Macroeconomics 5th Edition by Olivier Blanchard

Exercise 2

Consider first the goods market model with constant investment that we saw in Chapter 3. Consumption is given by
C = c 0 + c 1 (Y - T)
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 = b 0 + b 1 Y - 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 c 1 + b 1 1.)
Next, write the LM relation as
M/P = d 1 Y - d 2 i
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.