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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.
The front page quotes the motto of J. Willard Gibbs: "Mathematics is a language."The book begins with this statement: The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.
In mathematical economics, the Arrow–Debreu model is a theoretical general equilibrium model. It posits that under certain economic assumptions (convex preferences, perfect competition, and demand independence), there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy.
Notes and Problems in Applied General Equilibrium Economics. North-Holland. ISBN 978-0-444-88449-7. ——, with Rimmer, Maureen T. (2002). Dynamic General Equilibrium Modelling for Forecasting and Policy: A Practical Guide and Documentation of MONASH. Contributions to economic analysis (256). Amsterdam: Elsevier. ISBN 0444512608.
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An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes.
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio ...
In his paper, Koopmans states in a footnote that Cass independently obtained conditions similar to what he finds. Cass also considers the limiting case where the discount rate goes to zero in his paper. For his part, Cass notes that "after the original version of this paper was completed, a very similar analysis by Koopmans came to our attention.