Optimal Time Allocation Decision

An individual's preferences for consumption ($c$) and free time ($t$) are represented by the utility function u(t,c) = tc. Their daily budget is determined by the equation c = w(24 - t) + I, where 'w' is the hourly wage rate and 'I' is non-labor income. If this individual's non-labor income (I) increases, while their wage rate (w) remains constant, how will their optimal choice of daily free time be affected?

Consider an individual whose preferences for consumption ($c$) and free time ($t$) are described by the utility function u(t,c) = tc. They have 24 hours per day to allocate and earn an hourly wage ($w$), with no other source of income.

Statement: An increase in this individual's hourly wage rate will cause them to choose more free time because the higher income allows them to afford more of all goods, including leisure.

Calculating Optimal Leisure and Consumption

An individual's choice between consumption ($c$) and free time ($t$) is modeled by the utility function $u(t,c) = tc$ and the budget constraint $c = w(24-t) + I$, where 'w' is the hourly wage and 'I' is non-labor income. Match each economic concept to its correct mathematical representation in this specific model.

Analyzing Policy Effects on Labor-Leisure Choice

An individual's preferences for consumption ($c$) and free time ($t$) are represented by the utility function $u(t,c) = tc$. They have 24 hours available each day, which they can allocate between free time and work at an hourly wage of $w$. If this individual has no other source of income, they will optimally choose to work for ______ hours each day, regardless of the specific wage rate.

You are tasked with finding the optimal combination of free time (t) and consumption (c) for an individual. Their preferences are represented by the utility function u(t,c) = tc, and their choices are limited by a budget constraint c = w(24 - t) + I, where 'w' is the hourly wage and 'I' is non-labor income. Arrange the following steps in the correct logical order to solve for the individual's optimal choice.

Two individuals, Alex and Ben, have identical preferences for consumption (c) and free time (t), represented by the utility function u(t,c) = tc. They both have 24 hours per day to allocate. Alex has a job but no other source of income, so their budget is c = w_A(24 - t). Ben has a different job and also receives a daily non-labor income, so their budget is c = w_B(24 - t) + I, where I > 0. Based on this information, which of the following statements about their optimal choices of daily free time is correct?

Evaluating a Policy with a Work-Hour Restriction