Beta and Gamma produce vitamin A at a constant average cost of $5 per unit. Assume that low-price guarantees are illegal. Here are the possible outcomes: Price fixing (cartel). Each firm sells 30 units at a price of $20 per unit. Duopoly (no price fixing). Each firm sells 40 units at a price of $12 per unit. Underpricing (one firm charges $20 and the other charges $12). The low-price firm sells 70 units and the high-price firm sells 5 units. 1. Suppose Beta chooses a price first, followed by Gamma. Draw a game tree for the price-fixing game and predict the outcome. 2. Suppose the firms agree to pick the high price. Once Beta picks the high price, how much more could Gamma earn if it cheated on the price-fixing agreement? 3. Suppose the firms divide the market into two areas of equal size and assign each firm one of the areas. Each firm agrees to sell only in its assigned areas. Will this arrangement generate a successful cartel?