Insiders Outsiders, and Market breakdowns oped in the noisy rational expectations literature. First, given P, the riable T is fully revealed. This tells us that although there may be a nonlinear term in the price, the price is still a linear function of the normally distributed information variable of the insider, T, and it reveals this. Importantly, this revelation would not occur if the aggre gate demand function submitted by the outsiders was a correspon dence. In the Appendix, we prove that it is not optimal for the out. siders to submit such a correspondence. Second, even though the outsiders know T, they cannot fully identify e, since w also enters the equation. The general public is therefore left uncertain as to whether the primary motivation for trading by the informed is"hedging"or nformational. Third, if e is the only variable that the informed has n informational advantage in(o,=0), the market clearing price P fully reveals e. Fourth, although the uninformed cannot disentangle , they can learn something about Pi from the offer price P. We now proceed to analyze how this learning takes place 2.2 Problem of the uninformed competitors Equation (5) tells us that t is a linear function of two normally dis- tributed random variables, implying that it is also a normally distrib- uted random variable. Simple calculations can then be used to show that E(T)=0 and var()=02=02+6如2AsP1=μp+∈+nby construction, one also knows that Pi is a normally distributed random variable with E(P)=μ and var(P1)=σ2+ p(P,T)=σ/2(02+σ2)]/2 Hence, by observing the equilibrium price P, and thereby T, the uninformed update their priors on P,. The posterior distribution of Pi given P, using fact 1, is now normally distributed with E(P1|P=E(P1|) =p+o{r-0]1σ2=μp+σ{P-(p+a(P)/a2 var(P1|P)=Ⅴar(P1|r)=(2+a2)-0:/σ2. (7) Equations (6)and(7) make precise the " learning procedure""of the uninformed. Equation(6) gives them the posterior mean of P1 as a function of P, while Equation (7) is used to update the variance Notice that the posterior precision on P is higher than the prior precision, and this improvement does not depend on P(assuming P exists) The above arguments show that the final period 1 wealth of the ith 261