Econ140 Assignment - Econ140 Assignment Ben Wen - 300186459...

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Market Demand given P=10-q (where q is q1+q2) So q=10 –p Game 1 . The incumbent chooses an output level. The potential entrant decides whether to enter or not. The potential entrant chooses an output level (if they entered). In this game the incumbent has the advantage as they are the first mover. The second firm must observe the output that the incumbent has chosen and then decide on the profit maximizing output given what the incumbent has chosen. However, the incumbent will predict the reaction of firm 2 and so they have an advantage. TR for incumbent = P*Q1 = (10-q)*q1 = (10-(q1+q2))*q1 = 10q1- q1^2 – q1*q2 Therefore MR = 10 – 2q1 – q2 Firm 2’s Reaction Curve: TR2 = P*Q2 = (10-(q1+q2))*q2 =10q2 – q1q2 – q2^2 Therefore MR2 = 10-q1-2q2 Setting MR = MC : 10-q1-2q2 = 2 -q1- 2q2 = -8 -2q2 = -8 + q1 Q2* = 4 – q1/2 This means that for ever choice of q1, q2* is firm 2’s best choice of output. The incumbent knows that firm 2 will act along its reaction curve and that firm 2’s output will rely on its own choice of output. The incumbent’s total revenue can therefore be written as : TR1 = 10q1 – q1^2 – q1(4 – q1/2) MR1 = 10 – 2q1 – 4 +q1 = 6 – q1 Profit maximizing output for incumbent at MR = MC: 6 – q1 = 2 Q1 = 4 Firm 2 will produce at Q2* = 4 – q1/2 = 2 Market price = 4
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Econ140 Assignment - Econ140 Assignment Ben Wen - 300186459...

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