The Equivalence of a Fisher Competitive Equilibrium and a Perfect Foresight Competitive Equilibrium in a Multi-Sectoral Model of Capital Accumulation

Abstract

The purpose of this paper is to demonstrate the importance of the transversality condition for an intertemporal competitive equilibrium to be equivalent to a Fisher competitive equilibrium. The transversality condition also emerges to show the optimality of either equilibrium process.2 Another concern of this paper is the importance of assumptions about individual savings and expectations.3 The models of this paper derive an agent's savings decision from an explicit intertemporal optimization model under conditions of perfect capital markets and long-run perfect foresight. The perfect foresight assumption means that paths of prices, dividends, and rental rates expected to occur at any future time are realized in an intertemporal equilibrium, referred to as a perfect foresight competitive equilibrium. This paper provides a demonstration that a perfect foresight competitive equilibrium is equivalent to a Fisher competitive equilibrium. The abstract economy under consideration consists of a representative consumer and a production or investment opportunity sector. There are n capital goods used for investment goods and one pure consumption good produced under the condition of nojoint production. Capital goods are not consumed, nor do they depreciate;