Question

Question 9 6 pts Devah lives for two periods: period 1 in which she works and earns income, and period 2 in which she is retired and earns no income. At the start of her life, her utility over consumption is given by where c1 and c2 are consumption in periods 1 and 2, respectively (both measured in dollars), and S is a measure of myopia or "present bias" (0 1). Assume there is no time discounting. During period 1, Devah will have total income of $1800 that she can either devote to c1 or to savings, s. Any money that she saves can be used for consumption in period 2 (during which time she will not have any other source of income). Assume that interest on savings is zero Assume for now that δ-1. In that case, Devah's optimal consumption in period 1 (c) is $ her optimal private savings (s) are $ and her optimal consumption in period 2 (c2) is $ (enter only numbers in the blanks, and please round to the nearest whole number if necessary) Question 10 6 pts Consider Devah from the previous question. Suppose now that 8-0.5, but that the rest of the problem remains the same (including there being no interest on savings). Devah's optimal consumption in period 1 (c1) is $ , her optimal private savings (s) are $ and her optimal consumption in period 2 (c2) is $ (enter only numbers in the blanks, and please round to the nearest whole number if necessary)

Answer 1

$\small \text{If } \delta = 1, \\ U(c_1. c_2) = (c_1)^{2/3} + (c_2)^{2/3}$

$\small \text{Budget constraint: } c_1 + s_1 = 1800 \hspace{3em}c_2 = s_1 \\ \Rightarrow c_1 + c_2 = 1800$

Devah's Optimization Problem:

UO