Managerial Economics Ko University Graduate School of Business - - PDF document

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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

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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: MC1 = MC2 = 0 (for simplicity only) Lower price firm captures the entire market. If firms charge the same prices they split the market evenly.

Homogenous Product Bertrand

price 90 90 quantity 60 29 61 30 Cournot Equilibrium: Q1 = Q2 = 30 P = 30 > MC Is it still an equilibrium? 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 Same as the perfectly competitive market outcome! 30

A B

Profits in Cournot model = 900 Profits in Bertrand = 0 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
• utcome 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)

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Bertrand with Different Marginal Costs

Suppose MC1 = 5 and MC2 = 10 What is the equilibrium? Could it be P1 > P2 ? P2 ≥ 10 and Firm 1 profits = 0 Firm 1 can set price smaller than 10 and earn positive profits Could it be P1 = P2 ? Must be P2 ≥ 10. If Firm 1 sets P1 = P2 its profits = (90 – P2)(1/2)(P2 – 5) If Firm 1 sets P1 = P2 – ε its profits = (90 – P2 + ε)(P2 – ε – 5) For small ε, P2 – ε is better. Must be P1 < P2. Firm 1 captures the entire market One possible equilibrium is P1 = 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

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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)* Q1 = 63.42 – 3.98P1 + 2.25P2 Q2 = 49.52 – 5.48P2 + 1.40P1 P = dollars per 10 case (12 cans in each case) Q = millions of cases MC1 = 4.96, MC2 = 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)

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20.46 4.96 30.9 12.71

Coke’s quantity Coke’s price D8 MR8 MC If Pepsi’s price = $8 → Q1 = 63.42 – 3.98P1 + 2.25x8 P1 = 20.46 – 0.25Q1 MR = 20.46 – 0.5Q1 = 4.96 = MC → Q1 = 30.9, P1 = 12.71

Pepsi’s Price Coke’s Price

22.72 4.96 35.34 13.84

Coke’s quantity Coke’s price D12 MR12 MC If Pepsi’s price = $12 → Q1 = 63.42 – 3.98P1 + 2.25x12 P1 = 22.72 – 0.25Q1 MR = 22.72 – 0.5Q1 = 4.96 = MC → Q1 = 35.34, P1 = 13.84

8 12 13.84 12.71

Coke’s reaction function

The Algebra Behind Reactions Functions

Coke’s Profit Maximization Problem

Q1 = 63.42 – 3.98P1 + 2.25P2 Profits = (63.42 – 3.98P1 + 2.25P2)(P1 – 4.96) What is the profit maximizing price for Coke given an arbitrary price set by Pepsi? Maximize profits with respect to P1 given P2 FOC: 2.25P2 – 7.96P1 + 83.161 = 0 → Coke’s reaction function: P1 = 10.45 + 0.28P2

Pepsi’s Profit Maximization Problem

Q2 = 49.52 – 5.48P2 + 1.40P1 Profits = (49.52 – 5.48P2 + 1.40P1)(P2 – 3.96) What is the profit maximizing price for Pepsi given an arbitrary price set by Coke? Maximize profits with respect to P2 given P1 FOC: 1.4P1 – 10.96P2 + 71.221 = 0 → Pepsi’s reaction function: P2 = 6.50 + 0.13P1

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Pepsi’s Price Coke’s Price

8.13 12.74

Coke’s reaction function

6.50

Pepsi’s reaction function

P1 = 10.45 + 0.28P2 P2 = 6.50 + 0.13P1 Nash equilibrium of Bertrand Model with Differentiated Products P1 = $12.74 P2 = $8.13 Q1 = 31 (%58) Q2 = 22.8 (%42)

Actual average prices over the period of the analysis (1968-1986) 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 Percentage Contribution Margin (PCM)

PCM = (P – MC)/P For every dollar of sales, how much is left over to cover fixed costs (marketing expenses, company overhead, interest, and taxes, etc.) Can be used to compare profitability if fixed costs are the same

0.51 0.61 PCM 95.1 241.2 Profits 42% 58% Market Shares 22.83 30.98 Sales 8.13 12.74 Prices Pepsi Coke

20.46 1 38.7 10.7

Coke’s quantity Coke’s price D8 MR8 MC If Pepsi’s price = $8 MR = 20.46 – 0.5Q1 = 1 = MC → Q1 = 38.7, P1 = 10.7

Pepsi’s Price Coke’s Price

22.72 1 43.22 11.86

Coke’s quantity Coke’s price D12 MR12 MC If Pepsi’s price = $12 MR = 22.72 – 0.5Q1 = 1 = MC → Q1 = 43.22, P1 = 11.86

8 12 13.84 12.71

Coke’s old reaction function Coke’s new reaction function Profits = (63.42 – 3.98P1 + 2.25P2)(P1 – 1) FOC: 2.25P2 – 7.96P1 + 67.4 = 0 → Coke’s new reaction function: P1 = 8.47 + 0.28P2 (Old reaction function P1 = 10.45 + 0.28P2)

4.96 4.96

What happens if Coke’s MC decreases to 1?

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Pepsi’s Price Coke’s Price

8.13 12.74

Coke’s old reaction function

6.50

Pepsi’s reaction function

What happens if Coke’s MC decreases to 1?

P1 = 8.47 + 0.28P2 P2 = 6.50 + 0.13P1 P1 = $10.69 P2 = $7.86 Q1 = 38.6 (%64) Q2 = 21.4 (%36)

Coke’s new reaction function

10.69 7.86

• Direct effect:

Coke’s price decreases because of a MC decrease

• Strategic effect:

Pepsi responds by decreasing its price This leads Coke to reduce its price further

Click here for bertrand.xls

What happens as Horizontal Differentiation Changes?

• Stronger horizontal differentiation means that demand for the product becomes less

sensitive to the other product’s price.

• As an example suppose that demand functions for Coke and Pepsi change in the

following manner Q1 = 63.42 – 3.98P1 + 0.5P2 Q2 = 49.52 – 5.48P2 + 0.5P1

Reaction Functions

2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 Coke's Price Pepsi's Price Scenario 1 - Coke Scenario 1 - Pepsi Scenario 2 - Coke Scenario 2 - Pepsi

• Reaction functions become less sensitive to

the rival’s price changes

• More freedom in pricing
• As horizontal differentiation becomes weaker

firms become more interdependent in their pricing and tougher price competitors

was 2.25 was 1.40

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What happens as Vertical Differentiation Changes?

• At equal prices Coke sells more. So, it could still capture 50% of the market at a price premium
• Now suppose Pepsi gains some more loyal customers. One way to reflect that is to increase the intercept in

Pepsi’s demand function For example Q1 = 63.42 – 3.98P1 + 2.25P2 Q2 = 63.42 – 5.48P2 + 1.40P1

Reaction Functions

2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 Coke's Price Pepsi's Price Scenario 1 - Coke Scenario 1 - Pepsi Scenario 2 - Coke Scenario 2 - Pepsi

• Pepsi’s reaction function shifts up
• Pepsi increases its price → Coke increases its

price as well Initial Equilibrium New Equilibrium

0.51 0.61 PCM 95.1 241.2 Profits 42% 58% Market Shares 22.83 30.98 Sales 8.13 12.74 Prices Pepsi Coke 0.58 0.62 PCM 164.7 264.8 Profits 48% 52% Market Shares 30.04 32.46 Sales 9.44 13.12 Prices Pepsi Coke

Dynamic Rivalry and Collusion So far we have assumed that market interaction is one-shot In reality firms compete in price or capacity repeatedly over time This changes their incentives and nature of strategic interaction Using the Bertrand model we have seen that firms have an incentive, whose strength is determined by the extent of horizontal differentiation, to undercut their rivals’ prices In a repeated interaction, a firm that cuts its price today to steal business from rivals may find that they retaliate with their own price cuts in the future, nullifying the “benefits” of the original price cut In some concentrated industries prices are maintained at high levels The U.S. steel industry until the late 1960s The U.S. cigarette industry until the early 1990s In other similarly concentrated industries there is fierce price competition Costa Rican cigarette industry in the early 1990s The U.S. airline industry in 1992

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Dynamic Pricing Rivalry

The market for a commodity chemical consists of two firms, Shell Chemical and Exxon Mobil Chemical Market demand curve: Q = 100 – P or P = 100 – Q Marginal costs are equal: MCS = MCE = 20 Lower price firm captures the entire market. If firms charge the same prices they split the market evenly

MR price ($/hundred pounds) 100 100 quantity (millions of pounds per year) MC 20 40 60

Bertrand Equilibrium price = MC = $20 Profits are zero Collusion Charge the monopoly price of $60 and produce 40 million pounds altogether If they divide the market 50:50, each makes an annual profit of $8 million Can Shell and Exxon Mobil sustain collusion? Suppose currently they both charge $40 and make $6 million each If Shell increases its price above $40 and Exxon does not follow suit, Shell will suffer a huge market loss and Exxon will make $12 million

Dynamic Pricing Rivalry

Explicit Collusion

• They could formally collude by discussing and jointly making their pricing decisions
• Illegal in most countries and subject to severe penalties

Most recently, in October 2005, Samsung admitted that it conspired with its rivals to fix prices between 1999 and 2002 and agreed to pay $300 million fine. Hynix Semiconductor Inc. pleaded guilty in May and agreed to pay $185 million. German firm Infineon Technologies pleaded guilty in 2004 and is paying $160 million. Micron Technology Inc. of Boise, Idaho, the largest U.S. DRAM firm, was the first in the ring to come forward with evidence and will probably be spared prosecution under an amnesty program. Five individuals have served criminal sentences and seven executives are open to prosecution.

Implicit Collusion

• Could they collude without explicitly fixing prices?
• There must be some rewards/punishments mechanism to keep firms in line
• Repeated interaction provides the opportunity to implement such mechanisms
• One such mechanism is Tit-for-Tat Pricing: mimic your rival’s last period price
• A firm that contemplates undercutting its rivals faces a trade-off
• short-term increase in profits (maybe longer-term if market share increase becomes

permanent)

• long-term decrease in profits if rivals retaliate by lowering their prices
• Depending upon which of these forces is dominant collusion could be sustained
• What determines the sustainability of implicit collusion?

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Tit-for-Tat Pricing

• Suppose both currently charge $40 and Shell raises its price to $60
• If Exxon Mobil does not follow suit it will capture the entire market and make an annual profit of $12

million, much higher than the collusive profit of $8 million

• Let’s assume that
• prices can be changed on a weekly basis and Shell can take back its price increase in a week
• both firms can observe each other’s prices
• both firms use a 10% annual rate to discount future profits (a weekly rate of .2%)
• Shell considers two scenarios:
• Bad Scenario: Exxon Mobil sticks with the current price of $40. Then we will take our price back

to $40 after a week. This will give Exxon a week’s worth of extra profits

• From 6/52 = $0.1154 million to 12/52 = $0.2308 million
• This will however last only for a week until we take our rice back
• Discounted present value of Exxon’s profits under this scenario will be

0.2308 + 0.1154/(1.002) + 0.1154/(1.002)2 + 0.1154/(1.002)3 + … = $57.93 million

• Good Scenario: Exxon Mobil follows us and raises its price to $60. We will each earn $8 million

annually or $0.1538 weekly. Therefore, by following our price hike Exxon’s discounted profits will be 0.1538 + 0.1538/(1.002) + 0.1538/(1.002)2 + 0.1538/(1.002)3 + … = $77.05 million If Exxon is rational it will follow our price increase and we will increase our profits significantly. If it does not follow, then we will loose only a week’s worth of profits. Worth a try!

Tit-for-Tat Pricing

• Exxon could be rational and able to do all these calculations but still may not follow Shell if it is not

sure that Exxon will take back its price increase

• It is important that Shell communicates its intentions to do so
• Shell could make a commitment to its customers that “We will not be undersold”
• We have seen that Tit-for-Tat gives incentives to increase prices.
• It also discourages price cutting to steal business from competitors because such a move will be

matched by the competitors and the benefits of undercutting will be transitory

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What determines the sustainability of implicit collusion?

• Let there be N firms in the industry and πm be the industry monopoly profit. Also let πd be the

industry profit at the prevailing price.

• If each firm charges the monopoly price and shares the market evenly, each makes πm/N
• Assume that firms compete with each other over an infinite horizon and discounts the future profits

using a discount factor 0 ≤ δ <1

• Next period’s $1 is worth $δ today for each firm
• This could reflect value of time as well as the probability of an interaction next period
• If a firm expects the rest of the industry to increase the price to the monopoly price, it faces a

decision: Keep charging the current price or increase price to the monopoly price

• If a firm charges the monopoly price, the discounted sum of profits will be
• If it does not increase the price, its profit today is πd. Starting next period, however, the other firms

will all charge the same price and hence this firm will get πd/N. Therefore, the discounted sum of profits will be

( )

... 1

2

+ + +

m m m

N π δ δπ π

( )

... 1

2

+ + +

d d d

N π δ δπ π

payoff to colluding → payoff to undercutting →

What determines the sustainability of implicit collusion?

• Collusion through Tit-for-Tat can be sustained if

( ) ( )

( )

N N

m d d m d m

π π π π δ π π δ − ≥ + − + − ... 1

2

• LHS is the (long-term) benefit of colluding and RHS is the (short-term) benefit of undercutting
• We can re-write this condition as

( )

N N

m d d m

π π δ π π − ≥ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − 1 1 1

• Four determinants of sustainability of collusion

1. Size of the short-term benefit to undercutting: smaller the better 2. Size of the industry-wide single period benefit to colluding: larger the better 3. Number of firms: smaller the better 4. Discount factor:

• more patience is better
• more likely the firm will be there next period the better

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Why Tit-for-Tat?

• Folk Theorem: if firms are sufficiently patient, then any price between the monopoly price and

marginal cost can be sustained as an equilibrium

• Another strategy that sustains monopoly price for high enough discount factor is “grim-trigger”
• Starting this period we will charge the monopoly price. In each subsequent period, if any firm

undercuts we will drop our price to marginal cost in the next period and keep it there forever

• Promises infinite price war
• Tit-for-Tat has advantages over other strategies in sustaining collusion:

1. It is simple, easy to describe, easy to understand

• Firms can announce “We will not be undersold” or “We will match any price” to signal

intentions 2. It is forgiving. If there is a misunderstanding collusion can be restored.

• the strategy may need to be modified a little
• ignore what appears to be a uncooperative move by a competitor if the competitor

reverts back to cooperative behavior in the next period

Market Structure and Cooperative Pricing

• Market Concentration: higher the market share larger are the benefits from cooperation and smaller

the benefits from undercutting

• easier to coordinate on a common strategy
• easier to detect cheaters
• Reaction speed: higher speed facilitates cooperation
• infrequent interaction due to lumpiness of orders
• Detection lags and ambiguities make it more difficult to sustain collusion
• secret deals: ambiguities in identifying who is cutting the price
• volatile demand conditions: there is a drop in your sales. Is it due to (a) price cutting by

rivals, or (b) an unanticipated decrease in demand?

• partitioning the market geographically or by product characteristics may help
• Asymmetries among firms
• no single focal price; more difficult to coordinate
• small firms have more incentive to defect from cooperative pricing
• large firms benefit more from cooperative pricing
• small firms may anticipate that large firms are less likely to punish defection by a small

firm, because the market share a small firm steals would be relatively small

• Price sensitivity of buyers: when buyers are price sensitive, a firm that undercuts its rivals’ prices by

even a small amount may be able to achieve a significant boost in its volume