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Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0

where c1 and c2 are consumption in period 1 and period 2 respectively

(Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2. The gross market rate of interest is R. I Write the inter-temporal budget constraint of the consumer and interpret it. While deriving thee inter-temporal budget constraint using the budget constraint of the first period eliminate s from the second period budget constraint. Il Set up the consumer optimization problem IlII Derive first order conditions and interpret them in terms of marginal cost and marginal benefit of optimal choices. IV Derive optimal capital investment, k. Now suppose that R changes by one unit. How does it affect optimal capital investment?

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