S m. D m0. D m1 Q m Amount of money demanded and supplied

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1 Rate of interest, i (p ercent) Chapter - Interest Rates and Monetary Policy Chapter Interest Rates and Monetary Policy QUESTIONS 1. What is the basic determinant of (a) the transactions demand and (b) the asset demand for money? Explain how these two demands can be combined graphically to determine total money demand. How is the equilibrium interest rate in the money market determined? Use a graph to show the impact of an increase in the total demand for money on the equilibrium interest rate (no change in money supply). Use your general knowledge of equilibrium prices to explain why the previous interest rate is no longer sustainable. LO1 Answer: (a) The level of nominal GDP. The higher this level, the greater the amount of money demanded for transactions. (b) The interest rate. The higher the interest rate, the smaller the amount of money demanded as an asset. On a graph measuring the interest rate vertically and the amount of money demanded horizontally, the two demands for the money curves can be summed horizontally to get the total demand for money. This total demand shows the total amount of money demanded at each interest rate. The equilibrium interest rate is determined at the intersection of the total demand for money curve and the supply of money curve. S m i 1 i 0 D m0 D m1 Q m Amount of money demanded and supplied With an increase in total money demand, the previous interest rate (i 0) is unsustainable because with the new demand for money (D m1), the quantity of money demanded will exceed the quantity of money supplied. There would be a shortage of funds and upward pressure on the interest rate. 2. What is the basic objective of monetary policy? What are the major strengths of monetary policy? Why is monetary policy easier to conduct than fiscal policy? LO2-1

2 Answer: The basic objective of monetary policy is to assist the economy in achieving a full-employment, non-inflationary level of total output. The major strengths of monetary policy are its speed and flexibility compared to fiscal policy, the Board of Governors is somewhat removed from political pressure, and its successful record in preventing inflation and keeping prices stable. The Fed is given some credit for prosperity in the 1990s and early 2000s. Monetary policy is formed by the 7 members of the Board of Governors. Fiscal policy requires the consent of both houses in Congress, plus the President. One of the implications is that monetary policy has a much shorter administrative lag than fiscal policy.. Use commercial bank and Federal Reserve Bank balance sheets to demonstrate the impact of each of the following transactions on commercial bank reserves: LO2 a. Federal Reserve Banks purchase securities from banks. b. Commercial banks borrow from Federal Reserve Banks at the discount rate. c. The Fed reduces the reserve ratio. d. Commercial banks borrow from Federal Reserve Banks after winning an auction held as part of the term auction facility. Answer: In the tables below, columns a through c show the changes caused by the answers to the questions. It is assumed the initial reserve ratio is 20 percent. Thus, as the first column shows, the commercial banks are initially completely loaned up. The answers are not cumulated: We return to the first column each time to show the resulting change in column a, b, or c. If you would rather not use numbers, it would be acceptable to substitute with + or - signs, using symbols to represent numbers. For example, part (a) could read the Fed purchases x dollars worth of securities, and instead of the $2 billion changes on the balance sheet, you would indicate + x. Note: Any numbers could demonstrate this if direction is same. The answer to part (d) is similar to that of part (b) conditional on winning the auction. (a) It is assumed the Fed buys $2 billion worth of securities. This should increase commercial bank reserves by $2 billion, and reduce securities by $2 billion. With demand deposits of $200 billion, required reserves are $40 billion, (= 20 percent of $200 billion). Therefore, excess reserves are $2 billion (= $42 billion - $40 billion) and the banking system can increase the money supply (by making loans) by $10 billion more (= $2 billion x 5). (b) It is assumed the commercial banks borrow $1 billion from the Fed. The commercial banks may now increase the money supply (through making loans) by $5 billion (= $1 billion x 5). (c) Changing the reserve ratio in itself does not change the balance sheets. However, if we assume the reserve ratio has been decreased from 20 percent to 19 percent, required reserves are now $8 billion (= 19 percent of $200 billion) and the commercial banks can now increase the money supply (through making loans) by $10.5 billion [= $2 billion (1/0.19)]. Proof: 19 percent of $210.5 billion is $40 billion. -2

3 CONSOLIDATED BALANCE SHEET: ALL COMMERCIAL BANKS A B C Assets: Reserves Securities Loans $ $ $ $ Liabilities and net worth: Checkable deposits Loans from the Federal Reserve Banks Assets: Securities Loans to commercial banks CONSOLIDATED BALANCE SHEET: TWELVE FEDERAL RESERVE BANKS A B C $28 2 $285 2 $28 $28 2 Liabilities and net worth: Reserves of commercial banks Treasury deposits Federal Reserve Notes Other liabilities and net worth Distinguish between the Federal funds rate and the prime interest rate. Why is one higher than the other? Why do changes in the two rates closely track one another? LO Answer: The Federal funds interest rate is the interest rate banks charge one another on overnight loans needed to meet the reserve requirement. The prime interest rate is the interest rate banks charge on loans to their most creditworthy customers. The Federal funds rate is lower than the prime interest rate for a number of reasons. Federal funds are loaned overnight, so lenders don t have to wait long for repayment. The reserves loaned would otherwise generate no interest, so even loaning at the lower Federal funds rate is beneficial to lenders. Interest rates also depend on risk. It is less risky to lend overnight to other banks than it is to lend for longer periods to non-bank businesses and households. Both rates are related to the relative scarcity or availability of reserves. If there are less reserves available for lending, the price to borrow those reserves (the interest rate) will rise whether the customers are banks, businesses, or households. 5. Why is a decrease in the supply of Federal funds shown as an upshift of the supply curve in Figure., whereas an increase in Federal funds is shown as a downshift of the supply curve? LO -

4 Answer: The decrease in the supply of Federal funds is shown as an upshift in the supply curve because the FED will ensure that the quantity of funds supplied equals the quantity of funds demanded at the targeted rate of 4.5%. In effect, the FED creates a perfectly elastic (horizontal) supply curve to target the rate of 4.5%. This logic applies to an increase in Federal funds where we observe a downshift in the supply curve. Here the FED targets the rate of.5%, so the amount of funds in the market are constantly adjusted to match demand at this targeted rate. Again, in effect the supply curve is perfectly elastic(horizontal). 6. Suppose that you are a member of the Board of Governors of the Federal Reserve System. The economy is experiencing a sharp rise in the inflation rate. What change in the Federal funds rate would you recommend? How would your recommended change get accomplished? What impact would the actions have on the lending ability of the banking system, the real interest rate, investment spending, aggregate demand, and inflation? LO, LO4 Answer: To reduce inflation, the Federal funds rate should be raised. This would be accomplished typically through open-market operations (selling bonds), but could also be achieved with an increase in the reserve ratio or discount rate. The restrictive monetary policy would reduce the lending ability of the banking system, increase the real interest rate, reduce investment spending, reduce aggregate demand, and reduce inflation. 7. Explain the links between changes in the nation s money supply, the interest rate, investment spending, aggregate demand, real GDP, and the price level. LO4 Answer: A change in the nation s money supply (achieved by changing reserves in the banking system) will cause an opposite change in the interest rate. A reduction in the money supply will make funds increasingly scarce and drive up their price (interest rate). The interest rate and investment spending are also inversely related. A rising interest rate will make some investments (capital spending projects) unprofitable, so spending on those will decline. Investment spending is part of aggregate demand, so they will move together, as will real GDP. A decline in spending (AD) will reduce inflationary pressure (and will reduce prices if they are downwardly flexible). 8. What do economists mean when they say that monetary policy can exhibit cyclical asymmetry? How does the idea of a liquidity trap relate to cyclical asymmetry? Why is this possibility of a liquidity trap significant to policymakers? LO5 Answer: Cyclical asymmetry refers to the condition that a restrictive monetary policy is relatively potent at contracting economic activity, while an expansionary monetary policy is relatively weak at stimulating an economy. The weakness in expansionary monetary policy results when, even though the Fed increases liquidity (reserves) in the system, potential borrowers are unwilling to spend (often because of uncertainty over general weakness in the economy). This is often referred to as a liquidity trap. -4

5 Cyclical asymmetry, and the potential for a liquidity trap, is important to policymakers because it suggests that while monetary policy can effectively fight inflation, it may not be as successful in bringing an economy out of a recession. As Japan learned in the 1990s, expansionary monetary policy may be inadequate, and an expansionary fiscal policy may be necessary to stimulate recovery. 9. LAST WORD What are the three main aggregate supply factors that determine a nation s potential (or full employment) level of real output? What are the four main components of aggregate demand? Explain: Aggregate supply factors determine a nation s potential GDP whereas aggregate demand factors determine whether or not the nation achieves its full employment GDP. How does fiscal and monetary policy relate to aggregate demand? PROBLEMS Answer: From the Figure we see that the three main aggregate supply factors that determine a nation s potential (or full employment) level of real output are: (1) Inputs (2) Productivity and () the legal-institutional environment. Also from the figure we see that the four main components of aggregate demand are: (1) Consumption (2) Investment () Net Export spending and (4) Government spending. The reason that aggregate supply factors determine a nation s potential GDP is because it is this set of factors that determines what, and how much, an economy can produce. However, aggregate demand factors determine whether or not the nation achieves its full employment GDP. For example, the economy may be able to produce goods, but if no one is willing to purchase the goods they will not be produced. Fiscal and Monetary policy can potentially guide aggregate demand to the appropriate level to achieve full-employment. 1. Assume that the following data characterize the hypothetical economy of Trance: money supply = $200 billion; quantity of money demanded for transactions = $150 billion; quantity of money demanded as an asset = $10 billion at 12 percent interest, increasing by $10 billion for each 2-percentage-point fall in the interest rate. LO1 a. What is the equilibrium interest rate in Trance? b. At the equilibrium interest rate, what are the quantity of money supplied, the total quantity of money demanded, the amount of money demanded for transactions, and the amount of money demanded as an asset in Trance? Answer: (a) 4% (b) $200; $200; $150; $50 Feedback: Consider the following example. Assume that the following data characterize the hypothetical economy of Trance: money supply = $200 billion; quantity of money demanded for transactions = $150 billion; quantity of money demanded as an asset = $10 billion at 12 percent interest, increasing by $10 billion for each 2-percentage-point fall in the interest rate. LO1-5

6 Part a: What is the equilibrium interest rate in Trance? To answer this part of the question we use the table below. The first column is the interest rate and the second column is the quantity of money demanded as an asset at each rate. The third column us the quantity of money demanded for transactions, which is independent of the interest rate. The fourth column is actual (total) quantity of money demanded at each interest rate, which is the sum of the columns 1 and 2. The fifth column is the quantity of money supplied at each interest rate. Interest Rate Asset Demand for Money Transactions Demand Combined Demand for Money Money Supply 12% % % % % % We find the equilibrium interest rate by equating the quantity supplied with the quantity demanded, which occurs at the interest rate of 4%. Part b: b. At the equilibrium interest rate, what are the quantity of money supplied, the total quantity of money demanded, the amount of money demanded for transactions, and the amount of money demanded as an asset in Trance? It also follows from the answer above that the equilibrium quantity of money supplied is $200 and the equilibrium quantity demanded is $200. We can decompose the quantity demanded into its separate components, where the amount of money demanded for transactions is $150 and the amount of money demanded as an asset is $ Suppose a bond with no expiration date has a face value of $10,000 and annually pays a fixed amount of interest of $800. In the table provided, calculate and enter either the interest rate that the bond would yield to a bond buyer at each of the bond prices listed or the bond price at each of the interest yields shown. Round your answer to the nearest thousandth. What generalization can be drawn from the completed table? LO1-6

7 Answer: The generalization is that Bond price and interest rate are inversely related. Feedback: Consider the following example. Suppose a bond with no expiration date has a face value of $10,000 and annually pays a fixed amount of interest of $800. Compute and enter in the spaces provided in the accompanying table either the interest rate that the bond would yield to a bond buyer at each of the bond prices listed or the bond price at each of the interest yields shown. What generalization can be drawn from the completed table? To answer this question we use the formula for a perpetuity. Bond Price = Fixed Payment Amount / Interest Yield or Interest Yield = Fixed Payment Amount / Bond Price Bond Price $8,000: Interest Yield = $800/$8000 = 0.10 (or 10%) Interest Yield 8.9%: Bond Price = $800/.089 = $9000 (rounded to nearest thousandth) Bond Price $10,000: Interest Yield = $800/$10,000 = 0.08 (or 8%) Bond Price $11,000: Interest Yield = $800/$11,000 = (or 7.272%) Interest Yield 6.2%: Bond Price = $800/.062 = $1,000 (rounded to nearest thousandth) Note here that the Face Value does not enter the equation because it has no expiration date (you could actually drop this part of the question). The generalization is that bond price and interest rate are inversely related.. In the accompanying tables you will find consolidated balance sheets for the commercial banking system and the 12 Federal Reserve Banks. Use columns 1 through to indicate how the balance sheets would read after each of transactions a to c is completed. Do not cumulate your answers; that is, analyze each transaction separately, starting in each case from the numbers provided. All accounts are in billions of dollars. LO2-7

8 a. A decline in the discount rate prompts commercial banks to borrow an additional $1 billion from the Federal Reserve Banks. Show the new balance-sheet numbers in column 1 of each table. b. The Federal Reserve Banks sell $ billion in securities to members of the public, who pay for the bonds with checks. Show the new balance-sheet numbers in column 2 of each table. c. The Federal Reserve Banks buy $2 billion of securities from commercial banks. Show the new balance-sheet numbers in column of each table. d. Now review each of the above three transactions, asking yourself these three questions: (1) What change, if any, took place in the money supply as a direct and immediate result of each transaction? (2) What increase or decrease in the commercial banks reserves took place in each transaction? () Assuming a reserve ratio of 20 percent, what change in the money-creating potential of the commercial banking system occurred as a result of each transaction? Answer: (a) Commercial Bank Balance Sheet (Column 1): Reserves = $4, Securities = $, Loans = $, Checkable deposits = $150, Loans from the Federal Reserve Banks = $4; The 12 Federal Reserve Banks Balance Sheet (Column 1): Securities = $, Loans to commercial banks = $4, Reserves of commercial banks = $4, Treasury deposits = $, Federal Reserve Notes = $27-8

9 (b) Commercial Bank Balance Sheet (Column 2): Reserves = $0, Securities = $, Loans = $, Checkable deposits = $147, Loans from the Federal Reserve Banks = $; The 12 Federal Reserve Banks Balance Sheet (Column 2): Securities = $57, Loans to commercial banks = $, Reserves of commercial banks = $0, Treasury deposits = $, Federal Reserve Notes = $27 (c) Commercial Bank Balance Sheet (Column ): Reserves = $5, Securities = $58, Loans = $, Checkable deposits = $150, Loans from the Federal Reserve Banks = $; The 12 Federal Reserve Banks Balance Sheet (Column ): Securities = $62, Loans to commercial banks = $, Reserves of commercial banks = $5, Treasury deposits = $, Federal Reserve Notes = $27 (d) Transaction (a) 1: No immediate effect on the money supply; 2: Reserves increased from $ to $4 billion; : Money-creating potential increased by $5 billion Transaction (b) 1: Immediate decrease in the money supply by $ billion; 2: Reserves fall from $ to $0 billion; : Money-creating potential decreased by $12 billion Transaction (c) 1: No immediate effect on the money supply; 2: Reserves increased from $ to $5 billion; : money-creating potential increased by $10 billion Feedback: Consider the following example for the data and questions below. In the accompanying tables you will find consolidated balance sheets for the commercial banking system and the 12 Federal Reserve Banks. Use columns 1 through to indicate how the balance sheets would read after each of transactions a to c is completed. Do not cumulate your answers; that is, analyze each transaction separately, starting in each case from the figures provided. All accounts are in billions of dollars. -9

10 To answer these questions we use the values immediately following the transaction. That is, do not work through the monetary multiplier process (we will do this in part d). Part a: A decline in the discount rate prompts commercial banks to borrow an additional $1 billion from the Federal Reserve Banks. Show the new balance-sheet numbers in column 1 of each table. Since the decline in the discount rate prompts commercial banks to borrow an additional $1 billion from the Federal Reserve Banks, the commercial banks' reserves increase by $1 billion in column (1). Thus, on the asset side the banks' reserves increase from $ billion to $4 billion. Security and Loans do not change. On the liability side Loans from the Federal Reserve Banks increase from $ billion to $4 billion. For the Twelve Federal Reserve Banks we see loans to commercial banks increase from $ billion to $4 billion on the asset side and Reserves of commercial banks increase from $ billion to $4 billion on the liability side (also in column (1)). Part b: The Federal Reserve Banks sell $ billion in securities to members of the public, who pay for the bonds with checks. Show the new balance-sheet numbers in column 2 of each table. Since the Reserve Banks sell $ billion in securities to members of the public, who pay for the bonds with checks, checkable deposits fall from $150 billion to $147 billion in column (2) on the liability side. The Federal Reserve Banks then reduce the reserves held by the commercial banks for the amount of $ billion (the Federal Reserve Banks 'clear' the check). This causes reserves to fall from $ billion to $0 billion on the commercial bank asset side. For the Twelve Federal Reserve Banks we see a decrease in securities by $ billion, from $ billion to $57 billion in column (2) on the asset side. On the liability side we see a decrease of reserves of commercial banks (the check 'clears') from $ billion to $0 billion. -10

11 Part c: The Federal Reserve Banks buy $2 billion of securities from commercial banks. Show the new balance-sheet figures in column of each table. Since the Federal Reserve Banks buy $2 billion of securities from commercial banks the securities held by the commercial banks falls from $ billion to $58 billion. The Federal Reserve Banks credit the commercial banks with an additional $2 billion in reserves. Both in column (). For the Twelve Federal Reserve Banks we see an increase of securities from $ billion to $62 billion. We also see an increase in liabilities, reserves of commercial banks, from $ billion to $5 billion. Also in column () CONSOLIDATED BALANCE SHEET: ALL COMMERCIAL BANKS (1) (2) () Assets: Reserves Securities Loans $ $4 $0 $5 58 Liabilities and net worth: Checkable deposits Loans from the Federal Reserve Banks Assets: Securities Loans to commercial banks CONSOLIDATED BALANCE SHEET: TWELVE FEDERAL RESERVE BANKS (1) (2) () $ $ 4 $57 $62 Liabilities and net worth: Reserves of commercial banks Treasury deposits Federal Reserve Notes $ 27 $4 27 $0 27 $5 27 Part d: Now review each of the above three transactions, asking yourself these three questions: (1) What change, if any, took place in the money supply as a direct and immediate result of each transaction? (2) What increase or decrease in the commercial banks reserves took place in each transaction? () Assuming a reserve ratio of 20 percent, what change in the money-creating potential of the commercial banking system occurred as a result of each transaction? Transaction (a): -11

12 There is no immediate effect on the money supply because the banks checkable deposits (and loans) have not changed immediately after the transaction. Reserves increased from $ to $4 billion. Assuming a 20% reserve ratio, the money-creating potential of the commercial banking system has increased by $5 billion. The monetary multiplier here is 5 (=1/0.20) and the increase in reserves is $1 billion. Transaction (b): There is an immediate effect on the money supply here because the banks checkable deposits have fallen to $147 billion immediately after the transaction. Thus, there is an immediate decrease in the money supply by $ billion. Reserves fall from $ to $0 billion. Assuming a 20% reserve ratio, the money-creating potential of the commercial banking system has decreased by $12 billion. This one takes a little more thought. Reserves have fallen by $ billion. Given the monetary multiplier is 5 (=1/0.20) this results in a decrease in money-creating potential of $15 billion (=5 x $ billion). However, checkable deposits have also fallen by $ billion. This implies that the bank has additional excess reserves of $0.6 billion (=.20 (required reserve ratio) x $ billion (decrease in checkable deposits)) relative to reserves prior to the transaction. The bank can lend out these additional excess reserves. Again, given the monetary multiplier is 5 (=1/0.20) this results in an increase in money-creating potential of $ billion (=5 x $.06 billion). Combining these two effects the money-creating potential of the commercial banking system has decreased by $12 billion as stated above (= decrease of $15 billion due to the direct fall in reserves minus the $ billion increase resulting from the decrease of checkable deposits and reduced need for required reserves.) Transaction (c): There is no immediate effect on the money supply because the banks checkable deposits (and loans) have not changed immediately after the transaction. Reserves increased from $ to $5 billion. Assuming a 20% reserve ratio, the money-creating potential of the commercial banking system has increased by $10 billion. The monetary multiplier here is 5 (=1/0.20) and the increase in reserves is $2 billion. 4. Refer to Table.2 and assume that the Fed s reserve ratio is 10 percent and the economy is in a severe recession. Also suppose that the commercial banks are hoarding all excess reserves (not lending them out) because of their fear of loan defaults. Finally, suppose that the Fed is highly concerned that the banks will suddenly lend out these excess reserves and possibly contribute to inflation once the economy begins to recover and confidence is restored. By how many percentage points would the Fed need to increase the reserve ratio to eliminate one-third of the excess reserves? What would be the size of the monetary multiplier before and after the change in the reserve ratio? By how much would the lending potential of the banks decline as a result of the increase in the reserve ratio? LO2-12

13 Answer: 5 percentage points; 10 before, 6.67 after; $16,667. Feedback: Consider the following example. Refer to Table.2 and assume that the Fed s reserve ratio is 10 percent and the economy is in a severe recession. Also suppose that the commercial banks are hoarding all excess reserves (not lending them out) because of their fear of loan defaults. Finally, suppose that the Fed is highly concerned that the banks will suddenly lend out these excess reserves and possibly contribute to inflation once the economy begins to recover and confidence is restored. By how many percentage points would the Fed need to increase the reserve ratio to eliminate one-third of the excess reserves? At the 10% reserve ratio the amount of excess reserves is $000. If the Fed wants to reduce a third of these excess reserves. eliminate $1000 of excess reserves, it should raise the reserve ratio to 15%. This will result in excess reserves of $2000 (between $000 and $1000). Thus, the Fed should raise the reserve ratio by 5 percentage points What would be the size of the monetary multiplier before and after the change in the reserve ratio? The monetary multiplier before the change is 10 (= 1/0.1). The monetary multiplier after the change is 6.67 (= 1/0.15). By how much would the lending potential of the banks decline as a result of the increase in the reserve ratio? Before the change the banks' lending potential was $0,000 (= 10 (monetary multiplier) x $000 (excess reserves)). After the change the banks' lending potential was $1,40 (= 6.67 (monetary multiplier) x $2000 (excess reserves)). Thus, the decline in lending potential is $16,6. 5. Suppose that the demand for Federal funds curve is such that the quantity of funds demanded changes by $120 billion for each 1 percent change in the Federal funds interest rate. Also, assume that the current Federal funds rate is at the percent rate that is targeted by the Fed. Now suppose that the Fed retargets the rate to.5 percent. Assuming no change in demand, will the Fed need to increase or decrease the supply of Federal funds? By how much will the quantity of Federal funds have to change for the equilibrium to occur at the new target rate? LO -1

14 Answer: Decrease the supply of Federal funds; decrease by $ billion. Feedback: Consider the following example. Suppose that the demand for Federal funds curve is such that the quantity of funds demanded changes by $120 billion for each 1 percent change in the Federal funds interest rate. Also, assume that the current Federal funds rate is at the percent rate that is targeted by the Fed. Now suppose that the Fed retargets the rate to.5 percent. Assuming no change in demand, will the Fed need to increase or decrease the supply of Federal funds? By how much will the quantity of Federal funds have to change for the equilibrium to occur at the new target rate? Since the current Federal funds rate is at the percent rate and Fed retargets the rate to.5 percent, the Fed will need to reduce the supply of Federal funds by $ billion. This will cause the quantity demanded to fall by $ billion as well (the increase in half a percentage point of The Federal funds rate will reduce the quantity of funds demanded by $ billion, or half of $120 billion). Thus achieving the higher targeted rate. 6. Suppose that inflation is 2 percent, the Federal funds rate is 4 percent, and real GDP falls 2 percent below potential GDP. According to the Taylor rule, in what direction and by how much should the Fed change the real Federal funds rate? LO Answer: Decrease by 1%. Feedback: Consider the following example. Suppose that inflation is 2 percent, the Federal funds rate is 4 percent, and real GDP falls 2 percent below potential GDP. According to the Taylor rule, in what direction and by how much should the Fed change the real Federal funds rate? The Taylor rule assumes that the Fed has a 2 percent target rate of inflation that it is willing to tolerate and that the FOMC follows three rules when setting its target for the Federal funds rate: When real GDP equals potential GDP and inflation is at its target rate of 2 percent, the Federal funds target rate should be 4 percent, implying a real Federal funds rate of 2 percent (= 4 percent nominal Federal funds rate 2 percent inflation rate). For each 1 percent increase of real GDP above potential GDP, the Fed should raise the real Federal funds rate by ½ percentage point. For each 1 percent increase in the inflation rate above its 2 percent target rate, the Fed should raise the real Federal funds rate by ½ percentage point. (Note, though, that in this case each ½ percentage point increase in the real rate will require a 1.5 percentage point increase in the nominal rate in order to account for the underlying 1 percent increase in the inflation rate.) Here we only need to use first two parts of this rule. Since real GDP is 2 percentage points below potential GDP the Fed should lower the Federal funds rate by 1 percentage point. This reduction is half a 1/2 a percentage point for each percentage point actual real GDP is below potential GDP. The new Federal funds rate is percent. -14

15 7. Refer to the accompanying table for Moola to answer the following questions. LO4 What is the equilibrium interest rate in Moola? What is the level of investment at the equilibrium interest rate? Is there either a recessionary output gap (negative GDP gap) or an inflationary output gap (positive GDP gap) at the equilibrium interest rate, and, if either, what is the amount? Given money demand, by how much would the Moola central bank need to change the money supply to close the output gap? What is the expenditure multiplier in Moola? LO4 Answers: 5 percent; $20; $20 billion recessionary output gap; $100 increase; 2 Feedback: Consider the following example. Refer to the accompanying table for Moola to answer the following questions. What is the equilibrium interest rate in Moola? The equilibrium interest rate occurs at the interest rate where the quantity of money supplied equals the quantity of money demanded. Thus, the equilibrium interest rate is 5%. What is level of investment at the equilibrium interest rate? Investment at this interest rate is $20. Is there either a recessionary output gap (negative GDP gap) or an inflationary output gap (positive GDP gap) at the equilibrium interest rate, and if either, what is the amount? At the interest rate of 5% potential GDP is $50 and actual GDP is $0. Since actual GDP is less than potential GDP there is a recessionary (negative) GDP gap. The gap is the difference, so the amount of the recessionary gap is $20. Given money demand, by how much would the Moola central bank need to change the money supply to close the output gap? What is the expenditure multiplier in Moola? -15

16 To eliminate the recessionary gap, that is to move actual GDP to $50 so that it equals potential GDP, the Fed will need to increase the money supply $0. When the money supply is $0 the equilibrium interest rate is now 4% and investment $0. To find the expenditure multiplier we can divide the change in actual GDP by the change in investment. multiplier = ($50 - $0)/($0 - $20) = $20/$10 =

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