Leightons utility function is represented by U(w)=2(w^1/2). Leighton has just purchased a new home worth $100,000 and his home represents all of his wealth. The statistics show that in any year there is a two percent (0.02) chance that his home may burn down. If Leightons house does burn down then the value of the scraps is $30,000.

1. Using the information above draw Leightons utility function, plot utility against wealth)
2. Is Leighton risk averse? Explain
3. The insurance for the house costs 2.5 cents per dollar insured, based on Leightons preferences how much insurance will he buy?
4. Leightons brother also owns a house that is valued at $100,000. His brothers house also has a 2% risk of burning down, if this occurs then the value of the scrap is worth $30,000. Determine the expected utility for Leighton if the two brothers share the losses equally. Also assume that the event of both houses burning down are independent.