EC120 HW Set 3

Assumptions:

1. The nonbank public holds checkable deposits and money market mutual fund shares, M³ (There is no currency in this model.) The nonbank public desires to hold $2 of M³F for every $1 of D (deposits). M2 = D + M³F. Let “f” = desired ratio of M³F to D.
2. Banks are required to hold $.10 of reserves for every $1 of D they issue (r_D =.1). In addition, they desire to hold $.10 of excess reserves for every $1 of D they issue (e=.1). There (initially) is no reserve requirement on money market mutual fund shares. Money market mutual funds invest all of their shares in loans.
3. There are $5000 of government securities outstanding, $1000 of which are owned by the nonbank public, $1000 of which are owned by the banking system, and $3000 of which are owned by the Federal Reserve Banks. These are the only assets owned by the Federal Reserve Banks.

(Note: The monetary base will equal the total liabilities of the Federal Reserve Banks, and consists only of reserves in this problem, since there is no currency.)

Questions:

1. Use the Sources = Uses method to derive the money supply equations for D and M2. Identify the algebraic expressions for the D and M2 multipliers; and determine the numerical value of each multiplier.

2. Show the initial balance sheets of the Federal Reserve Banks, the Treasury, the nonbank public, the banking system, and the money market mutual funds. What is the total credit extended to the nonbank public from banks and money market mutual funds combined?

In questions 3, 4, and 5, refer back to your answer to #2 as the starting point.

3. The Federal Reserve Banks sell $500 of government securities to the banking system. Determine the quantitative effect of this transaction on:

1. bank reserves (same as monetary base in this problem)
2. M2 (use the M2 multiplier)
3. the flow of funds to borrowers

4. Money market mutual funds desire to expand their loans more quickly, so they raise the interest rate they pay on the shares that they issue to attract funds. Find the quantitative effect of a rise in “f” from 2 to 4 on:

1. M2 (use the M2 multiplier)
2. the new flow of funds to borrowers

5. The Federal Reserve, determined to stem the growth of credit, decides to put a reserve requirement on money market mutual fund shares (r_MF), and sets the reserve ratio on M³F at .0125 (1.25%). The value of f is 4, as in part 4; all other initial assumptions and values hold.

Use the Sources = Uses method to derive the money supply equations for D and M2. Identify the algebraic expressions for the D and M2 multipliers; also determine their algebraic values.

6. Show the new balance sheets of the Federal Reserve Banks, the Treasury, the nonbank public, and the banking system. As compared with your answer to #4 above, how has the new flow of funds to borrowers changed? Has the Federal Reserve achieved its goal?

Part II: The Fed-Funds Market

1. Short answer questions
2. Explain why the fed funds rate is never > the discount rate.

2. Explain why in normal conditions, the Fed sets the discount rate at a level greater than the fed funds rate.

3. Explain why the Fed started paying interest on banks’ reserve balances.

4. Explain why the fed funds rate should not in theory fall below the interest rate on reserve balances.

1. Graphical analysis.

Assume that initially the discount rate > the fed funds rate and borrowed reserves = 0. Assume also that the Fed wants to keep the spread between the discount rate and the fed funds rate constant.

1. Using the graph of the fed funds market, show two ways that the Fed could cause the fed funds rate to rise. For each policy, state how the discount rate and total reserves change (if at all).

2. Using the logic of the article “Money creation in the modern economy”, explain how a policy of increasing the fed funds rate will lead to a fall in bank deposits.