Problem Set 3 Answers

Transcription

1 Social Analysis 10 Spring 2006 Problem Set 3 Answers Question 1 (a) Liabilities and Net Worth Reserves $2,500 Checking Deposits $6,000 Loans $5,500 Net Worth $2,000 Total $8,000 Total $8,000 (b) Money Supply = Cash held by the Public + Checking Deposits Cash held by public = $4,000 Checking Deposits = $6,000 Money Supply = $4,000+$6,000= $10,000 (c) The required reserve ratio is the fraction of deposits banks are required by law to keep in reserve. Let R be the reserve required ratio. Then, Required reserves = R*Deposits. and R= Required reserves/ Deposits If Bank A holds only required reserves, Required reserves = $2,500; Deposits=$6,000. Hence, R=$2,500/$6,000=0.416 or 41.6%. (d) If the required reserve ratio R is 10%, Bank A has to hold $600 as required reserves. Required reserves = R*Deposits=0.10*$6,000=$600 Given that total reserves of Bank A are $2,500, Bank A is holding $1,900 of excess reserves. Excess reserves = Total Reserves- Required Reserves. 1

2 (e) 1 The money multiplier is equal to. R + E R=0.10 E= Excess Reserves/Deposits = $1,900/$6,000 = The money multiplier is equal to = Question 2 (a) Before the bank robbery $1 million in reserves allows for $10 million deposits, given the 10% required reserve ratio. The robbery decreases reserves and net worth by $500,000. This lower quantity of reserves can sustain only $5 million in deposits. Thus deposits decrease by $5,000,000. Another way to see this is to take the initial change in reserves and use the money multiplier: Δdeposits = -$500,000 x 1/R = -$500,000 x 1/0.1 = -$5,000,000 Therefore change in total deposits is -$5,000,000. But money supply also includes cash held by the public (criminals included!). $500,000 saw its way from the vault of the bank (i.e., not in the money supply) to the storage place of the crook (so that it now is a part of the money supply). ΔMoney Stock = ΔTotal Deposits + ΔCash Held By Public = -$5,000,000 + $500,000 = -$4,500,000 Thus, the Money Supply decreases by $4,500,000 at most. (Assuming banks hold no excess reserves and people do not hold extra cash.) (b) The resulting balance sheet is: Liabilities and Net Worth Reserves: $500,000 Deposits: $5,000,000 Loans: $7,000,000 Net Worth: $2,500,000 Total: $7,500,000 Total: $7,500,000 2

3 Reserves fall to $500,000 and can only support deposits of $5,000,000. Net worth is decreased by the amount of the theft. Loans fall by $5,000,000. Question 3 (a) Total money stock is equal to the sum of cash held by the public and the total checking deposits. Therefore, it is equal to $10m + $80m = $90m. (b) The buyer of the bonds has to withdraw from the banks to purchase the treasury bonds. But since the proceeds are distributed back to him, they are eventually deposited back to the checking accounts (given the assumption that the amount of cash held by the public never changes). Therefore on the assets side of the buyer s balance sheet, checking deposits do not change; only the amount of bonds held increases by $5m. Also, his liabilities are not affected he holds the same amount of bank loans as before. His net worth hence increases by $5m. Change in bonds held = +$5m Liabilities (nothing changes) Net Worth Change = +$5m (c) The total money stock remains unchanged at $90m because trade in treasury bonds involves only transfer of money, and neither creation nor destruction of money. (d) For open market operation, the central bank should buy bonds from the residents to increase the money supply. By how much? Notice that the money multiplier is 1/(reserve ratio) = 10. Therefore the central bank has to buy $2m worth bonds in order to create $20m in money stock. The bonds purchased will show up on the assets side of the central bank s balance sheet. This item will be balanced by the corresponding increase in cash on the liabilities side. The net worth hence will remain unchanged. Change in bonds held = +$2m Liabilities Change in reserves = +$2m Net Worth (nothing changes) 3

4 Question 4 In order to decrease the money supply by $10m, the central bank has to sell $1m worth of bonds. Since the public does not hold cash, Money Supply = Total Deposits =(1/R)*(original withdrawal) = (1/0.10)*(original withdrawal). We know that Money Supply = $10m. Solving the equation for original withdrawal tell us the amount worth of bonds that the central bank has to sell. Original withdrawal = $10m*0.10=$1m Question 5 The growth rates form of the quantity equation states that: %ΔM + %ΔV = %ΔP + %ΔY We assume that the %ΔV = 0% in the long run. Rearranging, we get that: %ΔP = %ΔM %ΔY We know that %ΔM = 10% and that %ΔY = 2%. Therefore, %ΔP = 10% 2% = 8% 4

5 Question 6 (a) i M 1 S M 0 S i 1 i 0 M0 D M 1 D M 1 M 0 M Since Y is increasing and P is stable, nominal GDP (PY) is also increasing. This means there will be greater demand for money at every interest rate in order to facilitate a higher volume of transactions. Hence, the money demand curve shifts to the right. The increase in the reserve requirement means that banks will be able to lend out less of their reserves. This will lower the amount of deposits in the economy, and contract the money supply, shifting the money supply curve to the left as shown above. These two actions together mean that the equilibrium interest rate will be unambiguously higher. (b) The FED sale of bonds reduces the money supply; the rising price level increases money demand. The two changes drive the interest rate higher. 5

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