3. Emmitt is a risk averse investor whose preferences over dollar wealth are given by the utility function u($) = l/(Hmmitt has the option to buy a portfolio of precious metals. If there is high ination in the future then the portfolio will he worth $ 1 ,t}. If there is low ination then the portfolio will he worth only $64M. Emmitt considers high and low ination to he equally likely. a} What is the expected value of the portfolio of precious metals? What is the certainty equivalent to this portfolio? 1What is the risk premium? h} Illustrate the expected utility of this portfolio in a diagram. Be sure to lahel the expected value, expected utility, certainty equivalent and risk premium Suppose that the likelihood of high ination falls to 22.5% and that the value of the portfolio of precious metals rises to $14,4 in the high ination state {the value in the low ination state remains unchanged at $64M). c} 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}. He sure to indicate the new certainty equivalent and the new risk premium