How to Collude

How to Collude - T /2 everywhere you see Q 1 or Q 2 in the...

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How to Collude I wanted to make the process of collusion clear for the whole class. The idea is that the firms will maximize joint profits. To solve for P, Q 1 2 , go through the following steps (which, for my class, is different than how I showed you). 1) Set up the total profit function π t = P(Q T ) – TC 1 – TC 2 2) Solve the market demand function for P, and substitute into the total profit function. 3) Each total cost function will be given in terms of the firm’s own quantity, Q 1 2 . If the firm’s costs are symmetric, each firm will produce half the total output, so put in Q
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Unformatted text preview: T /2 everywhere you see Q 1 or Q 2 in the Total Cost functions. 4) Take the derivative of profit with respect to Q T and set that equal to zero. Solving for Q T yields the quantity that maximizes industry profit. 5) Plug Q T into the market demand equation to find the industry price. 6) Q T /2 gives you Q 1 & Q 2 . Thats it. Six steps and youre done. Note: Step 3 only works where the firms costs are symmetric. Solving with asymmetric costs is takes a little extra work and we havent shown you how, so it wont come up on the final....
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