VoL.70N0.3 GROSSMAN AND STIGLITZ:EFFICIENT MARKETS 399 as A rises,the expected utility of informed EV(W) traders does go down relative to uninformed traders. EV(W) Note that the function y(0)=eac(Var(u* 0)/Var u*)1/2.Figure 1 illustrates the de- termination of the equilibrium A.The figure assumes that y(0)<1<y(1). e ac var(u"1e) G.Characterization of Equilibrium vor u We wish to provide some further char- acterization of the equilibrium.Let us define FIGURE 1 (16a) Note that (19)holds for y(0)<I<y(1),since these conditions insure that the equilibrium A is between zero and one.Equation (19b) (16b) n= shows that the equilibrium informativeness of the price system is determined completely by the cost of information c,the quality of Note that m is inversely related to the the informed trader's information n,and the informativeness of the price system since the degree of risk aversion a. squared correlation coefficient between P* and 0*,pa is given by H.Comparative Statics 1 (17) p6=1+m From equation(19b),we immediately ob- tain some basic comparative statics results: Similarly,n is directly related to the quality 1)An increase in the quality of infor- of the informed trader's information be- mation (n)increases the informativeness of cause n/(1+n)is the squared correlation the price system. coefficient between and u*. 2)A decrease in the cost of information Equations (14)and (15)show that the increases the informativeness of the price cost of information c,determines the equi- system. librium ratio of information quality be- 3)A decrease in risk aversion leads tween informed and uninformed traders informed individuals to take larger posi- (Var(u*))/Var(u*wa).From (1),(A11)of tions,and this increases the informativeness Appendix A,and (16),this can be written as of the price system. Further,all other changes in parameters, (18) such that n,a,and c remain constant, do not change the equilibrium degree of in- formativeness of the price system;other Var(u*wx)1+m+nm changes lead only to particular changes in A of a magnitude to exactly offset them.For Substituting(18)into (14)and using (15) example: we obtain,for 0<A<1,in equilibrium 4)An increase in noise (o)increases e2ac-I the proportion of informed traders.At any (19a) m=- given入，an increase in noise reduces the +n-e2ac informativeness of the price system;but it or increases the returns to information and leads more individuals to become informed; the remarkable result obtained above estab- (19b) lishes that the two effects exactly offset each