# On the foundations of intertemporal economic models

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- Purdue University
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## Abstract

In the second chapter, we investigate the existence of a competitive equilibrium in a deterministic intertemporal economy with infinitely many consumers when the aggregate wealth is restricted to be finite. After we show the existence we discuss the efficiency of the equilibrium in relation with the existence of price bubbles. We also provide an example with Stochastic Differential Equation as an application of our construction of commodity-price dual system. In the third chapter, we prove the existence of equilibrium for the overlapping generations economy when the commodity-price dual system is vector lattice dual system. In the fourth chapter we prove that the uniformly proper preferences defined on convex subset of a topological vector space is extendable to a set with nonempty interior. In the last chapter, the economy is an incomplete, stochastic overlapping generations model. The main contribution of this section is that the distribution of the endogenous variables are not restricted to be absolutely continuous with respect to Lebesgue Measure. This enables to use the measures with mass points for the endogenous variables. However because of this discontinuity, we are usable to use the dynamic programming techniques to show the existence of a rational expectations equilibrium. We prove the existence by techniques of the infinite dimensional economies. ^

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