3. A decision maker is faced with a choice between a lottery with a 30% chance of a payoff of $30 and a 70% chance of a payoff of $80, and a guaranteed payoff of $65. a. If the decision makers utility function is U = 1/2 what is the risk premium associated with this choice? b. If the decision makers utility function is U = | + 500, what is the risk premium associated with this choice? Please %3D

Suppose that 20 risk neutral competitors participate in a rent seeking game with a fixed prize of $500. Each player may invest as much money as he wishes in the political contest. The probability of winning is directly proportional to the candidate's share of the total rent-seeking investment. 1. What is the expected net benefit of a player if all other players invest $20 each? Write the net benefit as a function of the player's investment. 2. Solve the maximization problem to arrive at the profit-maximizing investment. Round to the nearest cent.

In a large casino, the house wins on its blackjack tables with a probability of 50.9%. All bets at blackjack are 1 to 1, which means that if you win, you gain the amount you bet, and if you lose, you lose the amount you bet. a. If you bet $1 on each hand, what is the expected value to you of a single game? What is the house edge? b. If you played 150 games of blackjack in an evening, betting $1 on each hand, how much should you expect to win or lose? c. If you played 150 games of blackjack in an evening, betting $3 on each hand, how much should you expect to win or lose? d. If patrons bet $7,000,000 on blackjack in one evening, how much should the casino expect to earn? a. The expected value to you of a single game is $ (Type an integer or a decimal.)

Are the following preferences consistent with von Neumann Morgenstern’s axioms to maximize expected utility? Explain. a. You would rather have a sure $200 to a gamble with p=0.7 chance of $200, p=0.1 chance of $50, p=0.2 chance of $300. b. You prefer the gamble of p=2/3 chance of $300 and p=1/3 chance of $50 than a sure $250 win.