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  First Welfare Theorem and Economics of Welfare

First Welfare Theorem:

• In the Wealth of Nations Adam Smith utilized the illusion of an invisible hand to present his famous case for a decentralized system of market transactions – capitalism.

• According to Smith (1776) all of us are ‘led by an invisible hand to promote a [social] end which was no part of his intention.’

• Smith highlights the role of markets in directing resources to where they are valued most thus his standard for evaluating economic systems – his end – loosely fits the net benefit criterion (e.g. consumer’s surplus).

• Smith’s Invisible Hand transforms into the modern era as the First Welfare Theorem of

Economics: If (x, p) is a competitive that is Walrasian equilibrium then x is Pareto optimal.

Proof: Suppose not as well as let x′ be a feasible allocation that all agents prefer to x. Then x′ should not be affordable to each agent

That is, pxi′ > pωi for i = 1,..., I. Sum these over i to find

48_pareto optimal.jpg

which is a contradiction. Thus the theorem is true.

If the equilibrium allocation is inside the box therefore choices are interior solutions then proof is simple – Agents equate MRS (marginal rates of substitution) to price ratios so MRSs are equated across agents which mean indifference curves are tangent (see the diagram below).

1983_first welfare problem.jpg

 (First Welfare Theorem: Interior)

135_first welfare theorem edge.jpg

(First Welfare Theorem: Edge)

• The substance of the First Welfare Theorem is that all the gains from trade are exhausted in a competitive equilibrium.

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