Georgetown University
Last Time
 The
Analytics of Profit maximizing Prices
 The economics of cost pass-throughs
Review
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Why study pricing?
In a market economy, what factors determine
prices, in general?
In a consideration of prices what is the role of
costs?
What is the Inverse Elasticity Rule?
How does the production of substitutes
(complements) affect optimal pricing?
In a world in which you control price, how does
one determine optimal cost pass-through rates?
Review:
Elasticity and Pricing
Colas
Coffees
Brand
Elasticity of
Demand
Royal Crown
-2.4
Coke
-5.2 to -5.7
Folgers
-6.4
Maxwell House
-8.2
Chock full o’Nuts
-3.6
Who has more pricing power in the Cola market?
In the coffee market? Explain.
Suppose that the marginal cost of Royal Crown is 40 cents
per 12 oz can. What is its profit maximizing price?
How does Coke’s pricing
change if it buys Royal Crown?
(Pi - ∂C/ ∂qi)/Pi = 1/ εii – [(pj- ∂C/ ∂qj)Qj εij] / Ri εii.
1.
2.
3.
4.
5.
The higher is the RC PCM, the higher the price increase
The higher are RC volumes, the higher the price increase
The higher the cross-price elasticity, the higher the price increase
The higher the volume of Coke sales, the lower the price increase
The higher the Coke own-price elasticity, the lower the price increase
Coffee bean prices have risen…
What should Maxwell House
do?
TAKE AWAY ON COST-PASS THROUGH
If constant elasticity of demand
If linear demand
If semi-log demand
dp/dMC = [ε/(1+ ε)]
dp/dMC = ½
dp/dMC = 1
A Pint-Sized Problem
What has been the reaction of beer suppliers to rising input prices?
A Pint-Sized Problem?
The Role of Industrial Organization
on Pricing

Competition v. Monopoly

Strategic Interactions Among Competitors

Oligopoly (Few competitors; Barriers to entry)

Possible reactions to price changes:
• Competitors match price decreases, but not price increases

Models: 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 rely upon Nash equilibrium concept
Prices, Industry Supply & Demand, and
the Role of Industrial Organization
CS = Consumer Surplus
$
mc
S
ac
D
Suppose you are in a competitive
market with a cost advantage?
CS = Consumer Surplus
$
mc
S
ac
ac1
D
For as long as you have a cost advantage, p = AC of competitors (-δ)
Monopoly and Competition
$
mc
ac
Pm
Pc
D
mr
Prices are higher under Monopoly than competition
Next lecture will deal with industrial structure and prices
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)
If considering a price change …must consider rivals’ reaction…
Possible reactions to price 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
• Dynamic Pricing: Tit-for Tat

Models rely upon Nash equilibrium concept
Sweezy Oligopoly
P
If competitors follow price
Decreases, but not increases
A kinked demand results
P3
P1
mr2
D2
P2
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
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
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
Cournot- Nash Equilibrium
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)
Note that in our previous example,
increases in Q2 were met with reductions in Q1
Q1
Competitive equilibrium
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
Price Determination in Cournot Oligopolies
Cournot oligopoly
(P-MC)/P = s/ε
Pricing
(where s is market share)
Cournot oligopoly w/
Identical frims
(P – MC)/P = 1/(nε)
Take-aways:
1. Each firm has some market power
2. Cournot prices are “in-between” competitive and monopoly prices
3. Greater elasticity reduces prices
4. Mark-ups are higher for higher market shares (if differentiated)
5. As the number of competitors grows, prices approach
competitive levels
Bertrand Oligopoly
 Assume
that firms compete against each
other through prices

Homogeneous
• Suppose that P= 30-Q and mc1 = mc2 = 3
• Nash Equilibrium?
 Differentiated
Joseph Bertrand
Bertrand Oligopoly
 Assume
that firms compete against each
other through prices

Homogeneous
• Suppose that P= 30-Q and mc1 = mc2 = 3
• Nash Equilibrium?
 Differentiated
Joseph Bertrand
Differentiated Bertrand
 Suppose
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
2 firms each with fixed costs of 20.
Q1 = 12 - 2P1 +P2 (demand facing firm 1)
Q2 = 12 – P2 +P1 (demand facing firm2)
Find π = P1 (12 -2P1 +P2 )
Set ∂dπ/ ∂ p1 = 0, to get firm 1’s reaction
function:
• P1 = 3 + 1/4P2, and similarly for firm 2,
• P2 = 3 + 1/4P1
Differentiated Goods, Bertrand Reaction functions
P1
P2 = 3 + 1/4P1
P1 = 3 + 1/4P2
4
Nash Equilibrium
4
P2
Cola Wars: Coke and Pepsi
 Bertrand
competition in prices with a
differentiated product
 Rival’s prices do affect the firm’s demand
function, but because products are
differentiated a lower price does not steal
the entire market
 Each firm has a Bertrand profit-maximizing
“best response function” for the price to
charge in response to the price its rival
charges
Cola Wars: Coke and Pepsi
 Demand
equations estimated from
detailed monthly price data:
 qC(PC,PP) = 63.42 – 3.98PC + 2.25PP
 qP(PC,PP) = 49.52 – 5.48PP + 1.40PC
 Unit CostC = 4.96 Unit CostP
 Unit is a 10 cases of 24 12 oz cans.
= 3.96
Source: “Econometric Analysis of Collusive Behavior in a Soft-Drink Market” by Gasmi,
Laffont and Vuong in Journal of Economics & Management Strategy, 1992, vol. 1, issue
2, pp. 277-311
Cola Wars: Coke and Pepsi
 How
should Coke and Pepsi price in
response to their rival?
 Need to find Best Response Function for
each cola producer
 Solve for profit-maximizing PRICE (in a
Bertrand game price is the choice
variable)
Cola Wars: Coke and Pepsi
 How
do we find profit-maximizing price?

Set MR = MC!!
 Solve for MR (in terms of change in PC):
 TRC = PC * qC = PC * qC(PC, PP)
 TRC = PC * (63.42 – 3.98PC + 2.25PP)
 MRC(PC, PP) = 63.42 – (2)* 3.98PC +
2.25PP
 MRC = 63.42 – 7.96PC + 2.25PP
Cola Wars: Coke and Pepsi
 How
do we find profit-maximizing price?

Set MR = MC!!
 Solve for MR (in terms of change in PC):
 TRC = PC * qC = PC * qC(PC, PP)
 TRC = PC * (63.42 – 3.98PC + 2.25PP)
 MRC(PC, PP) = 63.42 – (2)* 3.98PC +
2.25PP
 MRC = 63.42 – 7.96PC + 2.25PP
Cola Wars: Coke and Pepsi
 Solve
for MC (again, in terms of PC):
 TCC = UCC * qC = UCC * qC(PC, PP)
 TCC = 4.96 * (63.42 – 3.98PC + 2.25PP)
 MCC(PC, PP) = -19.74
(MC with respect to PRICE – if price goes up,
quantity goes down)
Cola Wars: Coke and Pepsi
 Profit
maximizing price is where MR = MC
 MRC = 63.42 – 7.96PC + 2.25PP
 MCC = -19.74
 MRC = MCC
 63.42 – 7.96PC + 2.25PP = -19.74
 PC(PP) = 10.44 + 0.2826PP
 “Best Response Function”
Cola Wars: Coke and Pepsi
 Can
do the same thing for Pepsi - Best Response Function for Pepsi
 PP(PC) = 6.49 + 0.1277PC
 PC(PP) = 10.44 + 0.2826PP
 2 equations and 2 unknowns:
 PC(PP) = 10.44 + 0.2826 *(6.49 +
0.1277PC)
 PC(PP) = 12.73; PP(PC) = 8.11

Actual average prices over this period: C=12.96, P=8.16
Price Determination
Competitive
P=MC
Competitive w/
cost advantage
P=MC(competitors) - δ
Monopoly Pricing:
(P-MC)/P = 1/ε
Cournot oligopoly
(P-MC)/P = s/ε
Pricing
(where s is market share)
Cournot oligopoly w/
Identical firms
(P – MC)/P = 1/(nε)
Bertrand
(identical product)
P=MC
Bertrand Differentiated
P> MC
Price Leadership
The Dominant Firm Model
a. Assumes a single “dominant”
firm facing a competitive “fringe”
b. The dominant firm calls out a
price
c. The competitive fringe responds
as a price taker setting its output
The Dominant Firm-Competitive Fringe Model
P
S=Σmc
d=D-S
d
P1
mc
D
mr
Qd
Q
Pricing in a Dominant Firm
Competitive Fringe Industry
(P-MC)/P = S/[ηm + (1-S)ef]
1. Market share (S)
2. Elasticity of Market demand (ηm)
3. Elasticity of Supply of the fringe
firms (ef)
Suppose S=.8, ηm = 2, and ef = 2, What is the value of the
price cost mark up?
Collusion
Price Collusion
“People of the same trade seldom meet together even
for merriment and diversion, but the conversation ends
in a conspiracy against the public, or in some
contrivance to raise prices.”
Adam Smith
The Wealth of Nations
The Simple economics of collusion?
$/q
$/q
mc
S= Σmc
AC
Pm
P
D
MR
qm
q
Firm
q
Qm
Industry
Q
Q
Competition (?) in the Airline Industry
Crandall: I think it's dumb as hell ... to sit here and pound the (deleted) out
of each other and neither one of us making a (deleted) dime. ...
We can both live here [Dallas] and there ain't no room for Delta. But there's, ah,
no reason that I can see, all right, to put both companies out of business.
Putnam: Do you have a suggestion for me?
Crandall: yes, I have a suggestion for you. raise your goddamn fares twenty
percent. I'll raise mine the next morning. ... You'll make more money, and I will too.
Putnam: We can't talk about pricing.
Crandall: Oh (deleted), Howard. We can talk about any goddamn thing we want to
talk about.
Economic conditions conducive to
and destructive of Collusion
 Number
of firms (market concentration)
 Barriers to entry
 Product homogeneity
 Elasticity of market demand
 Ability to detect cheating
 Cost symmetry/asymmetry
Economic research indicates that despite obstacles, economic
barriers to successful collusion can often be overcome
Rebates in Real Estate
Commissions
“If we give rebates and inducements, it would
get out of control and all clients would be
wanting something. The present law keeps it
under control.”
 “This would turn into a bidding war, lessen our
profits and cheapen our ‘so-called’ profession.”
 “If inducements were allowed, they could lead to
competitive behavior, which would make us look
unprofessional in the eyes of the public.”
 “I think this would just take money right out of
our pocket.”

http://www.usdoj.gov/atr/public/real_estate/rebates.htm