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Market Structure And Competition

Chapter 13. Market Structure And Competition. Chapter Thirteen Overview. Introduction: Cola Wars A Taxonomy of Market Structures Monopolistic Competition Oligopoly – Interdependence of Strategic Decisions Bertrand with Homogeneous and Differentiated Products

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Market Structure And Competition

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  1. Chapter 13 Market Structure And Competition

  2. Chapter Thirteen Overview • Introduction: Cola Wars • A Taxonomy of Market Structures • Monopolistic Competition • Oligopoly – Interdependence of Strategic Decisions • Bertrand with Homogeneous and Differentiated Products • The Effect of a Change in the Strategic Variable • Theory vs. Observation • Cournot Equilibrium (homogeneous) • Comparison to Bertrand, Monopoly • Reconciling Bertrand, and Cournot • The Effect of a Change in Timing: Stackelberg Equilibrium Chapter Thirteen

  3. Market Structures Four Key Dimensions • The number of sellers • The number of buyers • Entry conditions • The degree of product differentiation Chapter Thirteen

  4. Product Differentiation Definition:Product Differentiation between two or more products exists when the products possess attributes that, in the minds of consumers, set the products apart from one another and make them less than perfect substitutes. Examples: Pepsi is sweeter than Coke, Brand Name batteries last longer than "generic" batteries. Chapter Thirteen

  5. Product Differentiation • "Superiority" (Vertical Product Differentiation) i.e. one product is viewed as unambiguously better than another so that, at the same price, all consumers would buy the better product • "Substitutability" (Horizontal Product Differentiation) i.e. at the same price, some consumers would prefer the characteristics of product A while other consumers would prefer the characteristics of product B. Chapter Thirteen

  6. Types of Market Structures Chapter Thirteen

  7. Oligopoly • Assumptions: • Many Buyers and Few Sellers • Each firm faces downward-sloping demand because each is a large producer compared to the total market size • There is no one dominant model of oligopoly. We will review several. Chapter Thirteen

  8. Cournot Oligopoly • Assumptions • Firms set outputs (quantities)* • Homogeneous Products • Simultaneous • Non-cooperative • *Definition: In a Cournot game, each firm sets its output (quantity) taking as given the output level of its competitor(s), so as to maximize profits. • Price adjusts according to demand. • Residual Demand: Firm i's guess about its rival's output determines its residual demand. Chapter Thirteen

  9. Simultaneously vs. Non-cooperatively Definition: Firms act simultaneously if each firm makes its strategic decision at the same time, without prior observation of the other firm's decision. Definition: Firms act non-cooperatively if they set strategy independently, without colluding with the other firm in any way Chapter Thirteen

  10. Residual Demand Definition: The relationship between the price charged by firm i and the demand firm i faces is firm is residual demand In other words, the residual demand of firm i is the market demand minus the amount of demand fulfilled by other firms in the market: Q1 = Q - Q2 Chapter Thirteen

  11. Residual Demand Price Residual Marginal Revenue when q2 = 10 10 units Residual Demand when q2 = 10 MC Demand 0 Quantity q1* Chapter Thirteen

  12. Profit Maximization Profit Maximization: Each firm acts as a monopolist on its residual demand curve, equating MRr to MC. MRr = p + q1(p/q) = MC Best Response Function: The point where (residual) marginal revenue equals marginal cost gives the best response of firm i to its rival's (rivals') actions. For every possible output of the rival(s), we can determine firm i's best response. The sum of all these points makes up the best response (reaction) function of firm i. Chapter Thirteen

  13. Profit Maximization q2 Example: Reaction Functions, Quantity Setting Reaction Function of Firm 1 • q2* Reaction Function of Firm 2 0 q1 q1* Chapter Thirteen

  14. Equilibrium Equilibrium: No firm has an incentive to deviate in equilibrium in the sense that each firm is maximizing profits given its rival's output • What is the equation of firm 1's reaction function? • Firm 1's residual demand: • P = (100 - Q2) - Q1 • MRr = 100 - Q2 - 2Q1 • MRr = MC  100 - Q2 - 2Q1 = 10 • Q1r = 45 - Q2/2 firm 1's reaction function • Similarly, one can compute that • Q2r = 45 - Q1/2 • P = 100 - Q1 - Q2 • MC = AC = 10 • What is firm 1's profit-maximizing output when firm 2 produces 50? • Firm 1's residual demand: • P = (100 - 50) - Q1 • MR50 = 50 - 2Q1 • MR50 = MC  50 - 2Q1 = 10 Chapter Thirteen

  15. Profit Maximization • Now, calculate the Cournot equilibrium. • Q1 = 45 - (45 - Q1/2)/2 • Q1* = 30 • Q2* = 30 • P* = 40 • 1* = 2* = 30(30) = 900 Chapter Thirteen

  16. Bertrand Oligopoly (homogeneous) • Assumptions: • Firms set price* • Homogeneous product • Simultaneous • Non-cooperative *Definition: In a Bertrand oligopoly, each firm sets its price, taking as given the price(s) set by other firm(s), so as to maximize profits. Chapter Thirteen

  17. Setting Price • Homogeneity implies that consumers will buy from the low-price seller. • Further, each firm realizes that the demand that it faces depends both on its own price and on the price set by other firms • Specifically, any firm charging a higher price than its rivals will sell no output. • Any firm charging a lower price than its rivals will obtain the entire market demand. Chapter Thirteen

  18. Residual Demand Curve – Price Setting Price Market Demand Residual Demand Curve (thickened line segments) • Quantity 0 Chapter Thirteen

  19. Residual Demand Curve – Price Setting Assumptions • Assume firm always meets its residual demand (no capacity constraints) • Assume that marginal cost is constant at c per unit. • Hence, any price at least equal to c ensures non-negative profits. Chapter Thirteen

  20. Best Response Function • Each firm's profit maximizing response to the other firm's price is to undercut (as long as P > MC) • Definition: The firm's profit maximizing action as a function of the action by the rival firm is the firm's best response (or reaction) function • Example: • 2 firms • Bertrand competitors • Firm 1's best response function is P1=P2- e • Firm 2's best response function is P2=P1- e Chapter Thirteen

  21. Equilibrium If we assume no capacity constraints and that all firms have the same constant average and marginal cost of c then: For each firm's response to be a best response to the other's each firm must undercut the other as long as P> MC Where does this stop? P = MC (!) Chapter Thirteen

  22. Equilibrium Key Points • 1. Firms price at marginal cost • 2. Firms make zero profits • 3. The number of firms is irrelevant to the price level as long as more than one firm is present: two firms is enough to replicate the perfectly competitive outcome. • Essentially, the assumption of no capacity constraints combined with a constant average and marginal cost takes the place of free entry. Chapter Thirteen

  23. Stackelberg Oligopoly Stackelberg model of oligopoly is a situation in which one firm acts as a quantity leader, choosing its quantity first, with all other firms acting as followers. Call the first mover the “leader” and the second mover the “follower”. The second firm is in the same situation as a Cournot firm: it takes the leader’s output as given and maximizes profits accordingly, using its residual demand. The second firm’s behavior can, then, be summarized by a Cournot reaction function. Chapter Thirteen

  24. Stackelberg Equilibrium vs. Cournot q2 Profit for firm 1 at A…0 at B…0 at C…1012.5 at Cournot Eq…900 • A Former Cournot Equilibrium • • C Follower’s Cournot Reaction Function B (q1= 90) • q1 Chapter Thirteen

  25. Dominant Firm Markets A single company with an overwhelming market share (a dominant firm) competes against many small producers (competitive fringe), each of whom has a small market share. Limit Pricing – a strategy whereby the dominant firm keeps its price below the level that maximizes its current profit in order to reduce the rate of expansion by the fringe. Chapter Thirteen

  26. Bertrand Competition – Differentiated • Assumptions: • Firms set price* • Differentiated product • Simultaneous • Non-cooperative • *Differentiation means that lowering price below your rivals' will not result in capturing the entire market, nor will raising price mean losing the entire market so that residual demand decreases smoothly Chapter Thirteen

  27. Bertrand Competition – Differentiated Example Q1 = 100 - 2P1 + P2"Coke's demand" Q2 = 100 - 2P2 + P1"Pepsi's demand" MC1 = MC2 = 5 What is firm 1's residual demand when Firm 2's price is $10? $0? Q1(10) = 100 - 2P1 + 10 = 110 - 2P1 Q1(0) = 100 - 2P1 + 0 = 100 - 2P1 Chapter Thirteen

  28. Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Coke’s Price Pepsi’s price = $0 for D0 and $10 for D10 100 MR0 Coke’s Quantity 0 Chapter Thirteen

  29. Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Coke’s Price 110 Pepsi’s price = $0 for D0 and $10 for D10 100 D10 D0 Coke’s Quantity 0 Chapter Thirteen

  30. Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Coke’s Price 110 Pepsi’s price = $0 for D0 and $10 for D10 100 D10 D0 MR10 MR0 0 Coke’s Quantity Chapter Thirteen

  31. Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Coke’s Price 110 Pepsi’s price = $0 for D0 and $10 for D10 100 D10 D0 MR10 5 MR0 0 Coke’s Quantity Chapter Thirteen

  32. Key Concepts Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Coke’s Price 110 Pepsi’s price = $0 for D0 and $10 for D10 100 30 27.5 D10 D0 MR10 5 MR0 45 50 0 Coke’s Quantity Chapter Thirteen

  33. Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC • Example: • MR1(10) = 55 - Q1(10) = 5 • Q1(10) = 50 • P1(10) = 30 • Therefore, firm 1's best response to a price of $10 by firm 2 is a price of $30 Chapter Thirteen

  34. Key Concepts • Residual Demand, Price Setting, Differentiated Products • Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC • Example: • Solving for firm 1's reaction function for any arbitrary price by firm 2 • P1 = 50 - Q1/2 + P2/2 • MR = 50 - Q1 + P2/2 • MR = MC => Q1 = 45 + P2/2 Chapter Thirteen

  35. Key Concepts • Residual Demand, Price Setting, Differentiated Products • Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC • And, using the demand curve, we have: • P1 = 50 + P2/2 - 45/2 - P2/4 or • P1 = 27.5 + P2/4 the reaction function Chapter Thirteen

  36. Equilibrium and Reaction Functions Price Setting and Differentiated Products Pepsi’s Price (P2) P2 = 27.5 + P1/4 (Pepsi’s R.F.) 27.5 Coke’s Price (P1) Chapter Thirteen

  37. Equilibrium and Reaction Functions Price Setting and Differentiated Products Pepsi’s Price (P2) P1 = 27.5 + P2/4 (Coke’s R.F.) P2 = 27.5 + P1/4 (Pepsi’s R.F.) • 27.5 Coke’s Price (P1) P1 = 110/3 27.5 Chapter Thirteen

  38. Equilibrium and Reaction Functions Price Setting and Differentiated Products Pepsi’s Price (P2) P1 = 27.5 + P2/4 (Coke’s R.F.) P2 = 27.5 + P1/4 (Pepsi’s R.F.) Bertrand Equilibrium P2 = 110/3 • 27.5 Coke’s Price (P1) P1 = 110/3 27.5 Chapter Thirteen

  39. Equilibrium • Equilibrium occurs when all firms simultaneously choose their best response to each others' actions. • Graphically, this amounts to the point where the best response functions cross. Chapter Thirteen

  40. Equilibrium • Example: Firm 1 and Firm 2, continued • P1 = 27.5 + P2/4 • P2 = 27.5 + P1/4 • Solving these two equations in two unknowns. • P1* = P2* = 110/3 • Plugging these prices into demand, we have: • Q1* = Q2* = 190/3 • 1* = 2* = 2005.55 •  = 4011.10 Chapter Thirteen

  41. Equilibrium Notice That: • Profits are positive in equilibrium since both prices are above marginal cost! • Even if we have no capacity constraints, and constant marginal cost, a firm cannot capture all demand by cutting price. • This blunts price-cutting incentives and means that the firms' own behavior does not mimic free entry Chapter Thirteen

  42. Equilibrium Notice That: • Only if I were to let the number of firms approach infinity would price approach marginal cost. • Prices need not be equal in equilibrium if firms not identical (e.g. Marginal costs differ implies that prices differ) • The reaction functions slope upward: "aggression => aggression" Chapter Thirteen

  43. Cournot, Bertrand, and Monopoly Equilibriums • P > MC for Cournot competitors, but P < PM: • If the firms were to act as a monopolist (perfectly collude), they would set market MR equal to MC: • P = 100 - Q • MC = AC = 10 • MR = MC => 100 - 2Q = 10 => QM = 45 • PM = 55 • M= 45(45) = 2025 • c = 1800 Chapter Thirteen

  44. Cournot, Bertrand, and Monopoly Equilibriums A perfectly collusive industry takes into account that an increase in output by one firm depresses the profits of the other firm(s) in the industry. A Cournot competitor takes into account the effect of the increase in output on its own profits only. Therefore, Cournot competitors "overproduce" relative to the collusive (monopoly) point. Further, this problem gets "worse" as the number of competitors grows because the market share of each individual firm falls, increasing the difference between the private gain from increasing production and the profit destruction effect on rivals. Therefore, the more concentrated the industry in the Cournot case, the higher the price-cost margin. Chapter Thirteen

  45. Cournot, Bertrand, and Monopoly Equilibriums Homogeneous product Bertrand resulted in zero profits, whereas the Cournot case resulted in positive profits. Why? The best response functions in the Cournot model slope downward. In other words, the more aggressive a rival (in terms of output), the more passive the Cournot firm's response. The best response functions in the Bertrand model slope upward. In other words, the more aggressive a rival (in terms of price) the more aggressive the Bertrand firm's response. Chapter Thirteen

  46. Cournot, Bertrand, and Monopoly Equilibriums Cournot: Suppose firm j raises its output…the price at which firm i can sell output falls. This means that the incentive to increase output falls as the output of the competitor rises. Bertrand: Suppose firm j raises price the price at which firm i can sell output rises. As long as firm's price is less than firm's, the incentive to increase price will depend on the (market) marginal revenue. Chapter Thirteen

  47. Chamberlinian Monopolistic Competition • Market Structure • Many Buyers • Many Sellers • Free entry and Exit • (Horizontal) Product Differentiation • When firms have horizontally differentiated products, they each face downward-sloping demand for their product because a small change in price will not cause ALL buyers to switch to another firm's product. Example: Restaurants, Local markets for doctors Chapter Thirteen

  48. Monopolistic Competition – Short Run • 1. Each firm is small each takes the observed "market price" as given in its production decisions. • 2. Since market price may not stay given, the firm's perceived demand may differ from its actual demand. • 3.If all firms' prices fall the same amount, no customers switch supplier but the total market consumption grows. • 4. If only one firm's price falls, it steals customers from other firms as well as increases total market consumption Chapter Thirteen

  49. Perceived vs. Actual Demand Price d (PA=20) Quantity Chapter Thirteen

  50. Perceived vs. Actual Demand Price Demand assuming no price matching d (PA=50) d (PA=20) Quantity Chapter Thirteen

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