The second welfare theorem of economics states that if preferences are convex, then any Pareto optimal allocation could be achieved as a competitive equilibrium after some reallocation of initial endowments.

Second Welfare Theorem

An economic principle stating that under certain conditions, any efficient allocation of resources can be attained through a competitive equilibrium, assuming perfect markets and price flexibility.

Pareto Optimal

A distribution state of resources where trying to improve the status of one individual inevitably leads to the decline of another's.

Competitive Equilibrium

A state in a market-based economy where supply equals demand, and prices are stable, facilitating the optimal distribution of resources.