Economics 450 - Assignment 1
Q1. 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.
a. 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.
b. Draw the budget line on your graph. Pick any three points on the budget line and measure the MRS at these points.
c. 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.)
d. Suppose the wage increases to $8 per hour. Would this person choose to supply more labor at $8 than at $4?
e. 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?
Q2. 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.
Q3. 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?