Strategic Pricing:
Theory, Practice and Policy
Professor John W. Mayo
mayoj@georgetown.edu
Prices, Industry Supply & Demand, and the Role of
Industrial Organization
CS = Consumer Surplus
$
mc
S
ac
D
Pricing above competitive levels imposes economic welfare losses
Monopoly and Competition
$
mc
ac
cs
D
mr
Prices are higher under Monopoly than competition
The Role of Market Structure in Pricing
• Suppose that:
• Market Demand Q=1000-1000P
• MC = $.28
• How do optimal prices compare depending on
Market Structure and the nature of competition?
Perfect Competition
Industry
Regardless of Market demand
Price is driven by the equality
Of price and marginal cost
MC
P=.28
D
720
Q
Monopoly
Firm
π = PQ - .28Q
π = [1 – (1/1000Q)]Q -.28Q
π = Q - .001Q2 -.28Q
So, taking the first derivative
And setting equal to 0:
P=.64
MC
P=.28
Dπ/dQ = 1 - .002Q - .28 =0
D
mr
360
720
Q = 360
Q
Plugging into the demand function
P= .64.
The Role of Industrial Organization on Pricing
• Competition v. Monopoly
• Strategic Interactions Among Competitors
• Oligopoly
• Few competitors
• Barriers to entry
• Possible reactions to price/output changes:
• Competitors match price decreases, but not price increases
• Model: Sweezy oligopoly
• Price is determined by market output. Each competitors set output to
maximize profit given the output of rivals
• Model: Cournot Oligopoly
• Firms constantly seek to undercut competitors’ prices
• Model: Bertrand oligopoly
• Price leadership (One or more firm calls out price and others follow)
• Model: Dominant Firm-Competitive fringe
• Models most typically rely upon Nash equilibrium concept
• Each firm is optimizing given the behavior of its rivals
Sweezy Oligopoly
P
Suppose price is initially at P0.
If competitors follow price
decreases, but not increases, then
a kinked demand results
P0
mr2
D2
D1
mr1
Q
Sweezy Oligopoly
P
Implications: prices are non-responsive
to changes in mc over a range –
consider mc1 and mc2
mc1
mc2
mr2
D2
D1
mr1
Q
Nash equilibrium
In a Nash equilibrium, each firm is optimizing,
given the behavior of other firms
John Nash
1994 Nobel Laureate
Cournot Oligopoly
• Price is determined by total market output
(relative to demand)
• So my strategy must account for the output of
rivals
• If duopoly:
• Q1* =r1(Q2) and Q2* = r2(Q1)
Cournot Model: Nash equilibrium as number
of firms changes
Assume mc=0
$
With an initial equilibrium of Qm,Pm,
consider the output of a second firm.
The second firm takes the output of
Firm 1 as given, then optimizes on the
Residual demand curve (the lower
Half of the original demand)
Pm
The result is P2.
P2
What is Firm 1’s reaction?
D1
Qm mr1
mr2
Qc
Q
Cournot Model: Nash equilibrium as number
of firms changes
The result is P2.
What is Firm 1’s reaction?
Firm 1, then takes the output of firm
2 as given and reduces its output.
Why? Because firm 2 has taken ¼
of market.
Pm
P2
D1
mr1
mr2
Cournot Quantity Adjustments
Reaction Functions
In Cournot, each firm seeks to maximize profit given
the output of its rival.
So, we can examine how firm 1’s output changes as firm 2 has different
outputs. Denote Q1*(Q2)
Q1
Note that in our previous example,
increases in Q2 were met with reductions in Q1
Q2*(Q1)
Similarly, for Q2*(Q1)
Cournot- Nash equilibrium
Q1*(Q2)
Q2
Cournot: A linear demand example
Suppose that market demand is P= 30-Q and MC1=MC2 = 0.
What is firm 1’s reaction function?
Revenue for firm 1 = PQ1 = (30-Q)Q1 = (30 – Q1- Q2)Q1
= 30Q1 – Q12 – Q1Q2
Thus, MR = 30-2Q1-Q2
Set MR=MC and solve for Q1: Q1 = 15 - 1/2Q2
Similarly, Q2 = 15-1/2Q1
Cournot: linear demand (cont.)
Solving the reaction functions simultaneously:
Q1
Q1 = 15 - 1/2Q2
Q2 = 15 - 1/2Q1
How does this compare with a
Competitive equilibrium for the firms?
How does this compare with the case of
Collusion?
10
10
Q2
Stackelberg
• Consider that firms compete in quantities, but
now…
• Suppose that instead of firms choosing outputs
simultaneously, one firm is the leader and output
is sequential
Stackelberg
If firm 1 goes first, then it will maximize profit given the reaction
function of firm 2
Recall that in our example
Rev1 = PQ1 = 30Q1 – Q12 –Q1Q2
But firm 1 knows how firm 2 will react to its output, so substituting
in the reaction function from 2, we get
Rev1 = 15Q1 -1/2Q12, so MR = 15 –Q1, so Q1* = 15, Q2* = 7.5.
Why is the equilibrium different from simultaneous Cournot?
Bertrand Oligopoly
• Homogeneous
• Differentiated
Dynamic Pricing Considerations
• Cournot and Bertrand are static
• What if playing (in competition with) a rival
repeatedly?
Pricing: Dynamic considerations
• Suppose rivals announce intention to raise price
• If cooperate, then your profits are $10 per period, forever.
• If “cheat”, then profits increase (say to $50) this period with
zero thereafter.
Pricing: Dynamic considerations
• Look at NPV of cooperative behavior compared to NPV of
non-cooperative behavior
• Assume infinitely repeated
• NPV = p0 + S p’t * (1/(1+r))t = [(1 + r)/r]p0
• NPVCO = 10 + S 10 * (1/(1+r))t = 10 + 10*1/r
• NPVNC = 50 + S 0 * (1/(1+r))t = 50
• NPVCO > NPVNC if r < .25
• In this example, if very impatient, cheat. Otherwise
cooperate with price increase.
• Pricing strategy will depend upon discount rates and
the relative payoff from defection
IF competing in long-run
• Folk Theorem – says that with a low discount rate,
any price between MC and PM can be equilibrium
• Engendering cooperation
• Focal prices [Knittle and Stango (AER 2003)]
• Standardize timing of price changes
• Pre-announcement of price changes (upward)
• Trigger Strategies (tit-for-tat; grim trigger)
• Most Favored Customer Clause
• Match rivals’ price (create “whistle blowing” consumers)
• “Giant now honoring Safeway coupons”
Price Ceilings as Focal Points
• Knittle and Stango study the credit card market
• 1450 bank-issued cards
• 90 % of states in late 70s/early 80s had interest rate
ceilings (18% was most common)
• Find tacit collusion consistent with price ceilings
serving as focal points
• Tacit collusion is more likely when:
• (a) concentration is higher
• (b) costs are higher
• (c ) firms are larger
• (d) but lower when demand is high