396 THE AMERICAN ECONOMIC REVIEW JUNE 1980 since 0 and e are uncorrelated.Throughout Then,we can write for the uninformed this paper we will put a above a symbol to individual emphasize that it is a random variable. Since Wi:is a linear function of e,for a given portfolio allocation,and a linear func- (7)E(v(Wi)IP)=-exp-aE[WilP-] tion of a normally distributed random vari- able is normally distributed,it follows that -2 var[WilP"]) Wi;is normal conditional on 0.Then,using (2)and (3)the expected utility of the in- formed trader with information 0 can be --exp-a(RWo+Xu(E[u*lP*]-RP) written (7) E(V(W)川8)= -号xar[u*p*]}] -exp(-afE[Wil]-var[wi])) The demands of the uninformed will thus be a function of the price function P*and the actual price P. --cxp(-aRWo+X,(E(u*l0)-RP) (8)Xu(P;P*) =E[*P*(0,x)=P]-RP -x好varu*o)]） a var[u*P*(0.x)=P] C.Equilibrium Price Distribution --exp(-aRWo+x(0-RP) If A is some particular fraction of traders who decide to become informed,then define -x]） an equilibrium price system as a function of (0,x),P(0,x),such that for all (0,x)per capita demands for the risky assets equal where X,is an informed individual's de- supplies: mand for the risky security.Maximizing (7) with respect to X,yields a demand function (9) 入X（P(8,x),9) for risky assets: X,(P.0)=0-RP +(I-入)X(P(9x):P*)=x (8) a03 The function P(6,x)is a statistical The right-hand side of(8)shows the familiar equilibrium in the following sense.If over result that with constant absolute risk aver- time uninformed traders observe many re- sion,a trader's demand does not depend on alizations of (u,P),then they learn the wealth;hence the subscript i is not on the joint distribution of (u*,P*).After all learn- left-hand side of(8). ing about the joint distribution of (u*,P*) We now derive the demand function for ceases,all traders will make allocations and the uninformed.Let us assume the only form expectations such that this joint dis- source of "noise"is the per capita supply of tribution persists over time.This follows the risky security x. from (8),(8),and (9),where the market- Let P*()be some particular price func- clearing price that comes about is the one tion of (,x)such that u*and P*are jointly which takes into account the fact that unin- normally distributed.(We will prove that formed traders have learned that it contains this exists below.) information