Quetion: 1. A consumer lives for two periods (the present and the future). His income in period 1 is 100. His income in period 2 is 200. Prices of the single consumption good are $1 per unit in both periods. The interest rate at which he can lend or borrow is 20% per period. Consumption in the present and the future periods is C1 and C2. The utility function is U (C1,C2) = C1 * C2.
a. Solve the optimization problem of the consumer. (Non-round number of units is ok, if that's the solution)
b. Is the consumer a borrower or a lender? Is the result intuitive to you? (please calculate savings explicitly as part of the answer)
c. If the consumer wins the lottery today, and that increases his future, 2nd period income by 300, will he change his borrowing decision? Is the result intuitive to you?