Bob is a restaurant owner who faces an uncertain World with two possible states, COVID (c) and no COVID (n). Bob has money holding Mc when there is COVID, and has money holding Mn > Mc when there is no COVID. Denote the money bundle as M = (Mc, Mn). The COVID state is realized with probability = 41 and the no COVID state is realized with probability 1 . Bob's preferences are characterized by expected utility function, U(M) = ln Mc (1 ) ln Mn. (1) How does Bob rank the following bundles M1 = (10, 10), M2 = (7, 11), M3 = (1, 13)? (2) What is Bob's expected money holdings for the three bundles? What is the certainty equivalent of the three bundles? Is Bob risk averse, neutral, or loving? Calculate the risk premium associated with each bundle. Now, suppose that Bob has the bundle M3 = (1, 13). An insurance company offers an actuarially fair insurance, which charges price m = b and pays b in the case of COVID. Bob can choose the coverage, b. (3) What is the value of ? (4) Suppose Bob purchases a coverage b. What isVersion:0.9 StartHTML:0000000105 EndHTML:0000006382 StartFragment:0000000141 EndFragment:0000006342

What is his money bundle M = (Mc, Mn)? What is his

utility U(M)?

(5) How much coverage does Bob buy? What is his money bundle after buying the insurance?

2Now, suppose that Bob's preferences are given by U(M) = (Mc)2 + (1 )(Mn)2.

(6) How does Bob rank bundles M1, M2, M3? What is the certainty equivalent of the three bundles?

Is Bob risk averse, neutral, or loving? Calculate the risk premium associated with each bundle.

(7) As in parts (3)-(5), assume the insurance is actuarially fair. Bob's money holdings in each state

must be non-negative (i.e., Mc, Mn 0). How much coverage would Bob buy?

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