A student has a maximum of 90 days to allocate between work and free time. After a wage increase to $130 per day, the student chooses to have 30 days of free time, earning and consuming $5,200. For this specific combination of free time and consumption to be the student's utility-maximizing choice, which of the following statements must be true at this point?

Evaluating an Optimal Labor-Leisure Choice

Analyzing the Optimal Labor-Leisure Trade-off

A student's wage increases to $130 per day, and their new utility-maximizing choice is to have 30 days of free time and $5,200 in consumption. Given this is their optimal choice, it must be true that they would be willing to work one additional day (i.e., reduce free time by one day) if it resulted in an additional $125 of consumption.

A student's wage is $130 per day, and they determine their optimal choice is to have 30 days of free time and $5,200 in consumption. Why would this student reject an alternative, feasible option of working one additional day to have 29 days of free time and $5,330 in consumption?

A student's wage increases to $130 per day, and they find their new utility-maximizing choice is to have 30 days of free time and $5,200 in consumption. At this specific point, the student's marginal rate of substitution—the amount of consumption they are willing to give up for one additional day of free time—is equal to $____.

Analyzing a Sub-Optimal Labor-Leisure Choice

A student's wage is $130 per day, and their utility-maximizing choice is to have 30 days of free time and $5,200 in consumption. Suppose the student is offered a one-time opportunity to work on what would have been their 30th day of free time for a special payment of $140. Assuming this is their only choice, what would be the utility-maximizing response and why?

Evaluating a Work-Life Balance Policy

Critiquing a Recommendation on Work-Leisure Balance

A student's wage increases to $130 per day, and their new utility-maximizing choice is to have 30 days of free time and $5,200 in consumption. Given this is their optimal choice, it must be true that they would be willing to work one additional day (i.e., reduce free time by one day) if it resulted in an additional $125 of consumption.