Sally owns a factory on the banks of a river that occasionally floods. She has no other assets. If there is no flood this spring, Sally's factory will be worth $500,000. If there is a flood, the factory will be worthless. Sally is an expected utility maximizer with a utility function u(W) = lnW where W is her wealth. She believes that the probability of a flood is 1/10. Sally is offered a chance to buy as much flood insurance as she likes at a cost of p per dollar's worth of insurance. To purchase C worth of flood insurance coverage she must pay a total of pC in insurance premiums. If there is a flood she receives a payment of C from the insurance company.
Write down a formula for the amount of insurance that Sally will buy as a function of the cost p per dollar of insurance. What is the price elasticity of demand of Sally's demand for insurance?