Strategic Pricing:
Theory, Practice and Policy
Professor John W. Mayo
mayoj@georgetown.edu
This Lecture:
Supply-side (Costs) and prices
• Basics: supply, demand and prices
• Costs and prices
• Relevant and irrelevant costs
• Cost changes and Price changes (Pass-through)
Prices, Industry Supply & Demand, and the
Role of Industrial Organization
$
$
mc
S
ac
D
q
Q
Demand Growth and Prices
$/Q
$/q
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mc
ac
P2
P1
D2
D1
q
With Demand growth, upward pressure exists for prices
Q
Supply Changes and Prices
$/Q
$/q
S1
mc
ac
S2
P2
P1
D2
D1
q
Increases in Supply create downward pressure on prices
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Monopoly and Competition
cs= consumer surplus
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mc
ac
cs
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mr
Prices are higher under Monopoly than competition
Next lecture will deal with industrial structure and prices
Costs and Prices
• What are the relevant costs to the determination of price?
• Incremental Costs
• Avoidable cost
• Opportunity Costs
• What are costs that are NOT relevant to the
determination of price?
• Fixed costs
• Sunk costs
Note: read Nagel and Holden for examples
Maximizing profits:
The economic approach
π = p*Q(p) –c[Q(p)]
dπ/dp = Q + p*dQ/dp – (dc/dQ)dQ/dp = 0. Rearranging,
p*dQ/dp – (dc/dQ)(dQ/dp) = - Q, or
[p - (dc/dQ)](dQ/dp) = - Q
[p - (dc/dQ)]= - Q /(dQ/dp)
Dividing through by p
[p - (dc/dQ)]/p= - [(Q/p) /(dQ/dp)] = -1/ε
The profit maximizing markup is inversely
related to the firm’s price elasticity of demand
Maximizing profits: Multiple Markets
Suppose the firm produces in multiple markets with
interdependent demands:
π = p1*Q1(p1,p2) + p2*Q2(p1,p2) –c[Q1(p1, p2)] - c[Q2(p1, p2) ]
∂dπ/ ∂ pi = 0
Solving…
(Pi - ∂C/ ∂qi)/Pi = -1/ εii - [(pj- ∂C/ ∂qj)Qj εij] / Ri εii.
where
εii is the own-price elasticity, [∂Q1/ ∂p1]/(p1/q1)
εij is the cross-price elasticity, [∂Q2/ ∂p1]/(p1/q2)
∂C/ ∂qi is the marginal cost wrt i, and
Ri is the revenue of the ith product
Pricing with Substitutes
(Pi - ∂C/ ∂qi)/Pi = -1/ εii - [(pj- ∂C/ ∂qj)Qj εij] / Ri εii.
Implications:
Suppose that the firm produces substitute products so εij > 0.
Then the optimal mark-up is larger than if the firm optimized
mark-ups on each product independent of the other.
Example: Say, e.g., the εii = 2, pj=10, ∂C/ ∂qj) = 5, Qj =100 and
εij = -.5. How does this change the value of the Lerner Index?
Pricing with Complements
(Pi - ∂C/ ∂qi)/Pi = -1/ εii - [(pj- ∂C/ ∂qj)Qj εij] / Ri εii.
Implications:
Suppose that the firm produces complementary products so εij < 0.
Then the optimal mark-up is smaller than if the firm optimized
mark-ups on each product independent of the other.
Example: Say, e.g., the εii = 2, pj=10, ∂C/ ∂qj) = 5, Qj =100 and
εij = -.5. How does this change the value of the Lerner Index?
Cost changes and Price changes
(Constant Elasticity)
Can we understand optimal price changes in the face of cost changes?
Profit maximization requires MR=MC = p[1 + (1/ε)]
Suppose demand is given by p = q 1/ε
Thus, for constant ε, we have a simple rule of thumb to optimal pricing:
TR = q 1/ε + 1 = q (ε + 1)/ ε , MR = [(ε + 1)/ ε]q1/ε = [(ε + 1)/ ε]p
Thus we have [(ε + 1)/ ε]p =MC or p = [ε/(ε + 1)]MC
dp/dMC = [ε/(1+ ε)]
Suppose that we knew that MC=10 and ε = -5. What is the optimal price?
Assuming ε is a constant, what is your recommendation
regarding price if costs increase to 20?
Prices and Costs with Constant Price Elasticity
60
Optimal Price
50
40
30
20
10
0
5
10
15
20
25
Marginal Cost
30
35
40
Cost changes and Price changes
(Linear Demand)
Suppose demand is given by p = α - βq
Thus,
TR = (α – βq)q
= αq
– βq2, MR = α – 2βq
Setting MR=MC, we have α – 2βq =MC, or q = (α/2β) – (1/2β)MC
Substituting q back into the inverse demand function,
p = α - βq = α – β[(α/2β) – (1/2β)MC ]
Or p = α - α/2 +(1/2)MC, so
Dp/dMC = ½. The optimal cost flow-through is always ½ the
change in the cost
When might it make sense to fully pass
through cost changes?
Consider a demand function facing the firm equal to
P= α –β ln Q. In this case, MR = p – β,
Setting MR=MC and solving, we get
Dp/dMC = 1.
In this instance cost changes are flowed through dollar for dollar.
Optimal Pricing in the Face of Cost Changes
Profit Maximizing Price
60
50
40
Constantt Elasticity
30
Linear Demand
Full pass-through demand
20
10
0
5
10
15
20
25
30
35
Marginal Cost
Notes: assumes ε=5; α = 5; Β= 2, respectively
40
A Pint-Sized Problem
• How have retailers addressed cost increases?
17
Next Lecture: The role of Industrial
Organization on Pricing
• Competition v. Monopoly
• Oligopoly
• Bertrand
• Cournot
• Dominant firm price leadership