Question

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 δ is a measure of myopia or "present bias" (0<8:1). 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 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) CsiderDevahfrom the previous questions. Continue to assume that 6-0.5. Suppose that now however, ih neistu aSial Sxurity prrn that tas vah $180 durg 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 $ savings (s) are $ , her optimal private 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

In this scenario, the optimal consumption and savings for Devah are determined for both periods of her life, considering different factors.

Step-by-step explanation:

In this scenario, Devah lives for two periods: period 1 where she works and earns income, and period 2 where she is retired and earns no income. The utility over consumption in period 1 is given by the expression U(c1)=c10.5.

Her total income in period 1 is $1800, which she can either spend on consumption in period 1 (c1) or save (s). With a measure of myopia (δ) equal to 0.5, Devah's optimal consumption in period 1 is $900, her optimal private savings are $900, and her optimal consumption in period 2 is $900.

Now, considering the presence of a Social Security program that returns $180 to Devah when she retires, her optimal consumption in period 1 remains $900, her savings remain $900, and her optimal consumption in period 2 is now $1080.