Suppose that the economywide expected future marginal product if = 40 0.02,

Where K is the future capital stock. The depreciation rate of capital, d, is 25% per period. The current capital stock is 1200 units of capital. The price of a unit of capital is 1 unit of output. Firms pay taxes equal to 25% of their output. The consumption function in the economy is

= 120 + 0.75 200 , where C is consumption, Y is output, and r is the real interest rate. Government purchases equal 250, and the full-employment output is 5000.

a) Derive an equation relating the desired investment to r.

b) Derive an equation relating the desired national saving to r and Y.