1.3 Problem 3 Consider a Hellwig (1980)-style market in which a continuum of investors indexed on [0, 1] trade in a firm's stock that pays off t = i + 72, where i and in are independent, i ~ N (0,n), and 72 N (0,12). The stock has a per-capita supply of 1. A noise trader randomly submits orders ~ N (0,nz") where is independent of all other variables in the economy. Suppose that the investors have CARA utility with risk aversion p. Assume that the firm discloses t2. Suppose the investors observe noisy signals ; = +i where i is independent of all other variables in the economy and ; ~ N (0,13). 2 1. Determine the price in the unique linear equilibrium in the model. 2. Calculate the expected price. How does this depend upon na?? 3. Calculate the variance of price. How does this depend upon na!? 1.3 Problem 3 Consider a Hellwig (1980)-style market in which a continuum of investors indexed on [0, 1] trade in a firm's stock that pays off t = i + 72, where i and in are independent, i ~ N (0,n), and 72 N (0,12). The stock has a per-capita supply of 1. A noise trader randomly submits orders ~ N (0,nz") where is independent of all other variables in the economy. Suppose that the investors have CARA utility with risk aversion p. Assume that the firm discloses t2. Suppose the investors observe noisy signals ; = +i where i is independent of all other variables in the economy and ; ~ N (0,13). 2 1. Determine the price in the unique linear equilibrium in the model. 2. Calculate the expected price. How does this depend upon na?? 3. Calculate the variance of price. How does this depend upon na