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Question: question 1 consumptionsaving problem suppose that a consumer lives for...

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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 with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first period and R be the gross market rate of interest. I Write the inter-temporal budget constraint of the consumer and interpret it. [Marks 0.5 II Set up the consumer optimization problem and illustrate its optimal choices using the indifference curve and inter-temporal budget constraint. [Marks III Derive first order conditions and interpret them in terms of marginal cost and marginal benefit of optimal choices. [ Marks 1 IV Derive optimal choices of the consumer. Now suppose that y changes by one unit. How does it affect optimal consumption pattern and saving? Marks 1.5

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