Homework #5

1. Consider a closed economy with consumption given by the equation C=200+2/3(Y- T). In addition, suppose that planned investment expenditure is 300 and the government runs a balanced budget with government spending equal to 300. Use your understanding of the Keynesian cross as a starting point to answer the following questions.

a. If Y is 1,500, what is planned expenditure? What is inventory accumulation or decumulation? Given your answer to the last question, would you expect equilibrium Y be higher or lower than 1,500? If you expect equilibrium Y to be different, explain the mechanism by which you would expect Y to change in this economy.

b. What is equilibrium Y?

c. What are equilibrium consumption, private savings, public savings, and national savings? [Hint: first solve for equilibrium consumption, then use the definitions that you already know.]

d. Now, recalculate equilibrium income when G is reduced to 200, but T stays the same as above. What is the multiplier for government spending?

2. Next consider an economy with consumption function C=200+0.75(Y-T) and investment function I=200-25r, and where fiscal policy is summarized by G=T=100.
a. Use Excel to graph the IS curve for values of r ranging from 0 to 15. [Hint: plug in the given expressions for C, I and G into the equation Y=C+I+G. Then solve for Y as a function of only r. Use the resulting expression as an Excel formula which takes r from a neighboring cell. Have your 0 through 15 values of r in a column, so you can then copy your formula down.]

b. Suppose the money demand curve is given by (M/P)^d = Y-100r. In addition, the money supply is 1000 and the price level is 2. Use Excel to graph the LM curve for values of r ranging from 0 to 15.

c. Find the equilibrium interest rate r and equilibrium level of income Y.

d. Suppose that government purchases are raised from 100 to 150. How much does the IS curve shift? What is the new equilibrium interest rate? What is the new equilibrium level of income?

e. Suppose instead that the money supply is raised from 1,000 to 1,200. How will the LM curve shift? What is the new equilibrium interest rate and what is the new level of income?

f. With the initial values for monetary and fiscal policy, suppose that the price level rises from 2 to 4. What is the new equilibrium interest rate? What happens to the level of income in equilibrium?

g. Build on your algebra from parts (a) and (b) to derive an equation for the aggregate demand curve. [Hint: Part (a) gave you an equation in terms of Y and r. Solve that equation for r. Part (b) gave you an equation in terms of P, r and Y. Solve this equation also for r. Now set the two equations equal and solve for P.] Now use Excel to graph the aggregate demand curve. Do this for values of Y equal to 1000, 1100, 1200, etc., up to 2000.

h. Next, modify your Excel formula from part (g) to show what happens to the aggregate demand curve if fiscal policy changes as it did in part (d) (i.e., government purchases increase from 100 to 150). Use Excel to graph the new aggregate demand curve for the same values of Y as in part (g). Explain in words what happens to the aggregate demand and why.

i. Similar to the last question, show what happens to aggregate demand monetary policy changes as it did in part (e) (i.e., the money supply increases from 1000 to 1200). Again, use Excel to graph the modified aggregate demand curve for the same values of Y as in part (g). Explain in words what happens to the aggregate demand and why.