Diego has $6,400. He plans to bet on a soccer game. Team A is a favorite to win. Assume no ties can occur. For $.80 one can buy a ticket that will pay $1 if team A wins and nothing if B wins. For $.20 one can buy a ticket that pays $1 if team B wins and nothing if A wins. Diego thinks the two teams are equally likely to win. He buys tickets so as to maximize the expected value of lnW (the natural log of his wealth). After he buys his tickets, team A loses a star player and the ticket price moves to $.50 for either team. Diego buys some new tickets and sells some of his old ones. The game is then played and team A wins. How much wealth does he end up with?
a. $5,000
b. $15,000
c. $6,400
d. $8,400
e. $10,000