Compensating Wage Differentials and Increased Worker Safety: Why would any worker choose to work in a profession (like coal mining) that is risky for the worker’s health and safety? The answer is that such jobs tend to pay more than other jobs which require similar skill levels. The difference in wages between such “safe” jobs and risky jobs is what labor economists call a compensating wage differential. In the following exercise, suppose that it takes similar skills to work in coal mines as it does to work on oil rigs —and that workers in industries other than these two cannot easily switch to these industries.

A. Suppose that initially the wages in coal mines and oil rigs are the same.

(a) Illustrate demand and supply in the labor markets for oil workers and coal miners in two separate graphs. What does the fact that wages are identical in the two sectors tell you about the level of risk a worker takes on by working in coal mining relative to the level of risk he takes on by working on oil rigs?

(b) Suppose a new mining technology has just been invented—a technology that makes working in coal mines considerably safer than it was before. (For simplicity, suppose it is essentially costless to coalmining firms to put this technology in place.) What will happen to the supply of workers in the oil industry — and what will happen to the supply of workers in the coal industry?

(c) What happens to wages in the two industries? How does this relate to the idea of compensating wage differentials?

(d) Are workers in either industry better off?

(e) Suppose next that the oil industry if very large compared to the coal industry—so large that the change in wages in the oil industry is imperceptibly small. Are any workers better off as a result of the safety innovation in coal mines?

(f) In the case of the very large oil industry (relative to the coal industry), are any producers better off?

(g) True or False: The more competitive the labor market is across industries, the greater is the incentive for a producer in a competitive industry to find ways of improving employment safety conditions.

B. Suppose all workers’ annual utility can be given by the function u(s,w) = (αs−ρ+(1−α)w−ρ)−1/ρ where s is a work safety index that ranges from 0 to 10 (with 0 the least safe and 10 the most safe) and w is the annual wage denominated in tens of thousands of dollars.

(a) Suppose that workers of the skill type of coal miners are currently getting utility u∗ in all sectors of the economy in which they are employed. Determine the relationship of the current wages offered to such workers in the economy as it relates to safety conditions—i.e. find w(s) (which will itself be a function of u∗, α and ρ).

(b) Suppose that α = 0.5 and ρ = 0.5, and suppose that workers in the coal mining and in the oil rigging industries currently face safety conditions 5 and earn an annual wage (in tens of thousands) of 8. What level of utility u∗ do workers like coal miners achieve in the economy?

(c) Suppose that school teachers — who face safety of 10 — could equally well have chosen to become coal miners. What is their wage? How much of the coal miners’ salary is therefore equilibrium compensation for the risk they face?

(d) Suppose that safety conditions in coalmines improve—to a safety index level of 6. Assuming the coal industry employs a small fraction of workers of this skill type, what will be the new equilibrium wage for coal miners? Are they better or worse off?

(e) Next, construct a table that shows how compensating wage differentials vary with the elasticity of substitution of safety for wage. Let the first column of your table give ρ and let the next 4 columns give u∗, the wage of workers on oil rigs, the wage of workers in coal mines (after the safety improvements have been made) and the wage of teachers—all in tens of thousands of dollars. (Continue to assume α = 0.5 and an initial annual wage of 8 in the coal and oil rigging industries (before the safety improvements in coal mining).) Fill in the table for the following values of ρ: -0.99, 0.01, 0.5, 5, 10.

(f) Interpret the results in your table. 741 Prices and Distortions across Markets