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Economics 111 Professor Flavin
Winter 2002
Problem Set 3
Solutions will be posted on the Econ 111 web page.
1. Consider two banks: Bank A has reserves of 30 million, marketable securities of 20 million, loans of 170 million, deposits of 200 million, and a net worth of 20 million. Bank B has reserves of 30 million, marketable securities of 40 million, loans of 250 million, deposits of 300 million, and a net worth of 20 million.
a) Write down the balance sheet for each bank.
b) The required reserve ratio against deposits is 10%. Calculate the excess reserves of each bank.
c) Suppose bank B sells $10 million in securities to bank A. Show the new balance sheets for each bank.
d) Starting from the balance sheets obtained in part c, assume that a person with an account at Bank A writes a check for $1 million and uses the check to pay someone who has an account with Bank B, who duly deposits the check in his account (at Bank B). Show the balance sheets of the two banks after the check has cleared.
e) Calculate the excess reserves of each bank. If one or both banks have a reserve deficiency, discuss the ways the bank deficient in reserves could satisfy its reserve requirement.
2. Let
r = the required reserve ratio
c = the ratio of currency to deposits preferred by the nonbank private sector
e = the ratio of excess reserves to deposits preferred by banks
C = currency in circulation
M = the money supply
B = the monetary base
D = deposits
R = reserves
a) Derive the money multiplier using the “easy method” which treats the expansion of deposits () as an unknown, and solves for the total change in deposits which is induced by a given increase in the monetary base, after the banking system has returned to equilibrium.
b) Evaluate the money multiplier in part a), assuming that r = .10, c = .15, and e = .03 .
c) Still assuming that r = .10, what is the value of the money multiplier if c = 0 and e = 0?
d) Explain intuitively why c>0 and e>0 reduce the value of the money multiplier.
3. Suppose the Fed sells $2 million in Treasury bonds to Wells Fargo. On balance sheets (T-accounts) for both the Fed and Wells Fargo, show the changes induced by this transaction. What is the effect on the monetary base?
4. Consider the following statement:
“If reserve requirements on checkable deposits were set to zero (i.e., r = 0), the money multiplier would be infinity.”
Is this statement true, false, or uncertain? Explain.
5. During the early years of the Great Depression (1930-1933), the rash of bank runs caused banks to increase their holdings of excess reserves. At the same time, the wave of bank failures caused the public to distrust the safety of bank deposits and therefore hold relatively more of their money in the form of currency (as opposed to bank deposits). For a given level of the monetary base, what is the effect on the money supply of the increase in excess reserve holdings by banks and currency holding by the non-bank private sector?
6. a) Suppose that the Fed conducted an open market purchase of Godiva chocolates, paying for the chocolate in the same way that it pays for Treasury securities during an open market purchase of T-bills. What would be the effect of an open market purchase of Godiva chocolates on the monetary base and the money supply?
b) Is there some rational reason that open market operations are conducted via purchases or sales of Treasury securities instead of Godiva chocolates?
7. Suppose that Wells Fargo hasn’t been monitoring its reserve position carefully and, as a result of this oversight, suddenly discovers that if it does not take some corrective action immediately, it will end up with a reserve deficiency of $200 million for the current reserve reporting period.
a) What actions can Wells Fargo take in order to avoid having a reserve deficiency?
b) Considering not just Wells Fargo, but instead the banking sector as a whole, what effect will Wells Fargo’s actions in part a) have on:
i) the level of excess reserves
ii) the Federal funds rate
iii) the volume of discount lending.
8.The Fed sells $1000 worth of foreign assets, in particular, bonds denominated in the Euro, and does not sterilize the foreign exchange intervention. Trace through the effect on the international reserves of the Fed, the US money supply, and the exchange rate.
9.Consider the same intervention as in question 8, but assume that the Fed sterilizes the foreign exchange intervention. Discuss the effect on the international reserves of the Fed, the US money supply, and the exchange rate.
10.Under the gold standard, determine the exchange rate between the dollar and the franc is one dollar is convertible into 1/20 th ounce of gold and one franc in convertible into 1/60 th ounce of gold.
11.If a country’s par exchange rate was undervalued under the Bretton Woods fixed exchange rate regime, what kind of intervention would that country’s central bank be forced to take, and what effect would it have on the country’s international reserves and domestic money supply?