Search From A Known Distribution
George J. Stigler proposed thinking of searching for bargains or jobs as an economically important problem. John J. McCall proposed a dynamic model of job search, based on the mathematical method of optimal stopping, on which much later work has been based. McCall's paper studied the problem of which job offers an unemployed worker should accept, and which reject, when the distribution of alternatives is known and constant, and the value of money is constant. Holding fixed job characteristics, he characterized the job search decision in terms of the reservation wage, that is, the lowest wage the worker is willing to accept. The worker's optimal strategy is simply to reject any wage offer lower than the reservation wage, and accept any wage offer higher than the reservation wage.
The reservation wage may change over time if some of the conditions assumed by McCall are not met. For example, a worker who fails to find a job might lose skills or face stigma, in which case the distribution of potential offers that worker might receive will get worse, the longer he or she is unemployed. In this case, the worker's optimal reservation wage will decline over time. Likewise, if the worker is risk averse, the reservation wage will decline over time if the worker gradually runs out of money while searching. The reservation wage would also differ for two jobs of different characteristics; that is, there will be a compensating differential between different types of jobs.
An interesting observation about McCall's model is that greater variance of offers may make the searcher better off, and prolong optimal search, even if he or she is risk averse. This is because when there is more variation in wage offers (holding fixed the mean), the searcher may want to wait longer (that is, set a higher reservation wage) in hopes of receiving an exceptionally high wage offer. The possibility of receiving some exceptionally low offers has less impact on the reservation wage, since bad offers can be turned down.
While McCall framed his theory in terms of the wage search decision of an unemployed worker, similar insights are applicable to a consumer's search for a low price. In that context, the highest price a consumer is willing to pay for a particular good is called the reservation price.
Read more about this topic: Search Theory
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