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# A study in 1980s used statistical methods to estimate quarterly demand curved for Coke (Firm 1) and Pepsi (Firm 2): Q1 = 64 - 4P1 + 2P2 Q2 = 50 -...

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1. A study in 1980s used statistical methods to estimate quarterly demand curved for Coke (Firm 1) and Pepsi (Firm 2): Q 1 = 64 – 4P 1 + 2P 2 Q 2 = 50 – 5P 2 + P 1 The price is measured in dollars and the quantities are expressed as millions of units per quarter, where one unit is defined as 10 cases for cola. These demand curves imply that Coke and Pepsi are horizontally differentiated. Coke’s marginal cost is \$5 per unit and Pepsi’s marginal cost is \$4 per unit. (You can round the answers to two decimal places, or keep it as a fraction.) a) Solve for the Bertrand equilibrium. b) Suppose that because of additional advertising, Coke’s demand curve shifts to: Q 1 = 100 – 4P 1 + 2P 2 (with Pepsi’s demand curve remaining the same as it was before). Re-calculate the Bertrand equilibrium. c) Sketch a picture that shows what happened to the Bertrand equilibrium because of Coke’s advertising. Is Pepsi better off or worse off as a result of Coke’s advertising? 2. Take the setting of Cournot competition in class. Now suppose the two firms are instead asymmetric in their MC. We have C 1 = 10 and C 2 = 20. Assume quantity is continuous, meaning a firm can choose any non-negative real number as the quantity. Assume they can only use pure strategies and keep all other assumptions the same. a) Draw the new reaction functions. b) Solve for the pure strategy Nash Equilibrium. 3. Here is how we can think of N-firm Cournot competition. Assume all the firms have the same marginal cost C > 0. Firm 1 chooses Q 1 , Firm 2 chooses Q 2 , and so on. The market price P = A – (Q 1 + Q 2 + … + Q N ). Assume A > C. a) Solve for the Cournot (pure strategy) equilibrium. (Hint: the firms are all the same, so you should expect the equilibrium to be symmetric, that is, Q* 1 = Q* 2 = …= Q* N .) q 1 = (a – c –q 2 )/(2) b) Based on your answer to a), show whether the equilibrium profit of a firm increases or decreases in the number of firms, N.

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