Copyright (c)2014 John Wiley & Sons, Inc.

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Market Structures Four Key Dimensions • The number of sellers • The number of buyers • Entry conditions • The degree of product differentiation Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 = Q2 - 2Q1 MRr = MC  Q2 - 2Q1 = 10 Q1r = 45 - Q2/2 firm 1's reaction function Similarly, one can compute that Q2r = 45 - Q1/2 P = Q1 - Q2 MC = AC = 10 What is firm 1's profit-maximizing output when firm 2 produces 50? Firm 1's residual demand: P = ( ) - Q1 MR50 = Q1 MR50 = MC  Q1 = 10 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 (!) Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Equilibrium 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. Key Points Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Stackelberg Equilibrium vs. Cournot q2 Profit for firm 1 at A… at B…0 at C…1012.5 at Cournot Eq…900 • A Former Cournot Equilibrium • • Copyright (c)2014 John Wiley & Sons, Inc. C Follower’s Cournot Reaction Function B (q1= 90) • q1 Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Bertrand Competition – Differentiated Example Q1 = P1 + P2 "Coke's demand" Q2 = P2 + P1 "Pepsi's demand" MC1 = MC2 = 5 What is firm 1's residual demand when Firm 2's price is $10? $0? Q1(10) = P = P1 Q1(0) = P = P1 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. MR0 Coke’s Quantity Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. D10 D0 Coke’s Quantity Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. D0 MR10 MR0 Coke’s Quantity Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. D0 MR10 5 MR0 Coke’s Quantity Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. D0 MR10 5 MR0 Coke’s Quantity Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 = P2/4 the reaction function Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Equilibrium and Reaction Functions Price Setting and Differentiated Products Pepsi’s Price (P2) P2 = P1/4 (Pepsi’s R.F.) 27.5 Copyright (c)2014 John Wiley & Sons, Inc. Coke’s Price (P1) Chapter Thirteen

Equilibrium and Reaction Functions Price Setting and Differentiated Products Pepsi’s Price (P2) P1 = P2/4 (Coke’s R.F.) P2 = P1/4 (Pepsi’s R.F.) • 27.5 Copyright (c)2014 John Wiley & Sons, Inc. Coke’s Price (P1) 27.5 P1 = 110/3 Chapter Thirteen

Equilibrium and Reaction Functions Price Setting and Differentiated Products Pepsi’s Price (P2) P1 = P2/4 (Coke’s R.F.) P2 = P1/4 (Pepsi’s R.F.) Bertrand Equilibrium P2 = 110/3 • 27.5 Copyright (c)2014 John Wiley & Sons, Inc. Coke’s Price (P1) 27.5 P1 = 110/3 Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Equilibrium Example: Firm 1 and Firm 2, continued P1 = P2/4 P2 = 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* =  = Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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" Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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 = Q MC = AC = 10 MR = MC => Q = 10 => QM = 45 PM = 55 M= 45(45) = 2025 c = 1800 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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. Copyright (c)2014 John Wiley & Sons, Inc. Example: Restaurants, Local markets for doctors Chapter Thirteen

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 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Perceived vs. Actual Demand Price Demand (assuming price matching by all firms) • 50 Demand assuming no price matching Copyright (c)2014 John Wiley & Sons, Inc. d (PA=50) d (PA=20) Quantity Chapter Thirteen

Market Equilibrium The market is in equilibrium if: Each firm maximizes profit taking the average market price as given Each firm can sell the quantity it desires at the actual average market price that prevails Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Short Run Chamberlinian Equilibrium Price Demand (assuming price matching by all firms P=PA) • • Demand assuming no price matching Copyright (c)2014 John Wiley & Sons, Inc. d (PA=50) d(PA=43) Quantity Chapter Thirteen

Short Run Chamberlinian Equilibrium Price Demand (assuming price matching by all firms P=PA) • 50 • 43 Demand assuming no price matching Copyright (c)2014 John Wiley & Sons, Inc. d (PA=50) 15 mc d(PA=43) Quantity 57 MR43 Chapter Thirteen

Short Run Monopolistically Competitive Equilibrium Computing Short Run Monopolistically Competitive Equilibrium MC = $15 N = 100 Q = P + PA Where: PA is the average market price N is the number of firms Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Short Run Monopolistically Competitive Equilibrium A. What is the equation of d40? What is the equation of D? d40: Qd = P + 40 = P D: Note that P = PA so that QD = P B. Show that d40 and D intersect at P = 40 P = 40 => Qd = = 60 QD = = 60 C. For any given average price, PA, find a typical firm's profit maximizing quantity Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Inverse Perceived Demand P = 50 - (1/2)Q + (1/2)PA MR = 50 - Q + (1/2)PA MR = MC => 50 - Q + (1/2)PA = 15 Qe = 35 + (1/2)PA Pe = 50 - (1/2)Qe + (1/2)PA Pe = (1/4)PA Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Short Run Monopolistically Competitive Equilibrium D. What is the short run equilibrium price in this industry? In equilibrium, Qe = QD at PA so that 100 - PA = 35 + (1/2)PA PA = 43.33 Qe = 56.66 QD = 56.66 Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Monopolistic Competition in the Long Run At the short run equilibrium P > AC so that each firm may make positive profit. Entry shifts d and D left until average industry price equals average cost. This is long run equilibrium is represented graphically by: MR = MC for each firm D = d at the average market price d and AC are tangent at average market price Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Summary 1. Market structures are characterized by the number of buyers, the number of sellers, the degree of product differentiation and the entry conditions. 2. Product differentiation alone or a small number of competitors alone is not enough to destroy the long run zero profit result of perfect competition. This was illustrated with the Chamberlinian and Bertrand models. 3. Chamberlinian) monopolistic competition assumes that there are many buyers, many sellers, differentiated products and free entry in the long run. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Summary 4. Chamberlinian sellers face downward-sloping demand but are price takers (i.e. they do not perceive that their change in price will affect the average price level). Profits may be positive in the short run but free entry drives profits to zero in the long run. 5. Bertrand and Cournot competition assume that there are many buyers, few sellers, and homogeneous or differentiated products. Firms compete in price in Bertrand oligopoly and in quantity in Cournot oligopoly. 6. Bertrand and Cournot competitors take into account their strategic interdependence by means of constructing a best response schedule: each firm maximizes profits given the rival's strategy. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

Summary 7. Equilibrium in such a setting requires that all firms be on their best response functions. 8. If the products are homogeneous, the Bertrand equilibrium results in zero profits. By changing the strategic variable from price to quantity, we obtain much higher prices (and profits). Further, the results are sensitive to the assumption of simultaneous moves. 9. This result can be traced to the slope of the reaction functions: upwards in the case of Bertrand and downwards in the case of Cournot. These slopes imply that "aggressivity" results in a "passive" response in the Cournot case and an "aggressive" response in the Bertrand case. Copyright (c)2014 John Wiley & Sons, Inc. Chapter Thirteen

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