Transcript
246Miller•Economics Today, Nineteenth Edition
Chapter 16Domestic and International Dimensions of Monetary Policy239
Answers to Problems
16-1. Let’s denote the price of a nonmaturing bond (called a consol) as Pb. The equation that indicates this price is Pb = I/r, where I is the annual net income the bond generates and r is the nominal market interest rate.
a. Suppose that a bond promises the holder $500 per year forever. If the nominal market interest rate is 5 percent, what is the bond’s current price?
b. What happens to the bond’s price if the market interest rate rises to 10 percent?
a. $500/0.05 = $10,000.
b. Its price falls to $500/0.10 = $5,000.
16-2. On the basis of Problem 16-1, imagine that initially the market interest rate is 5 percent and at this interest rate you have decided to hold half of your financial wealth as bonds and half as holdings of non-interest-bearing money. You notice that the market interest rate is starting to rise, however, and you become convinced that it will ultimately rise to 10 percent.
a. In what direction do you expect the value of your bond holdings to go when the interest rate rises?
b. If you wish to prevent the value of your financial wealth from declining in the future, how should you adjust the way you split your wealth between bonds and money? What does this imply about the demand for money?
a. You expect that the value of your bond holdings will decline.
b. You would reduce your bond holdings, which implies a reallocation of wealth to money holdings. Consequently, the quantity of money that you desire to hold would increase.
16-3. You learned in an earlier chapter that if there is an inflationary gap in the short run, then in the long run a new equilibrium arises when input prices and expectations adjust upward, causing the short-run aggregate supply curve to shift upward and to the left and pushing equilibrium real GDP per year back to its long-run value. In this chapter, however, you learned that the Federal Reserve can eliminate an inflationary gap in the short run by undertaking a policy action that reduces aggregate demand.
a. Propose one monetary policy action that could eliminate an inflationary gap in the short run.
b. In what way might society gain if the Fed implements the policy you have proposed instead of simply permitting long-run adjustments to take place?
a. One possible policy action would be an open market sale of securities, which would reduce the money supply and shift the aggregate demand curve leftward. Another would be to increase the discount rate relative to the federal funds rate.
b. In principle, the Fed’s action would reduce inflation more quickly.
16-4. You learned in an earlier chapter that if a recessionary gap occurs in the short run, then in the long run a new equilibrium arises when input prices and expectations adjust downward, causing the short-run aggregate supply curve to shift downward and to the right and pushing equilibrium real GDP per year back to its long-run value. In this chapter, you learned that the Federal Reserve can eliminate a recessionary gap in the short run by undertaking a policy action that increases aggregate demand.
a. Propose one monetary policy action that could eliminate the recessionary gap in the short run.
b. In what way might society gain if the Fed implements the policy you have proposed instead of simply permitting long-run adjustments to take place?
a. One possible policy action would be an open market purchase of securities, which would increase the money supply and shift the aggregate demand curve rightward. Another would be to reduce the discount rate relative to the federal funds rate.
b. In principle, the Fed’s action would push real GDP per year back up more quickly.
16-5. Suppose that the economy currently is in long-run equilibrium. Explain the short-and long-run adjustments that will take place in an aggregate demand-aggregate supply diagram if the Fed expands the quantity of money in circulation.
The short-run effect is an upward movement along the short-run aggregate supply curve generated by an increase in aggregate demand. The equilibrium price level rises, and equilibrium real GDP increases. In the long run, input prices rise and people anticipate a higher price level, which causes the short-run aggregate supply curve to shift upward and to the left. The equilibrium price level rises once more, and equilibrium real GDP falls back to its long-run equilibrium level.
16-6. Explain why the net export effect of a contractionary monetary policy reinforces the usual impact that monetary policy has on equilibrium real GDP per year in the short run.
Because a contractionary monetary policy causes interest rates to increase, financial capital begins to flow into the United States. This causes the demand for dollars to rise, which pushes up the international value of the dollar and makes U.S. exports more expensive to foreign residents. They cut back on their purchases of U.S. products, which tends to reduce U.S. real GDP.
16-7. Suppose that, initially, the U.S. economy was in an aggregate demand-aggregate supply equilibrium at point A along the aggregate demand curve AD in the diagram below. Now, however, the value of the U.S. dollar suddenly appreciates relative to foreign currencies. This appreciation happens to have no measurable effects on either the short-run or the long-run aggregate supply curve in the United States. It does, however, influence U.S. aggregate demand.
a. Explain in your own words how the dollar appreciation will affect net export expenditures in the United States.
b. Of the alternative aggregate demand curves depicted in the figure—AD1 versus
AD2— which could represent the aggregate demand effect of the U.S. dollar’s appreciation? What effects does the appreciation have on real GDP and the price level?
c. What policy action might the Federal Reserve take to prevent the dollar’s appreciation from affecting equilibrium real GDP in the short run?
a. The dollar appreciation will raise the prices of U.S. goods and services from the perspective of foreign residents, so they will reduce their spending on U.S. exports. It will reduce the prices of foreign goods and services from the perspective of U.S. residents, so they will increase their spending on foreign imports. Thus, net export expenditures will decline.
b. The fall in net export expenditures will bring about a decrease in U.S. aggregate demand, so the aggregate demand curve AD2 will apply to this situation. In the short run, the equilibrium price level will fall from 118 to 116, and equilibrium real GDP, measured in base year dollars, will fall from $18.0 trillion to $17.5 trillion.
c. The Federal Reserve could engage in a policy action, such as open market purchases, that increase aggregate demand to its original level.
16-8. Suppose that the quantity of money in circulation is fixed but the income velocity of money doubles. If real GDP remains at its long-run potential level, what happens to the equilibrium price level?
The price level doubles. Because MsV = PY, V has doubled, and Y is unchanged; P must double
as well.
16-9. Suppose that following adjustment to the events in Problem 16-8, the Fed cuts the money supply in half. How does the price level now compare with its value before the income velocity and the money supply changed?
The price level remains at its original value. Because MsV = PY, V has doubled, and Y is unchanged; cutting Ms in half leaves P unchanged.
16-10. Consider the following data: The money supply is $1 trillion, the price level equals 2, and real GDP is $5 trillion in base-year dollars. What is the income velocity of money?
MsV = PY, so V = PY/Ms = (2 $5 trillion)/$1 trillion = 10.
16-11. Consider the data in Problem 16-10. Suppose that the money supply increases by $100 billion and real GDP and the income velocity remain unchanged.
a. According to the quantity theory of money and prices, what is the new equilibrium price level after full adjustment to the increase in the money supply?
b. What is the percentage increase in the money supply?
c. What is the percentage change in the price level?
d. How do the percentage changes in the money supply and price level compare?
a. MsV = PY, so P = MsV/Y = ($1.1 trillion 10)/$5 trillion = 2.2.
b. $100 billion/$1 trillion = 0.1, or 10 percent
c. 0.2/2 = 0.1, or 10 percent
d. Both the money supply and the price level increased by 10 percent.
16-12. Assuming that the Fed judges inflation to be the most significant problem in the economy and that it wishes to employ all of its policy instruments except interest on reserves, what should the Fed do with its three policy tools?
Open market sales, increase in the discount rate relative to the federal funds rate.
16-13. Suppose that the Fed implements each of the policy changes you discussed in Problem
16-12. Now explain how the net export effect resulting from these monetary policy actions will reinforce their effects that operate through interest rate changes.
Any one of these contractionary actions will tend to raise interest rates, which in turn will induce international inflows of financial capital. This pushes up the value of the dollar and makes U.S. goods less attractive abroad. As a consequence, real planned total expenditures on U.S. goods decline even further.
16-14. Imagine working at the Trading Desk at the New York Fed. Explain whether you would conduct open market purchases or sales in response to each of the following events. Justify your recommendation.
a. The latest FOMC Directive calls for an increase in the target value of the federal funds rate.
b. For a reason unrelated to monetary policy, the Fed’s Board of Governors has decided to raise the differential between the discount rate and the federal funds rate. Nevertheless, the FOMC Directive calls for maintaining the present federal funds rate target.
a. To push the equilibrium federal funds rate up to the new target value, the Trading Desk will have to reduce the money supply by selling U.S. government securities.
b. The increase in the differential between the discount rate and the federal funds rate will induce fewer depository institutions to borrow reserves from Federal Reserve banks. In the absence of a Trading Desk action, this would cause the equilibrium interest rate to increase. To prevent this from occurring, the Trading Desk will have to boost the money supply by purchasing U.S. government securities.
16-15. To implement a credit policy intended to expand liquidity of the banking system, the Fed desires to increase its assets by lending to a substantial number of banks. How might the Fed adjust the interest rate that it pays banks on reserves in order to induce them to hold the reserves required for funding this credit policy action? What will happen to the Fed’s liabilities if it implements this policy action?
To induce the banks to hold the reserves, the Fed would have to raise the interest rate it pays on the reserves. The increase in reserves owned by private banks would generate a rise in the Fed’s liabilities equal to the expansion of the Fed’s assets.
16-16. Suppose that to finance its credit policy, the Fed pays an annual interest rate of 0.5 percent on bank reserves. During the course of the current year, banks hold $1 trillion in reserves. What is the total amount of interest the Fed pays banks during the year?
$5 billion
16-17. During an interval between mid-2010 and early 2011, the Federal Reserve embarked
on a policy it termed “quantitative easing.” Total reserves in the banking system increased. Hence, the Federal Reserve’s liabilities to banks increased, and at the same time its assets rose as it purchased more assets—many of which were securities with private market values that had dropped considerably. The money multiplier declined, so the net increase in the money supply was negligible. Indeed, during a portion of the period, the money supply actually declined before rising near its previous value. Evaluate whether the Fed’s “quantitative easing” was a monetary policy or credit policy action.
The money supply did not change, so this did not actually constitute a monetary policy action. Instead, the Fed only expanded its reserves and, hence, its liabilities, which corresponded to the increase in the Fed’s holdings of privately issued assets. Consequently, the Fed’s “quantitative easing” was primarily a credit policy action.
16-18. Consider the two panels of Figure 16-2. Suppose that instructions in the latest FOMC Directive call for a monetary policy action aimed at pushing down the rate of interest prevailing in the economy. Use the appropriate panel of the figure to assist in explaining whether officials at the Federal Reserve Bank of New York’s Trading Desk should buy or sell existing bonds.
The appropriate panel of the figure is panel (b), in which the Trading Desk buys bonds. This action reduces the supply of existing bonds in the private marketplace. After this purchase, at
the initial bond price P1, an excess quantity demanded of bonds exists, so the bond price must
rise to P3.
16-19. Take a look at the two panels of Figure 16-2, and also consider Figure 16-1. Suppose that instructions in the latest FOMC Directive call for a monetary policy action aimed at inducing individuals and businesses to demand a smaller quantity of money. Use the appropriate panel of Figure 16-2 to assist in explaining whether officials at the Federal Reserve Bank of New York’s Trading Desk should buy or sell bonds.
Figure 16-1 indicates that the interest rate must rise to induce a lower quantity of money demanded. Generating a higher interest rate requires a lower price of bonds, so panel (a) of
Figure 16-2 is appropriate. When the Trading Desk sells bonds, the supply of existing bonds in the private marketplace rises. At the initial bond price P1, an excess quantity supplied of bonds exists, so the bond price must fall to P2.
16-20. Take a look at Figure 16-3. Discuss a policy action that the Trading Desk at the Federal Reserve Bank of New York could undertake in order to bring about the increase in aggregate demand displayed in this figure.
To generate an increase in aggregate demand, the Trading Desk would have to induce a rise in the price of bonds and a corresponding reduction in the interest rate, which would be associated with an increase in the quantity of money in circulation. To boost the price of bonds, the Trading Desk would buy existing bonds, which would reduce the supply of these bonds in the private marketplace.
16-21. Consider Figure 16-3. Discuss a policy action that the Trading Desk at the Federal Reserve Bank of New York could undertake in order to generate the decrease in aggregate demand displayed in this figure.
To bring about a decrease in aggregate demand, the Trading Desk would have to generate a fall
in the price of bonds and a related increase in the interest rate, which would be associated with a decrease in the quantity of money in circulation. To lower the price of bonds, the Trading Desk would sell existing bonds, which would raise the supply of these bonds in the private marketplace.
16-22. Take a look at Figure 16-6. Suppose that a multiple reduction in real GDP is the final outcome that the Fed desires in the last box in the figure. Explain the required directions
of effects—that is, increase or decrease—that must occur in the preceding boxes in the figure in order to yield this desired decrease in real GDP.
The required change in monetary policy would be an open market sale. This initial policy action which would bring about a reduction in excess reserves, a multiple reduction in the money supply, an increase in the interest rate (and corresponding decrease in bond prices), and a decrease in investment. The decline in investment would induce the Fed’s desired multiple reduction in real GDP.
16-23. Consider Figure 16-7. Discuss a specific monetary policy action that the Fed’s Trading Desk could implement in order to induce the effects traced out by this figure.
An open market purchase would generate an increase in excess reserves, a multiple increase in the money supply, a decrease in the interest rate (and related increase in bond prices), and an increase in investment. The rise in investment would bring about the increase in aggregate demand and short-run increase in equilibrium real GDP.
Appendix E
E-1. Suppose that each 0.1-percentage-point decrease in the equilibrium interest rate induces a $10 billion increase in real planned investment spending by businesses. In addition, the investment multiplier is equal to 5, and the money multiplier is equal to 4. Furthermore, every $20 billion increase in the money supply brings about a 0.1-percentage-point reduction in the equilibrium interest rate. Use this information to answer the following questions under the assumption that all other things are equal.
a. How much must real planned investment increase if the Federal Reserve desires to bring about a $100 billion increase in equilibrium real GDP?
b. How much must the money supply change for the Fed to induce the change in real planned investment calculated in part (a)?
c. What dollar amount of open market operations must the Fed undertake to bring about the money supply change calculated in part (b)?
a. Because the investment multiplier equals 5, a $20 billion increase in planned investment will generate a five-fold increase in equilibrium real GDP, or a rise of $100 billion.
b. A 0.2-percentage-point decrease in the equilibrium interest rate is required to bring about a $20 billion increase in planned investment. Thus, because every $20 billion rise in the money supply pushes the interest rate down by 0.1 percentage point, a $40 billion ($20 billion × 2) increase in the money supply is necessary.
c. The money multiplier is 4, so a $10 billion increase in reserves generated by a open market purchase is required to boost the money supply by 4 × $10 billion = $40 billion.
E-2. Suppose that each 0.1-percentage-point increase in the equilibrium interest rate induces a $5 billion decrease in real planned investment spending by businesses. In addition, the investment multiplier is equal to 4, and the money multiplier is equal to 3. Furthermore, every $9 billion decrease in the money supply brings about a 0.1-percentage-point increase in the equilibrium interest rate. Use this information to answer the following questions under the assumption that all other things are equal.
a. How much must real planned investment decrease if the Federal Reserve desires to bring about an $80 billion decrease in equilibrium real GDP?
b. How much must the money supply change for the Fed to induce the change in real planned investment calculated in part (a)?
c. What dollar amount of open market operations must the Fed undertake to bring about the money supply change calculated in part (b)?
a. Because the investment multiplier equals 4, a $20 billion decrease in planned investment
will generate a four-fold decrease in equilibrium real GDP, or a decline of $80 billion.
b. A 0.4-percentage-point increase in the equilibrium interest rate is required to bring about a $20 billion decrease in planned investment. Thus, because every $9 billion reduction in the money supply pushes the interest rate down by 0.1 percentage point, a $36 billion
($9 billion × 4) decrease in the money supply is necessary.
c. The money multiplier is 3, so a $12 billion decrease in reserves generated by a open market purchase is required to reduce the money supply by 3 × $12 billion = $36 billion.
E-3. Assume that the following conditions exist:
a. All banks are fully loaned up—there are no excess reserves, and desired excess reserves are always zero.
b. The money multiplier is 3.
c. The planned investment schedule is such that at a 6 percent rate of interest, investment is $1,200 billion; at 5 percent, investment is $1,225 billion.
d. The investment multiplier is 3.
e. The initial equilibrium level of real GDP is $18 trillion.
f. The equilibrium rate of interest is 6 percent. Now the Fed engages in expansionary monetary policy. It buys $1 billion worth of bonds, which increases the money supply, which in turn lowers the market rate of interest by 1 percentage point. Determine how much the money supply must have increased, and then trace out the numerical consequences of the associated reduction in interest rates on all the other variables mentioned.
Through its purchase of $1 billion in bonds, the Fed increased reserves by $1 billion. This ultimately caused a $3 billion increase in the money supply after full multiple expansion. The
1 percentage-point drop in the interest rate, from 6 percent to 5 percent, caused investment to rise by $25 billion, from $1,200 billion to $1,225 billion. An investment multiplier of 3 indicates that equilibrium real GDP rose by $75 billion, to $18,075 billion, or $18.075 trillion.
E-4. Assume that the following conditions exist:
a. All banks are fully loaned up—there are no excess reserves, and desired excess reserves are always zero.
b. The money multiplier is 4.
c. The planned investment schedule is such that at a 4 percent rate of interest, investment is $1,400 billion. At 5 percent, investment is $1,380 billion.
d. The investment multiplier is 5.
e. The initial equilibrium level of real GDP is $19 trillion.
f. The equilibrium rate of interest is 4 percent. Now the Fed engages in contractionary monetary policy. It sells $2 billion worth of bonds, which reduces the money supply, which in turn raises the market rate of interest by 1 percentage point. Determine how much the money supply must have decreased, and then trace out the numerical consequences of the associated increase in interest rates on all the other variables mentioned.
Through its sale of $2 billion in bonds, the Fed reduced reserves by $2 billion. This ultimately caused an $8 billion decrease in the money supply after full multiple contraction. The 1 percentage-point rise in the interest, from 4 percent to 5 percent, caused investment to fall by
$20 billion, from $1,400 billion to $1,380 billion. An investment multiplier of 5 indicates that equilibrium real GDP fell by $100 billion from $19,000 billion to $18,900 billion.
Selected References
Barro, Robert J., Macroeconomics, New York: John Wiley and Sons, 1984.
Barro, Robert J., The Cato Journal, Vol. 6, No. 2, Fall 1986, devotes an entire issue to “Money, Politics, and the Business Cycle.”
Dillard, Dudley, “The Theory of a Monetary Economy,” in Kenneth K. Kurihara, ed., Post Keynesian Economics, New Brunswick, NJ: Rutgers University Press, 1954.
Friedman, Milton, “The Role of Monetary Policy,” American Economic Review, Vol. 58, March 1968,
pp. 1–17.
Hayek, Frederich A., Unemployment and Monetary Policy, California: The Cato Institute, 1979.
Mann, Maurice, “How Does Monetary Policy Affect the Economy?” Federal Reserve Bulletin,
October 1968, pp. 803–809.
McCallum, Bennett T., Monetary Economics: Theory and Policy, New York: Macmillan, 1989.
Miller, Roger L. and David D. VanHoose, Modern Money and Banking, 3rd ed., New York:
McGraw-Hill, 1993.
Miller, Roger L. and Robert W. Pulsinelli, Macroeconomics, New York: Harper and Row, 1986.
Ritter, Lawrence S., “The Role of Money in Keynesian Theory,” in Deane Carson, ed., Banking and Monetary Studies, Homewood, IL: Irwin, 1963, pp. 134–150.
