1 / 53

Chapter 5

Chapter 5. Business Strategy in Oligopoly Markets. Introduction. In the majority of markets firms interact with few competitors In determining strategy each firm has to consider rival’s reactions strategic interaction in prices, outputs, advertising …

malorie-scholz
Télécharger la présentation

Chapter 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 5 Business Strategy in Oligopoly Markets EC 170 Industrial Organization

  2. Introduction • In the majority of markets firms interact with few competitors • In determining strategy each firm has to consider rival’s reactions • strategic interaction in prices, outputs, advertising … • This kind of interaction is analyzed using game theory • assumes that “players” are rational • Distinguish cooperative and noncooperative games • focus on noncooperative games • Also consider timing • simultaneous versus sequential games EC 170 Industrial Organization

  3. Oligopoly Theory • No single theory • employ game theoretic tools that are appropriate • outcome depends upon information available • Need a concept of equilibrium • players (firms?) choose strategies, one for each player • combination of strategies determines outcome • outcome determines pay-offs (profits?) • Equilibrium first formalized by Nash: No firm wants to change its current strategy given that no other firm changes its current strategy EC 170 Industrial Organization

  4. Nash Equilibrium • Equilibrium need not be “nice” • firms might do better by coordinating but such coordination may not be possible (or legal) • Some strategies can be eliminated on occasions • they are never good strategies no matter what the rivals do • These are dominated strategies • they are never employed and so can be eliminated • elimination of a dominated strategy may result in another being dominated: it also can be eliminated • One strategy might always be chosen no matter what the rivals do: dominant strategy EC 170 Industrial Organization

  5. An Example • Two airlines • Prices set: compete in departure times • 70% of consumers prefer evening departure, 30% prefer morning departure • If the airlines choose the same departure times they share the market equally • Pay-offs to the airlines are determined by market shares • Represent the pay-offs in a pay-off matrix EC 170 Industrial Organization

  6. What is the equilibrium for this game? The example (cont.) The Pay-Off Matrix The left-hand number is the pay-off to Delta American Morning Evening Morning (15, 15) (30, 70) The right-hand number is the pay-off to American Delta Evening (70, 30) (35, 35) EC 170 Industrial Organization

  7. The morning departure is also a dominated strategy for American and again can be eliminated The morning departure is a dominated strategy for Delta and so can be eliminated. If American chooses a morning departure, Delta will choose evening If American chooses an evening departure, Delta will still choose evening The example (cont.) The Pay-Off Matrix American The Nash Equilibrium must therefore be one in which both airlines choose an evening departure Morning Evening Morning (15, 15) (30, 70) Delta (35, 35) Evening (70, 30) (35, 35) EC 170 Industrial Organization

  8. The example (cont.) • Now suppose that Delta has a frequent flier program • When both airline choose the same departure times Delta gets 60% of the travelers • This changes the pay-off matrix EC 170 Industrial Organization

  9. However, a morning departure is still a dominated strategy for Delta (Evening is still a dominant strategy. If Delta chooses a morning departure, American will choose evening The example (cont.) American has no dominated strategy The Pay-Off Matrix But if Delta chooses an evening departure, American will choose morning American American knows this and so chooses a morning departure Morning Evening Morning (18, 12) (30, 70) Delta (70, 30) Evening (70, 30) (42, 28) EC 170 Industrial Organization

  10. Nash Equilibrium Again • What if there are no dominated or dominant strategies? • The Nash equilibrium concept can still help us in eliminating at least some outcomes • Change the airline game to a pricing game: • 60 potential passengers with a reservation price of $500 • 120 additional passengers with a reservation price of $220 • price discrimination is not possible (perhaps for regulatory reasons or because the airlines don’t know the passenger types) • costs are $200 per passenger no matter when the plane leaves • the airlines must choose between a price of $500 and a price of $220 • if equal prices are charged the passengers are evenly shared • Otherwise the low-price airline gets all the passengers • The pay-off matrix is now: EC 170 Industrial Organization

  11. The example (cont.) If Delta prices high and American low then American gets all 180 passengers. Profit per passenger is $20 If both price high then both get 30 passengers. Profit per passenger is $300 The Pay-Off Matrix If Delta prices low and American high then Delta gets all 180 passengers. Profit per passenger is $20 American If both price low they each get 90 passengers. Profit per passenger is $20 PH = $500 PL = $220 PH = $500 ($9000,$9000) ($0, $3600) Delta PL = $220 ($3600, $0) ($1800, $1800) EC 170 Industrial Organization

  12. There is no simple way to choose between these equilibria. But even so, the Nash concept has eliminated half of the outcomes as equilibria (PH, PH) is a Nash equilibrium. If both are pricing high then neither wants to change Nash Equilibrium (cont.) (PH, PL) cannot be a Nash equilibrium. If American prices low then Delta should also price low The Pay-Off Matrix Custom and familiarity might lead both to price high (PL, PL) is a Nash equilibrium. If both are pricing low then neither wants to change American (PL, PH) cannot be a Nash equilibrium. If American prices high then Delta should also price high There are two Nash equilibria to this version of the game PH = $500 PL = $220 “Regret” might cause both to price low ($9000, $9000) ($0, $3600) PH = $500 ($9000,$9000) ($0, $3600) Delta ($3600, $0) ($1800, $1800) PL = $220 ($3600, $0) ($1800, $1800) EC 170 Industrial Organization

  13. There is no simple way to choose between these equilibria, but at least we have eliminated half of the outcomes as possible equilibria (PH, PH) is a Nash equilibrium. If both are pricing high then neither wants to change There are two Nash equilibria to this version of the game Nash Equilibrium (cont.) (PH, PL) cannot be a Nash equilibrium. If American prices low then Delta wouldwant to price low, too. The Pay-Off Matrix (PL, PL) is a Nash equilibrium. If both are pricing low then neither wants to change American (PL, PH) cannot be a Nash equilibrium. If American prices high then Delta should also price high PH = $500 PL = $220 ($9000, $9000) ($0, $3600) PH = $500 ($9000,$9000) ($0, $3600) Delta ($3600, $0) ($1800, $1800) PL = $220 ($3600, $0) ($1800, $1800) EC 170 Industrial Organization

  14. The only sensible choice for Delta is PH knowing that American will follow with PH and each will earn $9000. So, the Nash equilibria now is (PH, PH) Suppose that Delta can set its price first Sometimes, consideration of the timing of moves can help us find the equilibrium Nash Equilibrium (cont.) Delta can see that if it sets a high price, then American will do best by also pricing high. Delta earns $9000 The Pay-Off Matrix This means that PH, PL cannot be an equilibrium outcome American This means that PL,PH cannot be an equilibrium PH = $500 PL = $220 Delta can also see that if it sets a low price, American will do best by pricing low. Delta will then earn $1800 ($3,000, $3,000) ($0, $3600) PH = $500 ($9000,$9000) ($0, $3600) Delta ($3600, $0) ($1800, $1800) ($1800, $1800) PL = $220 ($3600, $0) ($1800, $1800) EC 170 Industrial Organization

  15. Oligopoly Models • There are three dominant oligopoly models • Cournot • Bertrand • Stackelberg • They are distinguished by • the decision variable that firms choose • the timing of the underlying game • But each embodies the Nash equilibrium concept EC 170 Industrial Organization

  16. The Cournot Model • Start with a duopoly • Two firms making an identical product (Cournot supposed this was spring water) • Demand for this product is P = A - BQ = A - B(q1 + q2) where q1 is output of firm 1 and q2 is output of firm 2 • Marginal cost for each firm is constant at c per unit • To get the demand curve for one of the firms we treat the output of the other firm as constant • So for firm 2, demand is P = (A - Bq1) - Bq2 EC 170 Industrial Organization

  17. The Cournot model (cont.) If the output of firm 1 is increased the demand curve for firm 2 moves to the left P = (A - Bq1) - Bq2 $ The profit-maximizing choice of output by firm 2 depends upon the output of firm 1 A - Bq1 A - Bq’1 Marginal revenue for firm 2 is Solve this for output q2 Demand c MC MR2 = (A - Bq1) - 2Bq2 MR2 MR2 = MC q*2 Quantity A - Bq1 - 2Bq2 = c  q*2 = (A - c)/2B - q1/2 EC 170 Industrial Organization

  18. The Cournot model (cont.) q*2 = (A - c)/2B - q1/2 This is the best response function for firm 2 It gives firm 2’s profit-maximizing choice of output for any choice of output by firm 1 There is also a best response function for firm 1 By exactly the same argument it can be written: q*1 = (A - c)/2B - q2/2 Cournot-Nash equilibrium requires that both firms be on their best response functions. EC 170 Industrial Organization

  19. Cournot-Nash Equilibrium q2 If firm 2 produces (A-c)/B then firm 1 will choose to produce no output The best response function for firm 1 is q*1 = (A-c)/2B - q2/2 The Cournot-Nash equilibrium is at Point C at the intersection of the best response functions (A-c)/B Firm 1’s best response function If firm 2 produces nothing then firm 1 will produce the monopoly output (A-c)/2B The best response function for firm 2 is q*2 = (A-c)/2B - q1/2 (A-c)/2B C qC2 Firm 2’s best response function q1 (A-c)/2B (A-c)/B qC1 EC 170 Industrial Organization

  20. Cournot-Nash Equilibrium q*1 = (A - c)/2B - q*2/2 q2 q*2 = (A - c)/2B - q*1/2 (A-c)/B  q*2 = (A - c)/2B - (A - c)/4B + q*2/4 Firm 1’s best response function  3q*2/4 = (A - c)/4B (A-c)/2B  q*2 = (A - c)/3B C (A-c)/3B  q*1 = (A - c)/3B Firm 2’s best response function q1 (A-c)/2B (A-c)/B (A-c)/3B EC 170 Industrial Organization

  21. Cournot-Nash Equilibrium (cont.) • In equilibrium each firm produces qC1 = qC2 = (A - c)/3B • Total output is, therefore, Q* = 2(A - c)/3B • Recall that demand is P = A - BQ • So the equilibrium price is P* = A - 2(A - c)/3 = (A + 2c)/3 • Profit of firm 1 is (P* - c)qC1 = (A - c)2/9 • Profit of firm 2 is the same • A monopolist would produce QM = (A - c)/2B • Competition between the firms causes their total output to exceed the monopoly output. Price is therefore lower than the monopoly price • But output is less than the competitive output (A - c)/B where price equals marginal cost and P exceeds MC EC 170 Industrial Organization

  22. Numerical Example of Cournot Duopoly • Demand: P = 100 - 2Q = 100 - 2(q1 + q2); A = 100; B = 2 • Unit cost: c = 10 • Equilibrium total output: Q = 2(A – c)/3B = 30; • Individual Firm output: q1 = q2 = 15 • Equilibrium price is P* = (A + 2c)/3 = $40 • Profit of firm 1 is (P* - c)qC1 = (A - c)2/9B = $450 • Competition: Q* = (A – c)/B = 45; P = c = $10 • Monopoly: QM = (A - c)/2B = 22.5; P = $55 • Total output exceeds the monopoly output, but is less than the competitive output • Price exceeds marginal cost but is less than the monopoly price EC 170 Industrial Organization

  23. Cournot-Nash Equilibrium (cont.) • What if there are more than two firms? • Much the same approach. • Say that there are N identical firms producing identical products • Total output Q = q1 + q2 + … + qN • Demand is P = A - BQ = A - B(q1 + q2 + … + qN) • Consider firm 1. It’s demand curve can be written: This denotes output of every firm other than firm 1 P = A - B(q2 + … + qN) - Bq1 • Use a simplifying notation: Q-1 = q2 + q3 + … + qN • So demand for firm 1 is P = (A - BQ-1) - Bq1 EC 170 Industrial Organization

  24. The Cournot model (cont.) If the output of the other firms is increased the demand curve for firm 1 moves to the left P = (A - BQ-1) - Bq1 $ The profit-maximizing choice of output by firm 1 depends upon the output of the other firms A - BQ-1 A - BQ’-1 Marginal revenue for firm 1 is Solve this for output q1 Demand c MC MR1 = (A - BQ-1) - 2Bq1 MR1 MR1 = MC q*1 Quantity A - BQ-1 - 2Bq1 = c  q*1 = (A - c)/2B - Q-1/2 EC 170 Industrial Organization

  25. Cournot-Nash Equilibrium (cont.) q*1 = (A - c)/2B - Q-1/2 As the number of firms increases output of each firm falls How do we solve this for q*1? The firms are identical. So in equilibrium they will have identical outputs  Q*-1 = (N - 1)q*1 As the number of firms increases aggregate output increases  q*1 = (A - c)/2B - (N - 1)q*1/2 As the number of firms increases price tends to marginal cost As the number of firms increases profit of each firm falls  (1 + (N - 1)/2)q*1 = (A - c)/2B  q*1(N + 1)/2 = (A - c)/2B  q*1 = (A - c)/(N + 1)B  Q*= N(A - c)/(N + 1)B  P* = A - BQ* = (A + Nc)/(N + 1) Profit of firm 1 is P*1 = (P* - c)q*1 = (A - c)2/(N + 1)2B EC 170 Industrial Organization

  26. Cournot-Nash equilibrium (cont.) • What if the firms do not have identical costs? • Once again, much the same analysis can be used • Assume that marginal costs of firm 1 are c1 and of firm 2 are c2. • Demand is P = A - BQ = A - B(q1 + q2) • We have marginal revenue for firm 1 as before • MR1 = (A - Bq2) - 2Bq1 • Equate to marginal cost: (A - Bq2) - 2Bq1 = c1 Solve this for output q1 A symmetric result holds for output of firm 2  q*1 = (A - c1)/2B - q2/2  q*2 = (A - c2)/2B - q1/2 EC 170 Industrial Organization

  27. Cournot-Nash Equilibrium q*1 = (A - c1)/2B - q*2/2 q2 The equilibrium output of firm 2 increases and of firm 1 falls As the marginal cost of firm 2 falls its best response curve shifts to the right q*2 = (A - c2)/2B - q*1/2 What happens to this equilibrium when costs change? (A-c1)/B R1  q*2 = (A - c2)/2B - (A - c1)/4B + q*2/4  3q*2/4 = (A - 2c2 + c1)/4B (A-c2)/2B  q*2 = (A - 2c2 + c1)/3B C R2  q*1 = (A - 2c1 + c2)/3B q1 (A-c1)/2B (A-c2)/B EC 170 Industrial Organization

  28. Cournot-Nash Equilibrium (cont.) • In equilibrium the firms produce qC1 = (A - 2c1 + c2)/3B; qC2 = (A - 2c2 + c1)/3B • Total output is, therefore, Q* = (2A - c1 - c2)/3B • Recall that demand is P = A - BQ • So price is P* = A - (2A - c1 - c2)/3 = (A + c1 +c2)/3 • Profit of firm 1 is (P* - c1)qC1 = (A - 2c1 + c2)2/9B • Profit of firm 2 is (P* - c2)qC2 = (A - 2c2 + c1)2/9B • Equilibrium output is less than the competitive level • Output is produced inefficiently: the low-cost firm should produce all the output EC 170 Industrial Organization

  29. A Numerical Example with Different Costs • Let demand be given by: P = 100 – 2Q; A = 100, B =2 • Let c1 = 5 and c2 = 15 • Total output is, Q* = (2A - c1 - c2)/3B = (200 – 5 – 15)/6 = 30 • qC1 = (A - 2c1 + c2)/3B = (100 – 10 + 15)/6 = 17.5 • qC2 = (A - 2c2 + c1)/3B = (100 – 30 + 5)/3B = 12.5 • Price is P* = (A + c1 +c2)/3 = (100 + 5 + 15)/3 = 40 • Profit of firm 1 is (A - 2c1 + c2)2/9B =(100 – 10 +5)2/18 = $612.5 • Profit of firm 2 is (A - 2c2 + c1)2/9B = $312.5 • Producers would be better off and consumers no worse off if firm 2’s 12.5 units were instead produced by firm 1 EC 170 Industrial Organization

  30. Concentration and Profitability • Assume that we have N firms with different marginal costs • We can use the N-firm analysis with a simple change • Recall that demand for firm 1 is P = (A - BQ-1) - Bq1 • But then demand for firm i is P = (A - BQ-i) - Bqi • Equate this to marginal cost ci But Q*-i + q*i = Q* and A - BQ* = P* A - BQ-i - 2Bqi = ci This can be reorganized to give the equilibrium condition: A - B(Q*-i + q*i) - Bq*i - ci = 0  P* - Bq*i - ci = 0  P* - ci = Bq*i EC 170 Industrial Organization

  31. Concentration and profitability (cont.) The price-cost margin for each firm is determined by its own market share and overallmarket demand elasticity P* - ci = Bq*i Divide by P* and multiply the right-hand side by Q*/Q* The verage price-cost margin is determined by industryconcentration as measured by the Herfindahl-Hirschman Index P* - ci BQ* q*i = P* P* Q* But BQ*/P* = 1/ and q*i/Q* = si P* - ci si so: =  P* Extending this we have P* - c H = P*  EC 170 Industrial Organization

  32. Price Competition: Bertrand • In the Cournot model price is set by some market clearing mechanism • Firms seem relatively passive • An alternative approach is to assume that firms compete in prices: this is the approach taken by Bertrand • Leads to dramatically different results • Take a simple example • two firms producing an identical product (spring water?) • firms choose the prices at which they sell their water • each firm has constant marginal cost of $10 • market demand is Q = 100 - 2P Check that with this demand and these costs the monopoly price is $30 and quantity is 40 units EC 170 Industrial Organization

  33. Bertrand competition (cont.) • We need the derived demand for each firm • demand conditional upon the price charged by the other firm • Take firm 2. Assume that firm 1 has set a price of $25 • if firm 2 sets a price greater than $25 she will sell nothing • if firm 2 sets a price less than $25 she gets the whole market • if firm 2 sets a price of exactly $25 consumers are indifferent between the two firms • the market is shared, presumably 50:50 • So we have the derived demand for firm 2 • q2 = 0 if p2 > p1 = $25 • q2 = 100 - 2p2 if p2 < p1 = $25 • q2 = 0.5(100 - 50) = 25 if p2 = p1 = $25 EC 170 Industrial Organization

  34. Bertrand competition (cont.) Demand is not continuous. There is a jump at p2 = p1 • More generally: • Suppose firm 1 sets price p1 p2 • Demand to firm 2 is: q2 = 0 if p2 > p1 p1 q2 = 100 - 2p2 if p2 < p1 q2 = 50 - p1 if p2 = p1 • The discontinuity in demand carries over to profit 100 - 2p1 100 q2 50 - p1 EC 170 Industrial Organization

  35. Bertrand competition (cont.) Firm 2’s profit is: p2(p1,, p2) = 0 if p2 > p1 p2(p1,, p2) = (p2 - 10)(100 - 2p2) if p2 < p1 For whatever reason! p2(p1,, p2) = (p2 - 10)(50 - p2) if p2 = p1 Clearly this depends on p1. Suppose first that firm 1 sets a “very high” price: greater than the monopoly price of $30 EC 170 Industrial Organization

  36. If p1 = $30, then firm 2 will only earn a positive profit by cutting its price to $30 or less What price should firm 2 set? At p2 = p1 = $30, firm 2 gets half of the monopoly profit Bertrand competition (cont.) So, if p1 falls to $30, firm 2 should just undercut p1 a bit and get almost all the monopoly profit With p1 > $30, Firm 2’s profit looks like this: What if firm 1 prices at $30? The monopoly price of $30 Firm 2’s Profit p2 < p1 p2 = p1 p2 > p1 p1 $10 $30 Firm 2’s Price EC 170 Industrial Organization

  37. Bertrand competition (cont.) Now suppose that firm 1 sets a price less than $30 As long as p1 > c = $10, Firm 2 should aim just to undercut firm 1 Firm 2’s profit looks like this: What price should firm 2 set now? Of course, firm 1 will then undercut firm 2 and so on Firm 2’s Profit p2 < p1 Then firm 2 should also price at $10. Cutting price below costgains the whole market but loses money on every customer What if firm 1 prices at $10? p2 = p1 p2 > p1 p1 $10 $30 Firm 2’s Price EC 170 Industrial Organization

  38. Bertrand competition (cont.) • We now have Firm 2’s best response to any price set by firm 1: • p*2 = $30 if p1 > $30 • p*2 = p1 - “something small” if $10 < p1< $30 • p*2 = $10 if p1< $10 • We have a symmetric best response for firm 1 • p*1 = $30 if p2 > $30 • p*1 = p2 - “something small” if $10 < p2< $30 • p*1 = $10 if p2< $10 EC 170 Industrial Organization

  39. Bertrand competition (cont.) The best response function for firm 1 The best response function for firm 2 These best response functions look like this p2 R1 The Bertrand equilibrium has both firms charging marginal cost R2 $30 The equilibrium is with both firms pricing at $10 $10 p1 $10 $30 EC 170 Industrial Organization

  40. Bertrand Equilibrium: modifications • The Bertrand model makes clear that competition in prices is very different from competition in quantities • Since many firms seem to set prices (and not quantities) this is a challenge to the Cournot approach • But the Bertrand model has problems too • for the p = marginal-cost equilibrium to arise, both firms need enough capacity to fill all demand at price = MC • but when both firms set p = c they each get only half the market • So, at the p = mc equilibrium, there is huge excess capacity • This calls attention to the choice of capacity • Note: choosing capacity is a lot like choosing output which brings us back to the Cournot model • The intensity of price competition when products are identical that the Bertrand model reveals also gives a motivation for Product differentiation EC 170 Industrial Organization

  41. An Example of Product Differentiation Coke and Pepsi are nearly identical but not quite. As a result, the lowest priced product does not win the entire market. QC = 63.42 - 3.98PC + 2.25PP MCC = $4.96 QP = 49.52 - 5.48PP + 1.40PC MCP = $3.96 There are at least two methods for solving this for PC and PP EC 170 Industrial Organization

  42. Bertrand and Product Differentiation Method 1: Calculus Profit of Coke: pC = (PC - 4.96)(63.42 - 3.98PC + 2.25PP) Profit of Pepsi: pP = (PP - 3.96)(49.52 - 5.48PP + 1.40PC) Differentiate with respect to PC and PP respectively Method 2: MR = MC Reorganize the demand functions PC = (15.93 + 0.57PP) - 0.25QC PP = (9.04 + 0.26PC) - 0.18QP Calculate marginal revenue, equate to marginal cost, solve for QC and QP and substitute in the demand functions EC 170 Industrial Organization

  43. Bertrand competition and product differentiation Both methods give the best response functions: The Bertrand equilibrium is at their intersection PC = 10.44 + 0.2826PP PP Note that these are upward sloping RC PP = 6.49 + 0.1277PC These can be solved for the equilibrium prices as indicated RP $8.11 B $6.49 PC $10.44 $12.72 EC 170 Industrial Organization

  44. Bertrand Competition and the Spatial Model • An alternative approach is to use the spatial model from Chapter 4 • a Main Street over which consumers are distributed • supplied by two shops located at opposite ends of the street • but now the shops are competitors • each consumer buys exactly one unit of the good provided that its full price is less than V • a consumer buys from the shop offering the lower full price • consumers incur transport costs of t per unit distance in travelling to a shop • What prices will the two shops charge? EC 170 Industrial Organization

  45. Xm marks the location of the marginal buyer—one who is indifferent between buying either firm’s good Bertrand and the spatial model What if shop 1 raises its price? Assume that shop 1 sets price p1 and shop 2 sets price p2 Price Price p’1 p2 p1 xm x’m Shop 1 All consumers to the left of xm buy from shop 1 xm moves to the left: some consumers switch to shop 2 Shop 2 And all consumers to the right buy from shop 2 EC 170 Industrial Organization

  46. This is the fraction of consumers who buy from firm 1 Bertrand and the spatial model p1 + txm = p2 + t(1 - xm) How is xm determined? 2txm = p2 - p1 + t xm(p1, p2) = (p2 - p1 + t)/2t There are n consumers in total So demand to firm 1 is D1 = N(p2 - p1 + t)/2t Price Price p2 p1 xm Shop 1 Shop 2 EC 170 Industrial Organization

  47. Bertrand equilibrium Profit to firm 1 is p1 = (p1 - c)D1 = N(p1 - c)(p2 - p1 + t)/2t p1 = N(p2p1 - p12 + tp1 + cp1 - cp2 -ct)/2t Solve this for p1 This is the best response function for firm 1 Differentiate with respect to p1 N p1/ p1 = (p2 - 2p1 + t + c) = 0 2t p*1 = (p2 + t + c)/2 This is the best response function for firm 2 What about firm 2? By symmetry, it has a similar best response function. p*2 = (p1 + t + c)/2 EC 170 Industrial Organization

  48. Bertrand and Demand p2 p*1 = (p2 + t + c)/2 R1 p*2 = (p1 + t + c)/2 2p*2 = p1 + t + c R2 = p2/2 + 3(t + c)/2 c + t  p*2 = t + c (c + t)/2  p*1 = t + c p1 (c + t)/2 c + t EC 170 Industrial Organization

  49. Stackelberg • Interpret in terms of Cournot • Firms choose outputs sequentially • leader sets output first, and visibly • follower then sets output • The firm moving first has a leadership advantage • can anticipate the follower’s actions • can therefore manipulate the follower • For this to work the leader must be able to commit to its choice of output • Strategic commitment has value EC 170 Industrial Organization

  50. Stackelberg Equilibrium: an example Both firms have constant marginal costs of $10, i.e., c = 10 for both firms • Assume that there are two firms with identical products • As in our earlier Cournot example, let demand be: • P = 100 - 2Q = 100 - 2(q1 + q2) • Total cost for for each firm is: • C(q1) = 10q1; C(q2) = 10q2 • Firm 1 is the market leader and chooses q1 • In doing so it can anticipate firm 2’s actions • So consider firm 2. Demand is: • P = (100 - 2q1) - 2q2 • Marginal revenue therefore is: • MR2 = (100 - 2q1) - 4q2 EC 170 Industrial Organization

More Related