Third degree price
discrimination
Welfare Analysis
Third-degree price discrimination and
welfare

Does third-degree price discrimination reduce
welfare?



not the same as being “fair”
relates solely to efficiency
so consider impact on total surplus
Example 1 – Welfare decreases
Two markets

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
Market B:
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


All identical
Na=100 consumers
Reservation value pa=2
No discrimination:
p=4, p=(4-1)*50=150
Market A:


1.
p=2, p=(2-1)*200 = 200
2.
Discrimination:
pa=2, pb=4, p=100+150
Less consumers are served
Two types.
N1 =N2 = 50 of each
Reservation values p1 =4, p2 = 2.
Constant mg. cost c=1.
Example 2 – Welfare increases
Two markets

Market A:






No discrimination:
p=4, p=(4-1)*120=360
All identical
p=2, p=(2-1)*200 =200
Na=100 consumers
2. Discrimination:
Reservation value pa=4
Market B:


1.
Two types.
N1 =20, N2 = 80.
Reservation values p1 =4,
p2 = 2.
Constant mg. cost c=1.
pa=4, pb=2, p=300+100
•
Total output increases
•
More consumers
served
Price discrimination and welfare
Suppose that there are two markets: “weak” and “strong”
The discriminatory
price in the weak
market is P1
Price
D1
The maximum The uniform
gain in surplus price in both
in the weak market is P
U
market is G
PU
The discriminatory
price in the strong
market is P2
Price
D2
The minimum
loss of surplus in
the strong
market is L
MR2
P2
PU
P1
MR1
G
L
MC
ΔQ1
Quantity
MC
ΔQ2 Quantity
Price discrimination and welfare
Price
D1
Price discrimination
cannot increase
surplus unless it
increases aggregate
output
PU
Price
D2
MR2
P2
PU
P1
MR1
G
L
MC
ΔQ1
Quantity
MC
ΔQ2 Quantity
It follows that ΔW < G – L = (PU – MC)ΔQ1 + (PU – MC)ΔQ2
= (PU – MC)(ΔQ1 + ΔQ2)
Price discrimination and welfare
(cont.)
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Previous analysis assumes that the same markets
are served with and without price discrimination
This may not be true



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uniform price is affected by demand in “weak” markets
firm may then prefer not to serve such markets without
price discrimination
price discrimination may open up weak markets
In the two market case, if price discrimination opens
one market, welfare always increases:


In the only market that was originally served, price and
quantity don’t change (why?)
The previously excluded market is now served
New markets: an example
Demand in “North” is PN = 100 – QN ; in “South” is PS = 100 - QS
Marginal cost to supply either market is $20
North
South
$/unit
Aggregate
$/unit
$/unit
100
100
Demand
MC
MC
MC
MR
Quantity
Quantity
Quantity
The example: continued
Aggregate demand is P = (1 + )50 – Q/2
provided that both markets are served
$/unit
Aggregate
Equate MR and MC to get equilibrium
output QA = (1 + )50 - 20
Get equilibrium price from aggregate
demand P = 35 + 25
P
Demand
MC
MR
QA
Quantity
The example: continued
Aggregate
Now consider the impact of a
reduction in 
Aggregate demand changes
Marginal revenue changes
It is no longer the case that both
markets are served
$/unit
PN
Demand
MC
The South market is dropped
Price in North is the monopoly
price for that market
MR
MR'
D'
Quantity
The example again
Previous illustration is too extreme
$/unit
MC cuts MR at two points
So there are potentially two equilibria
with uniform pricing
At Q1 only North is served at the
monopoly price in North
PN
At Q2 both markets are served at
the uniform price PU
PU
Switch from Q1 to Q2:
decreases profit by the red area
increases profit by the blue area
If South demand is “low enough” or
Q1 Q2
MC “high enough” serve only North
Aggregate
Demand
MC
MR
Quantity
Price discrimination and welfare
(cont.)
In this case only North is served
with uniform pricing
But MC is less than the
reservation price PR in South
So price discrimination will
lead to South being supplied
$/unit
Aggregate
PN
PR
Price discrimination leaves
surplus unchanged in North
But price discrimination generates
profit and consumer surplus in
South
Q1
So price discrimination increases welfare
Demand
MC
MR
Quantity
Price discrimination and welfare again
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
Suppose only North is served with a uniform price
Also assume that South will be served with price
discrimination
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Welfare in North is unaffected
Consumer surplus is created in South: opening of a new
market
Profit is generated in South: otherwise the market is not
opened
As a result price discrimination increases welfare.