Question 3. Suppose a decision maker has an exponential utility function. The profit distribution for two uncertain alternatives are given below. Uncertain Alternative-1 Uncertain Alternative-2 2 3 1.20 2.00 3.00 4.00 5.00 6.00 6.50 P{X1 = x} 0.05 0.10 0.30 0.25 0.05 0.05 0.20 0.00 2.00 3.00 4.60 5.00 6.10 9.00 P{X2 = x} 0.20 0.25 0.20 0.05 0.10 0.15 0.05 (a) Assume that the decision maker has a risk tolerance p = 00. Find the certainty equivalents and the risk premiums of both alternatives. Find the preferred alternative. (b) Assume that the decision maker has a risk tolerance p = 5. Find the certainty equivalents and the risk premiums of both alternatives. Find the preferred alternative. (c) What should be the risk tolerance if both alternatives are equally pre- ferred? (d) Comment why the preference order for the two alternatives varies by changing the risk tolerance in the above cases