A risk-averse consumer has utility function log(W) where W is his wealth. He has an asset whose payoff is a lottery as follows:

{(1000,500);(0.9,0.1)}

He can purchase K0 units of insurance.

Part a

Find the fair insurance premium for one unit of insurance, denoted by .

Part b

Show that the consumer, maximizing his expected utility, would acquire full insurance when presented the opportunity to buy fair insurance.