Most questions will ask you to “explain” or “describe” your answer. Make sure to explain your reasoning and/or write down your derivation steps to be considered for full marks. Simply writing a numerical value as your answer is insufficient.
This assignment is worth 8 points in total.
- (4 points) Consider two firms, Firm A and B. A job has two attributes: wages (W) and fringe benefits (F). Assume that Firm A earns a predetermined sales revenue of $500 when it employs one worker and it costs the firm $50 per unit of fringe benefits. Therefore, the firm’s total cost can be expressed as TC
= W + 50F. Firm B’s predetermined sales revenue is $300 when employing one worker and the firm’s cost of providing one unit of fringe benefits is $20. Firm B’s total cost can be expressed as TC=W+20F. For simplicity, assume that each firm hires only one worker.
- (1 point) Draw the isoprofit schedule for both Firm A and B when both firms earn zero profits. Make sure to draw the two isoprofit schedules on the same graph (place W on the vertical axis and F on the horizontal axis). Graphically illustrate the employer’s offer curve.
- (3 points) Suppose there are three workers, David, Kate, and John with different preferences over wages and fringe benefits. Assume that their utility functions can be expressed as follows:
- David: U(W,F)=WF
- Kate: U(W,F) = min{W,20F}
- John: U(W,F) = W+ 30F
For each worker, do the following:
- Solve for the optimal (W*, F*).
- Explain which firm the worker would prefer to work at.
- Graphically illustrate how the optimum is found.
- (4 points total) Suppose Adam has just graduated from high school. For simplicity, assume that his working life consists of three periods. Adam faces the following three career options:
Option 1
Work for three periods. Each period, his salary is Y1.
Option 2
Attend community college in the first period and work during the next two periods. It costs Adam C1 in the first period to attend community college. Once he graduates, his salary is Y2 each period (for two periods).
Option 3
Attend university in the first two periods and work during the final third period. Attending university costs C2 each period. Upon graduation, Adam’s salary is Y3 in the third period.
Denote the market interest rate in each period as r.
- (1 point) Write down the net present value of earnings for each of the three career options. Your answer should be expressed in terms of r, Y1, Y2, Y3, C1, and C2.
b) (0.5 points) Suppose r=0, Y1=20,000, Y2=40,000, Y3=90,000, C1=5,000, and C2=10,000.
Which career option would Adam choose? Briefly explain.
c) Now, suppose the government decides to provide a subsidy b for university students. This lowers the per-period cost of attending university from C2 to C2-b. Suppose the government sets b=6,000. The remaining values for r, Y1, Y2, Y3, C1, and C2 are the same as in part (b).
c-1) (1 point) Express Adam’s net present value of earnings for Option 3 in terms of r, Y3, C2, and r. Furthermore, numerically calculate this value based on the parameter values given above.
c-2) (0.5 points) What is Adam’s optimal education choice given the government subsidy of b=6,000? Did the government subsidy alter Adam’s education choice compared to his optimal education choice in part (b)? Briefly explain.
c-3) (1 point) What is the minimum amount of government subsidy for Adam to choose Option 3? You must show your derivations.