19.1 PROBLEMS

Question 19.1

Leandro has 16 hours per day that he can allocate to work or leisure. His job pays a wage rate of $20. Leandro decides to consume 8 hours of leisure. His indifference curves have the usual shape: they slope downward, they do not cross, and they have the characteristic convex shape.

  1. Draw Leandro’s time allocation budget line for a typical day. Then illustrate the indifference curve at his optimal choice.

    Now Leandro’s wage rate falls to $10.

  2. Draw Leandro’s new budget line.

  3. Suppose that Leandro now works only 4 hours as a result of his reduced wage rate. Illustrate the indifference curve at his new optimal choice.

  4. Leandro’s decision to work less as the wage rate falls is the result of a substitution effect and an income effect. In your diagram, show the income effect and the substitution effect from this reduced wage rate. Which effect is stronger?

Question 19.2

Florence is a highly paid fashion consultant who earns $100 per hour. She has 16 hours per day that she can allocate to work or leisure, and she decides to work for 12 hours.

  1. Draw Florence’s time allocation budget line for a typical day, and illustrate the indifference curve at her optimal choice.

    One of Florence’s clients is featured on the front page of Vague, an influential fashion magazine. As a result, Florence’s consulting fee now rises to $500 per hour. Florence decides to work only 10 hours per day.

  2. Draw Florence’s new time allocation budget line, and illustrate the indifference curve at her optimal choice.

  3. In your diagram, show the income effect and the substitution effect from this increase in the wage rate. Which effect is stronger?

Question 19.3

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.

  1. Draw Tamara’s time allocation budget line for a typical week. Also illustrate the indifference curve at her optimal choice.

    The government changes the tax scheme. 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. But 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 exactly equally as well off as before. That is, her new optimal choice is on the same indifference curve as her initial optimal choice.

  2. Draw Tamara’s new time allocation budget line on the same diagram. 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.

  3. Will Tamara work more or less than before the changes to the tax scheme? Why?