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Week 4 – ECMC02 – Oligopoly Objectives for this week (and part of next): 1. Finish up discussion of price discrimination, presenting material on third-degree price discrimination 2. Introduce theory of oligopoly 3. Cournot model 4. Cartel or joint-monopoly model 5. Quasi-competitive model 6. Stackelberg leader model 7. Bertrand model 8. Bertrand model with differentiated products 9. Dominant firm/price leadership model 10. Compare and contrast different models of oligopoly behaviour 1 Third-degree price discrimination Not first degree (perfect) Not second degree (same menu of prices for all) But third…segmenting customers into different groups – dividing the market Not personalized pricing, not versioning, but group pricing Must be able to identify customers with different purchasing characteristics (essentially different elasticities of demand) Must be able to prevent resale between groups E.g., student discounts on TTC, senior citizen discounts on TTC and elsewhere, sales into different markets in the same country or different countries, men’s and women’s haircuts 2 Graphically: 3 Rule for profit maximization: Set MR in each market equal to MC (one production facility) MR1 = MR2 = MC But, since MR1 = MR2, And because MR = P(1 + 1/ED) We know that P1(1 + 1/ED1) = P2(1 + 1/ED2) Or, P1/P2 = (1 + 1/ED2)/(1 + 1/ED1) 4 Let’s say elasticity of demand in Market 1 is -4 and elasticity of demand in Market 2 is -2. What will be the ratio of the prices in these two markets when the monopolist sells in both? Since P1/P2 = (1 + 1/ED2)/(1 + 1/ED1) = (1 – ½)/(1 – ¼) = (1/2)/(3/4) = 2/3 In other words, the price in Market 1 will be 2/3rds of the price charged in Market 2 5 Imagine a monopoly provider of satellite TV signals selling into Vancouver and Toronto. You have to imagine that there are no close substitutes. Imagine demand is given by: QV = 50 – 1/3 PV QT = 80 – 2/3 PT Where Q is measured in thousands of subscriptions per year and P is the subscription price Costs are given by TC = 1000 + 30Q So MC = dTC/dQ = 30 (the cost of servicing one more subscription) 6 Turning around the demand functions, we have PV = 150 – 3QV PT = 120 – 3/2 QT Therefore, MRV = 150 – 6QV MRT = 120 – 3QT Therefore, in Vancouver MRV = 150 – 6QV = 30 or QV* = 20 And substituting into Vancouver’s demand function PV* = 150 – 3QV = 150 – 60 = $90 And in Toronto MRT = 120 – 3QT = 30 or QT* = 30 And substituting into Toronto’s demand function PT* = 120 – 3/2 QT = 120 – 45 = $75 7 How would you calculate demand in the combined markets if you wanted to calculate the monopoly solution when markets could not be segmented? 8 Oligopoly What is it? Why are there so many models? Oligopoly is a market in which there are only a few sellers. How many? So few that they feel the effects of each other’s decisions. Oligopoly markets are ones in which producers engage in strategic behaviour…. …there is strategic interaction 9 What form does competition between these sellers take? Could be collusion, could be a price war, could be an implicit agreement to share the market, could be an advertising war for market share but no price-cutting or, perhaps, one producer will have a dominant position and become a price leader, or a leader in decisions about output. Many other possibilities too. Therefore, many models All contributing to our understanding…. 10 Two broad types of models 1. Good sold is essentially same across producers (Oligopoly models) 2. Good sold differs in important ways from producer to producer (monopolistic competition or product differentiation) Other major issue: What do we assume about entry conditions? In this whole group of models today, entry is assumed blocked in some way In other models, blocking entry is a central strategic concern 11 Cournot Model Augustin Cournot (1838) A simple model assuming simple interaction. Each producer chooses its output assuming other producers will not react (will keep output same) In other words, each producer profit maximizes according to “residual” demand (However, each producer does, in fact, react) We are assuming a stable mature market of producers who do not want to rock the boat Homogeneous good. Assume duopoly. No entry. Firms choose output. 12 Mineral Water – e.g., Evian and Perrier Market Demand: P = 100 – Q or Q = 100 - P Total Costs for each firm TC = 10q Two firms, so that q1 + q2 = Q Firm 1 assumes Firm 2’s output remains constant (q2), so 13 P 100 Market Demand q2 (100 – q2) Residual demand curve for Firm 1 is q1 = (100 – q2) – P or P = (100 – q2) – q1 14 100 Q Therefore, along the residual demand curve… MR1 = (100 – q2) – 2q1 Since MC = dTC/dq = 10, profit max occurs where (100 – q2) – 2q1 = 10 or q1 = 45 – 0.5q2 [Reaction function for Firm 1] Often designated as R1 or R1(q2) 15 Firm 2’s reaction function is identical So q2 = 45 – 0.5q1 [Reaction function for Firm 2] Often designated as R2 or R2(q1) 16 On a graph: R1(q2) q1 90 R2(q1) 45 R1(q2) 45 90 17 q2 Only at “equilibrium point” do Firm 1 and Firm 2 not have incentives to change their output given the output of the other firm (check this) So q1 = 45 – 0.5q2 = 45 – 0.5(45 – 0.5q1) = 22.5 – 0.25 q1 So .75q1 = 22.5 Or q1 = 30 and q2 = 30 18 This equilibrium concept is called a Nash equilibrium after John Nash Sometimes, Cournot-Nash equilibrium In a Nash equilibrium, neither firm/player has any incentive to change his strategy (given the strategy of the other players/firms). 19 We know the outputs. What price will be charged? Each firm produces 30 units of output. Since market demand is P = 100 – Q, we have P = 100 – 60 = $40 Profit is TR – TC For each producer, Π = (40 x 30) – (10 x 30) = $900. Total profit in the industry is $1,800. 20 Cartel or Joint Monopoly Successful cartels - OPEC, bauxite (1970’s), uranium (1970’s), mercury (1930-1970), iodine (1878-1940), cement Unsuccessful cartels – copper, tin, coffee, tea, cocoa Try to jointly act like a monopolist. Restrict output to monopoly level to drive price up. 21 Faced with same market demand as above, how would cartel behave? P = 100 – Q TC = 10Q MR = 100 – 2Q = 10, so Q* = 45 (or q1 = q2 = 22.5, if there are two producers in the cartel) P* = 100 – 45 = $55 Π = TR – TC = (55 x 45) – (10 x 45) = $2025 Or Π1 = Π2 = $1012.50 22 Quasi-competitive model (for comparison purposes) Each firm acts as a price taker, sets P = MC, ignoring potential market power If P = 100 – Q and TC = 10Q, Then 100 – Q = 10 or Q* = 90 Then, P* = 100 – 90 = $10. So Π = 0 23 Comparison QuasiCournot competitive Duopoly Quantity Price Profit 90 $10 $0 60 $40 $1,800 Cartel – Joint Monoopoly 45 $55 $2,025 Cournot Model gives result between competitive and monopoly Firms do not acquire and use knowledge about other firms 24 Stackelberg Model Heinrich von Stackelberg (1930’s) Amendment to Cournot model. Two firms. One firm knows the reaction function of the other firm and maximizes profit subject to the behaviour of the other firm (as described by the reaction function). This firm is the Stackelberg leader 25 Assume Firm 1 is the Stackelberg leader Firm 1 knows Firm 2’s reaction function R2(q1) = 45 – 0.5q1 Therefore, q1 = (100 – q2) – P Or q1 = (100 – [45 - 0.5q1]) – P or P = 55 - 0.5q1 Therefore, MR1 = 55 - q1 = 10 So, q1* = 45 26 Since Firm 2 follows its reaction function q2 = R2(q1) = 45 – 0.5q1 or 45 – 22.5 = 22.5 Therefore, Q* = 45 + 22.5 = 67.5 P* = 100 – Q = $32.50 Π1 = (32.50 x 45) – (10 x 45) = $1012.50 Π2 = (32.50 x 22.5) – (10 x 22.5) = $506.25 Total Π = $1518.75. 27 Comparison QuasiCournot Cartel – competitive Duopoly Joint Monoopoly Quantity 90 60 45 Price $10 $40 $55 Profit $0 $1,800 $2,025 28 Stackelberg 67.5 $32.50 $1518.75