1. Finance 30210: Managerial Economics
Strategic Pricing Techniques

2. Recall that there is an entire spectrum of market structures
Perfect Competition
Many firms, each with zero market share
P = MC
Profits = 0 (Firm’s earn a reasonable rate of return on invested capital)
NO STRATEGIC INTERACTION!
Monopoly
One firm, with 100% market share
P > MC
Profits > 0 (Firm’s earn excessive rates of return on invested capital)
NO STRATEGIC INTERACTION!

3. 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)
Anheuser-Busch: 49% Miller/Coors: 29% Crown Imports: 5% Heineken USA: 4% Pabst: 3%
Music Recording (2005)
Universal/Polygram: 31% Sony: 26% Warner: 25% Independent Labels: 18%

4. The key difference in oligopoly markets is that price/sales decisions can’t be made independently of your competitor’s decisions
Your Price (-)
Monopoly
Oligopoly
Your N Competitors Prices (+)
Oligopoly markets rely crucially on the interactions between firms which is why we need game theory to analyze them!

5. Market shares are not constant over time in these industries!
Airlines (1992)
Airlines (2002)
American
American
United
United
Delta
Delta
Northwest
Northwest
Continental
Continental
US Air
SWest
While the absolute ordering didn’t change, all the airlines lost market share to Southwest.

6. Another trend is consolidation
Retail Gasoline (1992)
Retail Gasoline (2001)
Shell
Exxon/Mobil
Chevron
Shell
Texaco
BP/Amoco/Arco
Exxon
Amoco
Chev/Texaco
Mobil
Total/Fina/Elf BP
Conoco/Phillips
Citgo
Marathon
Sun
Phillips

7. Confess Don’t Confess -4 -4 0 -8 -8 0 -1 -1
Recall the prisoners dilemma game…
Clyde
Confess
Don’t Confess
Jake
The prisoner’s dilemma game is used to describe circumstances where competition forces sub-optimal outcomes

8. 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
$225M
SGL Carbon
Graphite Electrodes
$135M
UCAR International
1998
$110M
Archer Daniels Midland
Lysine & Citric Acid
1997
$100M
Haarman & Reimer
Citric Acid
$50M
HeereMac
Marine Construction
$49M
In other words…Cartels happen!

9. Each has a marginal cost of $80.
Suppose that we have two firms in the market. They face the following demand curve…
Each has a marginal cost of $80.
Firm 1’s output
Firm 2’s output
If these firms formed a cartel, they would operate jointly as a monopolist.
Each firm agrees to sell 20 units at $240 each.
Each firm makes $3200 in profits

10. Firm 1 cheats and earns more profits!
However, given that firm 2 is producing 20 units, what should firm 1 do?
Firm 1’s output
Firm 2’s output
Firm 1 cheats and earns more profits!

11. But if they both cheat and produce 30 units…

12. Cooperate Cheat $3200 $3200 $2400 $3600 $3600 $2400 $2400 $2400
Cartels - The Prisoner’s Dilemma
The problem facing the cartel members is a perfect example of the prisoner’s dilemma !
Clyde
Cooperate
Cheat
$ $3200
$ $3600
$ $2400
$ $2400
Jake
Cheating is a dominant strategy!

13. 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!

14. Perhaps cartels can be maintained because the members are interacting over time – this brings is a possible punishment for cheating.
Clyde
Cooperate
Cheat
$ $3200
$ $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!” 1 2 3 4 5
Time
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision

15. Clyde should cooperate, right?
Cheat
$ $3200
$ $3600
$ $2400
$ $2400
“I plan on cooperating…if you cooperate today, I will cooperate tomorrow, but if you cheat today, I will cheat forever!”
Jake
Cooperate:
$3200
$3200
$3200
$3200
$3200
$3200
Clyde 1 2 3 4 5
Time
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Cheat:
$3600
$2400
$2400
$2400
$2400
$2400
Cooperate: $19,200
Cheat: $15,600
Clyde should cooperate, right?

16. We need to use backward induction to solve this.
Jake
Clyde 1 2 3 4 5
Time
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Cooperate
Cheat
$ $3200
$ $3600
$ $2400
$ $2400
Regardless of what took place the first four time periods, what will happen in period 5?
What should Clyde do here?

17. We need to use backward induction to solve this.
Jake
Clyde 1 2 3 4 5
Time
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Cheat
Cooperate
Cheat
$ $3200
$ $3600
$ $2400
$ $2400
Given what happens in period 5, what should happen in period 4?
What should Clyde do here?

18. We need to use backward induction to solve this.
Jake
Clyde 1 2 3 4 5
Time
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Make Strategic Decision
Cheat
Cheat
Cheat
Cheat
Cheat
Cooperate
Cheat
$ $3200
$ $3600
$ $2400
$ $2400
Knowing the future prevents credible promises/threats!

19. 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

20. High Price Low Price $12 $12 $5 $14 $14 $5 $6 $6
Price Matching: A form of collusion?
High Price
Low Price
$12 $12
$5 $14
$14 $5
$6 $6
Price Matching Removes the off-diagonal possibilities. This allows (High Price, High Price) to be an equilibrium!!

21. The Stag Hunt - Airline Price Wars
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
P = $500
P = $220
$9,000
$3,600 $0
$1,800 60
180
What will the equilibrium be?
Delta

22. The Airline Price Wars P = $500 P = $220 $9,000 $3,600 $0 $1,800
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 = $500
P = $220
$9,000
$3,600 $0
$1,800
This game has multiple equilibria and the result depends critically on each company’s beliefs about the other company’s strategy
Delta

23. The Airline Price Wars: Mixed Strategy Equilibria
Suppose American charges $500 with probability
Charges $220 with probability
Charge $500:
American
Charge $220:
P = $500
P = $220
$9,000
$3,600 $0
$1,800
Delta
(6%)
(19%)
(19%)
(56%)
(75%)
(25%)

24. 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?

25. Cournot Competition: Quantity is the strategic choice variable
There are two firms in an industry – both facing an aggregate (inverse) demand curve given by D
Total Industry Production
Both firms have constant marginal costs equal to $20

26. 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 S Q1 P*
Profit = P*Q1 - TC D Q
Q1 + Q2
A centralized market determines the market price based on available supply and current demand Q2
Profit = P*Q2 - TC

27. For example…suppose both firms have a constant marginal cost of $20
Two manufacturers choose a production target
Two manufacturers earn profits based off the market price P S
Q1 = 1
$60
Profit = 60*1 – 20 = $40 D Q 3
A centralized market determines the market price based on available supply and current demand
Q2 = 2
Profit = 60*2 – 40 = $80

28. From firm one’s perspective, the demand curve is given by
Treated as a constant by Firm One
Solving Firm One’s Profit Maximization…

29. In Game Theory Lingo, this is Firm One’s Best Response Function To Firm 2
If firm 2 drops out, firm one is a monopolist!

30. What could firm 2 do to make firm 1 drop out?

31. 3 1 Firm 2 chooses a production target of 3
Firm 1 responds with a production target of 1

32. The game is symmetric with respect to Firm two…
Firm 2 responds with a production target of 2
Firm 1 chooses a production target of 1

33. Eventually, these two firms converge on production levels such that neither firm has an incentive to change
Firm 1
We would call this the Nash equilibrium for this model
Firm 2

34. Recall we started with the demand curve and marginal costs

35. The markup formula works for each firm

36. Had this market been serviced instead by a monopoly…

37. Had this market been instead perfectly competitive,

38. Monopoly
2 Firms
Perfect Competition

39. Recall, we had an aggregate demand and a constant marginal cost of production.
CS = (.5)(120 – 70)(2.5) = $62.5
Monopoly
$120
$62.5
$70 D
What would it be worth to consumers to add another firm to the industry?
2.5

40. Recall, we had an aggregate demand and a constant marginal cost of production.
CS = (.5)(120 – 53)(3.33) = $112
Two Firms
$112
$53 D
3.33

41. Suppose we increase the number of firms…say, to 3
Demand facing firm 1 is given by (MC = 20)
The strategies look very similar!

42. With three firms in the market…
CS = (.5)(120 – 45)(3.75) = $140
Three Firms
$140
$45 D
3.75

43. Expanding the number of firms in an oligopoly – Cournot Competition
N = Number of firms
Note that as the number of firms increases:
Output approaches the perfectly competitive level of production
Price approaches marginal cost.

44. Increasing Competition

45. Increasing Competition

46. The previous analysis was with identical firms.
Suppose Firm 2’s marginal costs increase to $30
Firm 1
50%
Firm 2
50%

47. Suppose Firm 2’s marginal costs increase to $30
If Firm one’s production is unchanged
Firm 2

48. Firm 1 Firm 2 42% 58% Firm 2’s market share drops
Firm 1’s Market Share increases
58%

49. Market Concentration and Profitability
Industry Demand
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

50. (58%)
(42%)
Industry
Firm 1
Firm 2

51. The previous analysis (Cournot Competition) considered quantity as the strategic variable. Bertrand competition uses price as the strategic variable.
Should it matter? P* D Q*
Just as before, we have an industry demand curve and two competing duopolies – both with marginal cost equal to $20.
Industry Output

52. Firm level demand curves look very different when we change strategic variables
Bertrand Case
Quantity Strategy
If you are underpriced, you lose the whole market
At equal prices, you split the market
If you are the low price you capture the whole market D D

53. Price competition creates a discontinuity in each firm’s demand curve – this, in turn creates a discontinuity in profits
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.

54. Firm One’s Best Response Function
Case #1: Firm 2 sets a price above the pure monopoly price:
Case #2: Firm 2 sets a price between the monopoly price and marginal cost
Case #3: Firm 2 sets a price below marginal cost
Case #4: Firm 2 sets a price equal to marginal cost
What’s the Nash equilibrium of this game?

55. 2 Firms
Monopoly
Perfect Competition
However, the Bertrand equilibrium makes some very restricting assumptions…
Firms are producing identical products (i.e. perfect substitutes)
Firms are not capacity constrained

56. 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
Each theatre has the capacity to handle 2,000 customers per day.
What will the equilibrium be in this case?

57. 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!”
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!

58. 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.
Example: D

59. Recall Firm 1 has a marginal cost of $20
Each firm needs to choose price to maximize profits conditional on the other firm’s choice of price.
Firm 1 profit maximizes by choice of price
Firm 2 sets a price of $50
Firm 1’s strategy D
$30
Firm 1 responds with $55

60. With equal costs, both firms set the same price and split the market evenly

61. 2 Firms
Monopoly
Perfect Competition

62. Suppose that Firm two‘s costs increase. What happens in each case?
Bertrand
With higher marginal costs, firm 2’s profit margins shrink. To bring profit margins back up, firm two raises its price
Firm 2
$30

63. Suppose that Firm two‘s costs increase. What happens in each case?
With higher marginal costs, firm 2’s profit margins shrink. To bring profit margins back up, firm two raises its price
Firm 1
A higher price from firm two sends customers to firm 1. This allows firm 1 to raise price as well and maintain market share!
Firm 2

64. Bertrand Cournot Firm 1 Firm 1 Firm 2 Firm 2
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
Cournot
Firm 1
Firm 1
Firm 2
Firm 2

65. 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.
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

66. Firm 2 has observed Firm 1’s output decision and faces the residual demand curve:
Firm 2’s strategy

67. Knowing Firm 2’s response, Firm 1 can now maximize its profits:
Firm 1 produces the monopoly output!

68. 2 Firms
Monopoly
Perfect Competition
(67%)
(33%)

69. Sequential Bertrand Competition
We could also sequence events using price competition.
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

70. Recall Firm 1 has a marginal cost of $20
From earlier, we know the strategy of firm 2. Plug this into firm one’s profits…
Now we can maximize profits with respect to firm one’s price.

71. Sequential Bertrand Competition
2 Firms
Monopoly
Perfect Competition

72. 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.

73. 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…
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

74. Knowing Firm 2’s response, We can adjust the demand curve:
This demand curve incorporates firm two’s behavior.

75. Now, we want to create firm 2’s profits:
MC = $20, FC = $5

76. We want to find the level of production by firm 1 that lowers Firm 2’s profits to zero…

77. Now, we can calculate profits…
Note: This was by design!
Firm one sacrifices some profits today to stay a monopoly!

78. A merger is generally a dominant strategy!!
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
It is difficult to make a credible threat (Remember the Chain Store Paradox)!
A merger is generally a dominant strategy!!

79. 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:
Can predatory pricing be a rational strategy?
Can we distinguish predatory pricing from competitive pricing?
If we find evidence for predatory pricing, what do we do about it?