1. 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 13% 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.
2. a) Assume for the time being that the insurance industry is competitive, and insurance is offered at a fair premium rate. Denote by WGKatie's wealth if she does not get her money stolen (the good state) and by WBher wealth if she does (the bad state). What are the equations for WGand WB(as functions of K)? Use these to work out the equation for Katie's budget constraint.