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

Calculate the amount of coverage α* demanded by the agent as a function of the agent's initial wealth level Wi, the loss L, the probability p and the price of the insurance q.