In
microeconomics
Microeconomics is a branch of mainstream economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics fo ...
, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting.
Search theory clarifies how buyers and sellers choose when to acknowledge a coordinating offer for a transaction. Search theory also provides an explanation for why frictional unemployment happens as people look for jobs and corporations look for new employees.
Search theory has been used primarily to explain labor market inefficiencies, but also for all forms of "buyers" and "sellers", whether products, homes or even spouses/partners. It can be applied. The clearing price will be met quickly as supply and demand react freely. However, this does not happen in the real world. Search theory tries to explain how.
Search theory has been applied in
labor economics to analyze
frictional unemployment resulting from
job hunting
Job hunting, job seeking, or job searching is the act of looking for employment, due to unemployment, underemployment, discontent with a current position, or a desire for a better position. The immediate goal of job seeking is usually to obtain ...
by workers. In
consumer theory
The theory of consumer choice is the branch of microeconomics that relates preferences to consumption expenditures and to consumer demand curves. It analyzes how consumers maximize the desirability of their consumption as measured by their pref ...
, it has been applied to analyze purchasing decisions. 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.
More precisely, search theory studies an individual's optimal
strategy
Strategy (from Greek στρατηγία ''stratēgia'', "art of troop leader; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the "art ...
when choosing from a series of potential opportunities of
random
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wikt:order, order and does not follow an intelligible pattern or combination. Ind ...
quality, under the assumption that delaying choice is costly. Search
models
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure.
Models c ...
illustrate how best to balance the cost of delay against the value of the
option to try again. Mathematically, search models are
optimal stopping
In mathematics, the theory of optimal stopping or early stopping
: (For French translation, secover storyin the July issue of ''Pour la Science'' (2009).) is concerned with the problem of choosing a time to take a particular action, in order to ...
problems.
Macroeconomists have extended search theory by studying
general equilibrium
In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an ov ...
models in which one or more types of searchers interact. These macroeconomic theories have been called '
matching theory', or 'search and matching theory.
Search from a known distribution
George J. Stigler
George Joseph Stigler (; January 17, 1911 – December 1, 1991) was an American economist. He was the 1982 laureate in Nobel Memorial Prize in Economic Sciences and is considered a key leader of the Chicago school of economics.
Early life and e ...
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
In mathematics, the theory of optimal stopping or early stopping
: (For French translation, secover storyin the July issue of ''Pour la Science'' (2009).) is concerned with the problem of choosing a time to take a particular action, in order to ...
, 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 Distribution may refer to:
Mathematics
*Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations
* Probability distribution, the probability of a particular value or value range of a vari ...
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
In labor economics, the reservation wage is the lowest wage rate at which a worker would be willing to accept a particular type of job. This wage is a theoretical representation of the hourly rate at which an individual values their own leisure ...
, 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
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more c ...
, 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 Wage differential is a term used in labour economics to analyze the relation between the wage rate and the unpleasantness, risk, or other undesirable attributes of a particular job. A compensating differential, which is also called a compensating w ...
between different types of jobs.
An interesting observation about McCall's model is that greater
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...
of offers may make the searcher better off, and prolong optimal search, even if he or she is
risk averse
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more c ...
. 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
In economics, a reservation (or reserve) price is a limit on the price of a good or a service. On the demand side, it is the highest price that a buyer is willing to pay; on the supply side, it is the lowest price a seller is willing to accept ...
.
Search from known distributions and heterogeneous costs
Opportunities might provide payoffs from different distributions. Costs of sampling may vary from an opportunity to another. As a result, some opportunities appear more profitable to sample than others. These problems are referred to as Pandora box problems introduced by
Martin Weitzman
Martin Lawrence Weitzman (April 1, 1942 – August 27, 2019) was an economist and a professor of economics at Harvard University. He was among the most influential economists in the world according to Research Papers in Economics (RePEc). His late ...
. Boxes have different opening costs. Pandora opens boxes, but will only enjoy the best opportunity. With
the payoff she discovered from the box
,
the cost she has paid to open it and
the set of boxes she has opened, Pandora receives
:
It can be proven Pandora associates to each box a reservation value. Her optimal strategy is to open the boxes by decreasing order of reservation value until the opened box that maximizes her payoff exceed highest reservation value of the remaining boxes. This strategy is referred as the Pandora's rule.
In fact, the Pandora's rule remains the optimal sampling strategy for complex payoff functions. Wojciech Olszewski and
Richard Weber show that Pandora's rule is optimal if she maximizes
:
for
continuous, non-negative, non-decreasing, symmetric and submodular.
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
The law of one price (LOOP) states that in the absence of trade frictions (such as transport costs and tariffs), and under conditions of free competition and price flexibility (where no individual sellers or buyers have power to manipulate prices ...
. 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 trade-off 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).
Search 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
In probability theory and machine learning, the multi-armed bandit problem (sometimes called the ''K''- or ''N''-armed bandit problem) is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices ...
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. Optimal search strategies for an unknown distribution have been analyzed using ''allocation indices'' such as the
Gittins index The Gittins index is a measure of the reward that can be achieved through a given stochastic process with certain properties, namely: the process has an ultimate termination state and evolves with an option, at each intermediate state, of terminati ...
.
Matching theory
More recently, job search, and other types of search, have been incorporated into
macroeconomic model
A macroeconomic model is an analytical tool designed to describe the operation of the problems of economy of a country or a region. These models are usually designed to examine the comparative statics and dynamics of aggregate quantities such as ...
s, using a framework called 'matching theory'.
Peter A. Diamond
Peter Arthur Diamond (born , 1940) is an American economist known for his analysis of U.S. Social Security policy and his work as an advisor to the Advisory Council on Social Security in the late 1980s and 1990s. He was awarded the Nobel Memoria ...
,
Dale Mortensen
Dale Thomas Mortensen (February 2, 1939 – January 9, 2014) was an American economist and winner of the Nobel Memorial Prize in Economic Sciences.
Early life and education
Mortensen was born in Enterprise, Oregon. He received his BA in econom ...
, and
won the 2010
Nobel prize in economics
The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel ( sv, Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award administered ...
for their work on matching theory.
In models of matching in the labor market, two types of search interact. That is, 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, others are simplified by ignoring wage differences, and just imply that workers pass through an unemployment spell of random length before beginning work.
See also
*
Frictional unemployment
*
Information economics
Information economics or the economics of information is the branch of microeconomics that studies how information and information systems affect an economy and economic decisions.
One application considers information embodied in certain types o ...
*
Job hunting
Job hunting, job seeking, or job searching is the act of looking for employment, due to unemployment, underemployment, discontent with a current position, or a desire for a better position. The immediate goal of job seeking is usually to obtain ...
*
Labor economics
*
Optimal stopping
In mathematics, the theory of optimal stopping or early stopping
: (For French translation, secover storyin the July issue of ''Pour la Science'' (2009).) is concerned with the problem of choosing a time to take a particular action, in order to ...
*
Price dispersion
In economics, price dispersion is variation in prices across sellers of the same item, holding fixed the item's characteristics. Price dispersion can be viewed as a measure of trading frictions (or, tautologically, as a violation of the law of one ...
*
Real options analysis
Real options valuation, also often termed real options analysis,Adam Borison ( Stanford University)''Real Options Analysis: Where are the Emperor's Clothes?''
(ROV or ROA) applies option valuation techniques to capital budgeting decisions.Campb ...
*
Reservation wage
In labor economics, the reservation wage is the lowest wage rate at which a worker would be willing to accept a particular type of job. This wage is a theoretical representation of the hourly rate at which an individual values their own leisure ...
*
Search cost Search costs are a facet of transaction costs or switching costs and include all the costs associated with the searching activity conducted by a prospective seller and buyer in a market. Rational consumers will continue to search for a better produ ...
References
{{DEFAULTSORT:Search Theory
Labour economics
Microeconomic theories