Topic 4 - Oligopoly - Fall 2011 Topic 4: Oligopoly Outline...

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Fall 2011 Topic 4: Oligopoly Outline Cournot Bertrand Edgeworth Differentiated oligopoly Horizontal mergers Conjectural variation Readings ch. 8 (pp. 231-74) ch. 23 (pp. 715-38) Lectures : 7, 8, 9, 10, 11 and 12 BU620 Topic 4: Classic models of oligopoly 1 of 23
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Fall 2011 Cournot : Assumptions and Matrix example Assumptions 1. Homogeneous product 2. Firms choose quantities 3. Constant MC, quantities determine capacity 4. Price adjusts to equate supply and demand 5. Nash equilibrium: Each firm chooses output to maximize profits, taking rival output as given . Example : P = 13 – Q , c 1 = c 2 = 1, π i = (12 – Q ) q i Firm 2’s output 3 4 6 Firm 1’s output 3 (18,18) (15,20) (9,18) 4 (20,15) (16,16) (8,12) 6 (18,9) (12,8) (0,0) (Pay-off to firm 1, Pay-off to firm 2) BU620 Topic 4: Classic models of oligopoly 2 of 23
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Fall 2011 Market power and market concentration Market concentration can be measured by the… …Herfindahl index given by …and is equivalent to 1/ H identical firms. Market power is …measured by the Lerner index, …related to H & η in Cournot (1) : market share, marginal cost efficiency and firm market power are positively related. (2) : market concentration and market power are positively related due to entry and MC variability. BU620 Topic 4: Classic models of oligopoly 3 of 23
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Fall 2011 Reaction functions and residual demand curves The Cournot response function of firm i… …indicates the profit maximizing response of firm i to any output chosen by rivals …slopes downward because a rise in rival output …shifts in firm i ’s residual demand …lowers firm i ’s marginal revenue …lowers firm i ’s profit maximizing output. Two approaches for deriving FOC in Cournot If firm i’ s marginal cost is c i and inverted demand is (1a) P ( Q ) = 120 2 Q (1b) where Q = q i + Q -i then its profits are π i = ( P ( Q ) – c i ) q i and its FOC is (2) (3) 120 2( q i + Q –i ) + q i (-2) = c i (4) RF i : Alternately, sub (1a) and (1b) into profits to get (5) i = (120 2( q i + Q –i ) – c i ) q i Differentiating with respect to q i yields (3). BU620 Topic 4: Classic models of oligopoly 4 of 23
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Fall 2011 Cramer’s rule and solving sets of linear equations x i :endogenous variables i = 1,…, n c i , a ij exogenous variables i = 1,…, n A system of linear equations can be written as or Cramer’s Rule : The solution to x i is given by 2 by 2 determinants 3 by 3 determinants BU620 Topic 4: Classic models of oligopoly 5 of 23
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Fall 2011 Solving symmetric Cournot models Let c i = c L for m low cost firms and c i = c H for n m high cost firms. By symmetry all firms with the same cost and demand will produce the same output in equilibrium and thus we obtain (6) q i = q L & Q -i = ( m –1) q L + ( n m ) q H if i = 1,…, m (7) q i = q H
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Topic 4 - Oligopoly - Fall 2011 Topic 4: Oligopoly Outline...

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