Bill has a utility of money given by u(x) = log(x) where x is the amount of Bill’s money. Bill can buy any amount of an asset (including fractions). One unit of the asset either pays $12 or $1200. The probability that the asset pays $1200 is 2/3. If the price of the asset is $780 and Bill has $50,000 of wealth initially.

1) What is Bill's expected utility if he buys X units of an asset?

2) What is the amount of the asset that will maximize his expected utility?