3 ECON3039WI Which option gives a higher max-min utility: the act h or the lottery p? Give an intuitive explanation for the preference that you find. Can you give some real-world economic examples where such preferences may help us understand behaviour? Hint: You can understand the lottery p as an act h' that results in objective lottery p in both states of the world, good and bad. [8]Al (25 points) Let Z = [0, co), representing monetary outcomes in L. Assume that Tom's preference over simple lotteries over outcomes in Z can be represented with an expected utility function based on some utility function (over outcomes) u : 7 - R. Consider the three lotteries p,q. and r such that: . p(130) = p(110) = 1/2 . q(140) = q(120) = 1/2 . r(140) = r(100) = 1/2 (a) Does one of these lotteries first-order stochastically dominate another one? [4] (b) Does one of these lotteries second-order stochastically dominate another one? [6] Now suppose *(#) = VE. (c) Compute the risk premium for the lotteries p and q. Which is larger? Relate your answer to the Arrow-Prat measure of absolute risk aversion. [7] (d) Now suppose that Tom faces a choice between the lottery p from above and an Anscombe-Aumann act / described as follows. There are two states: ? = {good, bad}. In the good state, he will end up with 130 pounds (for sure). In the bad state he will get 110 pounds (for sure). He does not know the probabilities of the two states. Suppose his preferences over such acts can be represented using a max-min expected utility function. Tom's attitude toward objective risk (as represented by w) is as above. For the probability of the good state, he considers all values possible between 4/10 and 6/10