Tamara earns $8 an hour and works 60 hours/week. Draw her labor-leisure budget constraint. What determines its slope? How does the position and slope of her budget constraint change if her wage increases to $16 per hour?
The correct answer and explanation is :
Tamara’s Labor-Leisure Budget Constraint
To draw Tamara’s labor-leisure budget constraint, we need to consider her total earnings and the time available for work and leisure. Tamara works 60 hours per week and earns $8 per hour. This means that her total weekly income is:
[
\text{Income} = \text{Wage} \times \text{Hours Worked} = 8 \times 60 = 480
]
Tamara has a total of 168 hours in a week (24 hours/day × 7 days/week). Out of these 168 hours, 60 are spent working, so the remaining 108 hours are available for leisure.
The budget constraint can be plotted on a graph with two axes: Leisure on the x-axis and Income on the y-axis. The maximum amount of leisure Tamara can enjoy is 108 hours, which happens when she works 0 hours. The maximum income Tamara can earn is $480, which happens when she works all 60 hours of the week.
Slope of the Budget Constraint
The slope of the budget constraint is determined by the wage rate. The wage rate represents the opportunity cost of leisure, as it tells us how much income Tamara sacrifices for each hour of leisure. The slope of the budget constraint can be calculated as:
[
\text{Slope} = \frac{\text{Change in Income}}{\text{Change in Leisure}} = \frac{\text{Wage}}{-1}
]
Thus, the slope of the budget constraint is the negative of the wage rate, since as Tamara takes more leisure time, her income decreases. In this case, the slope is:
[
\text{Slope} = -8
]
Effect of Wage Increase
If Tamara’s wage increases to $16 per hour, her total income for 60 hours of work becomes:
[
\text{Income} = 16 \times 60 = 960
]
The budget constraint will shift upward, as Tamara can now earn more income for the same amount of work. Additionally, the slope of the budget constraint will become steeper because the opportunity cost of leisure has increased. With a $16 wage, the slope will be:
[
\text{Slope} = -16
]
This means that for each hour of leisure Tamara chooses, she sacrifices $16 in income. The new budget constraint will have a steeper slope and higher income level.
Summary
- Original wage ($8/hr): The slope of the budget constraint is -8, and her total income is $480.
- Increased wage ($16/hr): The slope of the budget constraint becomes steeper at -16, and her total income increases to $960. The higher wage results in both a higher total income and a steeper opportunity cost of leisure.