324 REVIEW OF ECONOMIC STUDIES Regardless of the particular equilibrium concept used to obtain a symmetric linear equilibrium,the linearity and symmetry assumptions allow useful and intuitive measures of the informativeness of prices to be obtained as a consequence of Lemma 4.1,stated in Appendix A. Define TF as the precision of the forecast of the liquidation value based on all private information,i.e.T=var,...,iN).The assumptions that ,...,en are normally and independently distributed and that e1,...,ew have the same variance imply (from Lemma 4.1) TF =To+NTe. (13) To the prior precision To,one adds Te units of precision for each observation with error variance re to obtain the full-information precision TF.Now an individual informed or uninformed speculator does not observe i1,...,in but instead observes only the price and his own private signal,if any.Define precisions Tu for uninformed speculators and T,for informed speculators by TU =var p),TI=var p,in) (14) Normality makes ru and T constants,independent of the particular outcomes of p and in,while symmetry means that Tr does not depend on n.Since these precisions are bounded below by the prior precision To and above by the full-information precision TF, there exist constants and both in the interval [0,1],such that TU=To+PuNTe,TI=To+Te+pi(N-1)Te. (15) The parameters u and r are convenient indices measuring the "informational efficiency"with which prices aggregate private information of informed traders.The parameter u measures the fraction of the precision of the N informed traders revealed by prices to uninformed speculators.The parameter or measures the fraction of the precision of the other N-1 informed traders revealed by prices to one informed trader (whose prior,based on observing in alone,has precision T+re).Clearly,when u=0 orr=0,prices reveal no private information,and as u or tend to unity,prices become fully-revealing. Since the informational efficiency parameters u and r are discussed extensively in the following sections,some useful facts about them are collected here. Theorem 4.1.In a symmetric linear equilibrium,the parameters pu and o are given by NB2 (N-1)B2 PU-NB2+I(N-1)B+ (16) Let A=(Ny+Myu)denote the slope of the aggregate excess demand schedule.Itfollows that E(p)=PuT (A-6-Nu-Muu). (17) BTu E)=(A--Nur-MuU). (18) TI BTI Corollary 4.1.When the constants w and uu are zero,prices are unbiased (i.e. E{p}=p)if and only if ouTe=BATu