Existence of an Equilibrium for a Competitive Economy.¶
Arrow, K. J., & Debreu, G. (1954). Existence of an Equilibrium for a Competitive Economy. Econometrica, 22(3), 265-290.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Diminishing Returns (Law of)
- Hayek (1945)
This sourceProves existence of a competitive (Walrasian) equilibrium under convex, continuous technologies and preferences, including convex production sets
- Hayek (1945)
- Equilibrium
- where no player has a profitable unilateral deviation. General equilibrium theory and existence theorems
This sourceProves, via a Kakutani fixed-point argument on an abstract economy, the existence of a competitive general equilibrium under convexity and completeness assumptions. NOTE: the paper proves existence only, not uniqueness — see the prose-overreach flag on the Applied Example.
- where no player has a profitable unilateral deviation. General equilibrium theory and existence theorems
- Marginal Analysis
- The framework has been refined (partial equilibrium supplemented by general-equilibrium analysis per Arrow-Debreu 1954;
This sourceProves the existence of a general equilibrium allocation of goods and resources under specified conditions (convexity, completeness); establishes the fundamental welfare theorems linking competitive equilibrium to Pareto efficiency. Foundational theorem of mathematical economics.
- The framework has been refined (partial equilibrium supplemented by general-equilibrium analysis per Arrow-Debreu 1954;
- Pareto Efficiency
- Kenneth Arrow and Gérard Debreu's 1954 proof of general-equilibrium existence in a competitive economy (Econometrica),
This sourceProves the existence of a general equilibrium allocation of goods and resources under specified conditions (convexity, completeness); establishes the fundamental welfare theorems linking competitive equilibrium to Pareto efficiency. Foundational theorem of mathematical economics.
- Kenneth Arrow and Gérard Debreu's 1954 proof of general-equilibrium existence in a competitive economy (Econometrica),
- Price Mechanism
- Market failures map to specific breakdowns in the price-mechanism model and point to specific remedies (Pigouvian taxes, public-good subsidies, disclosure regulation, antitrust) rather than wholesale rejection of price coordination, with the diagnostic frame anchored in the welfare-theorem reasoning of Arrow and Debreu (1954).
This sourceProves the existence of a general equilibrium allocation of goods and resources under specified conditions (convexity, completeness); establishes the fundamental welfare theorems linking competitive equilibrium to Pareto efficiency. Foundational theorem of mathematical economics.
- Market failures map to specific breakdowns in the price-mechanism model and point to specific remedies (Pigouvian taxes, public-good subsidies, disclosure regulation, antitrust) rather than wholesale rejection of price coordination, with the diagnostic frame anchored in the welfare-theorem reasoning of Arrow and Debreu (1954).
Domain-specific¶
- Arrow–Debreu Model
- The Arrow–Debreu model (Kenneth Arrow and Gérard Debreu, 1954; Debreu, Theory of Value, 1959) is the canonical mathematical formalisation of general competitive equilibrium in an economy with finitely many commodities, finitely many price-taking consumers with convex continuous preferences and strictly positive endowments, and finitely many price-taking firms with convex production sets.
This sourceThe primary source for the model itself and for the assumption set the sentence enumerates (convex continuous preferences, strictly positive endowments, convex production sets). Carries the existence theorem and the fixed-point method: a price vector at which all markets clear simultaneously exists under the stated assumptions.
- The Arrow–Debreu model (Kenneth Arrow and Gérard Debreu, 1954; Debreu, Theory of Value, 1959) is the canonical mathematical formalisation of general competitive equilibrium in an economy with finitely many commodities, finitely many price-taking consumers with convex continuous preferences and strictly positive endowments, and finitely many price-taking firms with convex production sets.
- Competitive Equilibrium
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