Consider a two period economy where the preferences of a representative household are reflected by the following Cobb-Doug utility function:

 

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U (C1, C2) = C C Suppose that this representative household is expected to get income (in real terms) equal to 1000 in the first period, and 1300 in the second period. Moreover, assume that the market interest rate is 3%. 1.a. Write down the inter-temporal budget constraint and draw the graph. 1.b. Write down the consumption optimization equation, and intuitively describe what it states. 1.c. What is the marginal rate of substitution and explain what it means for this particular consumer. 1.d. Solve for the optimal values of consumption in periods 1 and 2 at the perfect equilibrium (C1* and C2"). Draw the graph. U (C1, C2) = C C Suppose that this representative household is expected to get income (in real terms) equal to 1000 in the first period, and 1300 in the second period. Moreover, assume that the market interest rate is 3%. 1.a. Write down the inter-temporal budget constraint and draw the graph. 1.b. Write down the consumption optimization equation, and intuitively describe what it states. 1.c. What is the marginal rate of substitution and explain what it means for this particular consumer. 1.d. Solve for the optimal values of consumption in periods 1 and 2 at the perfect equilibrium (C1* and C2"). Draw the graph.