The Formulation of Uncertainty : Prices and States

The formulation of uncertainty in terms of exogenous states, introduced by Arrow in 1952 (published 1953), has been extremely fruitful. The paper discusses informally the question, raised sporadically in the oral tradition and put in writing by Kurz in1974 and again recently, whether that formulation calls for including the spot prices prevailing at a future date-event in the definition of the event itelf. The discussion also bears on the comparison between the theories of temporary general equilibrium (TGE) and general equilibrium with incomplete markets (GEl). The following conclusions emerge: (i) The conceptual device of defining states comprehensively enough that market clearing prices are uniquely defined is consistent and useful, provided one recognises that many events are then unobservable, so that markets are inescapably incomplete. (ii) Whether one models the residual uncertainty associated with unobservable events through idiosyncratic expectations about states or about prices themselves does not seem to matter much; there is no reason to be dogmatic. (iii) Greater realism is obtained when it is recognised that prices are not observed perfectly, that different agents have different information, and that prices convey information. (iv) The revision of expectations on the basis of price observations is an essential feature in market economies; it can be modeled through information partitions or through price-dependent utility; there is again no reason to be dogmatic. (v) A GEl model with residual price uncertainty and price-dependent (expected) utilities is formally analogous to a TGE model with state-and-price dependent utilities. (vi) Much work remains to be done on GEI/TGE with incomplete price-contingent contracts. (vii) A positive theory of price-level determination and an extension of GEl to noncompetitive market clearing figure promeninently on the research agenda.