1 Marginal Propensity to Consume In Lecture 2, we saw an example where the household only lives for two periods. Now suppose that the N household lives for N periods. Therefore, the life time utility function is U = Z t_1u(ct). The income t=1 stream over the N periods is yt, where t = 1, 2, 3 - - - N. The interest rate is z'. 1. 2. Write down the objective function of the household. Write down the inter-temporal budget constraint. . Write down the Euler equation between Period t and t', where t' 7E t. (Hint: You may nd the Lagrange method useful in this case.) . For simplicity, we assume that the discount factor ,6 = 1 and interest rate 2' = 0. Solve for the optimal consumption plan for the N periods, 6;, where t = 1, 2, 3, - - - N. . What's the marginal propensity to consume in period t = l ? (You can explain in words.) . What's the marginal prepensity to conswne in period t = 2 '? (You can explain in words.)