Mathematical economics is the application of
mathematical methods to represent economic theories and analyze problems posed in
economics. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and
simplicity. By convention, the
applied methods refer to those beyond simple geometry, such as differential and integral
calculus,
difference and
differential equations,
matrix algebra, and
mathematical programming and other
computational methods.
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.
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.
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