Question

1.Currently, individuals can work up to 80 hours each week at a pre-tax wage of $20 per hour, but they face a constant 20% payroll tax, which reduces their after tax wage to $16 per hour. The government is considering imposing a negative income tax. Under this tax policy, everyone is given $300 each week, and everyone and anyone can supplement her income further by working. To pay for the negative income tax, the payroll tax rate will be increased to 50%.

a. Using the leisure-consumption model, draw the budget constraints faced by workers before and after the proposed negative income tax. Label the original constraint BL0and the post-policy constraint BL1. Make sure to label axes, intercepts, and intersection points.

b.True/False/Uncertain: A worker who maximizes utility by working 40 hours before the negative income tax is implemented will reduce her number of hours worked after the negative income tax is implemented. Support your response using both graphical and theoretical analysis. You may show your graphical analysis in your diagram in part A. You may assume the worker’s indifference curves have the typical shape.

Answer 1

a. Prior to the imposition of negative income tax, the budget constraint will be:

All work, no leisure: C (consumption) = $16*80 = $1280, and H (leisure hours) = 0

All leisure, no work C = 0, H = 80

After the negative income tax is imposed the budget constraint changes as follows:

All work, no leisure: C = $300+$10*80 = $1100, and H = 0

All leisure, no work C= $300, H=80

We can plot these below. Blue one is pre negative tax, and orange post negative tax

The two meet at 800,30, i.e., C=$800 and H=30, i.e., working for 50 hours gives the same income in both the situations

$16*50

$300+$10*50

b. We need to plot two indifference curves to check where this person will be before and after the negative tax. Blue IC is pre-negative tax and orange one is post-negative tax

Blue IC meets blue budget line at C=$640 and H=40

Orange IC meets orange budget line at C still close to $640 and H>40, since this person is able to generate $640 of income by working only 34 hours ($300+$10*34), she can reduce her working hours from the earlier 40, and still be at a higher IC (same income and more leisure hours)