Question

Tamara has 80 hours per week that she can allocate to work or leisure. Her job pays a wage rate of $20 per hour, but Tamara is being taxed on her income in the following way. On the first $400 that Tamara makes, she pays no tax. That is, for the first 20 hours she works, her net wage (what she takes home after taxes) is $20 per hour. On all income above $400, Tamara pays a 75% tax. That is, for all hours above the first 20 hours, her net wage rate is only $5 per hour. Tamara decides to work 30 hours. Her indifference curves have the usual shape. Draw Tamara's time allocation budget line for a typical week, with income on the vertical axis. Also illustrate the indifference curve at her optimal choice.

Based on your drawing, choose the correct statement.

A. The opportunity cost of leisure increases after she works the first 20 hours.

B. The opportunity cost of leisure decreases after she works the first 20 hours.

C. The opportunity cost of leisure does not change after she works the first 20 hours.

Answer 1

The leisure is depicted on the x-axis and the income on the y-axis.

If Tamara works for 80 hours, her income would be $700. For the first 20 hours, she gets $20, thus income $400. For the next 60 hours, she gets $5 her income $300. Thus total Income is $700. This gives us the vertical intercept at point A.

Point C depicts situation when she does not work and thus earns no income.

There is a kink in the budget of Tamara when leisure is 60 hours or labor is 20 hours. This kink implies the application of tax after working 20 hours. Thus after point B, the budget line becomes flatter.

Tamara is at equilibrium where the indifference curve is tangent to the budget line at point E, where she worked for 30 hours and enjoys the leisure of 50hours.

The opportunity cost of leisure decreases after she works the first 20 hours. We know the opportunity cost of leisure is nothing but the wage rate. Thus after 20 hours the after-tax wage rate decline from $20 to $5.