How useful Expected Utility is? The government is thinking of establishing a criterion under which schools potentially at risk of becoming infection hubs of a pandemic disease should be temporarily closed. The probability of a dangerous out-break of the disease among students is 1%. There are four possible outcomes:

A) No disease out-break; no school closure; B) No disease out-break; school closure; C) Disease out-break; school closed; D) Disease out-break and school open: huge spike in cases

Suppose the government is indifferent between sure outcome B and the lottery of A with probability p and D with probability 1 p. Moreover, the agency is indifferent between the sure outcome C and the lottery of A with probability q and D with probability 1 q. Suppose that it prefers A to D and that p (0, 1) and q (0, 1). Assume the conditions of the expected utility theorem are satisfied.

Construct a utility function of the expected utility of the government; Hint: Let the utility of the worst case scenario (which one is it?) be zero and the utility of the best case scenario (which one is it?) be one. Why you can do so?

Consider two different policy criteria:

Criterion 1: This criterion will result in a closure in 90% of the cases in which disease out-break will occur and an unnecessary closure in 10% of the cases in which no out-break occurs.

Criterion 2: This criterion is more conservative. It results in a closure in 95% of the cases in which disease out-break will occur and an unnecessary closure in 5% of the cases in which no out-break occurs. First, find the probability distribution over the four outcomes (A, B, C and D listed above) under each of the two criteria. Then, using the utility function you derived above, decide which criterion the government would prefer. The decision should depend upon two parameters.