Katie has £20,000 which she keeps in a safe in her flat. It is the only wealth which she has. She is thinking about using some of the money to insure against its theft. She thinks there is a (N+5)% chance that it will be stolen, in which case she will never see any of it again. She can fully insure against the loss of the money at a cost of £2000, or she can partially insure. Let K be the amount of insurance she buys and r be the premium rate at which insurance is offered (i.e. the price per £ of insurance) so that Katie spends rK on insurance. a) Assume for the time being that the insurance industry is competitive, and insurance is offered at a fair premium rate. Denote by WG Katie’s wealth if she does not get her money stolen (the good state) and by WB her wealth if she does (the bad state). What are the equations for WG and WB (as functions of K)? Use these to work out the equation for Katie’s budget constraint. b) Given Katie’s utility function over wealth is u(W) = √W, find out how much insurance Katie will buy. Does she fully insure? Explain why or why not. c) Suppose now that a cartel forms in the insurance industry and the premium rate is now double the fair one. How much insurance will Katie buy? Does she fully insure?
Katie has £20,000 which she keeps in a safe in her flat. It is the only wealth which she has. She
is thinking about using some of the money to insure against its theft. She thinks there is a
(N+5)% chance that it will be stolen, in which case she will never see any of it again. She can
fully insure against the loss of the money at a cost of £2000, or she can partially insure. Let K
be the amount of insurance she buys and r be the premium rate at which insurance is offered
(i.e. the price per £ of insurance) so that Katie spends rK on insurance.
a) Assume for the time being that the insurance industry is competitive, and insurance is
offered at a fair premium rate. Denote by WG Katie’s wealth if she does not get her
money stolen (the good state) and by WB her wealth if she does (the bad state). What
are the equations for WG and WB (as functions of K)? Use these to work out the
equation for Katie’s budget constraint.
b) Given Katie’s utility function over wealth is u(W) = √W, find out how much insurance
Katie will buy. Does she fully insure? Explain why or why not.
c) Suppose now that a cartel forms in the insurance industry and the premium rate is now
double the fair one. How much insurance will Katie buy? Does she fully insure?
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