Intermediate Macroeconomics Assignment
1. Consider the Keynesian Cross model, where consumption C = 100 + 0.75(Y - T), investment I = 175, and government expenditure G = 100 and taxes T = 100.
(a) Compute the equilibrium income.
(b) What is the marginal propensity to consume (MPC)? Find the fiscal multiplier and tax multiplier.
(c) Now suppose government expenditure increases to 150, how much does equilibrium income increase?
(d) Now suppose government expenditure increases to 150, and this increase is financed by increase in taxes (of the same amount). How much does equilibrium income increase?
2. In the IS-LM model, explain (1) what does the IS curve represent; (2) why is the IS curve downward sloping. Clearly label your curves if you use a diagram.
3. In the IS-LM model, explain (1) what does the LM curve represent; (2) why is the LM curve upward sloping. Clearly label your curves if you use a diagram.
4. Consider the following IS-LM model. Suppose consumption C = 100 + 0.75(Y - T). Taxes T = 100, government expenditure G = 100, and investment function I(r) = 100 - 5r, where r is interest rate.
Total nominal money supply M = 500, and the price level P = 2. The money demand function is given by
(M/P)d = Y - 10r
(a) Derive the IS curve.
(b) Derive the LM curve.
(c) Find equilibrium income and interest rate.
(d) Suppose government expenditure increases to 175. Re-compute the equilibrium income and interest rate. How much does income increase given larger government spending? Calculate the implied fiscal multiplier as the change in income divided by the change in government expenditure. Is the implied fiscal multiplier larger or smaller than the fiscal multiplier from the Keynesian Cross model, i.e., 1/(1 - mpc)? Can you explain why they are different?
(e) Suppose government expenditure decreases to 25, and the central bank decides to use expansionary monetary policy to stabilize income. Determine the amount of increase in money supply such that equilibrium income does not change despite the cut in government expenditure.
5. In this question, you are asked to derive the aggregate supply curve and the aggregate demand curve, and then solve for equilibrium price and income.
The goods market is characterized by the following equations
G = T = 100,
I(r) = 100 - r,
C(Y - T) = 100 + 0.75(Y - T).
The stock of nominal money is M = 300, and the demand for real money balance is given by L(r, Y) = Y - r.
For the production side, suppose that half of the firms are inflexible and half of the firms are flexible. Expected price level EP = 10. Long-run output level Y¯ = 300. The flexible firms set price according to
Pf = EP + 10(Y - Y¯).
Recall that the inflexible firms set price Pi = EP.
(a) Derive the aggregate demand (AD) curve.
(b) Derive the aggregate supply (AS) curve.
(c) Find equilibrium income and price level.