Suppose that market demand can be represented as p = 100 - 2Q. There are 10 identical firms producing an undifferentiated product, each with the total cost function TC = 50 + q2. Compare the competitive outcome with the cartel outcome
What is the individual firm's incentive to cheat on the cartel?
Each firm has MC = 2q, so that market supply is Q = 5p or joint MC = Q/5. As a cartel, they set joint MR = joint MC yielding 100 - 4Q = Q/5 or 100 = 4.2Q. Q = 23.8, and each firm will produce 2.38 units. The cartel price is 100 - 2(23.8 ) = $52.38. Each firm has the incentive to cheat because its marginal cost is $4.76 and the market price is $52.38. In a competitive market, supply equals demand. p = 100 - 2(5p) or 11p = 100. Price equals $9.09 and output equals 45.45 units.
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