Exercise Set 11
STEWART'S LABOR SUPPLY

Consider Mr. Jon Stewart's utility maximization problem. Mr. Stewart consumes two goods - apples (C) and leisure hours (R). The price of an apple is denoted by p, and the wage rate by w. All of Mr. Stewart's labor income is spent on apples. Mr. Stewart's utility function is: u(C,R) = 3CR2.

Note: R + L = 24, where L is the number of hours worked in a day.

  1. Write down Stewart's budget constraint.
  2. Sketch the budget constraint. Indicate the intercepts and slope.
  3. Set up Stewart's utility maximization problem formally.
  4. Use the FOC to determine L*, the optimal number of hours (in a day) that Stewart will work.
  5. Do the SOCs correspond to a maximum? Explain.
  6. Provide a sketch of the indifference curves in the earlier graph. Indicate the optimal amount of hours worked and the hours devoted to leisure.
  7. In a typical case, the amount of labor supplied increases with wage. Do you observe this result here?
  8. What is the effect of an increase in p on L* and R*?
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