Question

Suppose that for every hour you work, you can earn $10 before taxes. Furthermore, suppose that you can work up to 16 hours per day, 365 days per year. You pay an income tax of 10% on the first $5,000 earned annually, 20% on the next $10,000 earned annually, and 30% thereafter

Draw your annual budget constraint showing your before-tax income on the x- axis and after-tax income on the y-axis under the income tax schedule mentioned above. Clearly label the axes, slope(s), and any kink points in the budget constraint.

Answer 1

To draw an annual budget constraint under the provided income tax schedule, plot before-tax income on the x-axis and after-tax income on the y-axis of a graph. Calculate the kink points based on different tax rates and connect these points to represent the net income after taxes for each segment, with slopes changing as tax rates increase.

Step-by-step explanation:

The question involves drawing an annual budget constraint that accounts for different marginal tax rates based on an individual's before-tax income. To address the question:

1. Plot the before-tax income on the x-axis of a graph.
2. Plot the after-tax income on the y-axis of the graph.
3. Calculate the breakpoints for different tax brackets:
   
   At $10 per hour, working up to 16 hours a day for 365 days, the maximum before-tax income would be $58,400 (16 hours * 365 days * $10). The first $5,000 is taxed at 10%, so the first kink in the budget line is at $5,000, with after-tax income being $4,500.
   
   The next $10,000 is taxed at 20%, so the second kink is at $15,000 of before-tax income, with after-tax income at $4,500 + 0.8 * $10,000 = $12,500.
   
   Income above $15,000 will be taxed at 30%, decreasing the slope after this point.

1. Connect these points with straight lines. The slope of each line segment represents the net income after taxes for that segment. The slope becomes less steep as tax rates increase.

The changes in the slope of the budget constraint illustrate the impact of the progressive tax system on an individual's after-tax income.