Question

Period 1 is when Devah is working and earning money, and Period 2 is when she is retired and not working.

In the beginning of her life, she is provided with utility over consumption by U(c1,c2)=c1⁰.⁵+δ[(c2⁰.⁵)]
where c1 and c2 are consumption in periods 1 and 2, respectively (both measured in dollars), and delta(δ) is a measure of myopia or present bias (0<δ<1). Assume there is no time discounting.
During period 1, Devah will have total income of $1000 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.

Answer 1

Devah faces an intertemporal choice regarding her income allocation for consumption during her working years and for consumption in retirement, with a utility function considering present bias. There's no interest on savings, and the consumption function embodies the principle that consumption and savings combined equal total income.

Step-by-step explanation:

Intertemporal Choice and Consumption

The question revolves around an intertemporal choice model of consumption and savings, in which an individual named Devah must decide how much of her income to consume in period 1, when she is working, and how much to save and consume in period 2, her retirement. This decision is formulated within the utility function U(c1,c2) = c1^0.5 + δ[(c2^0.5)], where c1 and c2 represent consumption in periods 1 and 2 respectively, and δ is the measure of present bias. With no interest on savings, Devah's total income during period 1 is $1000, which must be allocated to either consumption or savings to be consumed in period 2.

The consumption function explains the relationship between income and consumption, which dictates that total consumption plus savings equals total income, as illustrated in various figures and tables referenced. An example to understand the concept may involve a given income amount where a certain percentage is set for consumption and the rest for savings. As income increases beyond the level needed for basic consumption, savings commence and grow.