# Unit 8: Imperfect Competition II oligopoly and monopolistic competition

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1 Unit 8: Imperfect Competition II oligopoly and monopolistic competition Prof. Antonio Rangel 1 Oligopoly Oligopoly: more than one firm, but not enough for perfect competition Firms have some market power Intermediate case between monopoly (F = 1) and perfect competition (F large) 1.1 Oligopoly with two firms Basic model Two firms q 1, q 2 = quantities produced by the two firms c i (q i ) cost function of each firm, no FCs or SFCs Key assumption: Each firm maximizes profits taking the action taken by the other firm as fixed Note: this assumes that firms anticipate each others actions correctly This gives rise to strategic considerations: Demand faced by firm i depends on choice of firm j Firm i s problem max q i 0 q ip D (q i + q j ) c i (q i ) 1

2 q j is taken as given in this problem. FOCs (also sufficient): dp D q i dq + pd = MC i }{{} MR w.r.t. q i given q j Key idea: firm s problem is as in the monopoly case, but with demand shifted due to other firm s actions Let q i (q j ) denote the solution to the problem for firm i, as a function of q j. Oligopoly equilibrium: q1 OL, q2 OL such that q1 OL = q1(q 2 OL ) and q OL q2(q OL 1 ) Remarks: 2 = 1. Model assumes rational expectations: each firm correctly anticipates other s action correctly in equilibrium 2. Firms best respond to each other 3. At equilibrium, firms have no incentive to deviate 4. Equilibrium concept generalizes to F > 2 (each firm best responds taking as given the choices of all other firms) 1.2 Example: Two identical firms Look at case of oligopolistic competition with two identical firms and linear aggregate demand F = 2, c(q i ) = µq i, i {1, 2} p D (q 1 + q 2 ) = p max m(q 1 + q 2 ) Demand faced by firm i is (p max mq j ) mq i Firm i s problem: max q i 0 q i(p max mq i mq j ) µq i 2

3 FOC: p max mq j 2mq i = µ Identical firms = symmetric equilibrium: q i = q j = q OL = q OL = pmax µ 3m DWL from oligopoly: Substituting in the inverse demand function: p OL = 2 3 µ pmax DWL then given by: DW L = 1 ( q opt 2q OL) (p OL p ) 2 = 1 ( ) ( ) m (pmax µ) 3 (pmax µ) = (pmax µ) 2 18m NOTE: There is a typo in the video lecture for this expression. This is the correct one. Distribution and oligopoly (table refers to graph in video lectures) Perfect Competition Oligopoly Change PS 0 B B CS A + B + C A -(B + C) SS A + B + C A + B -C 1.3 Example: Oligopoly vs. Monopoly Consider oligopoly market with two identical firms: F = 2, p D = p max mq, MC = µ for both firms What happens to DWL if the firms merge? Before: Oligopolistic equilibrium (as in previous section): q OL = pmax µ 3m 3

4 p OL = 2 3 µ pmax DW L OL = (pmax µ) 2 18m After: Monopolistic equilibrium (as in Unit 7): q mon = pmax µ 2m p mon = 1 2 µ pmax DW L mon = (pmax µ) 2 8m If follows that 2q OL > q mon (i.e., total oligopoly production is greater than total monopoly production) p OL < p mon DW L mon > DW L OL 1.4 Oligopoly with more than two firms Basic model: F > 2 Linear symmetric case: p D (q) = p max m i q i, MC i (q i ) = µ for all i Identical firms = q OL i = q OL j = q OL for all firms i, j Demand faced by firm i: ( p max (F 1)mq OL) mq i Optimal choice for i: MR i = MC i implies p max (F 1)mq OL 2mq i = µ Since firms are identical, in equilibrium must have q i = q OL for every firm i. Therefore, we get that each firm produces q OL = pmax µ (F + 1)m 4

5 Equilibrium price is then given by p OL = p max mf pmax µ (F + 1)m = 1 F + 1 pmax + F F + 1 µ Note: As F increases, p OL converges to µ, which is equal to the competitive equilibrium price How does the DWL change with number of firms? DW L(F ) = 1 2 (pol p )(q F q OL ) ( ) ( ) p max µ p max µ = 1 2 = 1 2m F + 1 (p max µ) 2 (F + 1) 2 m(f + 1) Note:DW L 0 with the square of the number of firms, so don t actually need many firms for the perfect competitive model to provide a good approximation of what happens in the market 2 Monopolistic competition Basic model: F 2 p D (q) = p max mq where q = i q i Firms: Can pay SFC of \$F to create a brand and then produce at constant MC of µ Not create a brand and set q i = 0 Key assumption: brands split the market equally and are monopolists within their brand Intuition: Each consumer becomes a loyal buyer of only one of the brands, but his demand curve for that brand is otherwise as before 5

6 Model solution I = number of firms that create a brand and produce a positive amount Each firm faces demand p max Imq Each firm sets MR = MC within its share of the market p max 2Imq = µ = q MC = pmax µ 2Im Equilibrium profits: Equilibrium number of firms: Remarks: = q tot = Iq MC = pmax µ 2m = p MC = p mon = pmax + µ 2 Π MC = (pmax µ) 2 4mI F I MC = max i such that (pmax µ) 2 4mi = qmon > F 1. Multiple equilibria: model gives number of firms that create brands, but doesn t say which firms create brands 2. Logic of equilibrium: some firms don t create brands because they correctly anticipate that other firms do, and given this creating additional brands is not profitable DWL analysis: q tot in M.C. = q mon = DW L MC = DW L mon + I MC F = (pmax µ) 2 8m Remarks: + I MC F 1. In oligopoly, DW L 0 as F. In contrast, in monopolistic competiting the DW L can increase as F 2. SFC of brand creation is socially wasteful 3. Brand creation induces decision mistakes by consumers in which Decision utility Experienced utility 6

7 3 Final remarks Here is a summary of the results Look at markets with 2 F < many firms Two types of markets to consider Oligopoly: Firms produce identical goods Equilibrium converges quickly to competitive case as F increases Monopolistic competition: Firms create brands that induce consumers to have very strong and artificial brand preferences Firms are monopolists within their brands Equilibrium outcome remains at monopolistic level as F increases 7

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