# Arrow-Debreu model

Arrow-Debreu model

The Arrow-Debreu model, also referred to as the Arrow-Debreu-McKenzie model (ADM model) is the central model in the General (Economic) Equilibrium Theory and often used as a general reference for other microeconomic models. It is named after Kenneth Arrow, Gerard Debreu and Lionel W. McKenzie.

Compared to earlier models, the Arrow-Debreu model radically generalized the notion of a commodity, differentiating commodities by time and place of delivery. So, for example, 'apples in New York in September' and 'apples in Chicago in June' are regarded as distinct commodities. The Arrow-Debreu model applies to economies with maximally complete markets, in which there exists a market for every time period and forward prices for every commodity at all time periods and in all places.

The model suggests that, should the assumptions made about the conditions under which it works hold (i.e. convexity, perfect competition and demand independence), then there will be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy.

The ADM model is one of the most general models of competitive economy and is a crucial part of general equilibrium theory, as it can be used to prove the existence of general equilibrium (or Walrasian equilibrium) of an economy. Once we can prove the existence of such an equilibrium, it is possible to show that it is unique.

Applications to finance theory

The Arrow-Debreu model specifies the conditions of perfectly competitive markets.

In financial economics the term Arrow-Debreu is most commonly used with reference to an Arrow-Debreu security. A canonical Arrow-Debreu security is a security that pays one unit of numeraire if a particular state of the world is reached and zero otherwise (a so called "state price"). As such, any derivatives contract whose settlement value is a function on an underlying whose value is uncertain at contract date can be decomposed as linear combination of Arrow-Debreu securities.

The concept of Arrow-Debreu security is a good pedagogical tool to understand pricing and hedging issues in derivatives analysis. Its practical use in financial engineering, however, has turned out to be very limited, especially in the multi-period or continuous markets.

The Black Scholes analysis and its extensions, despite their strong questionable assumptions, have proven more successful in practice and have led to an explosion of the derivatives industry.

ee also

*Model (economics)

References

*John Geanakoplos (1987). "Arrow-Debreu model of general equilibrium," "The ", v. 1, pp. 116-24.

* [http://www.hss.caltech.edu/~kcb/Notes/Arrow-Debreu.pdf Notes on the Arrow–Debreu–McKenzie Model of an Economy] , Prof. Kim C. Border California Institute of Technology
* [http://www.in-the-money.com/artandpap/IV%20Fundamental%20Theorem%20-%20Part%20I.doc "The Fundamental Theorem" of Finance] ; [http://www.in-the-money.com/artandpap/IV%20Fundamental%20Theorem%20-%20Part%20II.doc part II] . Prof. Mark Rubinstein, Haas School of Business
* [http://www.bus.lsu.edu/academics/finance/faculty/dchance/Instructional/TN97-13.pdf Option Prices and State Prices] , Prof. Don Chance Louisiana State University

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