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EC450 - Labor Economics

Problem Set 4

Instructions

Please fill out all answers to your best ability. You are allowed to col-laborate with up to 3 other students, if you do, please turn in your own assignment and list all members of the group on the top of the assignment. The problem set must be completed on a printed out copy and scanned as a single PDF file to be turned in on Canvas. If you don’t have access to a printer, you may complete your problem set digitally using adobe acrobat, LaTeX (if you want the LaTeX file for the assignments, email me), or on an iPad. Failure to follow the instructions will result in your grade being marked down by 50 percent.

Supplemental Readings

This problem set covers material from Chapters 8, 9, and 14 of Modern Labor Economics. For more related practice problems, please see the Review Questions and Problems sections of these chapters.

Hedonic Wage Theory

1. Suppose all workers have the same preferences represented by

where w is the wage and x is the proportion of the firm’s air that is composed of toxic pollutants. There are only two types of jobs in the economy, a clean job (x = 0) and a dirty job (x = 1). Let w0 be the wage paid by the clean job and w1 be the wage paid for doing the dirty job. If the clean job pays $16 per hour, what is the wage for dirty jobs? What is the compensating wage differential?

2. In the small town of Twisp, WA, people with experience in truck driv-ing have two different industries to choose from: first, they can work for a local logging company transporting lumber around the state. This job requires long hours with tough road conditions. The other option is to work for a local orchard that hires truck drivers to trans-port their crop to a distribution site out of town. Both jobs face the same demand curve by firms in town:

The labor supply curves differ between the two types of jobs due to the easier working conditions at the orchard company. Let LT represent the labor supply for the timber company and LO represent the labor supply for the orchard:

What is the compensating wage differential between the two jobs? (i.e. what is the ”price” workers charge the timber company for worse working conditions)

3. Recall the Deferred Acceptance Algorithm that we used to match workers to firms in class. For this example, suppose we’re looking at the free agent market for the National Basketball Association. The ”firms” in this context are the professional basketball teams and the ”workers” are the players.

Suppose that there are three highly sought after players (Lonzo Ball, Kyle Lowry, and Derrick Rose) and there are four teams (Miami Heat, New York Knicks, Orlando Magic, and Chicago Bulls) that are in the final running to sign either of them. Assume that the teams only have capacity to sign one of the players each (that means one team will miss out).

The preferences of the players are given by the following ta-ble:

The teams preferences over the players are given by the fol-lowing table:

Assuming that teams are the ”proposers” in this scenario, implement the DAA to find a stable match.

Education

4. Consider an individual that lives for two periods. In the first period, the individual will either work or go to school (but not both). In the second period, the individual will work regardless of what was done in the first period. If the individual foregoes schooling and decides to work, she will earn $1,000 in period 1 and $1,250 in period 2. If she decides to get an education in the first period, her wage in period 2 will be $2,850. The direct cost of schooling in period 1 is $500.

(a) If the individual’s discount rate is 10%, will she work or go to school in the first period (assuming her utility is solely a function of income)?

(b) Calculate her internal rate of return

5. The town of Quahog, RI has a population of 10,000 individuals that are entering the workforce. A recent survey of the area found that the income distribution for the town was described by the table below: 

Suppose that the best paying jobs in Quahog are at a company run by Mr. Pewterschmidt who believes a college degree serves as a signal for productivity. Anyone without a degree will get paid PV E1 = $1, 800, 000 while those without a degree get paid PV E2 = 2, 100, 000. The cost of education (e) is given by the following function:

Assume that the costs for education are higher per-year for those from lower income households than those from wealthier homes due to the need to take out student loans.

● Workers from the upper class have their tuition fully paid and don’t have to pay living expenses so the only costs they suffer are opportunity costs and the psychic costs of attending school:

● Workers from middle class homes don’t have to pay living ex-penses but still need to take out loans for tuition (and suffer the aforementioned opportunity and psychic costs):

● Last, workers from low income households need to take out enough loans to cover tuition and living expenses, in addition to working while going to school to help with living costs:

Given this information, how many people in Quahog will choose to get a college degree? In the context of this problem, do you see any issues with the use of education as a signal for ability?

Unemployment

6. In class, we went over the Stock-Flow Model of the labor market which emphasized the different flows between parts of the labor force. Sup-pose we’re looking at the fictional beach town of West Key City which has a working-age population of 5,000. There are 1,500 individuals not currently in the labor force (N = 1500). Assume that, over the course of a year, the following flows occur:

(a) Find the levels for employed workers, unemployed workers, and workers that aren’t in the labor force at the end of the year.

(b) What are the unemployment rates at the beginning of the year (u0) and at the end of the year (u1)?

(c) What are the labor force participation rates at the beginning of the year (l0) and at the end of the year (l1)?

(d) When comparing the changes to the unemployment and labor force participation rates, would you say this economy is better off or worse off than before? Explain your reasoning briefly.

7. Frictional unemployment arises naturally due to mobility costs. In class, we developed a model for job search where the odds of an in-dividual finding employment was determined by their relevant skills, the costs to searching for a job they face, and their reservation wage.

For this example, assume that firms pay their employees according to the skill level required for the position: w = 8k and where the range of skill levels across workers is k ∈ [1, 5].

(a) What is the range of possible wage offers in this market?

(b) Jasmine is currently unemployed and possesses a skill-level of k = 3. Assume she faces a constant marginal cost for job search given by c = 3. What is Jasmine’s reservation wage? rounding your answer to the nearest hundredth

(c) What is the probability that Jasmine will get hired?

(d) Now suppose that Jasmine underwent a training program to in-crease her skill-level to k = 4, however, she’s anxious about get-ting back into the labor market now, so her marginal cost for job search is c = 5. What is Jasmine’s new reservation wage? Is she more likely to get hired now?