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Consider an agent who lives for two periods. His income is Y1 in period 1 and Y2 in period 2. In period 1 he decides how much to consume C1, and how much to save, S. His second period consumption is denoted by C2. Savings are invested and earn interest rate R. The agent’s utility is U(C1, C2) = ln(C1) + ß ln(C2) where ln(x) is the natural logarithm of x and ß is the agent’s discount factor which measures his impatience (ß ? (0, 1)). Use the first and second period constraints to derive the agent’s lifetime budget con- straint. Maximize the agent’s utility subject to his lifetime budget constraint to find his optimal consumption for both periods and optimal savings as a function of his lifetime income, interest rate and discount factor.
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