A person owns a car worth 50,000 dollars which can get stolen with a probability of 1%. She can purchase coverage of the amount A at a premium of 0.05 dollars for each dollar covered (thus the total price of insurance is 0.05A ). Her utility function is U(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.