1. Suppose the marginal rate of return to capital invested in U.S. businesses Kb is rb = 20 − (2/3)Kb where rb is a percentage (that is, rb = 5 means a 5 percent rate of return)

and capital is measured in trillions of dollars. The marginal rate of return on housing investment is rh = 11 − (1/2)Kh.

The total amount of capital that can be invested in the United States is $25 trillion.

a. There is a 40 percent tax on capital income in the business sector and no tax in the housing sector. How much capital is invested in the business sector? In the housing sector? What is the pretax marginal rate of return in the business sector? In the housing sector? What is the pretax average rate of return in the business sector? In the housing sector? What is the post-tax marginal rate of return in the business sector? In the housing sector?

b. Suppose that a tax of 40 percent is instituted on returns to capital in the housing sector. How much capital shifts from housing to business?

c. What is the deadweight loss on an annual (flow) basis from the misallocation of capital stock?

d. How would the consequences of homeowners’ tax preferences be different if capital were perfectly elastically supplied on the world market at a post-tax rate of return of 6 percent?