(M8E12) [Microeconomics] First and Second Fundamental Theorem of Welfare Economics.

In this video, the speaker introduces three important theorems related to Walrasian equilibrium in economics: the First Fundamental Theorem of Welfare Economics, the Existence of Walrasian Equilibrium, and the Second Fundamental Theorem of Welfare Economics. The first theorem states that if each consumer's utility function is strictly increasing, every Walrasian equilibrium allocation is efficient, meaning that allowing free trade will lead to efficient outcomes without intervention based on the strict increase of utility with consumption.

The speaker raises the question of whether a Walrasian equilibrium exists in every economy and identifies necessary conditions for its existence. These conditions include continuous and strictly increasing concave utility functions and strictly positive endowments for each consumer. He notes that without these assumptions, a Walrasian equilibrium may not exist, particularly in cases where initial endowments are zero or utility functions may not be concave.

The Second Fundamental Theorem of Welfare Economics states that if consumers have strictly increasing, concave, and continuous utility functions with strictly positive endowments, then any Pareto efficient allocation can be achieved as a Walrasian equilibrium under some price ratio. This theorem emphasizes the relationship between efficient allocations and price vectors in exchange economies, again noting that production factors complicate these assumptions further.

Two examples are given to illustrate situations where the necessary assumptions for a Walrasian equilibrium fail. The first example has strictly positive endowments but fails the concavity assumption, resulting in no equilibrium. The second example has initial endowments that are not strictly positive, leading to a failure in establishing a Walrasian equilibrium due to similar reasons presented in the first example.