Third degree price discrimination

1
Third degree price discrimination

• Welfare Analysis

2
Third-degree rice 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

3
Example 1 Welfare decreases

• Two markets
• Market A
• All identical
• Na100 consumers
• Reservation value pa2
• Market B
• Two types.
• N1 N2 50 of each
• Reservation values p1 4, p2 2.
• Constant mg. cost c1.

• No discrimination
• p4, p(4-1)50150
• p2, p(2-1)200 200
• Discrimination
• pa2, pb4, p100150
• Less consumers are served

4
Example 2 Welfare increases

• Two markets
• Market A
• All identical
• Na100 consumers
• Reservation value pa4
• Market B
• Two types.
• N1 20, N2 80.
• Reservation values p1 4, p2 2.
• Constant mg. cost c1.

• No discrimination
• p4, p(4-1)120360
• p2, p(2-1)200 200
• Discrimination
• pa4, pb2, p300100
• Total output increases
• More consumers served

5
Price discrimination and welfare
Suppose that there are two markets weak and
strong
The discriminatory price in the strong market is
P2
The discriminatory price in the weak market is P1
Price
Price
D2
The minimum loss of surplus in the strong market
is L
The maximum gain in surplus in the weak market is
G
The uniform price in both market is PU
MR2
D1
P2
PU
PU
G
L
P1
MR1
MC
MC
?Q1
?Q2
Quantity
Quantity
6
Price discrimination and welfare
Price discrimination cannot increase surplus
unless it increases aggregate output
It follows that ?W lt G L
(PU MC)?Q1 (PU MC)?Q2
(PU MC)(?Q1 ?Q2)
7
Price discrimination and welfare (cont.)

• Previous analysis assumes that the same markets
  are served with and without price discrimination
• This may not be true
• 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 dont change (why?)
• The previously excluded market is now served

8
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
Aggregate
/unit
/unit
/unit
100
100?
Demand
MC
MC
MC
MR
Quantity
Quantity
Quantity
9
The example continued
Aggregate demand is P (1 ?)50 Q/2 provided
that both markets are served
Equate MR and MC to get equilibrium output QA
(1 ?)50 - 20
Get equilibrium price from aggregate demand P
35 25?
P
QA
10
The example continued
Now consider the impact of a reduction in ?
Aggregate demand changes
Marginal revenue changes
PN
It is no longer the case that both markets are
served
The South market is dropped
D'
Price in North is the monopoly price for that
market
MR'
11
The example again
Previous illustration is too extreme
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 MC high
enough serve only North
Q1
Q2
12
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
PR
Price discrimination leaves surplus unchanged in
North
But price discrimination generates profit and
consumer surplus in South
So price discrimination increases welfare
13
Price discrimination and welfare again

• Suppose only North is served with a uniform price
• Also assume that South will be served with price
  discrimination
• 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.