Question: 4. (20 marks in total) Consider a closed-cconomy. The cconomywide expected future marginal product of capital is M PK/ = 79.8 0.05K/, where K/ is

4. (20 marks in total) Consider a closed-cconomy. The cconomywide expected future marginal product of capital is M PK/ = 79.8 0.05K/, where K/ is the future capital stock. The depreciation rate of capital, o, is 14% per period. The current capital stock K is 1,000 units of capital. The rcal price of a unit of capital is 1 unit of output. Firms pay taxes cqual to 20% of their output. The consumption cquation is ) =100+ 0.5Y 3007, where ' is consumption, Y is output, and r is the real interest rate. Government spending equals 200 and full-employment output is 2,000. (a) (8 marks) 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

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