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.

Type

Journal article

Intellectual base

Primary research

Year

1954

DOI

10.2307/1907353

Link

https://doi.org/10.2307/1907353

Cited from

economics_finance, physics

Cited by

6 citations across 6 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

• 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.

• 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.

• 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.

• 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.

Domain-specific

• Competitive Equilibrium
  • Agents take prices as given; prices coordinate otherwise decentralized plans.

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