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

student submitted image, transcription available below

where c1 and c2 are consumption in periods 1 and 2, respectively (both measured in dollars), andstudent submitted image, transcription available belowis 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 thatstudent submitted image, transcription available below=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 thatstudent submitted image, transcription available below=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).

(C) 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).

(D) Consider Devah from the previous questions. Continue to assume thatstudent submitted image, transcription available belowδ=0.5. Instead of taxing Devah $180 during her working years and returning $180 to her when she retires, now assume that the government taxes Devah $180 during her working years and returns $90 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).

Answer 1

The intertemporal budgeting problem examines how Devah allocates her income for current and future consumption, considering present bias and varying levels of Social Security benefits. Accurate consumption and savings choices cannot be calculated without specific equations or numerical figures. The presence and structure of the Social Security program influence her private savings and consumption at different stages.

Step-by-step explanation:

The scenario presents an intertemporal choice problem where Devah must decide how to allocate her income between consumption in two periods of her life: her working years (period 1) and retirement years (period 2). With a present bias (represented by δ=0.5) and no interest on savings, her optimal choices alter when a Social Security program is introduced. This program either returns her contributions upon retirement or does not fully compensate for the taxed amount, potentially changing her private savings behavior.

Without solving the actual equations or having figures provided for different scenarios, we cannot precisely determine the amounts for optimal consumption (c1, c2) or savings (s). However, we can discuss how Devah might allocate her resources given her present bias and different government policies. If the Social Security program returns the full amount upon retirement, it may lead to reduced private savings by the amount of the tax as she would rely on the program for future consumption. If only a partial benefit is paid out, she might need to save more privately to secure her retirement consumption.