Consider the setup that we talked about in class (GS 1980), but without noise traders. Instead, each uninformed trader has wealth, given a position h in the security of Wi = wi + h(X-P) + zi Y, where X and Y are normally distributed with Y = + X + , and is mean zero and normally distributed independent of everything else. Think of zi Y as being random non-market income correlated (if 0) with X. Each individual knows their zi , but from the point of view of everyone else, zi is normally distributed with mean zero and independent of X and Y. Furthermore, zi = Z + i with z the standard deviation of Z and the standard deviation of i all of which are independent of each other. a. Derive the demand curve for sophisticated uninformed investors who have rational expectations and observe both P and zi (but do not solve for conditional expectations and volatilities) b. Derive the demand curve for the informed who as in class observe S = X + with independent of everything else. c. Show the nature of the equilibrium pricei.e. show that it is linear in two random variables and a constant (but do not solve for the constants) d. Let the number of agents get large and apply the law of large numbers to the equilibrium price. Show that an uninformed agent with rational expectations will use its knowledge of zi to form expectations. Specifically, E[X|P,zi ] is linear in P and zi (since everything is normally distributed) and puts non-zero weight on zi . You should use results from part c above. e. Explain why zi is useful for forecasting X.