Mathematical economics

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.

Much of modern economics can be presented in geometric terms or elementary mathematical notation. Mathematical economics, however, conventionally refers to use of such methods as calculus and matrix algebra in economic analysis.

Mathematical economics applications

• Arbitrage
• Black-Scholes equation
• Econometrics
• Game theory
• General equilibrium theory
• Growth theory
• Information theory
• Qualitative economics
• Wealth condensation

The scope of Mathematical Economics includes:

Economics theories in various fields based on rigorous mathematical reasoning.

Mathematical methods (e.g., analysis, algebra, geometry, and probability) motivated by economic theories.

Mathematical results of potential relevance to economic theory.

Historical study of mathematical economics.

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.

 

 

 

 

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