Gerard Debreu symbolizes the use of a new mathematical apparatus, an apparatus comprehended by most economists only abstractly. Nevertheless, his work has given us an improved intuitive understanding of the underlying economic relevance. His clarity and analytical rigor, as well as the distinction drawn by him between an economic theory and its interpretation, have given his work important bear...

To prove their Walrasian equilibrium existence theorem, Arrow and Debreu (1954) devised an abstract economy that Shapley and Shubik (1977) cricitized as a market game because, especially with untrustworthy traders, it fails to determine a credible outcome away from equilibrium. All this earlier work also postulated a Walrasian auctioneer with complete information about traders’ preferences and ...

This note provides an elementary short proof of the Knas t e r Kuratowski-Mazurkiewicz-Shapley ( K K M S ) Theorem based on Brouwer's fixed point theorem. The usefulness of the K K M S Theorem lies in the fact that it can be applied to prove directly Scarf's (1967) Theorem, i.e. any balanced game has a non-empty core. We also show that the K K M S Theorem and the Ga le -N ika ido -Debreu Theore...

In this paper, we describe and compare two approaches to analyzing transactions costs in a general equilibrium setting. In the first approach, which we label the transactions costs approach, the commodity space is the same as that used in models without transactions costs. In the second approach, which we label the valuation equilibrium approach, the commodity space is chosen so that the exchan...

We define a solution concept, perfectly contracted equilibrium, for an intertemporal exchange economy where agents are simultaneously price takers in spot commodity markets while engaging in efficient, non-Walrasian contracting over future prices. Without requiring that agents have perfect foresight, we show that perfectly contracted equilibrium outcomes are a subset of Pareto optimal allocatio...

Implicit in the prices of traded nancial assets are Arrow-Debreu prices or, with continuous states, the state-price density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and derive its asymptotic sampling theory. This estimator provides an arbitrage-free method of pricing new, complex, or illiquid securities while capturing those features of the data that a...

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The OLG model of Allais and Samuelson retains the methodological assumptions of agent optimization and market clearing from the Arrow–Debreu model, yet its equilibrium set has different properties: Pareto inefficiency, multiplicity, positive valuation of money, and a golden rule equilibrium in which the rate of interest is equal to population growth (independent of impatience). These properties...

The OLG model of Allais and Samuelson retains the methodological assumptions of agent optimization and market clearing from the Arrow-Debreu model, yet its equilibrium set has different properties: Pareto inefficiency, indeterminacy, positive valuation of money, and a golden rule equilibrium in which the rate of interest is equal to population growth (independent of impatience). These propertie...

We begin by looking at a set of theorems from various disciplines and how they relate to one another. From combinatorics, we take Sperner’s Lemma which we can use to prove Brouwer’s Fixed Point Theorem from topology. Brouwer’s Fixed Point Theorem can be used to prove the Arrow-Debreu Theorem from economics which states that general equilibria exist, and can also be used to prove Kakutani’s Fixe...