22 Inperfect Competition 3

22 Inperfect Competition 3 - 4/9/2009 Topic 9: Competition...

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4/9/2009 1 Topic 9: Competition between firms (3) USC Marshal Collusion, entry and other considerations Introduction • Some further issues: – Firms are engaged in repeated interactions – Firms can enter and exit industries – Firms make many other choices in addition to capacity/pricing USC Marshal – Welfare and antitrust legislation Collusion Collusion: – When interacting only once, the firms could not achieve an equilibrium that would have maximized their joint profits because each firm has incentives to deviate from that outcome and increase their individual profits USC Marshal – Can repeated interaction help? • Yes, as long as the firms don’t discount the future too much
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4/9/2009 2 Collusion Example: – Suppose there are two identical aluminum producers, each with marginal cost of 1. The product is homogeneous so the firms are engaged in Bertrand competition. The demand is given by Q=9 P USC Marshal Q=9-P. • Profit-maximizing outcome: P=5 and each firm makes $8 in profit • Bertrand equilibrium: P=1 and each firm makes $0 in profit Collusion Repeated game: – But firms don’t choose their prices only once. Can the firms do better than the Bertrand equilibrium if the game is repeated? • Let the discount factor be δ USC Marshal – Consider the following strategy for each firm: • “Begin by choosing the collusive price. If we both have always chosen the collusive price up until today, choose the collusive price again. However, if either one of us ever priced below the collusive price, then choose P=MC forever” Collusion Payoffs: – If I follow the strategy and expect the other to follow the strategy, then we end up choosing the collusive price forever. The present value of this profit stream is 8 8 2 8 3 8 8 8 USC Marshal – If I cheat today, I will choose a price just below 5, giving me the full market and profits of 16 – But then the market price collapses to marginal cost and I will make zero profit after that – Better to cooperate if ... 1 8 1 8 16 1 2
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4/9/2009 3 Collusion • In any game, determining whether collusion is possible and for what discount factors involves three steps: – Solve for the present value of profits from following the collusive strategy USC Marshal – Solve for the profit-maximizing deviation from the collusive strategy today and the profit associated with it – Solve for the present value of profits from tomorrow on, following the retaliation by the other firms – If first is greater than the sum of the latter two, then collusion is sustainable Collusion Factors inhibiting collusion: Number of competitors • The more competitors there are (N>2), the bigger the gain today relative to losses in the future USC Marshal • Example: Bertrand with N firms. Let Π i be the per-firm profit in the collusive equilibrium.
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22 Inperfect Competition 3 - 4/9/2009 Topic 9: Competition...

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