Analyzing Changes in Optimal Choice via Differentiation

An individual's preferences for consumption (c) and free time (t) are represented by the utility function U(c, t) = c * t. The individual has a total time endowment of T hours, earns a wage of 'w' per hour worked, and receives unearned income of 'I'. Which of the following expressions correctly represents the individual's optimal choices for consumption and free time as functions of their wage and unearned income?

Labor Supply Response to Unearned Income

Determinants of the Optimal Labor-Leisure Choice

Evaluating a Labor Supply Model

An individual's optimal choices for free time (t*) and consumption (c*) are described by the functions t*(w, I) = (wT + I) / (2w) and c*(w, I) = (wT + I) / 2, where 'w' is the wage rate, 'I' is unearned income, and 'T' is total time available. If this individual's unearned income 'I' increases, while their wage 'w' and total time 'T' remain unchanged, what is the predicted effect on their optimal choices?

Statement: For any individual who considers both consumption and free time to be normal goods, an increase in the wage rate will unambiguously lead them to choose less free time.

An individual has a total time endowment of T, earns a wage rate of 'w' per hour worked, and receives unearned income of 'I'. Their budget constraint is c = w(T-t) + I. Match each utility function representing their preferences for consumption (c) and free time (t) with the correct corresponding optimal choice function for free time, t*(w, I).

The Role of Preferences in Labor Supply Decisions

Policy Evaluation: Wage Subsidy vs. Cash Transfer

Analysis of a Tax and Transfer Policy

Evaluating a Labor Supply Model

Determinants of the Optimal Labor-Leisure Choice