course for micro econ and I am not so good with uncertainty

1. A wage earner, Mister T, with initial wealth to = $1600, has a Bernoulli utilityfunction u(:r) = fl. His monthly wage amounts to $2000. He can be sackedwith probability 0.2. An insurance company designs an insurance contract againstunemployment. If Mister T pays an insurance premium of $156, he will receive$1056 if he is sacked. There are only two periods: a first one at which decisions aretaken and a second one at which all uncertainty is resolved. Assume that Mister T’s preferences satisfy the conditions of the expected utility theorem. (a) Does Mr. T decide to insure himself against unemployment? (b) Supposing that the insurance premium is $156, what is the minimum amountof money that the insurance company must disburse to Mr. T in case of unemployment, if it wants Mr. T to buy a contract?

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