Consider a closed-economy. The economywide expected future marginal product of capital is M P Kf = 79.8 0.05Kf , where Kf is the future capital stock. The depreciation rate of capital, , is 14% per period. The current capital stock K is 1,000 units of capital. The real price of a unit of capital is 1 unit of output. Firms pay taxes equal to 20% of their output. The consumption equation is C = 100 + 0.5Y 300r, where C is consumption, Y is output, and r is the real interest rate. Government spending equals 200 and full-employment output is 2,000.

(a) Solve for the real interest rate that clears the goods market. What are the goods market-clearing values of consumption, saving, and investment? What is the desired amount of capital stock in this equilibrium?