Fundamental theorems of welfare economics

Two results connect competitive equilibrium with Pareto efficiency: under standard assumptions, competitive equilibria are efficient, and suitable redistribution can make efficient allocations competitive equilibria.

Competitive equilibrium: An allocation and price system in which consumers and firms optimize and markets clear. The first theorem starts from this market outcome and establishes its Pareto efficiency.
General equilibrium theory: The study of how prices and quantities across multiple markets are jointly determined. The theorems describe economy-wide links between market clearing and efficiency.
Market failure: A situation in which market outcomes fail to achieve an efficient allocation under the relevant social objective. Externalities, public goods, and other failures can break the link between equilibrium and efficiency.
Lump-sum tax: A tax fixed independently of an individual's choices or economic activity. The second theorem's redistribution is often modeled with transfers that do not distort subsequent choices.
Pareto efficiency: An allocation is Pareto efficient if no feasible change can make someone better off without making someone else worse off. This is the welfare criterion the first theorem guarantees for competitive equilibria.
Convexity in economics: A property of preferences or production sets that supports averaging and avoids certain nonconvex outcomes. Convexity is central to the second theorem’s claim that efficient allocations can be supported by prices.
Social welfare function: A rule that ranks social states by aggregating information about individual welfare. The theorems do not select among efficient allocations or determine a uniquely fair distribution.
First-best: An outcome that achieves the unconstrained optimum under a specified objective and set of resources. The theorems characterize when competitive markets can attain efficient, first-best allocations.
First welfare theorem: Under specified assumptions, every competitive equilibrium is Pareto efficient. It states the direction from market equilibrium to efficiency.
Local nonsatiation: A preference condition under which every consumption bundle has a nearby bundle the consumer strictly prefers. This assumption helps ensure that competitive equilibria are Pareto efficient.

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Gérard DebreuRelated: Debreu’s equilibrium framework helped give these efficiency results precise foundations.