ECON 320 – Intermediate Macroeconomic Theory Homework 2 1 The Money Multiplier Suppose that people hold no currency, the ratio of reserves to deposits is 0.1, and that the demand for money is given by the following: Md = Y (.8 − 4i) where Y is income and i is the interest rate. Initially, the monetary base is $100 billion and nominal income is $5 trillion.

1. What is the demand for central bank money?

2. Find the equilibrium interest rate by setting the demand for central bank money equal to the supply of central bank money.

3. What is the overall supply of money? Is it equal to the overall demand for money at the interest rate you found in part b?

4. What is the impact on the interest rate if central bank money is increased to $300 billion?

5. If the overall money supply increases to $3,000 billion, what will be the impact on i?

2 IS-LM Consider the following IS-LM model: C = 200 + .25YD I = 150 + .25Y − 1000i G = 250 T = 200 Md P = 2Y − 8000i M P = 1600 Where all variables (C, Y , M, etc.) are real. 1

1. Derive the IS relation (Hint: You’ll want to solve for Y ).

2. Derive the LM relation (Hint: You’ll want to solve for i).

3. Solve for equilibrium real output.

4. Solve for the equilibrium interest rate.

5. Sove for the equilibrium values of C and I, and verify the value you obtained for Y by adding up C, I, and G.

6. Now suppose that the money supply increases M/P = 1, 840. Solve for Y , i, C, and I, and describe in words the effects of an expansionary monetary policy.

7. Set M/P equal to its initial value of 1, 600. Now suppose that government spending incrteases to G = 400. Summarize the effects of an expansionary fiscal policy on Y , i, and C. 3 IS-LM and Central Bank Money Consider the following IS-LM model with a banking system: Consumption: C = 7 + 0.6YD Investment: I = 0.205Y − i Government expenditure: G = 10 Taxes: T = 10 Money demand: Md P = Y i Demand for reserves: R d = 0.375Dd Demand for deposits: Dd = (1 − 0.2)Md 2 Econ 320 – HW 2 Demand for currency

CUd = 0.2Md This says that consumers hold 20% (c = 0.2) of their money as currency and the required reserve ratio is 37.5% (θ = 0.375). Demand for central bank money (Hd ) is the total amount of currency being demanded plus the total demand for reserves. Suppose the price level is P = 1 and that the initial supply of central bank money is $100.

1. Solve for the money multiplier. Explain your work.

2. Solve for equilibrium output and the equilibrium interest rate at the initial supply of central bank money (ie. $100).

3. Suppose that the central bank sells $80 worth of bonds using open market operations. Solve for the new equilibrium output.

4. Solve for the the new equilibrium interest rate after the open market operations and use an IS-LM graph to explain what happened.