2 Expected value, expected utility, certainty equiv- alent, risk premium In this part, we examine some issues relating to the use of the expected utility repre- sentation of preferences to model choice over risky alternatives. Consider the following expected utility function where r and ro are monetary consumption levels in states 1 and 2, respectively, which occur with probabilities m and #2. Let m = #2 = 1/2. 2.1 For the lottery that pays 100 in state 1 and 400 in state 2, compute i) the expected utility of the lottery, if) the epected value of this lottery, ifi) the utility of receiving this expected value with certainty (ie. of receiving this expected value in both states). Which is larger-the expected utility of the lottery, or the utility of the expected value of the lottery? What does this tell you about this person's attitude toward risk? 2.2 The certainty equivalent of the lottery is an amount which, if received with certainty, would make the person indifferent between the lottery and receiving the certainty equivalent in each state. Compute the certainty equivalent of the lottery in 2.1. How does it compare to the expected value? 2.3 Use the definition of concavity to show in general, if one is risk averse, then the certainty equivalent of a lottery falls short of its expected value. The difference between these two is often called the risk premium for the lottery