CH-4 The Monetary System: What It Is and How It Works – Macroeconomics : Book Guide

Answers to Textbook Questions and Problems CHAPTER 4 The Monetary System: What It Is and How It Works Questions for Review 1. Money has three functions: it is a store of value, a unit of account, and a medium of exchange. As a store of value, money provides a way to transfer purchasing power from the present to the future. As a unit of account, money provides the terms in which prices are quoted and debts are recorded. As a medium of exchange, money is what we use to buy goods and services. 2. Fiat money is established as money by the government but has no intrinsic value. For example, a U.S. dollar bill is fiat money. Commodity money is money that is based on a commodity with some intrinsic value. Gold, when used as money, is an example of commodity money. 3. Open market operations are the purchase and sale of government bonds by the Federal Reserve. If the Fed buys government bonds from the public, then the dollars it pays for the bonds increase the monetary base and thus the money supply. If the Fed sells government bonds to the public, then the dollars paid to the Fed for the bonds decrease the monetary base and thus the money supply. 4. In a system of fractional-reserve banking, banks create money because they ordinarily keep only a fraction of their deposits in reserve. They use the rest of their deposits to make loans. The easiest way to see how this creates money is to consider the bank balance sheets shown in Figure 4-1. A. Balance Sheet – Firstbank Money Supply = $1,000 Assets Liabilities_______ Reserves $1,000 Deposits $1,000 B. Balance Sheet – Firstbank Money Supply = $1,800 Assets Liabilities_______ Reserves $200 Deposits $1,000 Loans $800 C. Balance Sheet – Secondbank Money Supply = $2,400 Assets Liabilities_______ Reserves $160 Deposits $800 Loans $640 Suppose that people deposit $1,000 into Firstbank, as in Figure 4-1(A). Although the money supply is still $1,000, it is now in the form of demand deposits rather than currency. If the bank holds 100 percent of these deposits in reserve, then the bank has no influence on the money supply. Yet under a system of fractional-reserve banking, the bank need not keep all of its deposits in reserve; it must have enough reserves on hand so that reserves are available whenever depositors want to make withdrawals, but it makes loans with the rest of its deposits. If Firstbank has a reserve–deposit ratio of 20 percent, then it keeps $200 of the $1,000 in reserve and lends out the remaining $800. Figure 4-1(B) shows the balance sheet of Firstbank after $800 in loans have been made. By making these loans, Firstbank increases the money supply by $800. There are still $1,000 in demand deposits, but now borrowers also hold an additional $800 in currency. The total money supply equals $1,800. Money creation does not stop with Firstbank. If the borrowers deposit their $800 of currency in Secondbank, then Secondbank can use these deposits to make loans. If Secondbank also has a reserve– deposit ratio of 20 percent, then it keeps $160 of the $800 in reserves and lends out the remaining $640. By lending out this money, Secondbank increases the money supply by $640, as in Figure 4-1(C). The total money supply is now $2,440. This process of money creation continues with each deposit and subsequent loans made. The text demonstrated that each dollar of reserves generates ($1/rr) of money, where rr is the reserve–deposit ratio. In this example, rr = 0.20, so the $1,000 originally deposited in Firstbank generates $5,000 of money. 5. The Fed influences the money supply through open-market operations, reserve requirements, and the discount rate. Open-market operations are the purchases and sales of government bonds by the Fed. If the Fed buys government bonds, the dollars it pays for the bonds increase the monetary base and, therefore, the money supply. If the Fed sells government bonds, the dollars it receives for the bonds reduce the monetary base and therefore the money supply. Reserve requirements are regulations imposed by the Fed that require banks to maintain a minimum reserve–deposit ratio. A decrease in the reserve requirements lowers the reserve–deposit ratio, which allows banks to make more loans on a given amount of deposits and, therefore, increases the money multiplier and the money supply. The discount rate is the interest rate that the Fed charges banks to borrow money. Banks borrow from the Fed if their reserves fall below the reserve requirements. A decrease in the discount rate makes it less expensive for banks to borrow reserves. Therefore, banks will be likely to borrow more from the Fed; this increases the monetary base and therefore the money supply. 6. To understand why a banking crisis might lead to a decrease in the money supply, first consider what determines the money supply. The model of the money supply we developed shows that M = m  B. The money supply M depends on the money multiplier m and the monetary base B. The money multiplier can also be expressed in terms of the reserve–deposit ratio rr and the currency–deposit ratio cr. This expression becomes Ø (cr+1) ø M =Œ œ B M = B. Œº (cr+rr)œß This equation shows that the money supply depends on the currency–deposit ratio, the reserve–deposit ratio, and the monetary base. A banking crisis that involved a considerable number of bank failures might change the behavior of depositors and bankers and alter the currency–deposit ratio and the reserve–deposit ratio. Suppose that the number of bank failures reduced public confidence in the banking system. People would then prefer to hold their money in currency (and perhaps stuff it in their mattresses) rather than deposit it in banks. This change in the behavior of depositors would cause massive withdrawals of deposits and, therefore, increase the currency–deposit ratio. In addition, the banking crisis would change the behavior of banks. Fearing massive withdrawals of deposits, banks would become more cautious and increase the amount of money they held in reserves, thereby increasing the reserve–deposit ratio. As the preceding formula for the money multiplier indicates, increases in both the currency–deposit ratio and the reserve–deposit ratio result in a decrease in the money multiplier and, therefore, a fall in the money supply. Problems and Applications 1. Money functions as a store of value, a medium of exchange, and a unit of account. a. A credit card can serve as a medium of exchange because it is accepted in exchange for goods and services. A credit card is, arguably, a (negative) store of value because you can accumulate debt with it. A credit card is not a unit of account because, for example, a car does not cost 5 VISA cards. b. A Rembrandt painting is a store of value only. c. A subway token, within the subway system, satisfies all three functions of money. Yet outside the subway system, it is not widely used as a unit of account or a medium of exchange, so it is not a form of money. 2. a. When the Fed buys bonds, the dollars that it pays to the public for the bonds increase the monetary base, and this in turn increases the money supply. The money multiplier is not affected, assuming no change in the reserve–deposit ratio or the currency–deposit ratio. b. When the Fed increases the interest rate, it pays banks to hold reserves. This gives banks an incentive to hold more reserves relative to deposits. The increase in the reserve deposit ratio will decrease the money multiplier. The decline in the money multiplier will lead to a decrease in the money supply. Since banks are holding more reserves (because they are making fewer loans), the monetary base will increase. c. If the Fed reduces its lending to banks through the Term Auction Facility, then the monetary base will decrease, and this in turn will decrease the money supply. The money multiplier is not affected, assuming no change in the reserve–deposit ratio or the currency–deposit ratio. d. If consumers lose confidence in ATMs and prefer to hold more cash, then the currency–deposit ratio will increase, and this will reduce the money multiplier. The money supply will fall because banks have fewer reserves to lend. The monetary base will increase because people are holding more currency, but will decrease because banks are holding fewer reserves. The net effect on the monetary base is zero. e. If the Fed drops newly minted $100 bills from a helicopter, then this will increase the monetary base and the money supply. If any of the currency ends up in the bank, then there will be a further increase in the money supply. If people end up holding more currency relative to deposits, then the money multiplier would fall. 3. a. If all money is held as currency, then the money supply is equal to the monetary base. The money supply will be $1,000. b. If all money is held as deposits, but banks hold 100 percent of deposits on reserve, then there are no loans. The money supply will be $1,000. c. If all money is held as deposits and banks hold 20 percent of deposits on reserve, then the reserve– deposit ratio is 0.20. The currency–deposit ratio is 0, and the money multiplier will be 1/0.2, or 5. The money supply will be $5,000. d. If people hold an equal amount of currency and deposits, then the currency–deposit ratio is 1. The reserve–deposit ratio is 0.2 and the money multiplier is (1 + 1)/(1 + 0.2) = 1.67. The money supply will be $1,666.67. e. The money supply is proportional to the monetary base and is given by M = m  B, where M is the money supply, m is the money multiplier, and B is the monetary base. Since m is a constant number defined by the currency–deposit ratio and the reserve–deposit ratio, a 10-percent increase in the monetary base B will lead to a 10-percent increase in the money supply M. 4. a. The money supply is equal to currency plus demand deposits or $5,000. The monetary base is equal to currency plus reserves. If we assume banks are not holding any excess reserves, then reserves must be 25percent of deposits, or $1,000. In this case the monetary base is equal to $2,000. The money multiplier is equal to the money supply divided by the monetary base, or 2.5. Alternatively, the money multiplier can be calculated using the formula m = (cr+1)/(cr+rr), where cr is the currency deposit ratio (0.25) and rr is the reserve deposit ratio (0.25). b. The bank balance sheet is illustrated below. If we assume the bank is not holding any excess reserves then reserves in the bank are 25 percent of deposits, or $1,000. This means outstanding loans must be $3,000. Table 4-1 Assets Liabilities ______ Reserves $1,000 Deposits $4,000 Loans $3,000 c. To increase the money supply the central bank should buy government bonds because this will increase reserves in the banking system, allowing loans, deposits, and the money supply to increase. We know that M=mB, so M = m B. If the central bank wants the money supply to increase by 10 percent then they want the change in the money supply to equal $400. We know the money multiplier is 2.5 so therefore the monetary base must increase by $160, meaning the central bank must buy $160 of government bonds. 5. a. Given that banks hold one third of their deposits on reserve, the reserve deposit ratio (rr) is 1/3. Given that people hold one third of their money in currency and two thirds in deposits, we can express the currency deposit ratio as = = = . Therefore, the money multiplier is equal to + 1 + 1 = = = 1.8. + 1 + 1 2 3 The money supply is equal to the monetary base times the money multiplier, or $1,800. b. If people hold half of their money in currency, then currency holdings are equal to deposits, and the currency deposit ratio is equal to 1. Therefore, the money multiplier is equal to 1.5, and the money supply is equal to $1,500. c. The central bank wants to increase the money supply by $300 so they will need to buy government bonds. We know M = m B, so therefore $300 = 1.5 B, and the central bank will want to buy $200 of government bonds. 6. The model of the money supply developed in Chapter 4 shows that M = mB. The money supply M depends on the money multiplier m and the monetary base B. The money multiplier can also be expressed in terms of the reserve–deposit ratio rr and the currency–deposit ratio cr. Rewriting the money supply equation: M =ØŒ (cr+1) øœ B . Œº (cr+rr)œß This equation shows that the money supply depends on the currency–deposit ratio, the reserve–deposit ratio, and the monetary base. To answer parts (a) through (c), we use the values for the money supply, the monetary base, the money multiplier, the reserve–deposit ratio, and the currency–deposit ratio from Table 4-2: Table 4-2 August 1929 March 1933 Money supply 26.50 19.00 Monetary base 7.10 8.40 Money multiplier 3.70 2.30 Reserve–deposit ratio 0.14 0.21 Currency–deposit ratio 0.17 0.41 a. To determine what would happen to the money supply if the currency–deposit ratio had risen but the reserve–deposit ratio had remained the same, we need to recalculate the money multiplier and then plug this value into the money supply equation M = mB. To recalculate the money multiplier, use the 1933 value of the currency–deposit ratio and the 1929 value of the reserve–deposit ratio: m = (cr1933 + 1)/(cr1933 + rr1929) m = (0.41 + 1)/(0.41 + 0.14) m = 2.56. To determine the money supply under these conditions in 1933: M1933 = mB1933. Plugging in the value for m just calculated and the 1933 value for B: M1933 = 2.56  8.4 M1933 = 21.504. Therefore, under these circumstances, the money supply would have fallen from its 1929 level of 26.5 to 21.504 in 1933. b. To determine what would have happened to the money supply if the reserve–deposit ratio had risen but the currency–deposit ratio had remained the same, we need to recalculate the money multiplier and then plug this value into the money supply equation M = mB. To recalculate the money multiplier, use the 1933 value of the reserve–deposit ratio and the 1929 value of the currency–deposit ratio: m = (cr1929 + 1)/(cr1929 + rr1933) m = (0.17 + 1)/(0.17 + 0.21) m = 3.09. To determine the money supply under these conditions in 1933: M1933 = mB1933. Plugging in the value for m just calculated and the 1933 value for B: M1933 = 3.09  8.4 M1933 = 25.96. Therefore, under these circumstances, the money supply would have fallen from its 1929 level of 26.5 to 25.96 in 1933. c. From the calculations in parts (a) and (b), it is clear that the decline in the currency– deposit ratio was most responsible for the drop in the money multiplier and, therefore, the money supply. 7. a. The introduction of a tax on checks makes people more reluctant to use checking accounts as a means of exchange. Therefore, they hold more cash for transactions purposes, raising the currency–deposit ratio cr. b. The money supply falls because the money multiplier, cr+1 , is decreasing in cr. Intuitively, the cr+rr higher the currency–deposit ratio, the lower the proportion of the monetary base that is held by banks in the form of reserves and, hence, the less money banks can create. c. The check tax was not a good policy to implement in the middle of the Great Depression because it resulted in a decrease in the money supply as people preferred to pay in currency rather than write a check. Banks had fewer reserves and were able to make fewer loans. 8. The leverage ratio is the ratio of a bank’s total assets to its bank capital. If the leverage ratio is 20, this means that for each dollar of capital contributed by the bank owners, the bank has $20 of assets, and therefore $19 of deposits and debts. The balance sheet below has a leverage ratio of 20: total assets are $1,200 and capital is $60. Assets Liabilities and Owners’ Equity__ Reserves $200 Deposits $800 Loans $600 Debt $340 Securities $400 Capital (owners’ equity) $ 60 If the value of the bank’s assets rises by 2 percent and deposits and debt do not change, then owner’s equity will rise by 2 percent of the asset value. Since the sum of the entries on each side of the balance sheet must be the same, a 2 percent rise in the asset value must be balanced by a 2 percent rise in the right-hand-side value. To reduce the bank’s capital to zero, assets must decline in value by $60, which is 5 percent of the current asset value. 9. a. JPM’s balance sheet is illustrated below. We know reserves are equal to $3,000 because total assets must equal total liabilities. Assets Liabilities and Owners’ Equity_____ Reserves $ 3,000 Deposits $14,000 Loans $10,000 Debt $ 4,000 Securities $ 7,000 Capital (owners’ equity) $ 2,000 The leverage ratio is the ratio of a bank’s total assets to its bank capital, or 10. b. If the value of the bank’s assets fall by 5 percent due to loan default, and deposits and debt do not change, then the value of owners’ equity will fall by 5 percent of the asset value. Loans and owner’s equity both fall by $500. Owners’ equity (JPM’s capital) fell by 25 percent. Assets Liabilities and Owners’ Equity_____ Reserves $3,000 Deposits $14,000 Loans $9,500 Debt $ 4,000 Securities $7,000 Capital (owners’ equity) $ 1,500 IN THIS CHAPTER, YOU WILL LEARN: ▪The definition, functions, and types of money ▪How banks “create” money ▪What a central bank is and how it controls the money supply Definition Money is the stock of assets that can be readily used to make transactions. Functions ▪ Medium of exchange we use it to buy stuff ▪ Store of value transfers purchasing power from the present to the future ▪ Unit of account the common unit by which everyone measures prices and values CHAPTER 4 The Monetary System Types 1. Fiat money ▪ has no intrinsic value ▪example: the paper currency we use 2. Commodity money ▪ has intrinsic value ▪ examples: gold coins, cigarettes in P.O.W. camps Two definitions ▪ The money supply is the quantity of money available in the economy. ▪ Monetary policy is the control over the money supply. The central bank and monetary control ▪ Monetary policy is conducted by a country’s central bank. ▪The U.S.’s central bank is called the Federal Reserve (“the Fed”). The Federal Reserve Building Washington, DC ▪To control the money supply, the Fed uses open market operations, the purchase and sale of government bonds. Banks’ role in the monetary system ▪ The money supply equals currency plus demand (checking account) deposits: M = C + D ▪ Since the money supply includes demand deposits, the banking system plays an important role. A few preliminaries ▪ Reserves (R ): the portion of deposits that banks have not lent. ▪ A bank’s liabilities include deposits; assets include reserves and outstanding loans. ▪ 100-percent-reserve banking: a system in which banks hold all deposits as reserves. ▪ Fractional-reserve banking: a system in which banks hold a fraction of their deposits as reserves. Banks’ role in the monetary system ▪To understand the role of banks, we will consider three scenarios: 1. No banks 2. 100-percent-reserve banking (banks hold all deposits as reserves) 3. Fractional-reserve banking (banks hold a fraction of deposits as reserves, use the rest to make loans) ▪In each scenario, we assume C = $1,000. SCENARIO 1: No banks With no banks, D = 0 and M = C = $1,000.SCENARIO 2: 100-percent-reserve banking ▪ Initially C = $1000, D = $0, M = $1,000. ▪Now suppose households deposit the $1,000 at “Firstbank.” ▪ After the deposit: Assets Liabilities reserves $1,000 deposits $1,000 FIRSTBANK’S balance sheet C = $0, D = $1,000, M = $1,000 ▪ LESSON: 100%-reserve banking has no impact on size of money supply. ▪ Suppose banks hold 20% of deposits in reserve, LESSON: In a fractional-reserve making loans with the rest. banking system, banks create money. ▪Firstbank will make $800 in loans. The money supply FIRSTBANK’S balance sheet now equals $1,800: Assets Liabilities ▪Depositor has $1,000 in reserves $$1200, 0 deposits $1,000 demand deposits. loans $800 ▪Borrower holds $800 in currency. ▪ Suppose the borrower deposits the $800 in Secondbank. ▪ Initially, Secondbank’s balance sheet is: SECONDBANK’S ▪Secondbank will balance sheet loan 80% of this Assets Liabilities deposit. reserves $16080 deposits $800 loans $6400 ▪ If this $640 is eventually deposited in Thirdbank, ▪ Then Thirdbank will keep 20% of it in reserve and loan the rest out: THIRDBANK’S balance sheet Assets Liabilities reserves $128640 deposits $640 loans $5120 Finding the total amount of money: Original deposit = $1000 + Firstbank lending = $ 800 + Secondbank lending = $ 640 + Thirdbank lending = $ 512 + other lending… Total money supply = (1/rr ) × $1,000 where rr = ratio of reserves to deposits In our example, rr = 0.2, so M = $5,000 Money creation in the banking system A fractional-reserve banking system creates money, but it doesn’t create wealth: Bank loans give borrowers some new money and an equal amount of new debt. ▪ Bank capital: the resources a bank’s owners have put into the bank ▪ A more realistic balance sheet: Assets Liabilities and Owners’ Equity Reserves $200 Deposits $750 Loans 500 Debt 200 Securities 300 Capital 50 ▪ Leverage: the use of borrowed money to supplement existing funds for purposes of investment ▪ Leverage ratio = assets/capital = $(200 + 500 + 300)/$50 = 20 Assets Liabilities and Owners’ Equity Reserves $200 Deposits $750 Loans 500 Debt 200 Securities 300 Capital 50 ▪ Being highly leveraged makes banks vulnerable. ▪ Example: Suppose a recession causes our bank’s assets to fall by 5%, to $950. ▪ Then, capital = assets – liabilities = 950 – 950 = 0 Assets Liabilities and Owners’ Equity Reserves $200 Deposits $750 Loans 500 Debt 200 Securities 300 Capital 50 Capital requirement: ▪ minimum amount of capital mandated by regulators ▪ intended to ensure banks will be able to pay off depositors ▪ higher for banks that hold more risky assets 2008-2009 financial crisis: ▪ Losses on mortgages shrank bank capital, slowed lending, exacerbated the recession. ▪ Govt injected billions of dollars of capital into banks to ease the crisis and encourage more lending. A model of the money supply exogenous variables ▪ Monetary base, B = C + R controlled by the central bank ▪ Reserve-deposit ratio, rr = R/D depends on regulations & bank policies ▪ Currency-deposit ratio, cr = C/D depends on households’ preferences Solving for the money supply: C D+ M C D= + = B = mB B where C D+ m = B C D+ (CD DD)+( ) cr+1 = = = C R+ (CD RD)+( ) cr rr+ The money multiplier cr+1 cr rr+ M mB=  , where m = ▪ If rr 1 ▪ If monetary base changes by ΔB, then ΔM = m × ΔB ▪ m is the money multiplier, the increase in the money supply resulting from a one-dollar increase in the monetary base. SOLUTION The money multiplier Impact of an increase in the currency-deposit ratio Δcr > 0. 1. An increase in cr increases the denominator of m proportionally more than the numerator. So m falls, causing M to fall. 2. If households deposit less of their money, then banks can’t make as many loans, so the banking system won’t be able to create as much money. The instruments of monetary policy The Fed can change the monetary base using: ▪open market operations (the Fed’s preferred method of monetary control) ▪To increase the base, the Fed could buy government bonds, paying with new dollars. ▪the discount rate: the interest rate the Fed charges on loans to banks ▪To increase the base, the Fed could lower the discount rate, encouraging banks to borrow more reserves. The instruments of monetary policy The Fed can change the reserve-deposit ratio using: ▪reserve requirements: Fed regulations that impose a minimum reserve-deposit ratio ▪To reduce the reserve-deposit ratio, the Fed could reduce reserve requirements. ▪interest on reserves: the Fed pays interest on bank reserves deposited with the Fed ▪To reduce the reserve-deposit ratio, the Fed could pay a lower interest rate on reserves. Why the Fed can’t precisely control M cr+1 M mB=  , where m = cr rr+ ▪ Households can change cr, causing m and M to change. ▪ Banks often hold excess reserves (reserves above the reserve requirement). If banks change their excess reserves, then rr, m, and M change. Quantitative Easing ▪ Quantitative easing: the Fed bought long-term govt bonds instead of T-bills to reduce long-term rates. ▪ The Fed also bought mortgage-backed securities to help the housing market. ▪ But after losses on bad loans, banks tightened lending standards and increased excess reserves, causing money multiplier to fall. ▪ If banks start lending more as economy recovers, rapid money growth may cause inflation. To prevent, the Fed is considering various “exit strategies.” Bank failures in the 1930s ▪From 1929 to 1933: ▪over 9,000 banks closed ▪money supply fell 28% ▪This drop in the money supply may not have caused The Great Depression, but certainly contributed to its severity. Bank failures in the 1930s cr+1 cr rr+ M mB=  , where m = ▪ Loss of confidence in banks: increases cr, reduces m ▪ Banks became more cautious: increases rr, reduces m Could this happen again? ▪ Many policies have been implemented since the 1930s to prevent such widespread bank failures. ▪ E.g., Federal Deposit Insurance, to prevent bank runs and large swings in the currency-deposit ratio. Money ▪ Definition: the stock of assets used for transactions ▪ Functions: medium of exchange, store of value, unit of account ▪ Types: commodity money (has intrinsic value), fiat money (no intrinsic value) ▪ Money supply controlled by central bank Fractional reserve banking creates money because each dollar of reserves generates many dollars of demand deposits. The money supply depends on the: ▪ monetary base ▪ currency-deposit ratio ▪ reserve ratio The Fed can control the money supply with: ▪ open market operations ▪ the reserve requirement ▪ the discount rate ▪ interest on reserves Bank capital, leverage, capital requirements ▪ Bank capital is the owners’ equity in the bank. ▪ Because banks are highly leveraged, a small decline in the value of bank assets can have a huge impact on bank capital. ▪ Bank regulators require that banks hold sufficient capital to ensure that depositors can be repaid. Solution Manual for Macroeconomics Gregory N. Mankiw 9781464182891, 9781319106058