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

U(c1,c2)=(c1)^0.5+?[(c2)^0.5]

where c1and c2are 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 $400 that she can either devote to c1or 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.

1. 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).
2. Continue to assume that?=0.5. Suppose that now, however, the government institutes a Social Security program that taxes Devah $40 during her working years, but returns that $40 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).
3. In the previous question about Devah's consumption and savings choices in the presence of the Social Security program, every $1 of Social Security benefits crowds out $of private savings for her retirement (enter a dollar amount in the blank, and please round to the second decimal place if necessary).
4. Consider Devah from the previous questions. Continue to assume that?=0.5. Instead of taxing Devah $40 during her working years and returning $40 to her when she retires, now assume that the government taxes Devah $40 during her working years and returns $80 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).

Consider Devah from the previous question. Suppose now that 6=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 (5) 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). Consider Devah from the previous questions. Continue to assume that 5=0.5. Suppose that now, however, the government institutes a Social Security program that taxes Devah $40 during her working years, but returns that $40 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 (5) are 55 , 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). In the previous question about Devah's consumption and savings choices in the presence of the Social Security program. every $1 of Social Security benets crowds out 55 of private savings for her retirement (enter a dollar amount in the blank, and please round to the second decimal place if necessary). Consider Devah from the previous questions. Continue to assume that 5=0.5. Instead of taxing Devah $40 during her working years and returning $40 to her when she retires, now assume that the government taxes Devah $40 during her working years and returns $80 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 (5) 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)