THE WORKER ‘S SUPPLY TO RISKY JOB Jobs differ in many charateristics which can give rise to conpensating wage differentials Adam smith, in fact, listed five such situations The five following are the[.]
THE WORKER ‘S SUPPLY TO RISKY JOB Jobs differ in many charateristics which can give rise to conpensating wage differentials Adam smith, in fact, listed five such situations The five following are the pricipal circumstances which, so far as i have been able to obserse, make up for a small pecuniary gain in some employments, and counter balance a great one in others: first, the agreeableness or disagreeableness of the employments themselves, secondly, the easiness and cheapness, or the difficultly and expence of learning them, thirdly, the constancy or inconstancy of employment in them, 4, the small or great trust which must be reposed in those who exercise them, and 5, the probability or improbability of sucess in them We begin by analyzing how compensating wage differenticals arise in the context of a very simple (and policy relevant ) example Suppose that jobs differ in only one characteristic: the probability that the worker will get mured while on the job We assume that the worker’s unility depends both on the wage (w) and on the probability that she will get injured on the job (p), and write the worker’s utilitic function as: 6.1 The marginal utility of income and the marginal utility of risk are defined as: 6.2 The marginal utility of income (MU) gives the change in utility resulting from a increase in the worker’s income, holding constant the risk on the job We assume that workers prefer highter wages, so that the marginal utinity resulting from a one unity change in the probanbility of injury, holding constant the worker’s income We assume innitially that risk is a bad, so that the marginal utility of risk is negative Some wokers may enjoy being exposted to the risk of injury (and the marginal utinity of risk is postive of these workers) We will ignore the existence of these “risk- lovers” until later in the discussion To simplity the discussion, we cosider initially a labor market where there are only two types of jobs Some jobs offer a completely safe inviroment., and the propability od injury in these jobs p is equal to Other jobs offers an inheretly riskly enviroment, and the probility of injury in those jobs is equal to one We will assume that the workers has complete information about the risk level assotucular job This assumption is extremely important because some risks may not be detectable for many years For instance, prior to the 1960s , asbestos products were regularly used to insulate buildings Few persons knew that continuous exposure to asbestos had adverse effects on health (in fact, it took a long time for the scientific evidence on the relationship between as bestos fibers and a host of health problems to becom widely known) We will discuss below how our analysis affectde if the worker is unaware of the true health riskers that she is being exposed to Suppose the “safe job” (that is job where wokers not get injured) offers a wage rare of wo Figure 6.1 illustrtes the worker’s indifference curve (Uo) that goes throught the point summarizing the “empoyment package” offered by the safe job At P the worker gets a wage of w0 and has a probability of in jury The indifferentce curve that describe a workes;s choises between income and risk of injured are upward sloping because risk is a bad Suppose that the worker is currently at P in the indiffence curve The only way to persuade the wokers to move to a riskers job and her wage declined, she would obvioussly be worse off The curvature of the difference curve refects the usual assumption that indiffrentce curves are convex THE RESERVATION PRICE It turn out that the slope of the indifference curve Uo provides a great deal of infomation about how much workers dislike being injured The worker in out analysis is obviously indifference between the job offer made by the safe firm at P and a potential job offer made by the risky firm at Q, where the risky firm offers her a wage of w1 and exposes her to a probability of injury equal to (so that she will surely get injured on this job) We define the worker’s reservation price as: 6.3 If the worker in come were in cereate by b as she swiched from the safe job to the risky job, she would be indifference about being exposed to the addtional risk The reservation price, there fore, is the worker’s answer to the age old questions of “How much would is take for u to smt that u would rather not do?” Is should be clear that if the worker dislikes risk, her indifference curve, would be very steep and the reservation price b would be very high If the worker does not mind being injured “too much” the indifference curve Uo would be flat and the reservation price would be low Supposre the safe job pays the market determined waged of Wo and risky job pays the market wage of W1 As usual, we assume that the woker has no influene over the wages that are paid by the various jobs Because we have assumed that all workers dislike risk, is follows that w1>w0 , so that risky jobs pay a higher wage than safe job If risky job were to pay less that safe job,a firm that offers a risky work enviroment would not attract any workers, is must offer a compensating wage differential The market compensating wage differential set If she accepts w1-wo SUMARY The worker’s reservation price gives the wage inceare that will persuade the worker to accept a job with an unpleasant characteristic, such as the risk of injury The worker will swith to the riskers job if the market compensating wage differential exceeds the worker’s reservation price Firms choose wherther to offer a risky enviroment or a safe enviroment to their workers Firms that offer a risky enviroment must pay higher wages, firms that offer a safe enviroment must invest in safety The firm offers whichever enviroment is more profitable 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 risker job If a few workers enjoy working in jobs that have a hight probability of injury and if these types of jobs demand relatively few wokers, the market wage differentstial will go the “wrong” way In other workers, risker jobs., risker jobs will pay lower wages than safe jobs There is a “marriage” of workers and firm in the labor maker Workers who dislike particular job characteristics (such as the risk of injury) match with firms that not offer those characteristics, workers who like the characteritics match with firms that provide them