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Problem 1. (Consumption smoothing) A consumer who lives for four periods have the following path of income y 60 0 60 0 Assume the consumer has log utility, u(a)-ing, and is infinitely patient, β-1. Also assume the interest rate is 0 so that the real rate of return is 1 b) What is the value of assets, at, of the consumer at the beginning of period 4? (c) If the consumer is not able to borrow at any point in time, what is the optimal consumption profile? d) What is the value of assets of the consumer at the beginning of period 4 in this case if the consumer cannot borrow?

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