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Suppose a firm hires workers from a large pool of

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Suppose a firm hires workers from a large pool of potential employees. Suppose further thatworkers come in two types, productive and unproductive, and that half the workers in thepopulation are of each type. Each productive worker hired by the firm will generate $80,000of revenue per year for the firm, while each unproductive worker will generate $40,000 ofrevenue per year for the firm.Each worker knows his own type. Also, each worker could choose not to work for thefirm, and instead generate an alternate income by being self-employed.Workers who aremore productive will get more value from being self-employed: suppose that each productiveworker could produce an income of $55,000 per year through self-employment, while eachunproductive worker could produce an income of $25,000 per year through self-employment.So if the firm could accurately determine the type of each job applicant, the situation wouldbe straightforward: the firm could oer a salary between $55,000 and $80,000 to each pro-ductive applicant, and a salary between $25,000 and $40,000 to each unproductive applicant,all job oers would be accepted, and both workers and the firm would benefit from each jobthat is taken at the firm.Unfortunately for the firm, it cannot reliably determine the type of each worker. So thefirm has to oer a uniform wage ofw, and simply hire workers who are willing to work atwagew.The firm is willing to oer a given wagewif and only if the average revenue itreceives from the workers it hires at this wage is at leastw.
716CHAPTER 22.MARKETS AND INFORMATIONEquilibria in the Labor Market.In our example, what wages can be oered, and whichworkers will be willing to work for the firm? The reasoning is very similar to the case of usedcars. We start by looking for a self-fulfilling expectations equilibrium. If the firm expects allworkers to be on the job market, then — since there are equal numbers of the two types ofworkers — its expected revenue per employee will be80,000 + 40,0002= 60,000,and hence it can oer a uniform wage of $60,000 per year.At this wage, both types ofworkers will be willing to accept the firm’s oers, and so the expectation will be confirmedby what happens — we have an equilibrium in which all workers are hired.By analogy with the used-car example, there is also another — less socially desirable —equilibrium. If the firm expects only unproductive workers to be on the job market, thenit expects to make only $40,000 per year per employee, and so this is the maximum wageit will oer.At this wage, only unproductive workers will be willing to accept jobs, andso again the firm’s expectations are confirmed. So there are two possible equilibria here —a high one and a low one, with dierent mixtures of workers in the applicant pool in thetwo equilibria.Essentially, the firm’sa priorilevel of confidence in the quality of its jobapplicants is self-fulfilling.

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Term
Spring
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Game Theory, Advanced material

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