity of money.
11. "An increase in the income tax rate will increase the income velocity of money." Comment on this statement. In your answer consider only the short-run effects of such a policy change.
Restrictive fiscal policy, such as an income tax increase, will affect GDP negatively and lead to lower interest rates, at least in the short run. Since the income velocity of money is positively affected by an increase in income and the interest rate, velocity should decrease. Another way of getting to the same result is to look at velocity as the ratio of nominal GDP to nominal money supply, that is,
V = (PY)/M.
Since restrictive fiscal policy leads to a (short-run) decrease in nominal GDP (PY), while nominal money supply (M) remains unaffected (the Fed was not involved in this fiscal policy measure), velocity (V) should decrease.
12. "Fiscal expansion will increase the income velocity of money." Comment on this statement.
Expansionary fiscal policy increases income and the interest rate. Since the income velocity of money is positively affected by increases in income and the interest rate, the income velocity should go up. Similarly, from the equation MV = PY, it follows that V = (PY)/M. Since expansionary fiscal policy raises nominal GDP (PY) but does not affect nominal money supply (M), we should expect velocity (V) to go up.
13. Assume you know that the supply of money (M) has increased by 6%, real output (Y) has increased by % and the income velocity (V) of money has dropped by 3%. What is the rate of inflation?
From the quantity theory of money equation (MV = PY) ==> % D M + % D V = % D P + % D Y ==>
% D P = % D M - % D Y + % D V ==> % D P = 6% - % + (-3%) = + %.
Therefore the rate of inflation (% D P) should be %.
Note: The equation that shows the percentage changes in money supply, output, velocity, and prices generally only applies for very small changes in these variables. Therefore, the result for this problem is just an approximation of the actual change we should expect in the price level.
14. Assume that M2 has increased by 8%, inflation has increased by 4%, and real output has grown at a rate of % over the same time period. What does this imply for V2, the income velocity of M2?
From the equation MV = PY, we get % D M + % D V = % D P + % D Y. It follows that
8% + % D V = 4% + % ==> % D V = - %,
that is, V2 must have decreased by %. (The note for question 14 applies here as well.)
CHAPTER 16
THE FED, MONEY, AND CREDIT
Solutions to the Problems in the Textbook :
Conceptual Problems:
1. The three tools the Fed has to conduct monetary policy are open market operations, discount rate changes, and reserve requirement changes. If the Fed wants to increase the money supply, it has the following options: first, the Fed can buy government bonds from the public (mostly banks), thereby increasing bank reserves. These open market purchases will induce banks to extend their loans, which will create more money. Second, it can lower the discount rate, so it becomes less costly for banks to borrow reserves from the Fed. This also will induce banks to create more money by extending more loans. Finally, the Fed can lower the required-reserve ratio, which again will allow banks to lend more.
2. The currency-deposit ratio is the ratio of currency outstanding to bank deposits. The Fed cannot directly influence this ratio, since it is determined by the behavior of the public and influenced by the convenience of obtaining cash and by seasonal patterns (increased Christmas shopping, for example). However, by changing either bank regulations (that would affect the ease of obtaining cash) or interest rates (that would change the opportunity cost of holding cash), the Fed may indirectly affect how much currency the public is willing to hold.
. . IS 2 .
i IS LM 2 i IS 1 LM
LM 1
i 2
i 2
i 1 i 1
0 0
Y 2 Y 1 Y Y 1 Y 2 Y
If most disturbances come from the money sector (a shift in money demand), interest rate targets work better than money targets. In the IS- LM diagram below we can see that as money demand increases due to changing expectations, the LM-curve will shift to the left and the interest rate will increase. By increasing money supply and shifting the LM-curve back to the right, the central bank can get the economy back to the original equilibrium.
. If most disturbances come from the expenditure sector, the central bank is better off targeting money supply. If spending increases, the IS-curve shifts to the right and the interest rate increases. If the central bank tried to get the interest rate back to its original level by increasing money supply, the disturbance would intensify, since the LM-curve would also shift to the right. Thus, the central bank should keep money supply (and thus the LM-curve) stable to keep the disturbance at a minimum.
. A bank run occurs when depositors, worried about the safety of their assets, rush to withdraw their deposits.
. If a bank is in trouble because it has made some bad investment decisions, people may expect it to fail. Thus they may want to withdraw their deposits before it is too late. Since other depositors are likely to behave in the same way, a run on the bank can be anticipated. Even a fairly financially sound bank may not be able to withstand a run, since most assets are tied up in loans. Almost all . banks are FDIC insured and therefore a run on a bank is very unlikely. With FDIC insurance, depositors know that they can get at least their principal back from the government should a bank fail, and therefore they do not panic easily.
. During the Great Depression, a large-scale run on banks lead to liquidity problems and bank failures. This decreased the lending power of the whole banking system. In other words, depositors lost their confidence in banks and withdraw their deposits. This increased the currency-deposit ratio, leading to a decrease in the money multiplier and a contraction in money supply.
. The existence of the FDIC increases the public's confidence in the banking system, so a run on banks is highly unlikely. Therefore the currency-deposit ratio is low and the value of the money multiplier is high. The money multiplier is also more stable since the public does not withdraw deposits any time a bank failure occurs.
. There are basically two reasons why the Fed does not adhere more closely to its monetary growth targets in the short run. The first is technical: due to the variability of the money multiplier and the lag in collecting data on money supply figures, the Fed is not always able to achieve its monetary growth target. The second reason is that the Fed, in the short run, uses interest rate targets concurrently with monetary growth targets, and it is impossible to succeed at both at the same time. Therefore, as the Fed responds to changes in the economy, it may move away at least temporarily from its monetary growth target. The Fed's desire to have some short-run flexibility while still maintaining long-run credibility, may cause a temporary deviation from the announced monetary growth target.
. The targeting of nominal interest rates can be self-defeating, especially in times of high inflation. If (nominal) interest rates increase, the Fed has to increase money supply to reduce interest rates to their original level. However, expansionary monetary policy will lead to more inflation and this will ultimately result in higher nominal interest rates. The so-called Fisher-equation states that the nominal interest rate (i n ) is equal to the real interest rate (i r ) plus the rate of inflation ( p ), that is,
i n = i r + p .
In the long run, the real interest rate will not be affected by expansionary monetary policy, but the nominal interest rate will be higher due to increased inflation. Another attempt to further reduce the nominal interest rate by expanding money supply even more will aggravate inflation even more and ultimately not succeed in bringing interest rates down.
. Nominal GDP is an ultimate target of monetary policy.
. The discount rate is an instrument of monetary policy.
. The monetary base is an immediate target of monetary policy.
. M1 is an intermediate target of monetary policy.
. The Treasury bill rate is an intermediate target of monetary policy.
. The unemployment rate is an ultimate target of monetary policy.
7. When banks ration credit, interest rates are no longer a good indication of existing market conditions. Credit is rationed when lending institutions limit the amount that their customers can borrow based on concerns that such borrowing may not be financially prudent. In this situation, the Fed should not use interest rate targets as a guide for its monetary policy, since interest rates no longer reflect true market conditions.
8. The Fed has much more control over intermediate targets (money supply or interest rates) than it does over ultimate targets (GDP, unemployment, or inflation). Changes in these intermediate targets do not have an immediate effect on the ultimate targets and therefore the Fed can easily reverse or re-enforce its policy measure. Because of the long lags associated with monetary policy, the Fed uses these intermediate targets to get feedback on the effects of a policy change and the likeliness that a policy measure will achieve its ultimate goal. However, concentrating solely on intermediate targets does not guarantee that the ultimate objectives will be achieved.
9. From the quantity theory of money equation MV = PY, we get
% D M + % D V = % D P + % D Y ==> % D P = % D M - % D Y + % D V.
If real GDP (Y) is assumed to grow at a rate of %, the Fed has to let money supply (M) grow at a rate of % to keep prices (P) stable, assuming that velocity (V) remains stable. The Fed can control nominal GDP through changes in nominal money supply only as long as the behavior of money demand (and thus velocity) is relatively predictable. The long-run GDP growth rate has been around %, far below the % mentioned here, and expansionary monetary policy will not achieve such a high growth rate. But there is a very close relationship between money supply changes and price changes in the long run, while real GDP growth is primarily influenced by other factors. If the Fed overestimates the rate at which potential GDP grows, then it is likely to stimulate the economy too much and induce high inflation. Therefore, nominal GDP targeting rather than real GDP targeting may be a better approach, since the former creates a policy tradeoff between unemployment and inflation. In other words, we will get less growth but also less inflation if potential GDP growth is overestimated.
Technical Problems:
1. Assume the Fed sells Treasury bills valued at $10 million to a bank.
Fed Balance Sheet: Assets Liabilities
Govt. securities - $10 Currency 0
Other assets 0 Bank deposits - $10
Bank Balance Sheet: Assets Liabilities
Deposits at the Fed - $10 Deposits 0
Govt. securities + $10
Other assets 0
The bank has now lost $10 million in reserves (deposits at the Fed). If required reserves are no longer sufficient, then the bank will have to acquire new reserves.
If a bank depositor buys the Treasury bills, then the balance sheet will be:
Bank Balance Sheet: Assets Liabilities
Reserves - $10 Deposits - $10
Other assets 0
Again, the bank may have to make up for the loss of reserves.
2. Assume the Fed buys $10 million worth of gold and then decides to sterilize the effect of this purchase on the monetary base through open market operations.
Fed Balance Sheet: Assets Liabilities
Gold + $10 Currency 0
Other assets 0 Member bank deposit + $10
The purchase of gold increased the monetary base (bank reserves) by $10 million.
Fed Balance Sheet
After Sterilization: Assets Liabilities
Gold + $10 Bank deposits (+10 -10) = $0
Govt. securities - $10
The sale of government securities to banks again decreased the monetary base (bank reserves) by $10 million, so there is no overall change in the monetary base.
. If the reserve-deposit ratio is 100%, then banks cannot create any loans and the money multiplier is equal to 1. This means that the Fed has total control over the money supply, since it has control over bank reserves. However, this would significantly change the banking industry, since banks no longer would be able to extend loans.
. Since banks would not be able to issue any loans, the assets side would contain only reserves.
. Banking could still remain profitable as long as banks were able to generate service charges to cover their operating costs.
4. In deciding whether monetary base targeting or interest rate targeting is better for the Fed in its conduct of monetary policy, it would be good to know whether the goods sector or the money sector is more prone to disturbances. If most disturbances occur in the goods sector (assume the IS-curve shifts to the right), then monetary base targeting is better, since interest rate targets would force the Fed to aggravate the disturbance. Under interest rate targeting, the Fed would be forced to change money supply (shifting the LM-curve to the right) and aggregate demand would be changed even more. If most disturbances occur in the money sector (assume the LM-curve shifts to the left), then interest rate targeting is better, since the Fed can easily offset the disturbance. Under interest rate targeting the Fed could change money supply (shifting the LM-curve to the right again) without affecting aggregate demand.
IS 2
i IS LM 2 i IS 1 LM
LM 1
i 2
i 2
i 1 i 1
0 0
Y 2 Y 1 Y Y 1 Y 2 Y
Additional Problems :
1. How does an increase in the currency-deposit ratio affect the money multiplier? What is the effect of an increase in the reserve-deposit ratio?
The money multiplier is defined as mm = (1 + cu)/(cu + re), where
cu = CU/D = currency-deposit ratio, and
re = R/D = reserve-deposit ratio.
An increase in the currency-deposit ratio means that people hold more currency and banks have fewer funds to create deposits. Therefore the money multiplier decreases. An increase in the reserve-deposit ratio means that banks now hold more reserves, so fewer deposits can be created. Again, the money multiplier decreases.
2. Assume that an increasing number of department and grocery stores accept credit and debit cards and more consumers use these cards to do their shopping. How will the money multiplier and money supply be affected?
If more consumers make purchases using credit or debit cards rather than cash, then less currency is held and the currency-deposit ratio will be lower. This implies a larger money multiplier and, given a fixed stock of high-powered money, an increase in money supply.
3. "The introduction of the FDIC after the Great Depression not only calmed the worries of the public but also made monetary policy easier for the Fed." Comment on this statement.
The introduction of the FDIC lowered the public's fear of new bank failures. Consumer confidence in the banking system increased and people held less currency. Banks also were able to reduce their excess reserves, since they no longer feared a widespread bank run. The currency-deposit and the reserve-deposit ratios both declined, and the size of the money multiplier increased. In addition, the money multiplier became more stable, since consumers became less likely to panic after a bank failure occurred. The larger and the more stable the money multiplier, the easier it is for the Fed to control money supply by changing the monetary base through open market operations.
4. Assume money supply (M) is $1,200 billion, total bank deposits (D) are $800 billion and the required reserve-deposit ratio is 10%. What would the Fed have to do to lower money supply by 5%? Explain your answer.
We know that M = CU + D ==> CU = M - D = 1,200 - 800 = 400.
If we assume that banks do not hold excess reserves, then
R = ()D = ()800 = 80 and H = CU + R = 400 + 80 = 480.
Thus the money multiplier is M/H = mm = 1,200/480 = .
If the Fed wants to reduce money supply by 5% or $60 billion, it has to reduce high-powered money (H) by $24 billion, by selling $24 billion worth of Treasury bills. In other words,
D M = mm( D H) == > - 60 = ( D H) ==> ( D H) = - 60/ = - 24
5. Assume the currency-deposit ratio is 30%, the required reserve-deposit ratio is 8% and the excess reserve-deposit ratio is 2%. How much would money supply change if the Fed made open market sales valued at $20 million?
The money multiplier is defined as: M/H = mm = (1 + cu)/(cu + re).
In this example the size of the money multiplier is equal to
mm = (1 + )/( + + ) = ()/() = .
An open market sale valued at $20 million would decrease high-powered money (H) by $20 million. Therefore, money supply (M) would decrease by $65 million, since
D M = mm( D H) = ()(-20) = - 65.
6. Assume bank deposits are $3,200 billion, the required reserve-deposit ratio is 10%, and currency outstanding is $400 billion. What should the Fed do to decrease money supply by $100 million?
Ms = Cu + D = 400 + 3,200 = 3,600 and H = Cu + R = Cu + ()D = 400 + 320 = 720
==> money multiplier = Ms/H = mm = 3,600/720 = 5
==> D Ms = mm( D H) ==> - 100 = 5( D H) ==> D H = - 20
If the Fed wants to decrease money supply by $100 million, bank reserves have to be decreased by $20 million through the open market sale of government securities. (Note: The assumption was that excess reserves are zero, which may not be true.)
7. True or false? Why?
"An open market sale raises the monetary base and therefore money supply."
False. An open market sale occurs when the Fed sells government bonds to the private sector, primarily banks, in return for currency. Reserves held in the form of deposits at the Fed decrease, and therefore the monetary base (the stock of high-powered money) decreases as does money supply, since banks cannot loan out as much as previously.
8. What problems would arise if the Fed tried to conduct open market operations via the stock market?
Theoretically, the Fed could change high-powered money and thus the supply of money by buying and selling stocks. The problem, however, would be how to decide which stocks to buy and sell, since the Fed's actions would affect the values of the stocks being bought or sold.
9. "Large open market sales may have a negative impact on the demand for money, the budget surplus, the income velocity of money, and consumption." Comment on this statement .
Open market sales decrease bank reserves and therefore money supply. This increases interest rates, leading to a lower level of investment and income. Since income tax revenues decrease in a recession, the budget surplus will also decrease. Since interest rates are higher, the interest payments on the national debt will increase. A lower level of income means a lower level of consumption. The income velocity of money generally declines in a recession. However, the decline in money occurs before the decline in income. Thus we first see an increase in velocity in the short run, followed by a decrease.
10. Which is the most useful tool for the Fed to conduct its monetary policy? In your answer discuss the advantages and disadvantages of each of the tools that the Fed has at its disposal.
The Fed has three basic tools to conduct monetary policy are open market operations, discount rate changes, and reserve requirement changes.
Open market operations are used most often by the Fed since it can be undertaken every business day, can be undertaken to a large or small degree, and can be easily reversed. Bank reserves are immediately affected to a desired degree with the initiative lying solely with the Fed.
The discount rate can be used as a signal for a change in monetary policy, but often a change in the discount rate simply reflects an adjustment to existing money market conditions. The disadvantage of using the discount rate is that it is up to banks to change the level of bank reserves. Bank reserves only change when banks borrow more or less from the Fed. Since this behavior cannot be anticipated, bank reserve changes cannot be accurately anticipated.
Reserve requirement changes are used only rarely, since this is an extremely blunt tool. A reserve requirement change will affect the money multiplier and have a huge effect on money supply. Generally banks are given ample time to adjust to changes.
11. Comment on the following statement:
"Changes in the discount rate are always a sign that the Fed has changed its monetary policy."
The discount rate is the rate at which banks can borrow from the Fed. The federal funds rate is the rate at which banks can borrow from each other. Banks generally prefer to borrow at the lowest rate. They do not like to borrow too often or too much from the Fed, however, since the Fed may then question their way of doing business. But if the demand for bank reserves increases and the difference between the federal funds rate and the discount rate gets too large, banks have an incentive to borrow from the Fed more often than usual. In this case total bank reserves will increase more than the Fed would like. As a result, the Fed may adjust the discount rate to bring it more in line with the federal funds rate. Therefore, while an increase in the discount rate may signal a shift in the Fed's policy, it may also simply reflect the Fed's response to a change in money market conditions.
12. In 1991-92, the Fed repeatedly lowered the discount rate, but failed to stimulate the economy. Explain this fact. Subsequently, the Fed lowered the reserve requirements for banks. In your opinion, what was the Fed's objective in doing this, and was the objective achieved?
Lowering the discount rate is not always successful in increasing money supply (and thus stimulating the economy), since it requires that banks take the initiative to change bank reserves. In 1991-92, the . was in a recession and negative business expectations persisted. Many banks needed to recover from loan losses they had incurred and did not want to extend credit even though they were encouraged to do so by the Fed.
The Fed finally lowered the reserve requirements for banks in a further effort to stimulate the economy but also to increase the profitability of banks. Banks do not earn interest on the reserves they hold, so a decrease in reserve requirements allowed them to increase their earnings and reduce their portfolio risk by buying Treasury-bills. While the economy was not immediately stimulated by new loans, at least the profitability of banks increased, creating more stability within the banking system.
13. "Open market sales are more effective than increasing the discount rate in changing money supply." Comment. In your answer explain the short-run effects of restrictive monetary policy on velocity, the budget surplus, and national saving.
With open market operations, the Fed has the initiative and bank reserves are immediately affected. Open market operations can be undertaken to a small or large extent on every business day, the Fed can determine the level of impact on bank reserves, and the Fed's actions can be easily reversed. Discount rate changes affect banks' cost of borrowing from the Fed, but leave the initiative to react to the banks. Thus, the Fed cannot easily predict the exact effect on bank reserves. For example, in 1991 the Fed changed the discount rate 15 times but banks did not borrow more from the Fed or increase their lending due to unfavorable economic conditions. If the Fed restricts money supply, interest rates will increase, leading to a decrease in economic activity. Initially, the income velocity (V = PY/M) will increase due to the lower money supply (M), but it will take time to affect income. But as national income (Y) decreases, income velocity will decline. Other results will include a decrease in the budget surplus (due to lower tax revenues) and national saving (due to lower income and a lower government surplus).
14. Assume the Fed lowered the discount rate. How would personal saving, the budget surplus and aggregate money demand be affected?
A lower discount rate is intended to encourage banks to borrow more from the Fed. It is not always clear that banks will respond as expected, but if they do, bank reserves will increase and so will money supply, as banks increase their lending activity. This will lower interest rates, leading to an increase in investment and national income. Personal saving will increase with a higher income level. Similarly, tax revenues will go up, increasing the budget surplus. Lower interest rates and higher income will increase money demand. (We also can see this from the fact that money supply has increased. Since the money sector has to move into a new equilibrium, money demand has to go up if money supply is increased.)
15. Should you expect the federal funds rate to be above the discount rate or vice versa? Explain.
The Fed is the lender of last resort and banks can always borrow from the Fed if the need arises. When banks borrow from the Fed, they are charged a rate called the discount rate. But banks also have the option to borrow from each other at the federal funds rate. Banks generally prefer to borrow at the lowest rate possible. However, they do not like to borrow too heavily from the Fed, since the Fed is a regulator of banks. Banks fear that their behavior will be questioned if the Fed takes notice and thus prefer to borrow from each other. In doing so, they drive the federal funds rate above the discount rate.
16. "Reserve requirements act as an unfair tax on banks." Comment on this statement.
Banks are forced to hold their reserves either as vault cash or as deposits at the Fed earning no interest in either case. Since other financial institutions have no such reserve requirement, it could be argued that this unfairly taxes banks. On the other hand, reserves guarantee a certain amount of liquidity for the banking system, which may be necessary, should there be a run on banks. The reserves held as deposits at the Fed also serve to facilitate the check clearing process. For these reasons, the tax can be viewed as necessary and therefore less "unfair."
17. Does the Fed have control over the federal funds rate and over bank reserves? If so, can the Fed control both simultaneously?
The Fed has indirect control over the federal funds rate, since it has control over the supply of total bank reserves in the banking system through open market operations. However, the Fed cannot control the demand for bank reserves. If the demand for bank reserves increases, the federal funds rate will rise. If the Fed chooses to peg the federal funds rate, it has to create additional bank reserves via open market purchases. On the other hand, if the Fed chooses to control the level of bank reserves, it has to let the federal funds rate fluctuate. Therefore, the Fed cannot control the federal funds rate and the level of bank reserves simultaneously.
18. "By lowering the reserve requirements for banks, the Fed reduces the budget deficit, national saving, and the income velocity of money." Comment on this statement.
If the Fed lowers the reserve requirement, banks have more money to lend out and can thus increase their earnings by making more loans or buying T-bills. If banks extend their loans, then money supply will increase and interest rates will decrease, stimulating investment and national income. Saving will increase with a higher level of income. Similarly, tax revenues will go up, reducing the budget deficit. Interest payments on the national debt will also decrease with lower interest rates, which will also help to lower the deficit. Velocity will initially decrease, since money supply will increase before income. But as income increases, then velocity will increase again. Ultimately, velocity may not change by much, since the income elasticity of money demand is close to one in the long run.
19. "Restrictive monetary policy over a long time period will lead to lower interest rates." Comment on this statement.
Long ‑ run effects of monetary policy are different from short ‑ run effects. Restrictive monetary policy leads to higher interest rates in the short run due to less liquidity (liquidity effect). But higher interest rates will reduce aggregated demand, which reduces prices and national income. Thus the level of interest rates will start to decline again (price ‑ income effect). Lower prices will eventually lead to lower inflationary expectations and thus lower nominal interest rates (price ‑ anticipation effect). In the end, real interest rates (i r ) will return to their original level and nominal interest rates (i n ) will be lower, since the inflation rate ( p ) is lower. This is shown in the so-called Fisher equation: i n = i r + p .
20. "The elimination of required reserves on bank deposits would decrease the Fed's control over money supply. But if money supply increased uncontrollably, then high rates of inflation would result." Comment on the following statement.
The Fed has a number of policy instruments at its disposal to control the level of bank reserves (and thus money supply). The required-reserve ratio is only one such instrument. The Fed can always influence bank reserves through the use of open market operations. Even if reserve requirements are abolished, the money multiplier will always have a finite value, since banks will always hold some (excess) reserves to meet their daily cash needs and emergency needs. If the reserve requirement were eliminated, the money multiplier would become larger, since banks would not choose to voluntarily hold as many reserves as the Fed required. However, large-scale open market operations would still enable the Fed to exercise great influence over bank reserves and therefore money supply.
21. "In order to keep national income stable, the FOMC has to purchase government securities whenever interest rates increase." Comment on the following statement with the help of an IS-LM diagram and explain the adjustment process.
Interest rates can go up for two reasons: either an increase in spending (a shift of the IS-curve to the right) or an increase in money demand (a shift of the LM-curve to the left). In the first case, to keep income stable the Fed has to sell (not purchase) government securities, to induce a decrease in bank reserves (and thus money supply) and shift the LM-curve to the left. But this will lead to even higher interest rates, lowering investment and thus future economic growth. In the second case, the Fed can succeed by buying government securities, shifting the LM-curve back to the right thus, in effect, negating the disturbance.
IS 1 LM 1
i IS o LM o 1 à 2 I Y md i I ¯ Y ¯
i 2 3
i 1 2 effect: Y i
i o 1 2 à 3 Ms ¯ i I ¯ Y ¯ md ¯ i ¯
effect: Y ¯ i
0 Overall effect: Y = const., as desired, i
Y o Y 1 Y
LM 1
i IS o LM o 1 à 2 md i I ¯ Y ¯ md ¯ i ¯
i 1 effect: Y ¯ i
i o 2 à 3 Ms i ¯ I Y md i
Effect : Y i ¯
0 Overall effect : Y = const., as desired, i ?
Y 1 Y o Y
22. Comment on the following statement:
"The Fed should always conduct open market purchases whenever interest rates increase."
If the increase in the interest rate is caused by an increase in spending (the IS-curve has shifted to the right), the Fed should not purchase government securities since this will shift the LM-curve to the right as well, making the disturbance worse.
i IS 2
IS 1 LM 1 LM 2
i 2
i 1
0
Y 1 Y 2 Y 3 Y
But when disturbances come from the money sector (assume an increase in money demand shifts the LM-curve to the left, increasing interest rates), the Fed can restore the original equilibrium by purchasing government securities, shifting the LM-curve back to the right.
23. True or false? Why?
"Money demand shocks will not affect the level of output as long as the Fed pegs the interest rate."
True. Assume money demand increases, shifting the LM-curve to the left and leading to an increase in the interest rate. If the Fed pegs the interest rate, it will respond by increasing the money supply. This will shift the LM-curve back to the right, moving the level of output demanded and the interest rate back to their original levels. A decrease in money demand requires a reduction in the money supply to bring interest rates and output back to their original levels.
i IS LM 2
LM 1
i 2
i 1
0
Y 2 Y 1 Y
CHAPTER 17
FINANCIAL MARKETS
Solutions to Problems in the Textbook :
Conceptual Problems:
1. Financial markets are markets in which assets are bought and sold. These markets transmit changes in government policies and other macroeconomic disturbances to the rest of the economy. For example, changes in interest rates affect peoples' wealth by changing the prices of stocks and bonds, peoples' ability to finance the purchase of a car or a house, and corporations' ability to finance investments. It is useful to look at financial markets to better understand this transmission mechanism. For example, many economists prefer to look at the flow of funds accounting rather than national income accounting when assessing the performance of the economy.
2. The concept of arbitrage implies that, in equilibrium, prices will make financial investors equally willing to buy or sell an asset. If investors are not equally willing to buy and sell an asset, then there is an opportunity for arbitrage. People buy or sell assets to take advantage of the resulting profit opportunity. But in doing so, they cause prices to adjust up to the point where no further arbitrage opportunity exists. If people always take advantage of profit opportunities, financial markets will always adjust to an equilibrium.
. The expectations theory of the term structure says that long-term interest rates are determined by the average of current and future expected short-term interest rates. If short-term interest rates are higher than long-term interest rates, people must expect that interest rates will decline in the future.
. Generally, interest rates decrease in a recession and increase in a boom. If people are expecting interest rates to decrease, they are probably anticipating a recession. However, this is not always the case. For example, if people expect interest rates to decline because of restrictive fiscal policy, then expectations about an upcoming recession may be warranted. But if they expect that interest rates may decline because of expansionary monetary policy, they should actually expect that the level of output will increase.
. The yield curve shows interest rates for government bonds of different maturities. If short-term interest rates are higher than long-term interest rates, the yield curve is downward sloping as indicated below.
yield
0
maturity
4. If stock prices follow a random walk, they cannot be predicted from existing information. Stock price changes only occur if (by surprise) new information becomes available. This implies that even the best-informed financial investors cannot make a killing in the stock market. In other words, either no riskless profit opportunities exits, or all such opportunities have already been taken advantage of. If stock prices did not follow a random walk, financial investors could find ways to reap great benefits by taking advantage of profit opportunities that have not yet been realized by others.
5. The price of a stock is the net present discounted value of the expected dividends. Any new information that will change expectations about future dividends will change the stock's price. Thus, if financial investors expect a recession, they expect no or at least lower dividend payments. This will immediately be reflected in lower stock prices, especially since some investors will try to avoid a capital loss by selling their stock before its price has adjusted to the new lower level.
Similarly, since the stock market and the bond market are linked, financial investors who expect a recession also expect lower interest rates. But lower interest rates imply higher bond prices. A capital gain can be made if bonds are bought at the current low price and sold later at the (expected) higher price. Therefore, some financial investors may switch their funds from stocks to bonds, lowering stock prices, if they expect a recession. This is why the stock market performance is often used a leading economic indicator.
6. If interest rates in the . increased relative to interest rates in Canada, then a flow of funds from Canada into the . would occur, since Canadian investors would want to take advantage of the higher rates. This would increase the demand for . dollars in the foreign exchange market, causing the value of the . dollar to appreciate and the Canadian dollar to depreciate. In other words the . dollar/Canadian dollar exchange rate would fall, since it would take more . currency to buy a Canadian dollar.
Technical Problems:
. According to the expectations theory of the term structure, the interest of a ten-year bond is simply the average of all one-year bond yields covering these ten years. In other words,
10
i 10 = (1/10) S i t .
t=1
. If there were no uncertainty, the interest rate of the ten-year bond should be exactly the average of all one-year bonds covering these ten years, in this case, 10%. The fact that the rate is 12%, reflects that there is uncertainty and that the ten-year bond offers a risk premium of 2%.
. The present value of the bond can be determined by the present discounted value formula, that is,
10 10
PV = S c/(1 + i) t + FV/(1 + i) 10 ==> 100 = S c/(1 + .1) t + 100/(1 + ) 10 .
t =1 t =1
Since the price is equal to the face value, the coupon rate has to be equal to the market interest rate, that is, 10%. Therefore, the coupon value has to be 10% of the face value, that is, c = 10.
. A drop in the interest rate will increase the net present value (price) of the bond. Since you bought the bond at a price PV = 100, you could now sell it for more. This can also be seen another way. The bond pays a coupon value of $10 each year, that is 10% of $100. But the market pays you only 5% or $5 out of $100. Therefore, people would be willing to buy this bond for a price higher than $100. The exact price can be calculated by the above formula with i = 5%.
3. If interest rates increase in Japan but remain the same in the ., we will have an outflow of funds from the . to Japan. The Japanese yen will appreciate and the . dollar will depreciate in value. In other words, the $/yen exchange rate (e) will rise. This can also be seen from the following equation:
( D e/e) = i US - i J ,
that is, if the Japanese interest rate (i J ) increases, then the $/yen exchange rate (e) has to increase.
4. The price of a stock is the net present discounted value of the expected dividends. If expected dividends go up, so will the price of the stock. If financial investors expect high future profits for . firms they are more likely to buy stocks in these firms, since they expect higher dividend payments. Therefore, the high average rate of return on . stock holdings is an indication that financial investors expect high future profit for . firms, indicating a strong performance for the . economy as a whole.
Additional Problems :
1. Explain why bond prices vary inversely with interest rates.
The present value (price) of a bond is the sum of the discounted yearly interest payments received plus the present discounted face value of the bond. In other words,
n
PV = S c/(1 + i) t + FV/(1 + i) n .
t =1
In the formula for the present value of a bond, the market interest rate is in the denominator, so an increase in the interest rate will decrease the present value (price) of the bond. The longer the time of maturity, the greater the change in value that comes from an interest rate change.
2. List some of the factors that determine the yield (interest rate) on different financial securities.
The yield (interest) that is paid on financial securities depends on some of the following factors:
· the lower the liquidity of a security, the higher the yield that has to be paid in order to attract financial investors;
· the higher the default risk of a corporation, the higher the yield that has to be paid to compensate for this increased risk;
· the longer the maturity, the higher the interest rate risk, and the higher the yield required to compensate for this higher risk;
· higher administration costs or different tax treatment also may affect the yield;
· foreign securities often have to pay higher yields to compensate for higher risk due to uncertain political circumstances or possible currency fluctuations.
3. If a previously upward-sloping yield curve starts to flatten out and eventually becomes downward sloping, how would you interpret this change?
Financial investors have expectations about whether interest rates will increase or decrease and they react accordingly. If they expect the economy to enter a recession, they expect that interest rates will fall. As they try to lock in high yields for the long term, the demand for long ‑ term securities increases, leading to an increase in long ‑ term security prices and thus a decrease in long ‑ term yields. The yield curve will flatten out and eventually become downward sloping. Naturally, such behavior is not always guaranteed and a downward-sloping yield curve can also be the result of decreasing inflationary expectations in the absence of a recession. However, in many cases, the yield curve can be a fairly reliable forecasting device.
4. If the yield curve becomes increasingly steeper over time, what kind of economic conditions would you forecast and why? In your answer explain why t he so-called expectations theory is self-fulfilling.
Financial investors respond to changing expectations about market interest rates. If the yield curve begins to get steeper, it is a sign that investors expect interest rates to go up in the future. If financial investors expect interest rates to rise, they fear a capital loss from holding long-term securities, so they try to sell them, driving prices down and yields up. They use the proceeds to buy short-term securities, leading to higher short-term security prices and lower short-term yields. The expectations have fulfilled themselves, as we will get an upward-sloping yield curve. Therefore the yield curve can serve as a forecasting tool. Since interest rates tend to rise in booms or periods of expected high inflation, we will see the yield curve getting steeper before such periods.
5. Explain the relationship between short-term and long-term interest rates according to the following three theories: (i) the expectations theory, (ii) the liquidity preference theory, and (iii) the market segmentation theory.
According to the expectations theory, long-term interest rates are an average of current and future expected short-term rates. If people expect interest rates to decrease they try to lock in high yields by buying long ‑ term securities. Therefore the demand for long ‑ term securities goes up and long ‑ term bond prices increase, that is, long ‑ term yields decline. As people shift out of short ‑ term securities, short ‑ term security prices decrease and short ‑ term yields go up. We get a downward-sloping yield curve if interest rates are expected to go down. (An analogous argument can be made for an upward-sloping yield curve.)
The liquidity preference theory suggests that long ‑ term securities have to offer a risk premium partly because of their higher interest rate risk, so the yield curve can be expected to slope upward.
Another explanation is provided by the market segmentation theory, which argues that different financial investors have different preferences in terms of the maturity of the securities they hold. Banks prefer to hold short-term maturity securities while pension plans prefer to hold long-term securities. The prices (and therefore the yields) of various securities are determined by the relative demand for and supply of these securities in the money or capital markets. Since the markets are sufficiently segmented, the shape of the yield curve is determined to some degree by who is in the market for specific securities at any given time.
6. How much would you be willing to pay for a one-year maturity bond with a 15% coupon rate and a face value of $4,400 if the market interest rate is 10%? Would you rather buy a consol that pays you $440 each year for that same price? Why or why not?
The present value of the one-year maturity bond is:
PV = 660/(1 + .1) + 4,400/(1 + ) = 600 + 4,000 = 4,600.
The present value of the consol is determined as follows:
PV = 440/() = 4,400
It would be a bad idea to buy the consol for $4,600.
7. Assume you bought a one-year maturity bond with a coupon rate of % and a face value of $10,000 for a price of $9,000. Calculate the current yield and the yield to maturity of this bond.
The current yield is the interest you receive on the funds you have invested, that is,
i = 810/9,000 = = %
The yield to maturity includes the interest you receive on the funds invested plus the capital gain that you receive from buying the security at less than face value. Thus the yield to maturity can be calculated in the following way:
9,000 = [810 + 10,000]/(1 + i) ==> 1 + i = 10,810/9,000 = ==> i = %
8. Assume you bought a zero percent coupon rate bond with a two-year maturity and a face value of $8,640 for $6,000. What is your rate of return? Should you have bought a consol, paying $720 a year instead for the same price? Why or why not?
The rate of return (yield to maturity) of the two-year maturity bond can be calculated as follows:
6,000 = 8,640/(1 + i) 2 ==> (1 + i) 2 = 8,640/6,000 = ==> (1 + i) = ==> i = = 20%.
The rate of return on the consol is determined as follows:
6,000 = 720/i ==> i = 720/6,000 = = 12%.
You should buy the two-year maturity bond.
9. Assume you paid $5,000 for Security A (a one-year maturity bond with a 5% coupon rate and a face value of $5,200), but you also could have bought Security B (a consol that pays you $810 every year you own it) for $9,000. Which of these securities offered you the highest rate of return? Please show all your calculations.
The rate of return (yield to maturity) of Security A can be calculated as follows:
5,000 = [260 + 5,200]/(1 + i) ==> 1 + i = 5,460/5,000 = ==> i = %.
The rate of return of Security B is as follows:
9,000 = 810/i ==> i = 810/9,000 = = 9%.
Since Security A offers a higher yield than Security B, you would prefer to buy Security A.
10. Assume the market interest rate is i = 20% and is not expected to change. Would you agree to buy a consol (a bond without maturity) that pays you $380 for every year you own it, if you had to pay $820 right now, an additional $744 in one year and a final payment of $576 in two years? Why or why not?
The present value of your consol is PV = R/i = 380/() = 1,900.
The present value of your payments is: PV = 820 + 744/() + 576/() = 820 + 620 + 400 = 1,840.
Since the present value of the consol is more than the present value of your payments, you would want to buy this consol.
11. Assume you had a winning ticket from the lottery, paying you $50,000 per year for the rest of your life. If the market interest rate is 5% and you could sell this ticket to anyone who wants it, about how much should you get for it?
The present value of this lottery ticket can be calculated by the sum of all yearly future payments, discounted using an appropriate discount rate. For simplicity, we can treat this as a perpetuity that pays you a fixed amount R = 50,000 every year forever. The present value of the ticket is therefore
PV = R/i = $50,000/ = $1,000,000.
12. Assume you are considering the purchase of rental property that is offered to you for a price of $100,000. Approximately how much would you have to charge in rent on average each month over the rest of your life so you can get a rate of return of 9% on your investment?
Since a house lasts a very long time, we can use the formula for a perpetuity to calculate the approximate present value of a rental property. In other words, the value of the property can be calculated in the following way:
PV = (yearly rent)/(interest rate) ==> yearly rent = PV*i ==>
yearly rent = 100,000() = 9,000 ==> monthly rent = 9,000/12 = 750.
13. Assume the going market rent for a rental property is $400 per month. Approximately how much would you pay for this property if the market interest rate is 5%?
We can use the formula for a perpetuity to calculate the approximate value of the house:
PV = (yearly rent)/(interest rate) = 12*400/(.05) = 4800/() = 96,000.
14. Explain how the value of a stock that pays a fixed dollar amount in dividends each year will change as interest rates decrease.
The value of a stock that pays a fixed dividend each year can be calculated in the same way as the value of a consol (a bond that has no maturity and pays a fixed amount R each year). The present value (price) of such a security is PV = R/i. As the market interest rate (i) decreases, the present value of the security (PV) increases.
15. "The efficient-markets theory states that monetary policy is more efficient than fiscal policy in stimulating economic activity." Comment on this statement.
While many people believe that monetary policy tends to be much more effective than fiscal policy, the efficient-markets theory does not say anything about fiscal or monetary policy. Instead, the efficient-markets theory suggests that current stock prices already contain all available information. New information is readily available and understood by all market participants who quickly react to new information. Therefore you cannot outperform the stock market, and you can't make profits by looking at old information or past patterns of price changes in a certain stock.
16. "The efficient-markets theory states that it does not pay to hire an expert to manage your portfolio; you can get the same return on your assets without any effort by randomly selecting securities." Comment on this statement.
The efficient-markets theory suggests that the current market price of a stock already reflects all available information. New information is readily available and understood by all market participants who quickly react to it. Nobody can consistently outperform the stock market nor can profits be made by looking at old information or past patterns of changes in stock prices. However, this does not consider the fact that some investors have more expertise in interpreting existing information and may be willing to take above-average risk. These investors might be able to achieve above-average returns--at least once in a while.
17. "The efficient-markets theory states that financial markets are more efficient than product markets." Comment on this statement.
The efficient-markets theory does not say anything about whether financial markets work better than product markets. Instead, the efficient-markets theory suggests that the current price of a stock already contains all available information. New information is readily available and understood by all market participants who quickly react. Therefore people cannot outperform the stock market nor can they make profits by looking at old information or past patterns of price changes of that stock.
18. "If interest rates in the . increase due to expansionary fiscal policy, then the . dollar will appreciate." Comment on this statement.
If . interest rates increase, there will be an inflow of funds, and the demand for the . dollar will increase. This will increase the value of the . dollar. This can be seen from the following equation:
( D e/e) = i us - i w .
If interest rates in the . (i us ) increase, but the interest rate (i w ) stays the same in the rest of the world, then the exchange rate of foreign currency/dollar (e) will increase.
