Assume the representative consumer lives in two periods and his preferences can be described by `a U(c, c0 ) = c^2/5 + (c 0 )^2/5 , where c is the current consumption, c 0 is next period consumption, and = 0.90. Let's assume that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an income y = 100 in the current period and y 0 = 150 in the next period. The government wants to spend G = 40 in the current period and G0 = 50 in the future period.

1. If the government sets t = 50, what will be the consumer's estimate of the value of t 0 ? [03 points]

2. Is it optimal for the consumer to consume his disposable income in each period? [03 points]

3. Solve the consumer's problem by finding the optimal allocations c ? and c 0? . [05 points]

4. Is the consumer a borrower or a lender? [02 points]

5. Is the economy at the equilibrium? Explain. [04 points]

6. What are the equilibrium values of c and c 0 ? [04 points]

7. What is the equilibrium interest rate? [03 points]

8. How will the equilibrium interest rate respond to a decrease in G? [03 points]

9. How will the equilibrium interest rate respond to a decrease in G0 ? [03 points]