## WAGE DIFFERENTIALS, PART 1

A. Suppose all workers have the same preferences represented by the utility function

U = W^(1/2) + S,

Where W is the wage rate and S is a measure of on the job safety. Suppose there are only two types of jobs in the economy: (1) a “safe” job (S=1) and a “dangerous” job (S=0). Let Ws be the wage rate in the “safe” job. Let WD be the wage rate in the “dangerous” job. If “safe” jobs pay $25 per hour, then what is the wage rate in the “dangerous” jobs? Demonstrate and explain. Is there a compensating wage differential? If so, how big is it? Demonstrate and explain. If not, explain why not. (8 points)

B. Now suppose worker preferences change to

U = W1/2 + 2S

Characterize what has happened to worker preferences. Suppose “safe” jobs still pay $25 per hour. What – if anything – becomes of the wage in “dangerous” jobs? Demonstrate and explain. What – if anything – becomes of the compensating wage differential? Demonstrate and explain (12 points)

WAGE DIFFERENTIALS, PART 2. (30 points in section)

Over a decade ago The Economist noted (“Pop, Crackle, Snap,” April 3, 2004). “Even desperate job seekers think twice about accepting hazardous work such as coal mining, cow slaughtering or cleaning up asbestos sites.” Suppose employers are able to provide different combinations of wages and job safety. Suppose individuals have different tastes for wages and safety.

Draw and identify the different worker’s indifferences curves for wages and safety. Explain which curve(s) represents which worker. (5 points)

Draw and identify the different firms isoprofit curves for wages and salary. Explain which curve(s) represents which firm. (5 points)

C. Given your answers in Parts A and B above, use suitable economic analysis to demonstrate whether or not people can be persuaded to do dangerous work. (10 points)

D. Aside from safety, what other factors that can result in equilibrium wage differentials? Explain how each factor can be expected to affect pay. (10 points)

LABOR MARKET DISCRIMINATION. (20 points in section)

A. Suppose there are two types of workers. Type A and Type B. Suppose the market wage for Type A workers is $20 while the wage for Type B workers is $16. Moreover, there are only 30 Type B persons in the labor pool, the rest of the labor supply consists of Type A persons. Furthermore, firms differ only with respect to their tendencies to be prejudiced about Type B workers. Suppose a firm sells output in a competitive market at a price of $4 per unit of output, recons it should produce 100 units of output, and faces the following production function:

Q = 5LA + 5LB

where Q is output, LA is the number of type A workers, and LB is the number of type B workers.

1. Are type A workers more productive than Type B workers? Demonstrate and explain (5 points)

2. Suppose Atlas Manufacturing Co seeks to minimize cost. How many workers of each type would it hire? Demonstrate and explain (5 points)

3. Suppose Ajax Enterprises exhibits a discrimination coefficient of 4. How many workers of each type would it hire? Demonstrate and explain (5 points)

4. Suppose Hidebound Industries exhibits a discrimination coefficient of 6. How many workers of each type would it hire? Demonstrate and explain. (5 points)

LABOR MARKET DISCRIMINATION? (30 points in section)

Suppose an employer cannot know your true productivity but can observe a “credential” that is correlated – imperfectly – with your productivity. Do you want the credential to be as informative as possible or “noisy”? Demonstrate and explain (10 points)

Suppose there are type types of workers, type 1 and type 2. Suppose schooling, S, and job experience, Exp, are factors that affect monthly pay, W. Specifically, suppose the earnings equation of type 1 and type 2 persons are given by:

W1 = 2,000 + 100S1 + 400 Exp1 & W2 = 1,900 +110S2 + 300Exp2

1. Show how much of any wage gap can be explained and how much of the gap may be due to discrimination.

2. Without doing any computations at all, can you tell if there is any pay discrimination going on? If so, who is favored? Demonstrate and explain.

3. Suppose type 1 workers average 10 years of schooling and type 2 workers average 15 years of schooling. Further, suppose type 1 workers average 20 years of job experience while type 2 workers average 10 years of job experience. Is most of the earnings gap due to discrimination or can most of it be explained? Demonstrate.