An individual has wealth w and is afraid that an accident will occur with probability p that will cause her a loss of D. The individual has to choose an amount, x, she will pay for insurance that will pay her λx (for some given ) if the accident occurs. 1. The insurer’s expected profit is x-λpx . Assume that λ makes this profit zero, so that λ=1/p. Show that if the individual is risk-averse she optimally chooses x=pD , so that she is fully insured: her net wealth is the same whether or not she has an accident. 2. Assume that pλ1 (that is, the insurer’s expected profit is positive). Show that if the individual is strictly risk-averse then she chooses partial insurance: λxD

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Given that Net Exfected profit Net wealth XX P 0 x xxp p Net wealth if accident happe... View the full answer