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Question 1: Suppose that a consumer has utility of the form u(c) = ln (c). Suppose that this consumer gets 2 units of income in the first period and 4 units in the second period.
(a) Derive his intertemporal budget constraint (ITBC), set up the utility maximization problem and derive the Euler equation. Then use the Euler equation and the ITBC to solve for his optimal consumption and saving functions.
(b) Suppose also that beta = 1 and 1 + r = 1. Solve for his consumption and saving each period.
(c) Suppose instead that beta = 0 and 1 + r = 1. Solve for his consumption and saving each period.
(d) Based on your answers to b) and c), which agent is richer at the beginning of the second period? How is this related to beta?
Question 2: Suppose that a consumer has utility in the first period of the form u(c) = ln (c) but utility in the second period is given by u (c) = c. Suppose that this consumer receives 2 units of income in the first period and 4 units in the second. Suppose also that beta = 1 and 1 + r = 1. Solve for his optimal consumption allocation. Explain how it differs from part b) of question 1.
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