Question

Assume that workers whose incomes are less than \(\$ 10,000\) currently pay no federal income taxes. Suppose a new government program guarantees each worker \(\$ 5000,\) whether or not he or she earns any income. For all earned income up to \(\$ 10,000\), the worker must pay a 50 -percent tax. Draw the budget line facing the worker under this new program. How is the program likely to affect the labor supply curve of workers?

Short answer

In terms of the budget line, the program creates a kinked budget line that starts at \$5000, continues with a 1:1 slope up to \$15,000 on the y-axis, and then retains a slope of 0.5 beyond that point. The labor supply might increase for those previously earning less than \$10,000, while it may decrease for those earning over \$10,000 due to the disincentive of a 50% tax.

Step-by-step solution

Preliminary Calculations and Assumptions

Assume that without the program, the worker can earn up to \$20,000 a year. Collectively with the guaranteed income (\$5000), the tax-free income (\$10,000 untaxed), and the taxed income (50% tax on everything over \$10000), we can calculate the maximum possible income with the new program.

Plotting the budget line without the program

Before the program, the budget line starts at 0 and has a slope of 1 (indicating 100% of earned income is kept), ending at \$20,000 on income (y) axis to represent the maximum income a year.

Plotting the budget line with the program

With the new program, the budget line starts at \$5000 on the y-axis as it presents the unconditional income. It continues with a slope of 1 until \$15,000 on the y-axis (\$10,000 in earnings + \$5000 unconditional income) as up to \$10,000 of earned income remains untaxed. From \$15,000 onwards, it has a slope of 0.5, indicating the 50% tax on all earnings above \$10,000.

Illustrating the effect on labor supply

Overall, the program is bound to influence the labor supply curve by making work over \$10,000 less appealing due to the 50% tax. It might encourage more labor supply for those earning below \$10,000 as the guaranteed income may supplement low wages, hence these workers could afford to work less. The actual effect, however, will depend on the balance between income and substitution effects for different groups of workers.

Key concepts

Federal Income Taxes

Understanding how federal income taxes influence individual's financial decisions is crucial, particularly for workers. Taxes can substantially impact disposable income, which is the income available after taxes. When incomes below a certain threshold, such as \(\$10,000\) in our exercise, are exempt from federal income tax, workers get to keep all their earnings up to that amount. This can act as a significant incentive for work.

On the other hand, introducing a guaranteed income, like the \(\$5,000\) in the exercise, paired with a 50-percent tax rate on all earned income above \(\$10,000\) alters this dynamic. While the guaranteed income provides a safety net that may encourage labor force participation by offering some financial security, the high marginal tax rate could dissuade additional work effort beyond the tax-free threshold, as half of the additional income will be taken in taxes. This taxation design intertwines with the concept of a 'budget line' to visually represent these effects on work incentives.

Budget Line

The 'budget line' is a fundamental concept in economics, illustrating the trade-off between two goods, often representing consumption and leisure. In the context of labor and income, the budget line helps to illustrate how much leisure (time not worked) a person can 'afford' given their potential earnings from labor (work time).

Initially, without the government program, the budget line in our exercise is a straight line from 0 to \(\$20,000\), reflecting that every hour worked directly increases the worker's income. However, the introduction of unconditional income and a tax scheme changes its shape. The guaranteed \(\$5,000\) shifts the budget line upwards, meaning that workers start with this income even without working. The slope remains the same up to \(\$15,000\) because earnings up to \(\$10,000\) aren't taxed. Beyond this point, the slope halves, indicating the 50% tax on additional earnings. This budget line graphically depicts the shift in financial incentives and potential changes in work-leisure trade-offs.

Income and Substitution Effects

Economic choices surrounding labor stem from two pivotal concepts: the income effect and the substitution effect. The income effect relates to how changes in a person's income influence their work-leisure balance. An increase in income, such as the guaranteed \(\$5,000\) in our scenario, might allow individuals to work less and enjoy more leisure, since they can maintain the same standard of living with fewer hours worked.

The substitution effect, conversely, is about how changes in wages affect the relative value of leisure versus work. If the wage, after taxes, decreases as a result of a new tax policy, leisure becomes relatively cheaper. Workers might be discouraged from putting in extra hours as the 'cost' of their time rises—they 'substitute' leisure for work.

In the textbook example, the interplay between these two effects would shape the labor supply curve. While the income effect of the guaranteed \(\$5,000\) might encourage more leisure, the substitution effect of the 50% tax above the \(\$10,000\) threshold might lead to reduced hours worked. The overall impact on the labor supply curve would vary across different workers based on their preferences for income versus leisure.