An agent with a logarithmic utility function of wealth tries to maximize his expected utility. He faces a situation in which he will incur a loss of L with probability . He has the possibility to insure against this loss. The insurance premium depends on the extent of the coverage. The amount covered is denoted by h and the price of the insurance per unit of coverage is p (hence the amount he has to spend on the insurance will be hp)

1. Calculate the amount of coverage h demanded by agent as a function of his wealth level Y , the loss L, the probability and the price of the insurance p.

2. What is the expected gain of an insurance company offering such a contract?

3. If there is perfect competition in the insurance market ( zero profit), what price p will the insurance company set?

4. What amount of insurance will the agent buy at the price calculated under point 3. What is the influence of the form of the utility function ?