Consider a market of risk-averse decision makers, each with a utility function U = √I. Each decision maker has an income of $90,000, but faces the possibility of a catastrophic loss of $50,000 in income. Each decision maker can purchase an insurance policy that fully compensates her for her loss. This insurance policy has a cost of $5,900. Suppose each decision maker potentially has a different probability q of experiencing the loss.
a) What is the smallest value of q so that a decision maker purchases insurance?
b) What would happen to this smallest value of q if the insurance company were to raise the insurance premium from $5,900 to $27,500?