7.3 Mathematical economics as a form of pure mathematics.7.2 Testing predictions of mathematical economics.7.1 Adequacy of mathematics for qualitative and complicated economics.6 Example: The effect of a corporate tax cut on wages.2.6 Agent-based computational economics.2.3.3 Variational calculus and optimal control.1.1 Marginalists and the roots of neoclassical economics.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. This rapid systematizing of economics alarmed critics of the discipline as well as some noted economists. 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. įormal 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. dynamic analysis, tracing changes in an economic system over time, for example from economic growth.comparative statics as to a change from one equilibrium to another induced by a change in one or more factors.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.optimization problems as to goal equilibrium, whether of a household, business firm, or policy maker.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.
Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics. Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity. 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. Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.
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