1. (10 points) Consumption Theory Consider a 2 period economy where the preferences of a representative household is reflected by the following Cobb-Douglas utility function: U(C_1,C_2)=C_1^{0.5}C_2^{0.5} (1) Suppose that this representative household is expected to get income (in real terms) equal to 100 in the first period, and 126 in the second period. Moreover, assume that the market interest rate is 5% (i.e. r = 0.05) and that the representative consumer has perfect foresight. a. Write down the flow budget constraints. b. Use your answers to part (a) above to write down the present value budget constraint. c. Calculate the marginal rate of substitution given preferences depicted in equation (1). d. Write down the consumption Euler equation and intuitively describe what it states. e. Solve for the optimal values of consumption in periods 1 and 2 at the perfect foresight equilibrium, i.e. C_1^* and C_2^*.
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The flow budget constraints for the two periods are as follows: For the first period: C1 ≤ Y1 = 100 For the second period: C2 ≤ (1+r) * (Y1 - C1) + Y2 = 1.05 * (100 - C1) + 126 b. The present value budget constraint is the sum of the present values of Show more…
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