Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets

Abstract

Consider a sequence of markets for goods and securities at successive dates, with no market at any date complete in the Arrow-Debreu sense. A concept of common expectations is proposed that requires traders to associate the same future prices to the same future exogenous events, but does not require them to agree on the (subjective) probabilities associated with those events. An equilibrium is a set ofprices at the first date,a set ofcomrnon price expectations for the future, and a consistent set of individual plans for consumers and producers such that, given the current prices and price expectations, each individual agent's plan is optimal for him, subject to an appropriate sequence of budget constraints. The existence of such an equilibrium is demonstrated under assumptions about technology and consumer preferences similar to those used in the typical Arrow-Debreu theory of complete markets. However, an equilibrium can fail to exist if some provision is not made for the elimination of "unprofitable" enterprises. The usual assumptions of "rationality" imply, in this model, that agents learn from experience and modify their expectations as Bayesians. 'The research on which this paper is based was supported in part by the National Science Foundation. A preliminary version of this was prepared while I was an Overseas Fellow at Churchill College, Cambridge, 1969-70, and I would like to thank the Master and Fellows of Churchill College and the Faculty of Economics of Cambridge for their facilitation of my research during that period. 289

Environmental Damage and Price Taking Behaviour by Firms and Consumers

“…Radner (1972), to a distribution of states and associated probabilities at some future date, say ten, …fty or one-hundred years from today. This idea extends the applicability of REED to the analysis of di¤erent climate scenarios with associated probability assessments, which would be relevant to study the economic impact of the rise in sea level.…”

Equilibrium analysis, banking and financial instability

“…Positive interest rates and bankruptcy penalties compactify the choice space by binding the potential transactions in the asset markets. Radner [50], instead, imposed artificial bounds on asset trades to show existence. The proof of the theorem also indicates that as the aggregate "outside" money becomes large then the necessary gains to trade for existence becomes arbitrarily large.…”

“…However, as the theorem asserts, such a Pareto improving intervention assumes no bankruptcy and binding capital requirements in the original equilibrium. When bankruptcy is allowed then a similar trade off exists as the one between severity of the bankruptcy code and efficiency 50 , but in this context the trade off is between regulatory policy and efficiency. The upshot of this discussion is that there exists optimal regulatory policy, which depends on the particular parameters of the economy.…”

“…49 The pioneering paper on the subject of constrained inefficiency in incomplete markets with numeraire goods was written by Geanakoplos and Polemarchakis [26]. 50 See [22], for an example of this tradeoff. But no general theorem has yet been provided on this.…”

Est-il rationnel d’avoir des anticipations rationnelles?

“…Cette affirmation a effectivement un sens dans un monde defirst best ou premier rang: la décentralisation d'un optimum parétien intertemporel de premier rang requiert que les agents aient une anticipation rationnelle des prix futurs, au sens précis donné à ce mot par le concept d'équilibre de plans de prix et d'anticipations de prix dû à R. Radner (1972). Cette justification, qui repose sur une foi très leibnizienne dans les vertus de l'organisation du monde, perd en outre toute sa force dès lors que le meilleur des mondes est, comme disent les anglo-saxons, le «second meilleur» (le second best plutôt que \tfirst best), c'est-à-dire, en langage technique, lorsqu'on passe du monde du premier rang à celui du second rang, du moindre mal, du pis aller.…”