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In welfare economics, a social planner is a hypothetical decision-maker who attempts to maximize some notion of social welfare. The planner is a fictional entity who chooses allocations for every agent in the economy—for example, levels of consumption and leisure—that maximize a social welfare function subject to certain constraints (e.g., a physical resource constraint, or incentive compatibility constraints). This so-called planner's problem is a mathematical constrained optimization problem. Solving the planner's problem for all possible Pareto weights (i.e., weights on each type of agent in the economy) yields all Pareto efficient allocations.
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Any Pareto efficient allocation is a solution to a planner's problem. However, the planner is a purely fictional entity; solving the planner's problem requires knowledge of consumers' preferences and all physical resource constraints in the economy. Thus, a natural question is whether a decentralized market could implement a Pareto efficient allocation, or conversely, whether the outcomes from a decentralized market are Pareto efficient. The fundamental theorems of welfare economics answer these questions, under certain key assumptions.[1]
The first welfare theorem states that, under certain conditions (for example, if there are no externalities), if an allocation and a set of prices constitute a competitive equilibrium, then the allocation is Pareto efficient.
The second welfare theorem states that, under certain conditions, any Pareto efficient allocation can be decentralized as a competitive equilibrium.
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