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A person owns a car worth 50,000 dollars which can get stolen with probability 1%. She can purchase coverage of the amount A at premium

A person owns a car worth 50,000 dollars which can get stolen with probability 1%. She can purchase coverage of the amountAat premium of 0.05 dollars for each dollar covered (thus the total price of insurance is0.05A). Her utility function isU(w)ln(w). Assume she has no other assets.

(a) How much insurance will she choose to buy?

(b) Does she buy full insurance? Why? Explain your answer.

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