Introductory Microeconomics (ES10001) Topic 6: Imperfect Competition 1

1.Introduction PC & Monopoly are useful benchmarks. But, in more than half of the 800 major UK manufacturing product categories, 70% of market is shared by 5 largest firms in the market. Real world markets are imperfectly competitive Imperfectly competitive (IC) firms cannot sell as much as want at going market price; they face a downward sloping demand curve. 2

1.Introduction Two models of imperfect competition Monopolistic Competition Oligopoly And in terms of Oligopoly Non-Collusive Collusive 3

2. Monopolistic Competition Theory originally developed by Chamberlain (USA) and Robinson (UK) in early 1930s Many sellers producing similar, but not identical, products that are close substitutes for each other Each firm has only a limited ability to affect the market price 4

2. Monopolistic Competition Assumptions: Large number of small firms; firms assume own behaviour has no influence on rivals actions; Similar, but not identical, products; Free entry and exit into industry 5

2. Monopolistic Competition Implication Each firm can, to some extent, influence its market share by changing its price relative to its competitors Demand curve is downward sloping because different firms’ products are only limited substitutes for each other Advertising; product differentiation 6

2. Monopolistic Competition Short-run equilibrium of typical monopolistically competitive firm Profit-maximising monopolist in its own brand Thus MR = MC and (we assume) profit > 0 7

p 0 Q SMC SAC Q0Q0 p0p0 LAC 0 D = AR MR Profit Figure 1: Monopolosit Competition (SR) π > 0 8

2. Monopolistic Competition Existence of supernormal profit induces other firms to enter industry with their own brands This shifts down/left demand curve facing existing monopolistically competitive firms Moreover, demand curve becomes more elastic since consumers now have a greater variety of choice Process continues until no more firms enter industry (i.e. all firms are earning normal profit) 9

p 0 Q AR 0 AR 1 Figure 2: Impact on AR of entry of rival brands 10

p 0 Q LMC LAC Q0Q0 p 0 = LAC 0 D = AR MR Figure 3: Monopolist LR Equilibrium π = 0 11

2. Monopolistic Competition Long-run tangency equilibrium where p = LAC Monopolistically competitive firms are neither electively nor productively efficient ‘... too many firms each producing too little output.’ (Chamberlain) But … ‘... excess capacity is the cost of differentness.’ 12

3. Oligopoly ‘Competition among the few’ Few producers, each of whom recognises that its own price depends on both its own output and the output of its rivals Thus, firms are of a size and number that each must consider how its own actions affect the decisions of its relatively few competitors. For example, firm must consider likely response of rivals before embarking on a price cutting strategy 13

3. Oligopoly Collusion or competition? Key element of all oligopolistic situations Collusion; agreement between existing firms to avoid competition with one another Can be explicit or implicit 14

3. Oligopoly For example, existing firms might collude to maximise joint profits by behaving as if they were a multi-plant monopolist i.e. restricting q to monopolist level, say q 0, and then negotiating over the division of q and monopoly profits Note, might not agree to divide up q equally; sensible for more efficient members of the cartel to produce q 15

p 0 q D = AR MR MC q 0 q 1 p0p0 p1p1 Figure 4: Collusion or Competition E0E0 16

3. Oligopoly But, since cartel p > MC, each firm has an incentive to renege on the collusive agreement... temptation to reach the ‘first best’ renders the ‘second best’ unsustainable and drives firms to ‘third best’ First-Best: I renege, you collude Second-Best: Neither renege; we both collude Third-Best: We both renege Cartels are inherently fragile! 17

p 0 q D = AR MR MC q 0 q 1 p0p0 p1p1 Figure 4: Collusion or Competition Cartel price is above cartel member’s marginal cost, thus incentive to renege (i.e. increase q) Normal profit equilibrium 18

3. Oligopoly Collusion is easiest when formal agreements between firms are legally permitted (e.g. OPEC). More common in 19th century, but increasingly outlawed Collusion is more difficult the more firms there are in the market, the less the product is standardised, and the more demand and cost conditions are changing in the absence of collusion 19

3. Oligopoly In absence of collusion, each firm’s demand curve depends upon how competitors react, and firms have to make assumptions about this A simple model of this was developed by Sweezy (1945) to explain that apparent fact that prices once set as a mark-up on average costs, tend not too change ‘Kinked Demand Curve’ model 20

3. Oligopoly Assume firm is at E 0 selling q 0 output at a unit price of p 0 Firm believes that if it raises price, its rivals will not raise their price (i.e. D A ), but that if it lowers price, then its rivals will follow him (i.e. D B ) Thus demand curve is kinked at E 0 being flatter for p > p 0 and steeper for p < p 0 21

p 0 q DADA DBDB q0q0 p0p0 Figure 5a: Kinked Demand Curve Model E0E0 22

3. Oligopoly Both the ‘no-follow’ demand curve (D A ) and the ‘follow’ demand curve (D B ) will have an associated MR curve (MR A, MR B ) Thus MR is discontinuous (i.e. vertical) at q 0 since an increase in q beyond q 0 will lead to a discontinuous fall in total revenue 23

p 0 q DADA DBDB q0q0 p0p0 Figure 5b: Kinked Demand Curve Model E0E0 MR B MR A 24

p 0 q D q0q0 p0p0 Figure 5c: Kinked Demand Curve Model E0E0 MR 25

3. Oligopoly Thus, fluctuations in marginal cost within the discontinuous part of the MR curve (i.e. within A-B) do not lead to a change in the firms profit- maximising level of output Sweezy used the model to model the inflexibility of US agricultural prices in the face of cost changes 26

p 0 q D q0q0 p0p0 Figure 5a: Kinked Demand Curve Model E0E0 MR LMC A B 27

3. Oligopoly But two key weaknesses: Empirical Further evidence suggested that agriculture prices did not behave asymmetrically Theoretical Model does not explain how we got to the initial equilibrium, or where we go if LMC moves outside of the discontinuity 28

3. Oligopoly Cournot (1833) Firms compete over quantities with ‘conjectural variation’ that other firm(s) will hold their output constant Cournot originally envisaged two firms producing identical spring water at zero cost 29

3. Oligopoly Two firms (a, b) costlessly produce identical spring water Assume normal (inverse) demand curve for spring water is: q d = 100 – 5p p d = 20 – 0.2q Assume that firm a believes that firm b will produce zero output (i.e. E a {q b }= 0); firm a’s optimal q is that which maximises firm a’s total revenue vis. 30

p 0 q D = AR MR Figure 6a: Cournot Competition Firm a’s optimal output if E a {q b }= 0 Ea1Ea1 31

3. Oligopoly However, if firm a were to produce 50 units, then firm b would presume that it (i.e. firm b) faces a (residual) demand curve of: i.e. a residual demand given by the market demand for the good less firm a’s output And firm b would make its optimal choice of output accordingly 32

p 0 q D´ = AR´ MR Figure 6b: Cournot Competition Ea1Ea1 MR´ Firm a’s supply Firm b’s (residual) demand 33

p 0 q D = AR MR Figure 6c: Cournot Competition Firm b’s residual demand Eb2Eb2 34

3. Oligopoly Thus, if q a = 50, then firm b would maximise its profit (i.e. revenue) by setting q b = 25 But this would imply that firm a would want to change its initial level of output; i.e. q a1 = 50 was optimal under the assumption that q b = 0 But now that q b = 25, firm a will want to revise its choice of q accordingly 35

3. Oligopoly Thus, firm a will choose the level of output that maximises total revenue given q b = 25 Firm a’s residual demand curve is thus: Such that 36

p 0 q D´ = AR´ Figure 6d: Cournot Competition E b2 MR´ Firm a’s supply Firm a’s (residual) demand 37

p 0 q D = AR MR Ea3Ea3 Figure 6e: Cournot Competition Firm a’s residual demand 38

3. Oligopoly This process will continue until neither firm ‘regrets’ its optimal choice of output i.e. until its ‘conjectural variation’ regarding the other firm’s response is validated The Cournot equilibrium is thus where: 39

p 0 q D = AR MR MR´ EaEa Figure 6d: Cournot Competition Cournot Equilibrium EbEb 40

3. Oligopoly Cournot market shares Round1234n Firm a Firm b

3. Oligopoly It can be shown that total (i.e. market) equilibrium output under Cournot competition is given by: where q c is the perfectly competitive level of output (i.e. where p = MC) N.B. Usually termed ‘Nash-Cournot’ equilibrium, hence superscript ‘n’ 42

3. Oligopoly Solution method without calculus: Firm a’s residual demand curve: 43

3. Oligopoly Thus: 44

3. Oligopoly Setting MR = 0 implies: 45

3. Oligopoly And similarly for Firm b, thus, two equations and two unknowns: Solving … 46

3. Oligopoly 47

3. Oligopoly Generally, assume: where And assume 48

3. Oligopoly Thus: 49

3. Oligopoly Generally: 50

3. Oligopoly Thus: 51

3. Oligopoly Thus: 52

3. Oligopoly Thus: 53

3. Oligopoly Thus: since 54

3. Oligopoly Recall: 55

3. Oligopoly Monopoly n = 1 q n = (1/2)q c Duopoly n = 2 q n = (2/3)q c Perfect Competition n = q n = q c 56

3. Oligopoly Cournot originally envisaged his model in term of sequential decision making on the part of firms But it would irrational for each firm to persist with the conjectural variation that its rival will hold output constant when they only do so in equilibrium Moreover, the model implies the existence of a future, in which case it can be shown that profitable collusion is sustainable 57

3. Oligopoly Economists have re-interpreted Cournot’s model in terms of a one-shot game i.e. only one amount of output actually put onto market vis. Cournot equilibrium level of output q n But, it is assumed that each firm goes through a rational sequential decision making process before implementing its output choice 58

3. Oligopoly The Cournot equilibrium may be re-interpreted in this sense as a Nash Equilibrium That is, an equilibrium in which each party is maximising his utility given the behaviour of all the other parties I am doing the best I can do, given what you are doing; and vice versa 59

3. Oligopoly Stackelberg competition Variation of Cournot in which firm a announces its output and, once that announcement is made, the output cannot be changed. i.e. one-shot game or repeated game in which firm a produces the same level of output in each period. 60

3. Oligopoly Assume: Firm 1 - market ‘leader’ Firm 2 - market ‘follower’ N.B. firm 1 has to be able to make a credible, binding commitment to a particular output level 61

p 0 q D´ = AR´ MR Figure 7: Stackelberg Competition E1E1 MR´ E2E2 EsEs 5 62

3. Oligopoly Bertrand Competition Both Cournot and Stackelberg assume that firms chose outputs with prices determined by the inverse demand functions. But in many oligopolistic markets firms appear to set prices and then sell whatever the market demands at those prices 63

3. Oligopoly In perfect competition and monopoly, it makes no difference whether we carry out analysis in terms of prices or quantities That is, price determines quantity and quantity determines price But in oligopoly the distinction is crucial 64

3. Oligopoly Bertrand presented an alternative to the Cournot model in his review of Cournot’s book. He asked the question, what would be the outcome if the two firms chose prices: (a) simultaneously (b) independently And then sold all the output that was demanded at these prices via the inverse demand functions 65

3. Oligopoly Conclusion Completely different result emerges Equilibrium which replicates perfectly competitive (i.e. allocatively efficient) equilibrium in which p = MC 66

3. Oligopoly Firms compete with each other by marginally undercutting the other’s price (assuming homogenous good, costs etc.) and thus taking the whole market Process continues until the only equilibrium is one where each firm sets price equal to marginal cost 67

3. Oligopoly Nash equilibrium in Bertrand is p 1 = MC = p 2 Rationalisation for the equilibrium is on the same lines as in Cournot model vis. no other pair of prices has the property of mutual consistency. Bertrand intended this to be a reductio ad absurdum and to demonstrate the weakness of Cournot’s approach 68

p 0 q D = AR MC = AC qbqb MR qmqm pbpb pmpm Figure 8: Bertrand Competition EmEm EbEb Bertrand Equilibrium Monopoly Equilibrium 69

3. Oligopoly Bertrand model yields a striking prediction from a quite reasonable model If outputs are homogenous, an increase in the number of firms in the market from one to two leads from the monopoly equilibrium directly to the perfectly competitive equilibrium! 70

4. Game Theory Game; situation in which intelligent decisions are necessarily interdependent The players in the game attempt to maximise their own payoffs via a strategy Strategy; game plan describing how the player will act (or move) in every conceivable situation. Equilibrium Concept - Nash 71

4. Game Theory Nash equilibrium occurs when each player chooses his best strategy, given the strategies of the other players. Consider … Prisoners’ Dilemma 72

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 73

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 74

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 75

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 76

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 77

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 78

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 79

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 80

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 81

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 82

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 83

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 84

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 85

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 86

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 87

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 88

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 89

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 90

4. Game Theory Prisoner’s Dilemma Player 2ConfessDeny Player 1 Confess-8, -80, -10 Deny-10, 0-1, -1 91

4. Game Theory Nash Equilibrium ; Confess, Confess Indeed, to confess is each player’s ‘dominant strategy vis. optimal strategy that is independent of the strategy of the other player(s) Recall, ‘collusion versus competition’ 92

4. Game Theory Collusion versus Competition Firm 2RenegeCollude Firm 1 Renege-8, -80, -10 Collude-10, 0-1, -1 93

4. Game Theory Collusion versus Competition Firm 2RenegeCollude Firm 1 Renege-8, -80, -10 Collude-10, 0-1, -1 94

4. Game Theory Collusion versus Competition Firm 2RenegeCollude Firm 1 Renege-8, -80, -10 Collude-10, 0-1, -1 95

4. Game Theory Collusion versus Competition Firm 2RenegeCollude Firm 1 Renege-8, -80, -10 Collude-10, 0-1, -1 96

4. Game Theory Collusion versus Competition Firm 2RenegeCollude Firm 1 Renege-8, -80, -10 Collude-10, 0-1, -1 97

3. Oligopoly First-best (i.e. dominant strategy) would be to renege given that the other firm colludes Second-best would to both collude (i.e. a voluntary agreement to maintain the cartel output – but restrictive practices are usually illegal and so agreements are usually tacit) Third-best is to both renege and compete 98

3. Oligopoly Again … … Temptation to reach the first-best renders the second- best unsustainable and so forces players to the third- best 99