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Finance 30210: Managerial Economics Strategic Pricing Techniques Recall that there is an entire spectrum of market structures Market Structures Perfect Competition Monopoly Many firms, each with zero One firm, with 100% market share market share P = MC Profits = 0 (Firm’s earn a P > MC Profits > 0 (Firm’s earn reasonable rate of return on invested capital) excessive rates of return on invested capital) NO STRATEGIC NO STRATEGIC INTERACTION! INTERACTION! Most industries, however, don’t fit the assumptions of either perfect competition or monopoly. We call these industries oligopolies Oligopoly Relatively few firms, each with positive market share STRATEGIES MATTER!!! Mobile Phones (2011) Nokia: 22.8% Samsung: 16.3% LG: 5.7% Apple: 4.6% ZTE:3.0% Others: 47.6% US Beer (2010) Music Recording (2005) Anheuser-Busch: 49% Miller/Coors: 29% Crown Imports: 5% Heineken USA: 4% Pabst: 3% Universal/Polygram: 31% Sony: 26% Warner: 25% Independent Labels: 18% The key difference in oligopoly markets is that price/sales decisions can’t be made independently of your competitor’s decisions Monopoly Q QP Your Price (-) Oligopoly Q QP, P1 ,...PN Your N Competitors Prices (+) Oligopoly markets rely crucially on the interactions between firms which is why we need game theory to analyze them! Market shares are not constant over time in these industries! Airlines (1992) Airlines (2002) American 21 United 20 15 Delta Northwest Continental 11 US Air 9 14 American 19 United 17 15 Delta Northwest 11 Continental 9 SWest 7 While the absolute ordering didn’t change, all the airlines lost market share to Southwest. Another trend is consolidation Retail Gasoline (1992) 9 Shell Chevron 8 8 8 Texaco Exxon Amoco 7 7 Mobil 5 5 4 4 24 Exxon/Mobil Shell 20 BP/Amoco/Arco 18 Chev/Texaco 16 10 6 BP Citgo Marathon Sun Phillips Retail Gasoline (2001) 7 Total/Fina/Elf Conoco/Phillips Recall the prisoners dilemma game… Clyde Jake The prisoner’s dilemma game is used to describe circumstances where competition forces suboptimal outcomes Confess Don’t Confess Confess -4 -4 0 -8 Don’t Confess -8 0 -1 -1 Price Fixing and Collusion Prior to 1993, the record fine in the United States for price fixing was $2M. Recently, that record has been shattered! Defendant Product Year Fine F. Hoffman-Laroche Vitamins 1999 $500M BASF Vitamins 1999 $225M SGL Carbon Graphite Electrodes 1999 $135M UCAR International Graphite Electrodes 1998 $110M Archer Daniels Midland Lysine & Citric Acid 1997 $100M Haarman & Reimer Citric Acid 1997 $50M HeereMac Marine Construction 1998 $49M In other words…Cartels happen! Suppose that we have two firms in the market. They face the following demand curve… Each has a marginal cost of $80. P 400 4q1 q2 Firm 1’s output Firm 2’s output If these firms formed a cartel, they would operate jointly as a monopolist. P 400 4Q MR 400 8Q 80 MC Each firm agrees to sell 20 units at $240 each. 240 8020 $3,200 Q 40 P $240 Each firm makes $3200 in profits However, given that firm 2 is producing 20 units, what should firm 1 do? P 400 4q1 20 Firm 1’s output P 400 4q1 80 Firm 2’s output P 400 430 20 $200 P 320 4q1 80 MR 320 8q1 80 MC Q 30 1 200 8030 $3,600 2 200 8020 $2,400 Firm 1 cheats and earns more profits! But if they both cheat and produce 30 units… P 400 430 30 $160 1 160 8030 $2,400 2 160 8030 $2,400 Cartels - The Prisoner’s Dilemma The problem facing the cartel members is a perfect example of the prisoner’s dilemma ! Clyde Cooperate Jake Cheat Cooperate $3200 $3200 $2400 $3600 Cheat $3600 $2400 $2400 $2400 Cheating is a dominant strategy! Cartel Formation While it is clearly in each firm’s best interest to join the cartel, there are a couple problems: With the high monopoly markup, each firm has the incentive to cheat and overproduce. If every firm cheats, the price falls and the cartel breaks down Cartels are generally illegal which makes enforcement difficult! Note that as the number of cartel members increases the benefits increase, but more members makes enforcement even more difficult! Perhaps cartels can be maintained because the members are interacting over time – this brings is a possible punishment for cheating. Clyde Cooperate Cheat Cooperate $3200 $3200 $2400 $3600 Cheat $3600 $2400 $2400 Jake Jake “I plan on cooperating…if you cooperate today, I will cooperate tomorrow, but if you cheat today, I will cheat forever!” 0 1 Make Strategic Decision Make Strategic Decision Time $2400 2 Make Strategic Decision 3 Make Strategic Decision 4 Make Strategic Decision 5 Make Strategic Decision “I plan on cooperating…if you cooperate today, I will cooperate tomorrow, but if you cheat today, I will cheat forever!” Jake Cooperate: $3200 Cooperate Cheat Cooperate $3200 $3200 $2400 $3600 Cheat $3600 $2400 $2400 $2400 $3200 $3200 $3200 $3200 $3200 0 1 2 3 4 5 Make Strategic Decision Make Strategic Decision Clyde Time Cheat: $3600 Cooperate: $19,200 Cheat: $15,600 $2400 Make Strategic Decision $2400 Make Strategic Decision $2400 Make Strategic Decision Make Strategic Decision $2400 $2400 Clyde should cooperate, right? We need to use backward induction to solve this. 0 1 Make Strategic Decision Make Strategic Decision Time Jake 2 Make Strategic Decision 3 Clyde 4 Make Strategic Decision 5 Make Strategic Decision Cooperate Regardless of what took place the first four time periods, what will happen in period 5? Make Strategic Decision Cheat Cooperate $3200 $3200 $2400 $3600 Cheat $3600 $2400 $2400 $2400 What should Clyde do here? We need to use backward induction to solve this. 0 1 Make Strategic Decision Make Strategic Decision Time Jake 2 3 Make Strategic Decision Clyde 4 Make Strategic Decision Make Strategic Decision 5 Make Strategic Decision Cheat Cooperate Given what happens in period 5, what should happen in period 4? Cheat Cooperate $3200 $3200 $2400 $3600 Cheat $3600 $2400 $2400 $2400 What should Clyde do here? We need to use backward induction to solve this. 0 1 Make Strategic Decision Make Strategic Decision Time Jake 2 Make Strategic Decision Cheat Cooperate Cheat Make Strategic Decision Cheat Cheat Cooperate $3200 $3200 $2400 $3600 Cheat $3600 $2400 $2400 $2400 3 Knowing the future prevents credible promises/threats! 4 Make Strategic Decision Cheat Clyde 5 Make Strategic Decision Cheat Where is collusion most likely to occur? High profit potential Inelastic Demand (Few close substitutes, Necessities) Cartel members control most of the market Entry Restrictions (Natural or Artificial) Low cooperation/monitoring costs Small Number of Firms with a high degree of market concentration Similar production costs Little product differentiation Price Matching: A form of collusion? High Price Low Price High Price $12 $12 $5 $14 Low Price $14 $6 $6 $5 Price Matching Removes the off-diagonal possibilities. This allows (High Price, High Price) to be an equilibrium!! The Stag Hunt - Airline Price Wars p Suppose that American and Delta face the given demand for flights to NYC and that the unit cost for the trip is $200. If they charge the same fare, they split the market $500 $220 American 180 What will the equilibrium be? P = $220 P = $500 $9,000 $9,000 $3,600 $0 P = $220 $0 $3,600 $1,800 $1,800 Q Delta 60 P = $500 The Airline Price Wars If American follows a strategy of charging $500 all the time, Delta’s best response is to also charge $500 all the time If American follows a strategy of charging $220 all the time, Delta’s best response is to also charge $220 all the time American P = $220 P = $500 $9,000 $9,000 $3,600 $0 P = $220 $0 $3,600 $1,800 $1,800 Delta This game has multiple equilibria and the result depends critically on each company’s beliefs about the other company’s strategy P = $500 The Airline Price Wars: Mixed Strategy Equilibria Suppose American charges $500 with probability pH Charges $220 with probability pL Charge $500: EV pH 9000 pL 0 Charge $220:EV pH 3600 PL 1800 American P = $500 P = $220 $9,000 $9,000 $3,600 $0 9000 pH 3600 pH 1800 pL Delta P = $500 pL 3 pH (6%) P = $220 $0 $3,600 (19%) pL 3 (75%) 4 pH 1 (25%) 4 (19%) $1,800 $1,800 (56%) Continuous Choice Games Consider the following example. We have two competing firms in the marketplace. These two firms are selling identical products. Each firm has constant marginal costs of production. What are these firms using as their strategic choice variable? Price or quantity? Are these firms making their decisions simultaneously or is there a sequence to the decisions? Cournot Competition: Quantity is the strategic choice variable There are two firms in an industry – both facing an aggregate (inverse) demand curve given by p P 120 20Q D Q Total Industry Production Q q1 q2 Both firms have constant marginal costs equal to $20 Consider the following scenario…We call this Cournot competition Two manufacturers choose a production target Two manufacturers earn profits based off the market price P Q1 S P* Profit = P*Q1 - TC D Q Q1 + Q2 Q2 A centralized market determines the market price based on available supply and current demand Profit = P*Q2 - TC For example…suppose both firms have a constant marginal cost of $20 Two manufacturers choose a production target P 120 20Q P Q1 = 1 Two manufacturers earn profits based off the market price S $60 Profit = 60*1 – 20 = $40 D Q 3 Q2 = 2 A centralized market determines the market price based on available supply and current demand Profit = 60*2 – 40 = $80 From firm one’s perspective, the demand curve is given by P 120 20q1 q2 120 20q2 20q1 Treated as a constant by Firm One Solving Firm One’s Profit Maximization… MR 120 20q2 40q1 20 100 20q2 q1 40 100 20q2 q1 40 In Game Theory Lingo, this is Firm One’s Best Response Function To Firm 2 q2 If firm 2 drops out, firm one is a monopolist! P 120 20q1 MR 120 40q1 20 q1 2.5 0 q2 0 q1 2.5 q1 100 20q2 q1 40 What could firm 2 do to make firm 1 drop out? q2 P 120 205 20 MC q2 5 q1 0 q2 0 q1 2.5 q1 P 120 20Q q2 100 20q2 q1 40 P 120 204 40 q2 5 q1 0 Firm 2 chooses a production target of 3 3 1 Firm 1 responds with a production target of 1 q2 0 q1 2.5 q1 1 401 201 20 2 403 203 60 The game is symmetric with respect to Firm two… P 120 20Q q2 100 20q1 q2 40 P 120 203 60 q1 0 q2 2.5 Firm 2 responds with a production target of 2 q1 5 q2 0 Firm 1 chooses a production target of 1 q1 1 601 201 40 2 602 202 80 Eventually, these two firms converge on production levels such that neither firm has an incentive to change 100 20q2 q1 40 q2 100 20q1 q2 40 100 201.67 1.67 40 Firm 1 We would call this the Nash equilibrium for this model q2* 1.67 Firm 2 q1* 1.67 q1 Recall we started with the demand curve and marginal costs P 120 20Q MC 20 q1* q2* 1.67M P 120 20(3.33) $53.33 1 53.331.67 201.67 $55.66 2 53.331.67 201.67 $55.66 The markup formula works for each firm P 120 20q2 20q1 86.6 20q1 MC $20 Q* 1.67 M P 86.6 20(1.67) $53.33 P MC .62 P 1 Q P 1 53.33 1.6 P Qi 20 1.67 1 .62 1.6 Had this market been serviced instead by a monopoly… P 120 20Q MC $20 Q* 2.5M P 120 20(2.5) $70 Q P 1 70 1.4 P Q 20 2.5 P MC .71 P 1 1 .71 1.4 Had this market been instead perfectly competitive, P 120 20Q MC $20 Q* 5M P 120 20(2.5) $20 P MC 0 P 1 1 0 P 120 20Q MC $20 Monopoly Q* 2.5M P $70 LI .71 HHI 10,000 2 Firms Q 3.33M q 1.67 P $53 LI .62 HHI 5,000 Perfect Competition Q* 5M P $20 LI 0 HHI 0 Recall, we had an aggregate demand and a constant marginal cost of production. P 120 20Q MC $20 Monopoly Q* 2.5M P $70 LI .71 HHI 10,000 CS = (.5)(120 – 70)(2.5) = $62.5 p $120 $62.5 $70 D What would it be worth to consumers to add another firm to the industry? 2.5 Q Recall, we had an aggregate demand and a constant marginal cost of production. P 120 20Q MC $20 Two Firms Q 3.33M q 1.67 P $53 LI .62 HHI 5,000 CS = (.5)(120 – 53)(3.33) = $112 p $112 $53 D 3.33 Q Suppose we increase the number of firms…say, to 3 P 120 20q1 q2 q3 P 120 20Q Demand facing firm 1 is given by (MC = 20) P 120 20q2 20q3 20q1 MR 120 20q2 20q3 40q1 20 q1 100 20q2 20q3 40 The strategies look very similar! With three firms in the market… P 120 20Q MC $20 CS = (.5)(120 – 45)(3.75) = $140 Three Firms p qi 1.25M Q 3q 3.75 P $45 $140 $45 LI .55 HHI 3,267 D 3.75 Q Expanding the number of firms in an oligopoly – Cournot Competition P A BQ MC c Ac qi ( N 1) B N A c Q ( N 1) B A N P c N 1 N 1 N = Number of firms Note that as the number of firms increases: Output approaches the perfectly competitive level of production Price approaches marginal cost. Increasing Competition 6 80 70 5 60 4 50 3 40 30 2 20 1 10 0 0 Number of Firms Firm Sales Industry Sales Price Increasing Competition 300 250 200 150 100 50 Num ber of Firm s Consumer Surplus Firm Profit Industry Profit 97 93 89 85 81 77 73 69 65 61 57 53 49 45 41 37 33 29 25 21 17 13 9 5 1 0 The previous analysis was with identical firms. P 120 20Q MC $20 100 20q2 q1 40 100 20q1 q2 40 Suppose Firm 2’s marginal costs increase to $30 q2 Firm 1 q2* 1.67 50% Firm 2 q1* 1.67 50% q1 P 120 20Q MC $30 q2 Suppose Firm 2’s marginal costs increase to $30 P 120 20q1 20q2 MR 120 20q1 40q2 30 90 20q1 q2 40 If Firm one’s production is unchanged 90 201.67 q2 1.41 40 q2* 1.67 1.41 Firm 2 q1* 1.67 q1 90 20q1 100 20q2 q2 q1 40 40 Q 1.33 1.83 3.16 P 120 203.16 $56.8 q2 1 56.81.83 201.83 67.34 2 56.81.33 301.33 35.64 Firm 1 HHI 42 2 582 5128 P MC .56 MC q2 1.33 42% Firm 2 q 1.83 * 1 58% q1 Firm 2’s market share drops Firm 1’s Market Share increases Market Concentration and Profitability N P A B qi Industry Demand i 1 P MC si P HHI P MC 10, 000 P The Lerner index for Firm i is related to Firm i’s market share and the elasticity of industry demand The Average Lerner index for the industry is related to the HHI and the elasticity of industry demand P 120 20Q MC1 20 q1 1.83 (58%) q2 1.33 (42%) MC2 $30 HHI 42 2 582 5128 Industry Q P 1 56.80 .90 P Qi 20 3.16 HHI 10,000 .5128 .56 .90 P $56.80 P MC .56 MC Firm 1 P MC 56.80 20 .58 .64 P 56.80 .90 Firm 2 P MC 56.80 30 .42 .47 P 56.80 .90 The previous analysis (Cournot Competition) considered quantity as the strategic variable. Bertrand competition uses price as the strategic variable. p Should it matter? P* D Q* P 120 20Q Industry Output Q Just as before, we have an industry demand curve and two competing duopolies – both with marginal cost equal to $20. Firm level demand curves look very different when we change strategic variables Bertrand Case Quantity Strategy Q 6 .05 P P 120 20q2 20q1 p p1 120 20q2 p2 D q1 If you are underpriced, you lose the whole market At equal prices, you split the market D q1 If you are the low price you capture the whole market Price competition creates a discontinuity in each firm’s demand curve – this, in turn creates a discontinuity in profits if p1 p2 0 6 .05 p1 1 p1 , p2 ( p1 20) if p1 p2 2 ( p 20)(6 .05 p ) if p p 1 1 2 1 As in the cournot case, we need to find firm one’s best response (i.e. profit maximizing response) to every possible price set by firm 2. Firm One’s Best Response Function Case #1: Firm 2 sets a price above the pure monopoly price: p2 pm p1 pm Case #2: Firm 2 sets a price between the monopoly price and marginal cost pm p2 20 p1 p2 Case #3: Firm 2 sets a price below marginal cost 20 p2 p1 p2 Case #4: Firm 2 sets a price equal to marginal cost c p2 p1 p2 c What’s the Nash equilibrium of this game? Monopoly Q* 2.5M P $70 LI 2.5 HHI 10,000 2 Firms Q 5M q 2 .5 P $20 LI 0 HHI 5,000 Perfect Competition Q* 5M P $20 LI 0 HHI 0 However, the Bertrand equilibrium makes some very restricting assumptions… Firms are producing identical products (i.e. perfect substitutes) Firms are not capacity constrained An example…capacity constraints Consider two theatres located side by side. Each theatre’s marginal cost is constant at $10. Both face an aggregate demand for movies equal to Q 6,000 60 P Each theatre has the capacity to handle 2,000 customers per day. What will the equilibrium be in this case? Q 6,000 60 P If both firms set a price equal to $10 (Marginal cost), then market demand is 5,400 (well above total capacity = 2,000) Note: The Bertrand Equilibrium (P = MC) relies on each firm having the ability to make a credible threat: “If you set a price above marginal cost, I will undercut you and steal all your customers!” 4,000 6,000 60P P $33.33 At a price of $33, market demand is 4,000 and both firms operate at capacity. Now, how do we choose capacity? Back to Cournot competition! With competition in price, the key is to create product variety somehow! Suppose that we have two firms. Again, marginal costs are $20. The two firms produce imperfect substitutes. p p1 40 q1 2 80 Example: p1 p2 40 q2 80 p2 40 p 80 q1 1 .0125 p1 D q1 Recall Firm 1 has a marginal cost of $20 1 ( p1 20) p2 p1 40 80 Each firm needs to choose price to maximize profits conditional on the other firm’s choice of price. q1 Firm 1 profit maximizes by choice of price p1 30 .5 p2 p2 Firm 2 sets a price of $50 Firm 1’s strategy D $30 Firm 1 responds with $55 p1 With equal costs, both firms set the same price and split the market evenly p1 30 .5 p2 p2 30 .5 p1 p2 Firm 1 Firm 2 $60 $30 $30 $60 p1 q1 .50 p1 $60 q2 .50 p2 $60 Monopoly Q* 2.5M P $70 LI .71 HHI 10,000 2 Firms P $60 LI .66 HHI 5,000 Perfect Competition Q* 5M P $20 LI 0 HHI 0 Suppose that Firm two‘s costs increase. What happens in each case? p1 p2 40 2 ( p2 20) 80 Bertrand p2 Firm 2 $30 p1 With higher marginal costs, firm 2’s profit margins shrink. To bring profit margins back up, firm two raises its price Suppose that Firm two‘s costs increase. What happens in each case? p2 With higher marginal costs, firm 2’s profit margins shrink. To bring profit margins back up, firm two raises its price Firm 1 Firm 2 p1 A higher price from firm two sends customers to firm 1. This allows firm 1 to raise price as well and maintain market share! Cournot (Quantity Competition): Competition is for market share Firm One responds to firm 2’s cost increases by expanding production and increasing market share – prices are fairly stable and market shares fluctuate Best response strategies are strategic substitutes Bertrand (Price Competition): Competition is for profit margin Firm One responds to firm 2’s cost increases by increasing price and maintaining market share – prices fluctuate and market shares are fairly stable. Best response strategies are strategic complements Bertrand p2 Cournot q2 Firm 1 Firm 1 Firm 2 Firm 2 p1 q1 Stackelberg leadership – Incumbent/Entrant type games In the previous example, firms made price/quantity decisions simultaneously. Suppose we relax that and allow one firm to choose first. P 120 20Q MC 20 Both firms have a marginal cost equal to $20 Firm 1 chooses its output first Firm 2 chooses its output second Market Price is determined Firm 2 has observed Firm 1’s output decision and faces the residual demand curve: P 120 20q1 20q2 q2 q2 5 q1 0 MR 120 20q1 40q2 20 100 20q1 q2 40 q2 0 q1 2.5 q1 Firm 2’s strategy Knowing Firm 2’s response, Firm 1 can now maximize its profits: P 120 20q2 20q1 100 20q1 q2 40 P 70 10q1 MR 70 20q1 20 q1 2.5 Firm 1 produces the monopoly output! q1 2.5 100 20q1 q2 1.25 40 Q 3.75 P 120 203.75 $45 1 452.5 202.5 62.50 2 451.25 201.25 31.25 2 Firms Monopoly Q* 2.5M P $70 LI .71 HHI 10,000 Q 3.75M q1 2.5 (67%) q2 1.25 (33%) P $45 LI .55 HHI 5,587 Perfect Competition Q* 5M P $20 LI 0 HHI 0 Sequential Bertrand Competition We could also sequence events using price competition. p2 p1 40 q1 80 p1 p2 40 q2 80 Both firms have a marginal cost equal to $20 Firm 1 chooses its price first Firm 2 chooses its price second Market sales are determined Recall Firm 1 has a marginal cost of $20 p2 p1 40 1 ( p1 20) 80 p2 30 .5 p1 From earlier, we know the strategy of firm 2. Plug this into firm one’s profits… .5 p1 70 1 ( p1 20) 80 Now we can maximize profits with respect to firm one’s price. Sequential Bertrand Competition p1 $80 p2 $70 q1 .38 q2 .62 2 Firms Monopoly Q* 2.5M P $70 LI .71 HHI 10,000 q1 .38 q2 .62 P $75 LI .73 HHI 5,288 Perfect Competition Q* 5M P $20 LI 0 HHI 0 Cournot vs. Bertrand: Stackelberg Games Cournot (Quantity Competition): Firm One has a first mover advantage – it gains market share and earns higher profits. Firm B loses market share and earns lower profits Total industry output increases (price decreases) Bertrand (Price Competition): Firm Two has a second mover advantage – it charges a lower price (relative to firm one), gains market share and increases profits. Overall, production drops, prices rise, and both firms increase profits. Predatory Pricing: A pricing strategy that makes sense only if it drives a competitor out of business. Suppose that a Cournot competitor decides to exploit the first mover advantage to drive its competitor out of business… P 120 20Q MC 20 Both firms have a marginal cost equal to $20, each also has a fixed cost equal to $5 Firm 1 chooses its output first Firm 2 chooses its output second Market Price is determined Knowing Firm 2’s response, We can adjust the demand curve: P 120 20q2 20q1 100 20q1 q2 40 P 70 10q1 This demand curve incorporates firm two’s behavior. Now, we want to create firm 2’s profits: 2 P MC q2 FC 100 20q1 2 70 10q1 20 5 40 100 20q1 q2 40 P 70 10q1 MC = $20, FC = $5 100 20q1 1 2 50 10q1 5 2 20 2 50 10q1 2 1 5 20 We want to find the level of production by firm 1 that lowers Firm 2’s profits to zero… 2 50 10q1 2 1 5 0 20 50 10q1 2 100 50 10q1 10 q1 4 100 20q1 q2 .5 40 P 70 10q1 30 Now, we can calculate profits… 1 P MC q1 FC 1 30 204 5 35 q1 4 q2 .5 P 30 2 P MC q2 FC 2 30 20.5 5 0 Note: This was by design! Firm one sacrifices some profits today to stay a monopoly! There have been numerous cases involving predatory pricing throughout history. Standard Oil American Sugar Refining Company Mogul Steamship Company Wall Mart AT&T Toyota American Airlines There are two good reasons why we would most likely not see predatory pricing in practice 1. It is difficult to make a credible threat (Remember the Chain Store Paradox)! 2. A merger is generally a dominant strategy!! The Bottom Line with Predatory Pricing… There have been numerous cases over the years alleging predatory pricing. However, from a practical standpoint we need to ask three questions: 1. Can predatory pricing be a rational strategy? 2. Can we distinguish predatory pricing from competitive pricing? 3. If we find evidence for predatory pricing, what do we do about it?
