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collusionII

# collusionII - Collusion in Practice ECO 171 1 Introduction...

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ECO 171 1 Collusion in Practice

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ECO 171 2 Introduction • Collusion is difficult to detect – no detailed information on costs – can only infer behavior – Facilitating practices can be forbidden • Where is collusion most likely? – Key considerations • Incentives to collude • Ability to detect cheating.
ECO 171 3 Collusion and number of firms N firms, identical marginal cost c • Bertrand equilibrium p=c, π =0 • Cooperative agreement: – Monopoly price p m – Equal share of monopoly q m / N – Profits of cooperating: π c = ( q m / N ) ( p m –c ) • Interest rate r • Immediate gain from cheating = ( N -1) π c • Cost of cheating = lost future profits = π c / r • Cooperate if r < 1/( N -1) • For any r there is a critical N * = (1/ r ) + 1 such that cooperation is possible only if N < N *

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ECO 171 4 Collusion and cost differences Suppose there are two firms with different costs Firm 1 has lower marginal cost Profit-possibility frontier describes maximum non- cooperative joint profit Maximum profits if only firm 1 produces Profits π 1 π 2 π m π m This is the profit- possibility curve This is maximum aggregate profit
ECO 171 5 Example of Collusion 2 Suppose that the Cournot equilibrium is at C π 1 π 2 M π 1m π 2m π m π m C Collusion at M is not feasible • firm 1 makes less than at C A side-payment from 1 to 2 makes collusion feasible on DE D E With no side-payment collusion is confined to AB (lower because the inefficient firm also produces) A B

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6 Collusion with different costs • Costs c 1 < c 2 . • Bertrand equilibrium price = c 2 • Agreement: price=p, q 1 = α D(p), q 2 =(1- α )D(p) • Market share: α for firm 1 and (1- α ) for firm 2. • Example: c 1 =0, c 2 =20, p=50, α =1/2 : does not work! • Firm 1’s incentives: – Deviation profits = (1 −α ) ( p-c 1 )D(p) – Deviation cost = [ ( p-c 1 ) αδ (p)-(c 2 -c 1 )D(c 2 )]/r – Higher r , higher α to be indifferent .
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collusionII - Collusion in Practice ECO 171 1 Introduction...

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