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Advanced Industrial Organization III. Dominant Firms and Market Power Instructor: Zhiqi Chen 1. Introduction Two models of imperfect competition that are less commonly studied in industrial organization theory:  The dominant firm model  The monopolistic competition model In some markets these models are better approximations of reality than either monopoly or oligopoly. For examples:  PC operating systems, PC CPU chips  Book publishing, restaurants 2. A General Model of Dominant Firm  A dominant firm: a near-monopoly  Small rivals of the dominant firm: the competitive fringe  The dominant firm sets the price  Fringe firms are price-takers  QM = QM(p): market demand  Qf = Qf(p): the supply function of the competitive fringe p 0 = min (AAC) where AAC denotes average avoidable costs  The residual demand for the dominant firm: Q D (p) = Q M (p) - Q f (p):  The dominant firm’s cost functions: TCD = cQD, MCD = c. A diagrammatic illustration The dominant firm’s optimization problem: max ( ) ( )[ ( ) ( )]D D M fp p c Q p c Q p Q p      The first-order condition: / ( )[ ' '] [ ] 0D M f M fd dp p c Q Q Q Q       [ ] / [ ' '] '/ ( / ) '/ M f D M D M f M M f M f f f f p c Q Q Q Q s p p Q Q pQ Q Q Q pQ Q s             where s j =Q j /Q M : market share of firm j (j = D, f) ε: elasticity of market demand, which measures demand substitution εf: elasticity of fringe supply, which measures supply substitution Note that the profitability of the dominant firm depends on s D , s f, ε and εf. An example of models that incorporates a dominant firm: Chen (2003 RAND) – It studies the effects of buyer power in the hands of a dominant retailer – In the model, a dominant retailer competes against a competitive fringe – The dominant retailer has buyer power against the supplier – Buyer power in the hands of the dominant retailer reduces consumer prices, but it causes potential efficiency loss in the provision of retail services – Economic efficiency does not always improve with the rise of buyer power 2. A Dynamic Model of Dominant Firm Implicit assumption in the dominant firm model:  There are high barriers to entry so that the number of fringe firms is fixed (i.e. the fringe supply curve is exogenously given) Alternatively, additional fringe firms may enter this market if there are profits to be made  Entry of additional fringe firms will shift the fringe supply curve to the right, reducing the residual demand for the dominant firm  Anticipating this, a low-cost dominant firm may set the price just below the minimum of fringe firms’ average cost curve to limit entry Berck and Perloff (1988 JEDC): In the long run, the competitive fringe is completely eliminated The Berck and Perloff Model The present value of the dominant firm’s profit stream: 0 [ ( ) ][ ( ) ( )] rtV p t c f p x t e dt     (1) where c: the average cost of the dominant firm f(p): the market demand function x(t): the level of sales by the competitive fringe (where each fringe firm produces one unit of output) x(0) = x0: the initial number of fringe firms The discounted value of profit stream of a fringe firm starting at t: ( )( ) [ ( ) ] r s tl t y t p s p e ds     (2) where pl is the limit price (the average cost of a fringe firm) An important assumption: pl > c (the dominant firm has a lower cost than a fringe firm) Aside. The Leibniz’ formula: ( ) ( ) ' ( ) ( ) ( , ) ( , ( )) '( ) ( , ( )) '( ) ( , ) v x v x x u x u x d f x t dt f x v x v x f x u x u x f x t dt dx     Use the Leibniz’s formula to differentiate (2) wrt t: ly ry p p   (3) The rate of entry is proportional to the discounted value of profit stream represented by (2) (“rational expectation”): ( ), where 0 is a constantx ky t k  (4) The number of fringe firms cannot be negative: x(t) ≥ 0 (5) The dominant firm chooses the time path of p(t) to maximize (1) subject to (3), (4) and (5). The current-value Hamiltonian: ( )[ ( ) ] ( )lH p c f p x zky v ry p p wx        where z and v are co-state variables, and w is a Lagrange multiplier The necessary conditions: ( ) ( ) '( ) 0pH f p x p c f p v      (6) [ ( ) ]xz rz H rz p c w       (7) ( )yv rv H rv zk vr zk       (8) 0 and 0wx w  (9) Consider the steady state, where 0.x y z v w        Then, (4) implies y* = 0 and (3) implies p* = pl. From (8), we obtain z = 0. Then (7) implies that w* = p* - c = pl - c > 0 Then (9) implies that x* = 0. That is, in the steady state the competitive fringe is completely eliminated. Berck and Perloff also consider the case of “myopic expectation” [first analyzed by Gasins (1971 JET)] Myopic expectation: A fringe firm assumes that the price will remain constant at the present level. In other words, its expected value of profit stream is ( )( ) [ ( ) ] [ ( ) ] /r s tl l t y t p t p e ds p t p r       (2’) Then (2’) and (3) can be combined into a single constraint: ( / )[ ( ) ]lx k r p t p  (4’) In this case, the dominant firm maximizes (1) subject to (4’) and (5). With myopic expectation, the steady state equilibrium may involve x* > 0. That is, the dominant firm eventually limits price with a positive number of fringe firms left in the market