1. The state lottery sells 10 million tickets, one of which is a winner. The winning ticket pays the holder $5 million; all other lottery tickets are losers and pay $0. The price of each ticket is $1. Calculate the expected value of the lottery, assume risk neutrality. Should a risk neutral player purchase a ticket?
2. In American Roulette, there are two white slots on the roulette wheel instead of one (thus there are 38 slots in total) Compute the expected value to a gambler betting $1 on the color red, and to the casino, for American Roulette.
3. Consider again the small business imperfect information game the game shown in the right panel, but with the following rule changes. Instead of losing all of his money if he opens a business in the bad state, an investor is subsidized, and gets a payoff of $10,000- also in this state. Otherwise payoffs are like those in Figure 2.6. Call this game Subsidized Small Business. Show that for all three attitudes, the strategy chosen is Open. Then interpret your result in terms of the economic policy bias against subsidies. (Note: You need not go case by case through the different risk attitudes. There is a global answer)
4. Consider a risk seeker with utility function u(x) = x2; a risk-neutral player with utility function u(x) = x; and a risk averter with utility function u(s) = x0.5 . Plot the utility function of each. Then show that the marginal utility of money for the risk (seeker/neutral/averter) is (increasing/constant/decreasing) as money increases.