Search theory

In economics, search theory (or just search) is the study of an individual's optimal strategy when choosing from a series of potential opportunities of random quality, given that delaying choice is costly. Search models illustrate how best to balance the cost of delay against the value of the option to try again.

The two most common settings for these models (and their empirical applications) are a worker's search for a job, in labor economics, and a consumer's search for a product they wish to purchase, in consumer theory. From a worker's perspective, an acceptable job would be one that pays a high wage, one that offers desirable benefits, and/or one that offers pleasant and safe working conditions. From a consumer's perspective, a product worth purchasing would have sufficiently high quality, and be offered at a sufficiently low price. In both cases, whether a given job or product is acceptable depends on the searcher's beliefs about the alternatives available in the market.

earch from a known distribution

George J. Stigler proposed thinking of searching for bargains or jobs as an economically important problem, [Stigler, George J. (1961), 'The economics of information'. Journal of Political Economy 69 (3), pp. 213-25.] [Stigler, George J. (1962), 'Information in the labor market'. Journal of Political Economy 70 (5), Part 2, pp. 94-105.] but the problem was first solved mathematically by John J. McCall. 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. [McCall, John J. (1970), 'Economics of information and job search'. Quarterly Journal of Economics 84, pp. 113-126.] 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. [Danforth, John P. (1979), 'On the role of consumption and decreasing absolute risk aversion in the theory of job search'. In S.A. Lippman and J.J. McCall, eds., "Studies in the Economics of Search". New York: North-Holland, ISBN 0444852220.] 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.

earch from an unknown distribution

When the searcher does not even know the distribution of offers, then there is an additional motive for search: by searching longer, more is learned about the range of offers available. Search from one or more unknown distributions is called a multi-armed bandit problem. The name comes from the slang term 'one-armed bandit' for a casino slot machine, and refers to the case in which the only way to learn about the distribution of rewards from a given slot machine is by actually playing that machine.

Endogenizing the price distribution

Studying optimal search from a given distribution of prices led economists to ask why the same good should ever be sold, in equilibrium, at more than one price. After all, this is by definition a violation of the law of one price. However, when buyers do not have perfect information about where to find the lowest price (that is, whenever search is necessary), not all sellers may wish to offer the same price, because there is a tradeoff between the frequency and the profitability of their sales. That is, firms may be indifferent between posting a high price (thus selling infrequently, only to those consumers with the highest reservation prices) and a low price (at which they will sell more often, because it will fall below the reservation price of more consumers). [Butters, G.R. (1977), 'Equilibrium distributions of sales and advertising prices'. Review of Economic Studies 44, pp. 465-91.] , [Burdett, Kenneth, and Kenneth Judd (1983), 'Equilibrium price dispersion'. Econometrica 51 (4), pp. 955-69.]

Matching theory

More recently, especially since the 1990s, many economists have been working on integrating job search into models of the macroeconomy, using a framework called 'matching theory' originally developed by Dale Mortensen and extended by Peter A. Diamond and Christopher A. Pissarides. In this framework, the rate at which new jobs are formed is assumed to depend both on workers' search decisions, and on firms' decisions to open job vacancies. While some matching models include a distribution of different wages, [Mortensen, Dale, and Christopher Pissarides (1994), 'Job creation and job destruction in the theory of unemployment'. Review of Economic Studies 61 (3), pp. 397-415.] others are simplified by ignoring wage differences. The simplified versions of the model focus instead on the main reduced form implication of search: namely, the fact that optimal job search takes time, so that workers are likely to pass through a spell of unemployment before beginning work. [Pissarides, Christopher (2000), "Equilibrium Unemployment Theory", 2nd ed. MIT Press, ISBN 0262161877.]

ee also

*Optimal stopping
*Job hunting
*Reservation wage
*Frictional unemployment
*Price dispersion
*Information economics
*Labor economics
*Real options analysis
*Search cost

References