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Innovation, Decentralization and Equilibrium. A Comment



Innovation, Decentralization and Equilibrium A Comment N I K O L A U S W O L I K * 1. INTRODUCTION In a recent issue of this journal GUNTER STEPHAN and GERHARD WAGENHALS (1990) addressed themselves to the important question of which conditions guarantee the existence of Pareto-optimal competitive equilibria in an overlapping generations econ- omy with production. Their"... approach is to present plausible intertemporal substitution conditions, which may be interpreted in terms of an economy's potential to innovate new techniques, and which guarantee that the competitive mechanism results in an allocation with these desired properties." The first substitution condition mentioned is a global form of roundaboutness, in its local form well-known from capital theory, and the second is the condition of superiority of roundaboutness. Their first result, Proposition 1, states that roundaboutness is a sufficient condition for the existence of competitive equilibria. The purpose of this note is to critically discuss this proposition. I argue that the assumption of roundaboutness is overly strong. The existence of competitive equilibria can be shown without making any additional assumption that would not be needed in finite horizon models. This is the main result of this note. 2. ROUNDABOUTNESS AND THE EXISTENCE OF COMPETITIVE EQUILIBRIA We start with a brief exposition of the model of STEPHAN and WAGENHALS:1 There are N perishable goods in every period t e IN and in every period a representative consumer is born and lives for two periods maximizing a strictly quasiconcave, strongly monotonie and continuous utility function ut by consuming non-negative amounts of goods ct when young and 2ct+\ when old. Goods may be also used as inputs xt in production. They yield an output of yt+\ one period later if (xtyt+i) e ^ c I R "+, the closed and convex technology set with the usual properties. Given a sequence w = (wi) of resources, initial stocks yi and consumption of the old ci,

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