Managerial Economics Koç University Graduate School of Business MGEC 501 Levent Koçkesen Oligopoly • Capacity Competition: Cournot Model – Firms take quantities or capacities of rivals as given – Price adjusts to clear the market – Firms commit to capacity beforehand and let the market determine the price – Firms can adjust prices more quickly than production – Examples: Automobile, mining, chemical processing • Price Competition: Bertrand Model – Firms take prices of the rivals as given • They set prices • Consumers decide how much to buy of each firm’s product • Firms satisfy that demand (they have enough capacity) – Firms believe that they can steal market share from competitors by price cuts and have enough capacity to satisfy the additional demand – Homogenous products • A flight between two airports • DRAM chips – Differentiated products • Coke versus Pepsi • Apple versus Wintel • Ready-to-eat breakfast cereals 1
Homogenous Product Bertrand Consider the same example we used for Cournot Model Two producers of DRAM chips (Firm 1 and Firm 2) Market demand curve: Q = 90 – P or P = 90 – Q Marginal cost of each producer is zero: MC 1 = MC 2 = 0 (for simplicity only) Lower price firm captures the entire market. If firms charge the same prices they split the market evenly. Cournot Equilibrium: price Q 1 = Q 2 = 30 � P = 30 > MC Is it still an equilibrium? 90 If Firm 1 decreases price to 29 it captures the entire market Its profit increases by A and decreases by B Each firm has an incentive to undercut the other’s price as long as it is above the MC Only possible equilibrium is P = MC = 0 30 B 29 Same as the perfectly competitive market outcome! A Profits in Cournot model = 900 Profits in Bertrand = 0 30 60 61 90 quantity Why the difference? Why are the Cournot and Bertrand Equilibria Different? 1. Time frames • Cournot: Firms first choose capacity and then compete as price setters given capacities. The outcome of this two-stage game is equivalent to Cournot outcome* • Bertrand: Short-run price competition when firms have enough capacity to satisfy demand at any price 2. Firms’ expectations about rivals’ reactions to competitive moves • Cournot: Firms take competitors’ output as given and assume they will match any price change so as to keep their sales constant - Makes more sense in industries in which capacity is difficult to change and inventories are costly - Examples: cement, steel, automobile, mining, petrochemical industry - It is difficult to steal customers from rivals → firms are less aggressive • Bertrand: Firms believe that they can steal customers by undercutting rivals’ prices and have enough capacity to satisfy additional demand - U.S. Airline industry in early 2000s: significant excess capacity → price cutting - Software industry - Encyclopedia Britannica’s 32 volume set sold for $1,600 - Early 1990s Microsoft started selling Encarta on CD for less than $100 - 2006 editions of both on CD were selling at less than $30 * See Kreps and Scheinkman (Bell J. of Econ., 1983) 2
Bertrand with Different Marginal Costs Suppose MC 1 = 5 and MC 2 = 10 What is the equilibrium? � Could it be P 1 > P 2 ? � P 2 ≥ 10 and Firm 1 profits = 0 � Firm 1 can set price smaller than 10 and earn positive profits � Could it be P 1 = P 2 ? � Must be P 2 ≥ 10. � If Firm 1 sets P 1 = P 2 its profits = (90 – P 2 )(1/2)(P 2 – 5) � If Firm 1 sets P 1 = P 2 – ε its profits = (90 – P 2 + ε )(P 2 – ε – 5) � For small ε , P 2 – ε is better. � Must be P 1 < P 2 . Firm 1 captures the entire market � One possible equilibrium is P 1 = 10 - ε (e.g. $9.99). � This assumes that price is a discrete (not a continuous) variable. Cost disadvantages could be deadly in homogenous product price competition Takeaways from Cournot and Bertrand Models 1. Capacity competition – Cournot and Stackelberg � Results in more than perfectly competitive but less than collusive profits � Moves that increase market share and profits � marginal cost reduction credible commitment to aggressive behavior � � example: sunk investment in capacity increase � collusion � could be hard to sustain, but there may be ways that do not involve going to jail 2. Price competition – Homogenous Product Bertrand � Results in zero profits: competing on price alone could be destructive � Moves that increase market share and profits � marginal cost reduction � collusion � product differentiation 3
Competition with Differentiated Products � Vertical Product Differentiation � One is considered better than the other � The better one can still get 50% of the market at a price premium � Example: Duracell batteries versus generic brands � Horizontal Product Differentiation � Consumers are divided on which is better � Equal price → both sell positive amounts � Example: Coke and Pepsi � Weak horizontal differentiation � demand is very sensitive to relative price changes � Strong horizontal differentiation � demand is not very sensitive to relative price changes Bertrand Price Competition with Differentiated Products Demand functions for Coke (denoted by 1) and Pepsi (denoted by 2)* Q 1 = 63.42 – 3.98P 1 + 2.25P 2 Q 2 = 49.52 – 5.48P 2 + 1.40P 1 P = dollars per 10 case (12 cans in each case) Q = millions of cases MC 1 = 4.96, MC 2 = 3.96 Firms set prices to maximize profits given what they believe the other firm will charge. What should each firm charge? * Gasini, Lafont, Vuong, J. of Econ. Man. Str. (1992) 4
If Pepsi’s price = $8 → Q 1 = 63.42 – 3.98P 1 + 2.25x8 Coke’s price P 1 = 20.46 – 0.25Q 1 MR = 20.46 – 0.5Q 1 = 4.96 = MC → Q 1 = 30.9, P 1 = 12.71 20.46 12.71 Pepsi’s Price D 8 Coke’s MC reaction 4.96 MR 8 function 30.9 Coke’s quantity 12 8 If Pepsi’s price = $12 → Q 1 = 63.42 – 3.98P 1 + 2.25x12 Coke’s price P 1 = 22.72 – 0.25Q 1 MR = 22.72 – 0.5Q 1 = 4.96 = MC → Q 1 = 35.34, P 1 = 13.84 22.72 12.71 13.84 Coke’s Price 13.84 D 12 MC 4.96 MR 12 35.34 Coke’s quantity The Algebra Behind Reactions Functions Coke’s Profit Maximization Problem Q 1 = 63.42 – 3.98P 1 + 2.25P 2 Profits = (63.42 – 3.98P 1 + 2.25P 2 )(P 1 – 4.96) What is the profit maximizing price for Coke given an arbitrary price set by Pepsi? Maximize profits with respect to P 1 given P 2 FOC: 2.25P 2 – 7.96P 1 + 83.161 = 0 → Coke’s reaction function: P 1 = 10.45 + 0.28P 2 Pepsi’s Profit Maximization Problem Q 2 = 49.52 – 5.48P 2 + 1.40P 1 Profits = (49.52 – 5.48P 2 + 1.40P 1 )(P 2 – 3.96) What is the profit maximizing price for Pepsi given an arbitrary price set by Coke? Maximize profits with respect to P 2 given P 1 FOC: 1.4P 1 – 10.96P 2 + 71.221 = 0 → Pepsi’s reaction function: P 2 = 6.50 + 0.13P 1 5
Nash equilibrium of Bertrand Model with Differentiated Products P 1 = 10.45 + 0.28P 2 P 1 = $12.74 Actual average prices over the period of Q 1 = 31 (%58) the analysis (1968-1986) P 2 = 6.50 + 0.13P 1 P 2 = $8.13 Q 2 = 22.8 (%42) Coke = $12.96 Pepsi = $8.16 Prices are well above marginal costs Product differentiation softens competition and increases profits When products are not perfect substitutes price cutting is less effective for stealing a rival’s business Pepsi’s Price Percentage Contribution Margin (PCM) Coke’s PCM = (P – MC)/P reaction For every dollar of sales, how much is left over to cover function fixed costs (marketing expenses, company overhead, interest, and taxes, etc.) Can be used to compare profitability if fixed costs are the same 8.13 Coke Pepsi Pepsi’s Prices 12.74 8.13 reaction 6.50 function Sales 30.98 22.83 Market Shares 58% 42% Profits 241.2 95.1 PCM 0.61 0.51 12.74 Coke’s Price What happens if Coke’s MC decreases to 1? Coke’s price If Pepsi’s price = $8 20.46 MR = 20.46 – 0.5Q 1 = 1 = MC → Q 1 = 38.7, P 1 = 10.7 Pepsi’s Price 10.7 D 8 Coke’s new Coke’s old reaction reaction 4.96 MR 8 MC function function 1 38.7 Coke’s quantity 12 8 If Pepsi’s price = $12 Coke’s price MR = 22.72 – 0.5Q 1 = 1 = MC → Q 1 = 43.22, P 1 = 11.86 22.72 12.71 13.84 Coke’s Price Profits = (63.42 – 3.98P 1 + 2.25P 2 )(P 1 – 1) FOC: 2.25P 2 – 7.96P 1 + 67.4 = 0 11.86 D 12 → Coke’s new reaction function: P 1 = 8.47 + 0.28P 2 MR 12 (Old reaction function P 1 = 10.45 + 0.28P 2 ) 4.96 MC 1 43.22 Coke’s quantity 6
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