Consider the two-period model we studied in class. A consumers income in the current period is Y1 = 300, and income in the future period is Y2 = 660. The interest rate R is 10%. Assume that the price level equals 1 in both periods.

(a) Write down the present-value budget constraint. What is the lifetime wealth of this con- sumer?

(b) Suppose the consumer has logarithm utility function. The total utility is log(C1) + log(C2). Suppose the discount factor = 0.8. Write down the optimality condition of this consumer. Solve for the optimal consumption in both periods. Is this consumer a borrower or a saver in the current period?

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(c) Now suppose the current-period income Y1 for this individual increases from 300 to 390. Solve for the optimal consumption in both periods for this individual. What is the marginal propensity to consume out of the additional income?

(d) Continue from part (b) and let Y1 = 300, Y2 = 660. Suppose the consumer faces the following credit constraint in period 1:

S1 Y2 . 6

That is, the consumer cannot borrow more than a quarter of her income in the future period. Are the optimal consumptions in part (b) still feasible? If yes, show your arguments. If not, what consumptions C1 and C2 will the consumer choose facing the credit constraint?

(e) Calculate the consumers utility in (b) and (d). Does the existence of the credit constraint reduce the consumers utility?