The second fundamental theorem of welfare economics suggests that we can achieve any possible Pareto optimal outcome using reallocation”

The second fundamental theorom of welfare economics postulates that when indifference curves are convex to orgin, every effficient allocation ( every point on contract curve for exchange) is a competitive equilibrium for intial allocation of goods or distribution of inputs. The significance of second fundamental theorem of welfare economics is that the issue of equity in distribution is logically seperable from issue of efficiency in allocation. Whatever the redistribution of income the society wants that would results exhaustion of all possible gains from exchange under perfect competition. Perfect competition leads to efficiency and pareto optimum in production and exchange at a particular point of time.

Paretto efficiency in production and exchange can be attained when

MRSxy =MRPTxy,( MRSxy of A =MRSxy of B=MRPTxy)

marginal rate of substitution of X for Y is equal to marginal rate of product transformation of X for Y

From the given graph efficiency in exchange and production is attained at point D. At this point slope of indifference curve (MRSxy ) and slope of production possibility curve (MRPTxy) are equal. At general equilibrium of production and exchange, it produces 12 x and 12y ( point M) and individual A receives 7x and 5 y and individual B receives 5x and 7 y at point D.

Locus of points on pareto equilibrium in production and exchange is termed as grand utility possibility

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