Abstract
We present versions of the fundamental theorems of welfare economics for the overlapping generations model with an infinite dimensional commodity space. Given Samuelson's example, one cannot hope for a version of the welfare theorems in terms of Pareto optimality. However, we show that for Malinvaud optimality both welfare theorems (as formulated by Debreu) do hold. The main result of this paper asserts that in an OLG model, an allocation is Malinvaud optimal if and only if it is a valuation equilibrium. A fundamental concern of general equilibrium theory, dating at least from Adam Smith's Wealth of Nations, is the optimality of the market mechanism. The relationship between competitive behavior and the efficient allocation of resources has its clearest and most satisfying formulation in the two welfare theorems of K. J. Arrow (1951) and G. Debreu (1954).
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