(Q2) Emmitt is a risk averse investor whose preferences over dollar wealth are given by the utility function u($)=In($). Emmitt has the option to buy a portfolio of precious metals. If there is high inflation in the future then the portfolio will be worth $10,000. If there is low inflation then the portfolio will be worth only $6,400. Emmitt considers high and low inflation to be equally likely. (a) What is the expected value of the portfolio of precious metals? What is the certainty equivalent to this portfolio? What is the risk premium? (b) Illustrate the expected utility of this portfolio in a diagram. Be sure to label the expected value, expected utility, certainty equivalent and risk premium (c) Suppose that the likelihood of high inflation falls to 22.5% and that the value of the portfolio of precious metals rises to $14,400 in the high inflation state (the value in the low inflation state remains unchanged at $6,400). Show that the expected value of the portfolio has not changed but that both the risk premium has risen? Illustrate the expected utility of the portfolio under the new circumstances in your diagram for part (b). Be sure to indicate the new certainty equivalent and the new risk premium