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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 is a measure of myopia or "present bias" (0

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.

(a)Consider Devah from the previous question. Suppose now that =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).

(b)Consider Devah from the previous questions. Continue to assume that =0.5. Suppose that now, however, the government institutes a Social Security program that taxes Devah $180 during her working years, but returns that $180 to her when she retires. In the presence of this Social Security program, 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).

C1, C2

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