First welfare theorem

The first welfare theorem states that, under assumptions such as price-taking behavior and locally nonsatiated preferences, every competitive equilibrium is Pareto efficient.

Competitive equilibrium: An allocation and price system in which agents optimize and markets clear. The theorem's starting point is an allocation satisfying these equilibrium conditions.
Pareto improvement: A change that makes at least one person better off and no one worse off. Efficiency is defined by the absence of any feasible Pareto improvement.
Second welfare theorem: A theorem stating, under suitable convexity assumptions, that Pareto-efficient allocations can be supported as competitive equilibria after redistribution. It reverses the direction of the first theorem: from efficiency to support by markets.
Welfare economics: The study of how economic arrangements affect social welfare and the allocation of resources. The theorem is a foundational result linking market equilibrium to welfare evaluation.
Léon Walras: A French economist who developed a mathematical theory of general competitive equilibrium. His equilibrium framework supplied a foundation for later welfare theorems.
Pareto efficiency: A state in which no feasible change can improve someone’s welfare without reducing another’s. This is the efficiency property the theorem guarantees for competitive equilibria.
Feasible allocation: An assignment of goods and resources that respects the economy’s aggregate resource constraints. The theorem compares equilibrium with alternatives that the economy can actually produce or distribute.
Market failure: A condition in which decentralized markets fail to produce an efficient allocation. Market failures identify settings where competitive equilibrium may not satisfy the theorem's conclusion.
First-best: An outcome that achieves the highest attainable objective without constraints from policy or market distortions. Pareto efficiency gives a benchmark for assessing whether an allocation is first-best.
Vilfredo Pareto: An Italian economist who developed the efficiency criterion now bearing his name. His criterion gave economists a way to define efficiency without comparing interpersonal utility.

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