The Journal of finance 4. WELFARE ASPECTS OF EQUILIBRIUM AND CONCLUSIONS Let Xei be the ith trader's endowment of the risky asset. Define (xmx)=E[O(小=E[(+)x+x)小](3) Consider the pure exchange economy where traders have utility function u* ()and endowments are(X, XEi). A competitive equilibrium for such an economy is Pareto efficient. The equilibrium Po()is an equilibrium for this economy because it gives each trader the information y, and this is equivalent to having y. The utility frontier of the central planner with information y is equivalent to the utility frontier with information y, since y is a sufficient statistic. Therefore the equilibrium P() is efficient to the extent that it yields allocations which a central planner with al the information y would choose as optimal. If there are any other equilibria they cannot yield more efficient allocations. Similarly the noisy equilibrium Po(y, x) cannot yield more efficient allocations The paradox we must face is that P(), by being so efficient, removes incentives for individuals to collect information. If information is costly then no individual will purchase it if he can observe Po. Therefore Po() is not an equilibrium if information is costly. Only an imperfect information equilibrium can be an equilibrium in an economy where information is costly. There may be imperfect information equilibria. These equilibria would have a chance of persisting in an economy where information is costly. Hayek ([1945], p. 527)has written We must look at the price system as,.. a mechanism for communicating information if we want to 2. Where Wor=XR+ Po()X 3. We have shown that for each y the central planner cannot dominate the competitive allocations of ection 3. However, if we consider a replicated economy the variance of y will make life more risky in uld counteract this by equil ations of y. Thus a central planner could achieve, for all i, higher Eu* than the competitive market of Section 3 even though the planner could not improve E[u* ly]for individual. This occurs because in Section 3 we have not given the competitive economy the ability to insure against the risks of variation in Wo due to variation in y. If before traders observe Po, we allow traders to trade promises to deliver income contingent on the realizations of y, then the competitive market will do as well as the central planner in allocating the risks associated with y. Once the market for risky assets opens the equilibrium price will be a sufficient statistic just as in Section 3 4. Because of the strong portfolio separation property of the utility functions, the competitive equilibrium holdings of risky assets will be the same when all traders have the same beliefs irrespective f which beliefs they have, as long as Pi is conditionally normally distributed. For a given y, the equilibrium allocations generated by Po, strictly Pareto dominate the allocations generated in the naive conomy where people observe only y, and prices are given by in(13a). However, the allocations rated by Po do not Pareto dominate the allocations generated by the competitive equilibrium where ll trader y and use only their prior distribution on P. This result that no information is as good as all the information is a pecularity of utility functions which have the strong roperty, and is of little interest. It will always be true that when prices are sufficient statistics the central planner with all information will not be able to Pareto dominate the competitive allocations nditional on y