Econ 4010 Lecture 26

Econ 4010 Lecture 26 - <Lecture 26> 12. Oligopoly We...

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<Lecture 26> 12. Oligopoly We have assumed that our two duopolists make their output decisions at the same time. Now let's see what happens if one of the firms can set its output first. Stackelberg Model Oligopoly model in which one firm sets its output before other firms do Duopoly Example: P = 30 – Q, MC 1 = MC 2 = 0. Suppose Firm 1 sets its output first and then Firm 2, after observing Firm 1's output, makes its output decision. In setting output, Firm 1 must therefore consider how Firm 2 will react. Firm 2's Reaction Curve: Q 2 = 15 – (1/2)Q 1 What about Firm 1? Max. π 1 => 1 / dQ 1 = 0 => Q 1 = 15 Substitute for Q 2 in the demand function, P = 30 – Q 1 – Q 2 = 30 – Q 1 – [15 – (1/2)Q 1 ] = 15 – (1/2)Q 1 . TR 1 = 30Q 1 – Q 1 2 – Q 2 Q 1 = 30Q 1 – Q 1 2 – [15 – (1/2)Q 1 ]Q 1 = 15Q 1 – (1/2)Q 1 2 , MR 1 = 15 – Q 1 . Equilibrium: Q 1 = 15, Q 2 = 15 – (1/2)Q 1 = 15/2, Q = 22.5, P = 7.5 Going first fives Firm 1 an advantage. Why? Announcing first creates a fait accompli : No matter what your competitor does, your output will be large. To maximize profit, your competitor must take your large output level as given and set a low level of output for itself. If your competitor produced a large level of output, it would drive price down and you would both lose money. So unless your competitor views "getting even" as more important than making money, it would be irrational for it to produce a large amount.
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Econ 4010 Lecture 26 - &lt;Lecture 26&gt; 12. Oligopoly We...

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