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.

The government changes the tax scheme in a few ways. First, now only the first $100 of income is tax-exempt. That is, for the first 5 hours she works, Tamara's net wage rate is $20 per hour. Second, the government reduces the tax rate on all other income to 50%. That is, for all hours above the first 5 hours, Tamara's net wage rate is now $10. After these changes, Tamara finds herself just as well off as before so that her new optimal choice is on the same indifference curve as her initial optimal choice.

Draw Tamara's new time allocation budget line on the same diagram as her initial time allocation budget, with income on the vertical axis. Also illustrate her optimal choice. Bear in mind that she is equally as well off (on the same indifference curve) as before the tax changes occurred. Choose the correct statement.

A. At her new optimal choice, Tamara consumes less leisure and has more income.

B. At her new optimal choice, Tamara consumes less leisure and has less income.

C. At her new optimal choice, Tamara consumes more leisure.

D. At her new optimal choice, Tamara consumes the same amount of leisure.

Answer 1

The maximum number of hours that Tamara can work = 80 hours. Given the first pay structure , for the first 20 hours, she earns 20*$20 = $400.

Therefore labour hours left is (80-20=) 60 hours.

The per hour wage rate is $5/hour for these 60 hours. Therefore maximum possible income by working these 6- hours = $5*60 = $300.

Therefore maximum possible income by working 80 hours full = $400+$300 = $700.

Similarly, when Tamara works 0 hours, she earns $0. This line joining the points $700 and 80 hours represents the time allocation budget line for Tamara (Labelled as AB). This has been plotted in Fig 1 on the vertical axis against leisure hours on the horizontal axis. On the same horizontal axis, Labour is read from right to left where Labour hours = (80- leisure hours). It is clear from the figure that when Tamara works for 80 labour hours, her Leisure hours is 0 and corresponding to those 0 leisure hours, her income is $700. Similarly, when she works for 0 hours, her leisure hours is 80 hours and her income corresponding to 80 leisure hours (and 0 labour hours) is $0.

It is given that she chooses to work for 30 hours, Therefore she earns ($20*20) + ($5*10) = $450. Her indifference curve which is downward sloping and convex, is tangent to AB at point T where her leisure hours = 50 and labour hours = 30, with an income of $450.

When the payment scheme changes, Tamara earns $100 @ $20/hour for the first 5 hours. Therefore labour hours left = 80-5 = 75 hours. The new per hour wage rate is $10/hour. Therefore maximum possible income by working for 75 more hours = $750.

Therefore, maximum possible income under the new income scheme by working 80 full hours = $100 + $750 = $850.This $850 on the vertical axis corresponds to 0 hours of leisure and 80 hours of labour on the horizontal axis. Here too, if Tamara works for 0 hours and enjoys 80 hours of leisre, she earns $0.

Therefore, the new time allocation budget line rotates to the right from AB to A’B. There is no change in point B because working for 0 hours still fetches $0 worth of income.

It is also mentioned that ‘Tamara finds herself just as well off as before so that her new optimal choice is on the same indifference curve as her initial optimal choice’.

When the IC is tangent to the budget line, the slope of the IC and the slope of the budget line become equal.

To make her lie on the same indifference curve (IC), yet equate the same IC with the new slope of the new time allocation budget line, an imaginary time allocation budget line is drawn in green, parallel to line A’B. This dotted line has the same slope as the new time allocation budget line (being parallel to it). The same IC is tangent to the dotted line at point T’ where it is clear that she enjoys less hours of leisure than the previously enjoyed 50 hours and earns higher income. That is, at point T’, Tamara’s labour hours exceed the labour hours at point T. Her Leisure hours at T’ is less than the leisure hours at T. Her income at T’ is greater than her income at T.

The correct statement is: A. At her new optimal choice, Tamara consumes less leisure and has more income.