This note is a drastic revision and extension of the author’s paper (1972). We recall the following theorem of Debreu (1970) for a pure exchange economy : One is given C1 demand functions, fi, . . ,, f,, of m consumers, satisfying a certain boundary condition. Then for almost all initial allocations of commodities to the m consumers, there are only a finite number of price equilibria. Our goal ...

In 1967, Gerard Debreu presented an integral of a correspondence by taking a higherdimensional point of view whereby a correspondence is seen as a function in a Banach space and thereby integrated as a consequence of the theory of Bochner integration. In this survey paper, we locate Debreu’s paper from the viewpoint of subsequent work, both in the theory of embeddings of convex-valued correspon...

The rational expectations equilibrium (REE), as introduced in Radner (1979) in a general equilibrium setting à la Arrow-Debreu-Mckenzie, often fails to have normative properties such as universal existence, incentive compatibility and efficiency. We resolve those problems by providing a new model which makes the standard REE a desirable solution concept. In particular, we consider an asymmetric...

In this paper the Aumann and the Debreu integrals are introduced and results about their comparison are given in countably and finitely additive setting. 1991 AMS Mathematics Subject Classification: 28B20, 26E25, 46B20, 54C60

The theory of general equilibrium with incomplete asset markets (GEI) studies the pricing of securities and commodities, and the interactions of perfectly competitive asset markets and commodity markets in determining consumption and investment. Since financial economics is fundamentally concerned with the pricing of securities, and since macroeconomics is fundamentally concerned with the real ...

We show that for a specific class of random matching Edgeworthian economies, the expectation of the limiting equilibrium price coincides with the equilibrium price of the related Walrasian economies. This result extends to the study of economies in the presence of uncertainty within the multi-period Arrow-Debreu model, allowing to understand the dynamics of how beliefs survive and propagate thr...

Restrictions that a class of general equilibrium models place upon the average returns of equity and Treasury bills are found to be strongly violated by the U.S. data in the 1889-1978 period. This result is robust to model specification and measurement problems. We conclude that, most likely, an equilibrium model which is not an Arrow-Debreu economy will be the one that Simultaneously rationali...

In the last two decades, the classical Arrow and Debreu result [3] on the existence of Walrasian equilibria has been generalized in many directions. MasColell [35] has first shown that the existence of an equilibrium can be established without assuming preferences to be total or transitive. Next, by using an existence theorem of maximal elements, Gale and Mas-Colell [20] gave a proof of the exi...

We derive tractable necessary and sufficient conditions for the absence of buy-and-hold arbitrage opportunities in a perfectly liquid, one period market. We formulate the positivity of Arrow-Debreu prices as a generalized moment problem to show that this no arbitrage condition is equivalent to the positive semidefiniteness of matrices formed by the market price of tradeable securities and their...