In mathematics, optimization refers to the general ideas of choosing some element of a set to maximize a function that is defined on the set. Abstractly, if one defines a function f (which is typically indexed by some set of parameters θ) from some general set S to the real numbers S, the function y = f ( s, θ); optimization is typically nothing more than asking which element of S produces the largest value of y. Notice that the set can contain complicated objects, including infinite sequences, or functions.
In economics, the notion of optimization has been used to model individual behavior. Indeed, neoclassical economic reasoning is typically predicated on the assumption that individual actors optimize in the sense that, subject to a set of constraints and beliefs about the consequences of their actions, agents choose actions that are optimal relative to their preferences. In a classic microeconomics problem, a consumer is assumed to choose a bundle of consumption goods to maximize utility subject to a budget constraint. This problem produces a relationship between relative prices and the marginal utilities of different goods. A more complicated version of this problem can ask what consumption/saving rules maximize a lifetime notion of utility in the presence of uncertainty about the future (cf. Brock and Mirman 1972). Under appropriate convexity assumptions, this type of stochastic growth model can be used to represent intertemporal general equilibrium in an economy with a representative consumer by the device of support prices constructed from the optimization problem. This approach has been fruitful in macroeconomics.
The notion that individual agents optimize is controversial from the perspectives of other social sciences. A gross simplification of this controversy is that sociologists focus much more on how social structures influence individual preferences and beliefs whereas psychologists emphasize empirically based descriptions of individual decisionmaking which can incorporate cognitive errors and limitations in the processing of information as well as what, from the perspective of the neoclassical economic theory of choice, are inconsistencies in preferences.
These alternative perspectives have become part of current economic reasoning. Herbert Simon was an early pioneer of work on bounded rationality, which emphasized limits to the ability of individuals to optimize. Simon advocated the alternative idea that individuals satisfice, that is, make acceptable rather than optimal actions. Simon’s views did not affect most economic practice. Rather, experimental research pioneered to a great extent by psychologists Amos Tversky and Daniel Kahneman created a strong case that the standard optimization assumptions in economics were flawed for many contexts. There is a rich literature that attempts to both empirically identify (again, via experiments) and formally model individual decisionmaking that accounts for limits to human reasoning in economically interesting environments. Efforts also exist to expand the formulation of preferences to account for social context and social preferences such as altruism, although this work seems less a challenge to the notion of optimization than a reconsideration of the objectives of individuals. Together, this work is known as behavioral economics.
An alternative approach to relaxing the standard optimization paradigm is to ask whether, in dynamic environments, individual behavior will evolve toward optimality. This question, which is a major theme of evolutionary game theory, does not admit a simple answer, as different models produce different results. But interesting environments have been identified where this convergence does occur.
Perhaps the appropriate lesson is that the appropriateness of optimization assumptions depends on contexts. For example, the empirically well established absence of arbitrage opportunities in financial markets suggests in modeling individual traders, they are optimizing to the extent that for the market as a whole, all such possibilities are eliminated. Also one should not underestimate the capacity of optimization models to explain seemingly irrational behaviors, as demonstrated by the Gary Becker and Kevin Murphy (1988) model of rational addiction. Efforts to move economic models away from optimization assumptions have yielded many valuable insights, but it is hardly the case that the optimization paradigm no longer has a key role to play in economic analysis.
A user-friendly introduction to mathematical methods of optimization relevant to economists is Rangarajan Sundaharam’s book A First Course in Optimization Theory (1996). Herbert Simon’s views are well summarized in his Reason in Human Affairs (1983). Colin Camerer’s Behavioral Game Theory (2003) provides an overview of behavioral approaches to economics. Drew Fudenberg and David Levine’s The Theory of Learning in Games (1998) is a standard text on learning and dynamics.
SEE ALSO Decisionmaking; Economic Model; Evolutionary Games; Maximization; Minimization; Partial Equilibrium; Satisficing Behavior; Theory of Second Best
Becker, Gary, and Kevin Murphy. 1988. A Theory of Rational Addiction. Journal of Political Economy 96: 675–700.
Brock, William, and Leonard Mirman. 1972. Optimal Economic Growth and Uncertainty: The Discounted Case. Journal of Economic Theory 4: 479–513.
Camerer, Colin. 2003. Behavioral Game Theory: Experiments in Strategic Interaction. Princeton, NJ: Princeton University Press.
Fudenberg, Drew, and David Levine. 1998. The Theory of Learning in Games. Cambridge: MIT Press.
Simon, Herbert. 1983. Reason in Human Affairs. Stanford, CA: Stanford University Press.
William A. Brock
Steven N. Durlauf