2. Consider first the goods market model with constant investment that we saw in Chapter 3. Consumption is given by

C = c0 + c11Y - T2 and I, G, and T are given.

a. Solve for equilibrium output. What is the value of the multiplier? Now let investment depend on both sales and the interest rate:

I = b0 + b1Y - b2i

b. Solve for equilibrium output. At a given interest rate, is the effect of a change in autonomous spending bigger than what it was in part (a)? Why? (Assume c1 + b1 < 1.) Next, write the LM relation as

M/P = d1Y - d2i

c. Solve for equilibrium output. (Hint: Eliminate the interest rate from the IS and LM relations.) Derive the multiplier (the effect of a change of one unit in autonomous spending on output).

d. Is the multiplier you obtained in part (c) smaller or larger than the multiplier you derived in part (a)? Explain how your answer depends on the parameters in the behavioral equations for consumption, investment, and money demand.

3. The response of investment to fiscal policy

a. Using the IS-LM diagram, show the effects on output and the interest rate of a decrease in government spending. Can you tell what happens to investment? Why? Now consider the following IS-LM model: C = c0 + c1 1Y - T2 I = b0 + b1Y - b2i M/P = d1Y - d2i

b. Solve for equilibrium output. Assume c1 + b1 6 1. (Hint: You may want to re-work through Problem 2 if you are having trouble with this step.)

c. Solve for the equilibrium interest rate. (Hint: Use the LM relation.)

d. Solve for investment.

e. Under what conditions on the parameters of the model (i.e., c0, c1, and so on) will investment increase when G decreases? (Hint: If G decreases by one unit, by how much does I increase? Be careful; you want the change in I to be positive when the change in G is negative.) f. Explain the condition you derived in part (e)