Compensating Wage Differentials 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.

All jobs are not the same 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. 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.

各行業受雇員工每人每月平均薪資 資料來源:行政院主計處

1. 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 → 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. → 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.

* 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. 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. Note: The predicted outcome of the compensating wage differential theory of job choice is not that employees working under “bad” conditions receive more than those working in “good” conditions. The prediction is that, holding worker characteristics constant, employees in bad jobs receive higher wages than those working under more pleasant conditions.

* 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.

2. 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. 3. 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.

2. 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.

(1) 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. 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. W U3 U2 U1 Risk

People differ in their aversion to the risk of being injured. Those who are very sensitive to this risk will require large wage increases for any increase in risk (UH), while those who are less sensitive will require smaller wage increases to hold utility constant (UL). Highly Averse to Risk W Moderately Averse to Risk UL UH Risk

(2) 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.

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.

→ The cost of reducing risk W 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. M N Risk

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

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

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.

W 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. Risk

* 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.

3. 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. 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.

2. 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.” Example: Firm Probability of Fatal Injury Annual Earnings X ρx wx Y ρx + .001 wx+ $5,000

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 0.001 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. 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.