40 marks) Jane owns a house worth $100,000. Assume that her wealth consists entirely of the house. In any given year, there is a 2% percent chance that the house will burn down. If it does, its scrap value will be

$30,000. Jane's utility function is U(w) = 2 w .

1. Draw Jane's utility function (plotting utility against wealth).
2. Show whether Jane is risk averse.

(20 marks) Suppose the value of timber (already planted on some given land) is the following function of time: V(t) =10000+6000t-10t2 in dollars. Assuming the continuously discount rate (lending and borrowing rate) is 5% and assuming zero upkeep cost during the period of timber growth,

(a) what is the optimal time to cut the timber for sale?

(b) What is the maximum present value of timber? (dV/dt=6000-20t).

c. If the insurance premium is 2.5 cents per dollar insured, how much insurance will Jane buy?

d. Heidi, Jane's sister, owns a house with the same value ($100, 000) and with the same chance (2%) of burning down. The scrap value of the burned house is also $30,000. Find the expected utility foe Jane if the two sisters share the losses equally. Assume the accidents of fire for the two houses are independent.