A small businesswoman faces a 10% chance of having a fire that will reduce her net worth to $1.00, a 10% chance that fire will reduce it to $50,000, and an 80% chance that nothing detrimental will happen, so that her business will retain its worth of $100,000.
What is the maximum amount she will pay for insurance if she has a logarithmic utility function? In other words, if U(W) = in W, compute the cost of the gamble. [Note: The insurance pays $99,999 in the first case; $50,000 in the second; and nothing in the third.]