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ProbSet5Ans_Solutions

# ProbSet5Ans_Solutions - AEM 331 Suggested Answers to...

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AEM 331 Suggested Answers to Problem Set #5 1. For both firms, solve for the lowest price where the average cost curve intersects demand. For firm 2, this is straightforward – average cost always equals 12, so this is the lowest price they could bid. For firm 1, we must find where: 100/ 1 102 Q Q + = - . Multiplying both sides by Q and rearranging, we have: 2 101* 100 0 Q Q - + = . The solutions are Q = 1 and Q = 100. At Q = 1, AC = 101, and at Q = 100, AC = 2; therefore, firm 1 can bid all the way down to 2. So, firm 1’s lowest bid is 2 while firm 2’s lowest bid is 12; therefore, firm 1 will win with a bid just under 12. 2. Now, solve for the monopoly profits each firm would make if they had control of the industry. For both firms, marginal revenue is 102 – 2Q. For firm 1, marginal cost is 1, so it will set 102 – 2Q = 1, to get Q = 50.5 and P = 51.5. This means total profits will be 51.5*50.5 – 100 – 50.5 = 2450.25. For firm 2, marginal cost is 12, so it will set 102 – 2Q = 12, to get Q = 45 and P = 57. This means total profits will be 57*45 – 12*45 = 2025. So, again firm 1 can “outbid” firm 2. Firm 1 wins with a bid just over 2025 and will set price at 51.5.

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