Figure 3.11 illustrates how additional, non-labor income affects an individual's optimal choice between free time and consumption. The figure shows that receiving a gift causes a parallel upward shift in the budget constraint. This expands the feasible set and typically leads the individual to choose more free time (working fewer days), as they can afford more leisure while maintaining or increasing consumption.

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While considering their optimal work-leisure plan, a student receives an unexpected offer from a mysterious benefactor: an unconditional gift of \$1,000. This sudden increase in non-labor income alters their financial situation, requiring them to re-evaluate their initial plan and determine a new optimal balance between free time and consumption.

The Student's Decision After Receiving a \$1,000 Gift

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CORE Econ - The Economy 2.0: Microeconomics

An increase in non-labor income, such as a monetary gift, shifts an individual's budget constraint but does not alter its slope. This is because the wage rate, which represents the opportunity cost of free time (the amount of consumption forgone for an additional unit of leisure), remains unchanged.

Non-Labor Income Does Not Affect the Opportunity Cost of Free Time

After receiving a \$1,000 gift, the student revises their plan and selects a new optimal bundle at point B. This new choice consists of 39 days of free time. Graphically, point B represents the tangency point on a higher indifference curve (IC3) where the student's marginal rate of substitution (MRS) is equal to the \$90 wage (the MRT).

The Student's New Optimal Choice at Point B (39 Free Days)

When an individual receives a fixed amount of non-labor income, such as a \$1,000 gift, their total income increases by that amount at every possible level of free time. This causes the budget constraint to shift vertically upwards in a parallel fashion, with the magnitude of the shift being equal to the amount of the gift.

Effect of a Fixed Cash Gift on the Budget Constraint

Following the receipt of a \$1,000 gift, the student's budget constraint is updated to include this non-labor income. The new formula is $c = 90(70 - t) + 1,000$, where $c$ is the maximum consumption, \$90 is the daily wage, 70 is the total number of days, and $t$ is the number of free days chosen. The additional \$1,000 is a fixed amount added to the income earned from work.

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