Mathematical economics

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Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods.[1][2] Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.[3]

Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics.[4] Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.[5]

Broad applications include:

  • optimization problems as to goal equilibrium, whether of a household, business firm, or policy maker
  • static (or equilibrium) analysis in which the economic unit (such as a household) or economic system (such as a market or the economy) is modeled as not changing
  • comparative statics as to a change from one equilibrium to another induced by a change in one or more factors
  • dynamic analysis, tracing changes in an economic system over time, for example from economic growth.[2][6][7]

Formal economic modeling began in the 19th century with the use of differential calculus to represent and explain economic behavior, such as utility maximization, an early economic application of mathematical optimization. Economics became more mathematical as a discipline throughout the first half of the 20th century, but introduction of new and generalized techniques in the period around the Second World War, as in game theory, would greatly broaden the use of mathematical formulations in economics.[8][7]

This rapid systematizing of economics alarmed critics of the discipline as well as some noted economists. John Maynard Keynes, Robert Heilbroner, Friedrich Hayek and others have criticized the broad use of mathematical models for human behavior, arguing that some human choices are irreducible to mathematics.

  1. ^ Elaborated at the JEL classification codes, Mathematical and quantitative methods JEL: C Subcategories.
  2. ^ a b Chiang, Alpha C.; Kevin Wainwright (2005). Fundamental Methods of Mathematical Economics. McGraw-Hill Irwin. pp. 3–4. ISBN 978-0-07-010910-0. TOC. Archived 2012-03-08 at the Wayback Machine
  3. ^ Debreu, Gérard ([1987] 2008). "mathematical economics", section II, The New Palgrave Dictionary of Economics, 2nd Edition. Abstract. Archived 2013-05-16 at the Wayback Machine Republished with revisions from 1986, "Theoretic Models: Mathematical Form and Economic Content", Econometrica, 54(6), pp. 1259 Archived 2017-08-05 at the Wayback Machine-1270.
  4. ^ Varian, Hal (1997). "What Use Is Economic Theory?" in A. D'Autume and J. Cartelier, ed., Is Economics Becoming a Hard Science?, Edward Elgar. Pre-publication PDF. Archived 2006-06-25 at the Wayback Machine Retrieved 2008-04-01.
  5. ^ * As in Handbook of Mathematical Economics, 1st-page chapter links:
         Arrow, Kenneth J., and Michael D. Intriligator, ed., (1981), v. 1
         _____ (1982). v. 2
         _____ (1986). v. 3
         Hildenbrand, Werner, and Hugo Sonnenschein, ed. (1991). v. 4. Archived 2013-04-15 at the Wayback Machine Description Archived 2023-07-01 at the Wayback Machine and Contents Archived 2023-07-01 at the Wayback Machine.
  6. ^ Chiang, Alpha C. (1992). Elements of Dynamic Optimization, Waveland. TOC & Amazon.com link Archived 2016-03-03 at the Wayback Machine to inside, first pp.
  7. ^ a b Samuelson, Paul (1947) [1983]. Foundations of Economic Analysis. Harvard University Press. ISBN 978-0-674-31301-9.
  8. ^ * Debreu, Gérard ([1987] 2008). "mathematical economics", The New Palgrave Dictionary of Economics, 2nd Edition. Abstract. Archived 2013-05-16 at the Wayback Machine Republished with revisions from 1986, "Theoretic Models: Mathematical Form and Economic Content", Econometrica, 54(6), pp. 1259 Archived 2017-08-05 at the Wayback Machine-1270.