1. Chapter5 Compensating Wage Differentials
It’s just a job. Grass grows, birds fly, waves pound the sand. I beat people up.
—Muhammad Ali

2. 5.1 Introduction
The model of competitive labor markets implies that as long as workers or firms can freely enter and exit the marketplace, there will be a single wage in the economy if all jobs are alike and all workers are alike.

3. 5.1 Introduction
The labor market is not characterized by a single wage: workers differ and jobs differ.
Adam Smith proposed the idea that job characteristics influence labor market equilibrium.

4. 5.1 Introduction
Compensating wage differentials arise to compensate workers for nonwage characteristics of the job.
Workers have different preferences and firms offer different working conditions.

5. 5.1 Introduction
All jobs are not the same. Adam Smith in 1776 argued that compensating wage differentials arise to compensate workers for the nonwage characteristics of jobs. It is not the wage that is equated across jobs in a competitive market, but the “whole of the advantages and disadvantages” of the job.

6. 5.1 Introduction
Workers differ in their preferences for job characteristics and firms differ in the working conditions that they offer. The theory of compensating differentials tells a story of how workers and firms “match and mate” in the labor market.

7. 5.2 Workers’ and Firms’ Choice with Risky Jobs
E.g.
Employer X: NT.$100 per hour, clean, safe work conditions
Employer Y: NT.$100 per hour, dirty, noisy factory

8. 5.2 Workers’ and Firms’ Choice with Risky Jobs
→ Most workers would undoubtedly choose employer X.
If employer Y decides not to alter working conditions, it must pay wage above NT.$100 to be competitive in the labor market.

9. 5.2 Workers’ and Firms’ Choice with Risky Jobs
→ The extra wage it must pay to attract workers is called a compensating wage differential because the higher wage is paid to compensate workers for the undesirable working conditions.
After the wage rise of firm Y, if both firms could obtain the quantity and quality of works they wanted, the wage differential would be an equilibrium differential, in the sense that there be no forces causing the differential to change.

10. 5.3 The Compensating Wage Differential Serves Two Purposes
It serves a social need by giving people an incentive to voluntarily do dirty, dangerous, or unpleasant work or a financial penalty on employers offering unfavorable working conditions.

11. 5.3 The Compensating Wage Differential Serves Two Purposes
At an individual level, it serves as a reward to workers who accept unpleasant jobs by paying them more than comparable workers in more pleasant jobs. Those who opt for more pleasant conditions have to buy them by accepting lower pay.
→ Compensating wage differentials provide the key to the valuation of the nonpecuniary aspects of employment.

12. 5.4 The Compensating Wage Differential Theory is Based on Three Assumptions
Utility Maximization
Workers seek to maximize their utility, not their income. Compensating wage differentials will only arise if some people do not choose the highest-paying job offered, preferring instead a lower-paying but more pleasant job.
→ Wages do not equalize in this case. The net advantage – the overall utility from the pay and the psychic aspects of the job – tend to equalize for the marginal workers.

13. 5.4 The Compensating Wage Differential Theory is Based on Three Assumptions
Worker Information
Workers are aware of the job characteristics of potential importance to them.
→ Company offering a “bad” job with no compensating wage differential would have trouble recruiting or retaining workers, trouble that would eventually force it to raise its wage.
Note: Our predictions about compensating wage differentials hold only for job characteristics that workers know about.

14. 5.4 The Compensating Wage Differential Theory is Based on Three Assumptions
Workers Mobility
Workers have a range of job offers from which to choose. It is the act of choosing safe jobs over dangerous ones that forces employers offering dangerous work to raise wages.

15. 5.5 The Hedonic Wage Function
A wage theory based on the assumption of philosophical hedonism that workers strive to maximize utility.
To simplify our discussion, we shall analyze just one dimension –risk of injury on the job – and assume that the compensating wage differentials for every other dimension have already been established.
→ To obtain a complete understanding of the job selection process and the outcomes of that process, it is necessary to consider both the employer and employee sides of the market.

16. 5.51 Employee Considerations
Some combinations of wage rates and risk levels that would yield the same level of utility can be represented by indifference curve map. W
Risk U1 U2 U3
U2 slopes upward because risk of injury is a “bad” job
characteristics. i.e., if risk
increases, wage must rise if
utility is to be held constant.

17. 5.51 Indifference Curves for Three Types of WorkersUC UB UA
Wage
Probability of Injury
Different workers have different preferences for risk. Worker A is very risk-averse. Worker C does not mind risk very much at all. Worker B is between the two.

18. 5.52 Employer Considerations
Assumptions:
It is presumably costly to reduce the risk of injury facing employees.
Perfect competition → Firms operate at zero profits.
All other job characteristics are presumably given or already determined.
→ If a firm undertakes a program to reduce the risk of injury, it must reduce wages to remain competitive.

19. 5.52 Employer Considerations
Forces on the employer side of the market tent to cause low risk to be associated with low wages and high risk to be associated with high wages, holding other things constant.
→The employer trade-offs between wages and levels of injury risk can be graphed through the use of isoprofit curves , which show the various combinations of risk and wage level that yield a given level of profits.

20. 5.52 Isoprofit Curves
An isoprofit curve gives all the risk-wage combinations that yield the same profits. Because it is costly to produce safety, a firm offering risk level ρ* can make the workplace safer only if it reduces wages (while keeping profits constant), so that the isoprofit curve is upward sloping. Note: higher isoprofit curves yield lower profits. P R p1 p0
Wage
Probability of Injury r* Q

21. 5.52 Isoprofit Curves W
Risk M N
The concavity of isoprofit curves is a representation of our assumption that there are diminishing marginal returns to safety expenditures.
→ The cost of reducing risk
levels is reflected in the slope of the isoprofit curve.

22. 5.52 Isoprofit Curves W
Risk X Y X’ Y’
Employers differ in the ease (cost) with which they can eliminate hazards.
→ Firm X can reduce risk more cheaply than firm Y.

23. 5.53 The Matching of Employer and Employees
Graphing worker indifference curves and employer isoprofit curves together can show which workers choose which offers. W
Risk
WBY
WAX
RAX
RBY A1 B1 A2 B2 X X’ Y Y’
A’s choice: (WAX, RAX)
→ value safety higher
If A took B’s offer
→ A1 < A2
B’s choice: (WBY, RBY)

24. 5.53 The Matching of Employer and Employees
Since X can produce safety more cheaply than Y, X will be a low-risk producer who attracts employees, like A, who value safety highly. Y attracts people like B, who have a relatively strong preference for money wages and a relatively weak preference for safety.
Note:
The only offers of jobs to workers with a chance of being accepted lie along XR’Y’.
→ The curve XR’Y’ can be called an “offer curve”, because only along XR’Y’ will offers employers can afford to make be potentially acceptable to employees.

25. 5.53 The Matching of Employer and EmployeesW
Risk
Offer Curve
The more types of firms there are in a market, the smoother this offer curve will be. It will always slope upward because of our assumptions that risk is costly to reduce and that employees must be paid higher wages to keep their utility constant if risk is increased.

26. Hedonic Wage Theory
Workers maximize utility by choosing wage-risk combinations that offer them the greatest amount of utility.
Isoprofit curves are upward sloping because production of safety is costly.
Isoprofit curves are concave because production of safety is subject to the law of diminishing returns.
Hedonic wage functions reflect the relationship between wages and job characteristics.

27. The Hedonic Wage Function
Different firms have different isoprofit curves and different workers have different indifference curves. The labor market marries workers who dislike risk (such as worker A) with firms that find it easy to provide a safe environment (like firm X); and workers who do not mind risk very much (worker C) with firms that find it difficult to provide a safe environment (firm Z). The observed relationship between wages and job characteristics is called a hedonic wage function. UC UB UA
Wage
Probability of Injury pZ pY pX PC PB PA
Hedonic Wage Function

28. Major Insights Wages rise with risk, other things equal.
→ There will be compensating wage differentials for job characteristics that are viewed as undesirable by workers.
Workers with strong preferences for safety will tend to take jobs in firms where safety can be generated most cheaply.
→ Firms and workers offer and accept jobs in a fashion that makes the most of their strengths and preferences.

29. 5.6 Policy Application: How Much is a Life Worth?
Studies report a positive relationship between wages and work hazards.
The statistical value of life is the amount that workers are jointly willing to pay to reduce the likelihood that one of them will suffer a fatal injury in a given year on the job.
The empirical evidence is ambiguous on the estimates of the value of a life.

30. 5.6 Policy Application: How Much is a Life Worth?
Empirical Evidences
Many studies estimate the hedonic function relating wages and the probability of injury on the job. This literature typically estimates regressions of the form:
wi = γρi + other variables
Where wi gives the wage of worker i and ρi. gives the probability of injury on the worker’s job. The coefficientγgives the wage change associated with a one-unit increase in the probability of injury.

31. 5.6 Policy Application: How Much is a Life Worth?
Many empirical studies report a positive relationship between wages and hazardous or unsafe work conditions, regardless of how the hazard or the unsafe nature of the work environment is defined.

32. 5.6 Policy Application: How Much is a Life Worth?
Calculating the Value of Life
The correlations of the wages and the probability of injury on the job allow us to calculate the “value of life.”

33. 5.6 Policy Application: How Much is a Life Worth?
The data suggests that each of the workers in firm Y is willing to give up $5,000 per year to reduce the probability of fatal injury in their job by units. Put differently, the 1,000 workers employed in firm Y are willing to give up $5 million (or $5,000x 1,000 workers) to save the life of the one worker who will almost surely die in any given year. The workers in firm Y, therefore, value a life at $5 million.

34. 5.6 Policy Application: How Much is a Life Worth?
This calculation instead gives the amount that workers are jointly willing to pay to reduce the likelihood that one of them will suffer a fatal injury in any given year. It is the statistical value of a life.

35. Summary
The worker’s reservation price gives the wage increase that will persuade the worker to accept a job with an unpleasant characteristic, such as the risk of injury.
The worker will switch to a riskier job if the market-compensating wage differential exceeds the worker’s reservation prices.

36. Summary
Firms choose whether to offer a risky environment or a safe environment to their workers. Firms that offer a risky environment must pay higher wages; firms that offer a safe environment must invest in safety. The firm offers whichever environment is more profitable.

37. Summary
The market compensating wage differential is the dollar amount required to convince the
marginal worker (that is, the last worker hired) to move to the riskier job.
If a few workers enjoy working in jobs that have a high probability of injury and if these
types of jobs demand relatively few workers, the market wage differential will go the
"wrong" way. In other words, risky jobs will pay lower wages than safe Jobs.

38. Summary
There is a "marriage" of workers and firms in the labor market. Workers who dislike
particular job characteristics (such as the risk of injury) match with firms that do not
offer those characteristics; workers who like the characteristics match With firms that
provide them.
The value of life can be calculated from the correlation between the worker's wage and
the probability of fatal injury on the job.

39. Summary
Workers with high earnings potential are likely to earn more and to have more generous job benefits. This positive correlation generates an ability bias that makes it difficult to find evidence that fringe benefits generate compensating wage differentials.