Suppose there are two periods, no discounting of future util- ity, no interest on savings, and...

Transcribed Image Text:

Suppose there are two periods, no discounting of future util- ity, no interest on savings, and overall utility function. u(C₁, C₂) = v(c₁) + v(c₂) where is strictly increasing, strictly concave, and differentiable. In period 1, the consumer is given a wealth of W, from which they can spend on period 1 consumption, or save for period 2 consumption. In the second period, the consumer faces a loss L<W with probability PL. € (0,1) (a) In class we explained the optimality condition determining as e'(₁) - PLU' (W-L-G₂)+(1-PI)e' (W-G₁) Explain this condition in a few words. (b) Setting v(r) - Inr, draw a figure of v'(r) (c) Set PL = 0.5, W = 4, and L= 2. Use the figure above to illus- trate why equalizing expected consumption across periods does not satisfy the optimality condition in (a). (d) Illustrate qualitatively in the figure why the optimal solution is to set c less than the expected consumption in period 2. Suppose there are two periods, no discounting of future util- ity, no interest on savings, and overall utility function. u(C₁, C₂) = v(c₁) + v(c₂) where is strictly increasing, strictly concave, and differentiable. In period 1, the consumer is given a wealth of W, from which they can spend on period 1 consumption, or save for period 2 consumption. In the second period, the consumer faces a loss L<W with probability PL. € (0,1) (a) In class we explained the optimality condition determining as e'(₁) - PLU' (W-L-G₂)+(1-PI)e' (W-G₁) Explain this condition in a few words. (b) Setting v(r) - Inr, draw a figure of v'(r) (c) Set PL = 0.5, W = 4, and L= 2. Use the figure above to illus- trate why equalizing expected consumption across periods does not satisfy the optimality condition in (a). (d) Illustrate qualitatively in the figure why the optimal solution is to set c less than the expected consumption in period 2.