Consider a closed economy with the following partcipants: households, rental firm, production firm and the government: (a)Production firm: the aggregate production function of the production firm can be described as: F(K, L) = 50K0.5L 0.5 . Assume that the total labor L=200 and total capital level K=200. (b )Households: households’ consumption depends on both disposable income Y − T and the real interest rate r (in percentage). Here we assume case II which means that when interest rate changes the substitution effects are greater than the income effects. Accordingly, C = 2400 + 0.6(Y − T) − 100r where C is consumption and T is tax. (c) Rental firm: rental firm makes investment decision which takes the real rental rate and the real interest rate as given. Assume that investment I is given by equation I = 3000 − 100r. The rental firm takes the rental rate set by the production firm as given. The production firm is selfish which set the rentral rate to maximize their profit. (d) Government collect lump-sum tax T=2000 and spend G=3000, which means a budget deficit of -1000. Use the condition above to answer the following questions: (1) (3 pts)What is the total output measured by the production method? (2) (9 pts) Solve the equilibrium real interest rate r, the equilibrium consumption C and the equilibrium investiment I. (3) (6 pts) Solve the private saving and the public saving in equilibrium. (4) (9 pts) Use the goods market equilibrium to graphically show what happens to the real interest rate and the output in equilibrium when the technology improves. (5) (9 pts) Use the loanable funds market to show what happens to the equilibrum level of the real interest rate and investment when the government spending increases. (6) (9 pts) Suppose now the government cut tax from T=2000 to T=1000, what is the new equilibrium real interest rate, output and investment.

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