Arrow–Debreu Model

In mathematical economics, the Arrow–Debreu model (also referred to as the Arrow–Debreu–McKenzie model) suggests 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.

The model is central to the theory of general (economic) equilibrium and it is often used as a general reference for other microeconomic models. It is named after Kenneth Arrow, Gérard Debreu, and sometimes also Lionel W. McKenzie for his later improvements in 1959.

The AD 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. In general, there may be many equilibria; however, with extra assumptions on consumer preferences, namely that their utility functions be strongly concave and twice continuously differentiable, a unique equilibrium exists. With weaker conditions, uniqueness can fail, according to the Sonnenschein–Mantel–Debreu theorem.

Read more about Arrow–Debreu ModelConvex Sets and Fixed Points, Economics of Uncertainty: Insurance and Finance

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Arrow–Debreu Model - Economics of Uncertainty: Insurance and Finance
... Compared to earlier models, the Arrow–Debreu model radically generalized the notion of a commodity, differentiating commodities by time and place of delivery ... 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 ... The Arrow–Debreu model specifies the conditions of perfectly competitive markets ...

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