An individual's preferences for consumption (c) and free time (t) are represented by the utility function u(t,c) = t(c+600). When this individual's wage rate increases, they consistently choose to work more hours, thereby reducing their free time. Which statement best analyzes the economic effects causing this outcome?

Predicting Labor Supply Changes

Analyzing Labor Supply Decisions

True or False: An individual's preferences for consumption (c) and free time (t) are described by the utility function u(t,c) = t(c+600). For this individual, it is possible that a very large increase in their wage rate could eventually cause them to increase their free time (work less).

Calculating Optimal Labor Supply

Analysis of Labor Supply with a Specific Utility Function

A policymaker argues that cutting taxes on wage income, which effectively increases the net wage rate, is a guaranteed way to encourage people to work more hours. An economist is analyzing a specific group of workers whose preferences for consumption (c) and free time (t) are well-represented by the utility function u(t,c) = t(c+600). Based on this model, which of the following presents the most accurate evaluation of the policymaker's argument for this specific group?

Evaluating a Labor Policy Model

An individual's preferences for consumption (c) and free time (t) are represented by the utility function u(t,c) = t(c+600). The mathematical relationship describing how their optimal choice of free time (t*) changes in response to a change in their wage rate (w) is given by the derivative: ∂t*/∂w = - (I + 600) / (2w^2), where I is non-labor income, which is non-negative (I ≥ 0). Given this relationship, for any increase in the wage rate, the change in the individual's optimal amount of free time will always be __________. (Enter 'positive', 'negative', or 'zero').

An individual's preferences for consumption (c) and free time (t) are represented by the utility function u(t,c) = t(c+600). When this individual's wage rate increases, there are two opposing pressures on their choice of free time:

1. The pressure to take less free time, because each hour of leisure now has a higher opportunity cost in terms of foregone earnings.
2. The pressure to take more free time, because their higher overall income allows them to afford more of all goods, including leisure.

For an individual with these specific preferences, how do these two pressures interact as their wage changes?