The Second Fundamental Theorem of Welfare Economics and the Existence of Competitive Equilibrium over an Infinite Horizon with General Consumption Sets

The purpose of this paper is to prove the second fundamental theorem of welfare economics and the existence of competitive equilibrium in production economies over an infinite horizon with general consumption sets. In the literature of the studies for an economy of infinite dimmentional commodity space, the second fundamental theorem of welfare economics was proved only approximately with uniform properness that is an assumption on consumers' preferences. The existence of competitive equilibrium was also shown under the assumption. However, when we turn to the study of the long run path of the economy, especially of sustainable growth, the assumption that uniformly bounds the rate of substitution among goods is inconsistent with some important preferences of growth theory. We proved the both theorems without uniform properness. The irreducibility of an economy and aggregate adequacy assumption plays the key role. Our model follows Boyd-McKenzie(1993) and generalize their strong irreducibility asuumption on the economy to the usual irreducibility.