In a two-period economy the interest rate is r = 0.2 and the consumer endowment is...

 

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In a two-period economy the interest rate is r = 0.2 and the consumer endowment is we during the first period (no endowment in period 2). The consumer has the following utility function U(c, c') = log (c) + log (c), where c stands for consumption in the current period and c' stands for consumption in the future period. 1. (15%) Write down the budget constraint, the maximization problem, and find the first-order conditions (FOC) for the consumer. 2. (20%) Find the optimal consumptions during the two periods c* and c* assuming that we = 61. Are optimal consumptions in both periods the same? Explain why. 3. (15%) Explain how the optimal savings in period 1 would change if the interest rate increased to 0.3. In a two-period economy the interest rate is r = 0.2 and the consumer endowment is we during the first period (no endowment in period 2). The consumer has the following utility function U(c, c') = log (c) + log (c), where c stands for consumption in the current period and c' stands for consumption in the future period. 1. (15%) Write down the budget constraint, the maximization problem, and find the first-order conditions (FOC) for the consumer. 2. (20%) Find the optimal consumptions during the two periods c* and c* assuming that we = 61. Are optimal consumptions in both periods the same? Explain why. 3. (15%) Explain how the optimal savings in period 1 would change if the interest rate increased to 0.3.

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The question pertains to a twoperiod intertemporal consumption model where a consumer decides how to allocate consumption over two periods to maximize ... View the full answer