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Class 17-2010

# Class 17-2010 - Managerial Econ Class 17 1 Stackelberg...

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11/9/2010 1 THE UNIVERSITY OF BRITISH COLUMBIA Managerial Econ: Class 17 1. Stackelberg Oligopoly – A Sequential Game 2. Multiple Equilibria and Pre-play Communication 3. Mixed Strategies 4. Repeated Games 5. Rationality, Information, and the Maximin Solution 6. Threats, Commitments and Entry Deterrence THE UNIVERSITY OF BRITISH COLUMBIA Announcements Assignment 2 The assignment has an online component and a component requiring answers to be turned in. The assignment is due in two weeks (Nov. 23) at the beginning of class. The rules are as before. Please read the instructions on the assignment. The online component is available on Vista and consists of 20 multiple choice questions. There are four longer questions that must be turned in. The assignment is on the website. Please download it and turn it in. The multiple choice questions are shown for your convenience but must be done on Vista.

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11/9/2010 2 THE UNIVERSITY OF BRITISH COLUMBIA 1. The Stackelberg Model – A Sequential Game The Stackelberg model is one in which one firm sets its output before other the other firm: (The Cournot model was based on simultaneous decisions.) Therefore, this model answers the question: What happens if one firm goes first? Assumptions: One firm can set output first MC = 0 Market demand is P = 40 - Q where Q is total output Firm 1 sets output first and Firm 2 then makes an output decision seeing Firm 1’s output. THE UNIVERSITY OF BRITISH COLUMBIA Firm 1: Must consider the likely response of firm 2 Firm 2: Takes firm 1’s output as fixed and determines its best response. What is the best response curve for firm 2? Determine firm 2’s best response curve by setting MR = MC. In this case R = PQ 2 = (40 – (Q 1 + Q 2 )Q 2 = 40Q 2 –Q 1 Q 2 –Q 2 2 so MR = dR/dQ 2 = 40 – Q 1 –2Q 2 = MC = 0. Therefore Q 2 = 20 - ½(Q 1 ). This is the best response curve for firm 2. We could draw it in the usual way. Sequential Decisions
11/9/2010 3 THE UNIVERSITY OF BRITISH COLUMBIA The Leader’s Decision Firm 1 knows firm 2 will choose output based on its best response curve. It can use firm 2’s best response curve to substitute for Q 2 in its own profit-maximization (MR= MC) problem. R = PQ 1 = (40 – (Q 1 + Q 2 ))Q 1 = 40Q 1 –Q 1 2 –Q 1 Q 2 = 40Q 1 –Q 1 2 –Q 1 (20 – ½ Q 1 ) = 20Q 1 –½Q 1 2 MR 1 = dR/dQ 1 = 20 - Q In this case MC = 0 so we set MR 1 = 0 or Q 1 = 20. What is Q

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Class 17-2010 - Managerial Econ Class 17 1 Stackelberg...

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