8. (Appendix 4.A) A consumer has initial real wealth of 20, current real income of 90, and future real income of 110. The real interest rate is 10% per period.

MPK K f

where K is the future capital stock. The depreciation rate of capital,

d, is 20% per period. The current capi tal stock is 900 units of capital. The price of a unit of capital is 1 unit of output. Firms pay taxes equal to 15% of their output. The consumption function in the economy is = + −

C Y r 100 0.5 200 , where C is con sumption, Y is output, and r is the real interest rate.

Government purchases equal 200, and full-employment output is 1000.

a. Suppose that the real interest rate is 10% per period.

What are the values of the tax-adjusted user cost of capital, the desired future capital stock, and the desired level of investment?

b. Now consider the real interest rate determined by goods market equilibrium. This part of the prob lem will guide you to this interest rate.

i.