KYLE INFORMED SPECULATION 319 monopsonists who observe their residual supply curves and utilize any information which the levels of these supply curves reveal about the liquidation value of the commodity. The plan of this paper is as follows.Section 2 outlines the basic structure,establishes notation,and makes special assumptions.Section 3 defines a rational expectations equilibrium with imperfect competition and provides a conceptual discussion of the particular equilibrium concept chosen.Section 4 introduces some indices measuring informational efficiency;these are useful in discussing both competitive and imperfectly competitive equilibria when linearity is assumed.Section 5 characterizes the unique symmetric rational expectations equilibrium with imperfect competition which has the property that optimal trading strategies are linear.Section 6 contains an analogous characterization of the competitive equilibrium,for the purpose of facilitating comparisons between the two.Section 7 compares the indices measuring the informativeness of prices which result from the two equilibrium concepts.Section 8 discusses the properties of equilibrium when the number of informed speculators is large.Section 9 shows how the model with imperfect competition can become one of monopolistic competition when traders are small,and characterizes all sequences of exogenous parameters in which the competitive and imperfectly competitive concepts have non-trivial,informationally equivalent limits.Section 10 introduces endogenous acquisition of costly private informa- tion,and shows that the strange properties of equilibrium associated with the"informa- tional efficiency"paradox go away when imperfect competition is introduced.Section 11 concludes by suggesting that since the equilibrium with imperfect competition is intellectually sensible and leads to properties different from those of the competitive equilibrium in important respects,its thorough study is justified. 2.STRUCTURE AND NOTATION Trading takes place in a one-period,partial equilibrium framework.A single risky asset is traded at a market clearing price p,realizes after trade occurs an exogenous liquidation value and thus generates returns o-p.Three kinds of traders participate in the market: noise traders,informed speculators,and uninformed speculators. Noise traders trade in aggregate an exogenous random quantity Z,which is not(in this paper)based on maximizing behaviour. There are N informed speculators,indexed n=1,...,N,and M uninformed specu- lators,indexed m=1,...,M.Each informed speculator is endowed with unique private information,represented as the outcome of a random variable in.After observing his private signal in,each informed speculator chooses a demand schedule X(;i)which depends upon that signal.Each uninformed trader chooses a demand schedule Ym(). The schedules X and Ym are the speculators'strategies.Given a market clearing price p,the quantities traded by informed and uninformed speculators can be written xn=Xn(p,in),n=1,...,N;ym=Ym(p),m=1,...,M. (1) In this notation,a tilde distinguishes a random variable from its realization.Thus, denotes the random variable generating the quantity traded by the nth informed trader, and xn is the quantity traded for a particular realization of.Similarly,X(;in)is a random variable defined over demand schedules,while X(,i)is a particular demand schedule corresponding to a particular realization of in.These are both different from X,the strategy rule of the nth informed speculator.We can interpret X either as a mapping from R'to R (i.e.X.=X(,))or as a mapping from R to the space of demand schedules (i.e.X=X(;))