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Total Costs: TC = 20Q P = the price of a basketball in $ US TC = the total cost of producing a given quantity of basketballs (in $ US) Show all of your work in solving the problems below. 1) The Cournot Model: Now assume that the two firms are Cournot competitors, and that all the assumptions of the Cournot model are met: no firm entry, homogeneous goods, a single period, and that the firms choose the quantities of basketballs to supply. Now, how many basketballs will be sold by each firm and at what price? What will be the total revenues, total costs, and the profits for each of the two firms? Demonstrate the model using graphs. (See Figs. 9-3 to 9-10) 2) The Stackelberg Model: Assume that the two firms are Stackelberg competitors, and that Wilson is the Stackelberg leader and Spalding the follower. All the assumptions of the Cournot model are met: no firm entry, homogeneous goods, a single period, and that the firms choose the quantities of basketballs to supply, but that Wilson gets to decide its strategy first, in full knowledge of Spalding's reaction function. Now, how many basketballs will be sold by each firm and at what price? What will be the total revenues, total costs, and the profits for each of the two firms? Demonstrate the model using graphs. (See Fig. 9-11) 3) The Bertrand Model: Now assume that the two firms are Bertrand competitors and that the firms compete by choosing price. How many basketballs will be sold by each firm and at what price? What will be the total revenues, total costs, and the profits for the two firms? Demonstrate the model using graphs. (See Bertrand Oligopoly) 4) The Cartel/Collusion Model: Assume that the two firms get together and form a cartel. How many basketballs will be sold in the market and at what price? What will be the total revenues, total costs, and combined profit for the two firms? Demonstrate the model using a graph. (See Figs. 9-9 to 9-10 on collusion.) 5) Comparison of the Four Structures: Compare the four industry structures based on quantity, price, profits, and price. (See Comparing Oligopoly Models.) 1 6) Game Theory: The Prisoners' Dilemma: Assume that the Wilson and Spalding athletic equipment companies are in a one-shot game for market share and profits, but that they have the option of choosing only one of two possible price strategies for basketballs: $20 or $80. Obviously if they choose different strategies, the firm with the lower price will win the entire market. The firms face the following payoff matrix (See Chap. 10). Wilson \Spalding Wilson $ 20 Price Wilson $ 80 Price Spalding $ 20 Price Spalding $ 400, $400 $1500, $0 $ 80 Price $ 0, $ 1500 $ 1000, $1000 What strategy will each firm choose? Why? Which strategy is dominant? Which strategy is preferred by each firm? What will be the outcome of the one-shot game? Where is the Nash equilibrium? Which outcome would be best for the two firms? What will happen if the game is repeated an infinite number of times? 2