Mathematical economics

Mathematical economics refers to the application of mathematical methods to represent economic theory or analyze problems posed in economics. Expositors maintain that it allows formulation and derivation of key relationships in the theory with clarity, generality, rigor, and simplicity (Chiang and Wainwright, 2005, pp. 1-2; Debreu, 1987, pp. 401-03). Thus, for example, Paul Samuelson's Foundations of Economic Analysis (1947) identifies a common mathematical structure across multiple fields in the subject.

Much of modern economics can be presented in geometric terms or elementary mathematical notation. Mathematical economics, however, conventionally makes use of calculus and matrix algebra in economic analysis. These are prerequisites for formal study, not only in mathematical economics but in contemporary economic theory generally. Thus, for example, The Journal of Economic Theory is one of the most-cited academic references in economics. According to the Editors, it is a non-specialist journal. For the diverse theoretical topics in economics examined in it, most articles there use a mathematical representation of the theory.

Applied mathematics

An economic problem often involves so many variables that mathematics is the only practical way of handling it - "handling" in the sense of solving it. For many academics interested on the subject, like Alfred Marshall, every economic problem which can be quantified, analytically expressed and solved, should be treated by means of mathematical work.^[1] Economic analysis relies more and more on mathematical foundations. Economics has become increasingly dependent on mathematical methods, and the mathematical tools it employs have become more sophisticated. As a result, mathematically competent professionals are needed in industry and government for dealing with the subject. Graduate programs in economics and finance programs in graduate schools of management require strong undergraduate preparation in mathematics for admission and are attractive to an increasingly high number of mathematicians. Applied mathematicians apply mathematical principles to practical problems, such as economic analysis and other economics-related issues, in such a way that many economic problems are often defined as being integrated into the scope of applied mathematics.^[2]

Criticism of mathematical economics

The methods of mathematical economics are widely, though far from exclusively used, in professional publications, but there are opponents, notably the Austrian School. Within it, the use of formal techniques has been criticized as projecting scientific exactness that, by nature of the eccentricities of its human subject matter, is infeasible, even in principle.

Proponents argue that the validity of the mathematical method derives from the distinctive modeling of economic decision-making and economic systems. These parallel mathematical concepts, such as optimization, to describe (i) rational, self-interested agents interacting in economic systems. From such assumptions and concepts, behavior of an agent or an economic system may in principle be compared against properties of the model using formal analytical techniques.

References

^ JSTOR: Marshall on Mathematics, in JSTOR
^ Sheila C Dow - THE USE OF MATHEMATICS IN ECONOMICS, For presentation to the ESRC Public Understanding of Mathematics Seminar, Birmingham, 21-2 May 1999

Alpha C. Chiang and Kevin Wainwright (2005). Fundamental Methods of Mathematical Economics, 4th edition, McGraw-Hill Irwin. ISBN 0-07-010910-9
Gerard Debreu (1987). "Mathematical Economics," The New Palgrave: A Dictionary of Economics, v. 3, pp. 399-404.
F.Y. Edgeworth ([1925] 1987). "Mathematical Method in Political Economy," The New Palgrave: A Dictionary of Economics, v. 3, pp. 404-05.
Eugene Silberberg and Wing Suen (2000). The Structure of Economics: A Mathematical Analysis, 3rd ed. McGraw-Hill.
Econometrica, leading journal in mathermatical economics and econometrics