For the following long question, assume that the consumption function is:
C = 200 + 0.75(Y - T)
The investment function is:
I(r) = 200 - 2.5r
Government spending is fixed at G = 100 and the government runs a balanced budget. The liquidity function is:
L(Y,r) = Y - 10r
Nominal money supply is 1,000. The price level is equal to 2.
a) Find the planned expenditure function and plot it on the Keynesian Cross diagram. Hint: PE=C+I+G and output is on the horizontal axis and planned expenditure is onthe vertical axis.
b) If the real interest rate is 10% then what is output?
c) Show the effects of an increase in government spending to G' = 200 on your diagram. What is the effect on output? Hint: I am asking for the gov- ernment spending multiplier.
d) Discuss the relationship between the multiplier and the marginal propensity to consume.
e) Draw the IS curve for the case when G = 100.
f) Now I want you to create a graph of the money market equilibrium with real money balances on the horizontal axis and the real interest rate on the vertical axis. Use the value of output that you found in part b).
g) Derive the LM curve for this economy. Plot it onthe same diagram that you plotted the IS curve from part e).
h) Suppose that the money supply increases from 1,000 to 1,200. Show the effects on the money market diagram in part f).
i) Solve for the real interest rate and the level of output in the IS-LM model.
j) Derive the IS curve for the case when G' = 200 and re-solve for output and the real interest rate.
k) Derive the LM curve for the case where M = 1,200 and re-solve for output and the real interest rate.