A person chooses between leisure and consumption. The utility derived from any combination of leisure and
consumption is given by the formula:
u = LC - 88C
where u is utility, L is the number of leisure hours per week, and C is the number of dollars spent on consumption per week. This person can work as many hours as desired each week, at a wage of $4 per hour. There is no other source of income.
- Using graph paper or a computer, draw a graph showing indifference curves for u = 6000, u = 6400, and u = 6800.
Measure the marginal rate of substitution (MRS) at some of the points on these indifference curves.
- Draw the budget line on your graph. Pick any three points on the budget line and measure the MRS at these
points.
- By trial and error (or by other means) find the utility maximizing combination of consumption and leisure. (Hint:
Starting from your answers to part (b) try to find a sequence of points which give increasing utility, guess where this
sequence will lead, and verify that your guess is at least approximately correct.)
- Suppose the wage increases to $8 per hour. Would this person choose to supply more labor at $8 than at $4?
- Now, instead of an increase in the straight-time wage, suppose overtime is offered at $8 per hour after
working 40 hours at $4 per hour. Will this person accept the overtime, and, if so, for how many hours?
A worker chooses to work X hours per week, at a wage of $9 per hour. An overtime rate of $12 per hour is then
offered, for hours in excess of 40; in this situation, the worker chooses to work Y hours per week. Finally, the $12
wage is offered for all hours worked, and the worker chooses to work Z hours per week. What can be said about the
relationship between X, Y and Z (for example, is Y greater than Z)? Explain your answer in terms of income and
substitution effects.
Borjas text, Problem 2-9.
(Among single, college-educated women aged 22 – 25, average annual hours worked is 2,160 and the average wage is $22.50. If the average wage increases to $25 per hour, average annual hours worked increases to 2,340. What is the elasticity of labor supply for this group of workers? )