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Review Exercise (1)

#3, p.344 PRGE

True or False? A profit maximizaing
monopoly faces a demand with constant
price elasticity of -2. His marginal cost is also
constant at 20$. If his marginal cost rises by
25%, the price he charges will also rise by
25%.
Review Exercise (1)

#3, p.344 PRGE

PM0 = MC0/(1+1/ED) = 20$/(1-1/2) = 40$

MC1 = (1+0.25)* MC0 = 25$

PM1 = MC1/(1+1/ED) = 25$/(1-1/2) = 50$

∆% PM ?= (PM1- PM0)/ PM0 = (50$-40$)/40$=...

10$/40$=25%

MC ∆ ↑25%  PM ∆ ↑25%

TRUE
Review Exercise (2)

True or False? A monopoly nerver produces
in the inelastic part of the demand curve.
Review Exercise (2)

True or False? A monopoly nerver produces in the
inelastic part of the demand curve.

In the inelastic part of the demand curve, by raising
the price the monopoly generates higher revenues
because the corresponding fall in the quantity
demanded is proportionally smaller. Furthermore,
the drop in quantity implies a fall in costs.

↑ revenus & ↓ coûts = ↑profits.

The producer would never maintain a level of
production in the inelastic part of the demand curve.
TRUE
Review Exercise (3)
#18 a) et b) p.346 PRGE
Profit maximizing monopoly;
Q = 144 / P2
CF=5 CVM=Q1/2
a) PM? QM? ProfitsM?
b) What happens if the government imposes a
price ceiling of 4$?
Review Exercise (3)
a) MR?
D: Q=144/P2 → P2=144/Q → P=12/Q1/2
Rev = P*Q = (12/Q1/2)*Q = 12 Q1/2,
MR = dRev / dQ = 6/Q1/2
MC? = dCT / dQ = dVC / dQ
VC? AVC=VC/Q  VC=AVC*Q
VC= Q1/2*Q = Q3/2
MC = dQ3/2 / dQ = 3/2*Q1/2
Review Exercise (3)
a) MR = MC
6/Q1/2 = 3/2*Q1/2 , 6 = 3/2*Q
12/3 = QM = 4
PM? D(QM)=12/(QM)1/2 = 12/2 = 6 = PM
Profits?
(PM*QM) – C(QM)
(6$*4) – (43/2$ + 5$)
24$ - 13$ = 11$ = πM
Review Exercise (3)
b) The State fixes a price ceiling at 4$.
D: Q = 144/P2 = 144/16 = 9 = QGOUV
Profits = (4$*9) – (93/2 + 5$) =
36$ - 27$ - 5$ = 4$
QM
QGOUV
10.00
9.50
9.00
8.50
8.00
7.50
D
7.00
MR
Rm
6.50
6.00
5.50
MC
Cm
5.00
4.50
12.00
4.00
3.50
3.00
2.50
2.00
1.50
1.00
14.00
AC
CM
10.00
8.00
6.00
PM
4.00
PGOUV
2.00
0.00
Pricing strategies
Introduction

Why do student discounts exist?

Why is a firm like Costco profitable?

Why is it that your neighbor on the plane
likely has not paid the same price as you
for his plane ticket?
Example: nightclub
Population:

100 men, each willing to pay 10$

100 women, each willing to pay 5$
What should the club’s cover charge be? (MC = 0)

If p = 10$, who will buy? π = ?

If p = 5$, same questions.
How can the club do better?
A possible solution
Price discrimination (PD) :
Charge different people different prices for the
same product.
Nightclub example:

charge 5$ for women

charge 10$ for men
 π = __________
Who can practice PD?
3 necessary conditions, on:
 the
ability to choose your selling price
 the
information about potential customers
 the
customers’ ability to resell the product
Explain in detail.
Perfect PD (1st degree)
Def: Charge each consumer his willingness to pay
p
Ex: Cupcake stand
MC ≡ $1.50 apiece (constant)
4
Who will buy a cupcake?
3
How much will each person
pay?
2
What will profits be?
Ali
Ben
Cat
MC
Dave
D
1
1
2
3
4
Q
Perfect price discrimination (cont.)
More generally, for a larger population.
p
Ex:
D : p = 40 - Q
40
S
S : MC = Q
How many units will be sold?
Compute CS, PS and W.
Compare with:
- Competition
- Traditional Monopoly
D
40
Q
Perfect price discrimination (end)
Interpretations :

Is perfect PD efficient?

Is it fair?

Is it realistic?
Give examples of markets approaching
perfect price discrimination.
Explicit market segmentation
(3rd degree PD)
Def.: Consumers can be differentiated
according to an observable characteristic
Examples :

_________________________________

_________________________________

_________________________________

….
Explicit market segmentation (cont.)
Example : Levi’s 501 jeans in Europe (E) and in
North America. ( MC ≡ $5 apiece )
p
p
45
35
DE
DNA
5
5
NA
Q
7000
MC
4500
QE
Explicit market segmentation (end)
What will the price be on each continent?
Give an interpretation in terms of priceelasticity?
Implicit market segmentation
(2nd degree PD)
Def.: Consumers are discriminated according to an
unobservable characteristic: their own preferences
 Price menus, block pricing
Examples :

_________________________________

_________________________________

_________________________________

….
Implicit market segmentation (cont.)
Example: Cell-phone plan (MC ≡ 10 ¢/mn)

Plan 1: 200 mn for 40 $/month

Plan 2: 400 mn for 70 $/month

Plan 3: 600 mn for 90 $/month
Two types of consumers:
Type 1: q1 = 650 - 20p
Type 2: q2 = 550 - 20p
Which plan will each type of consumer choose?
Type 1
Consumers
Chooses plan 2
b/c C > D
CS:
A+B+C-D
PS:
E+H+F+G+I+J
Type 2
Consumers
Chooses plan 1
b/c G > H
CS:
A-B
PS:
C+D+B+E+F
Monopoly pricing (no discr.)
Implicit market segmentation (cont.)
What pricing schedule does
this plan menu correspond
to?
In other words, what is the
per-minute price of the first
200mn?
What is the per-minute price
of the next 200mn? (from
200 to 400)
What is the per-minute price
for the last 200mn? (from
400 to 600)
p Draw the price « line »
20
15
10
200
400 600
Q
Implicit market segmentation (cont.)
p
Type 1 consumer:
d1 : q1 = 650 – 20p
30
d1
25
20
Which plan will she choose?
Why?
Show CS1 and PS1 graphically.
15
MC
10
200
400
600
Q
Implicit market segmentation (cont.)
p
Type 2 consumer:
d2 : q2 = 550 – 20p
30
25
d2
20
Which plan will she choose?
Why?
Show CS2 and PS2 graphically.
15
MC
10
200
400
600
Q
*Implicit market segmentation (end)
Exercise:
Consider a population of 100 consumers of each type
Compute the consumer surplus, producer surplus and
total welfare for this entire population
Compare with the traditional monopoly. [Hint: First draw
the demand curve of the entire population]
Conclusions

Several types of price discrimination:
 perfect
(or 1st degree)
 explicit
segmentation (or 3rd degree PD)
 implicit
segmentation (or 2nd degree PD)

Price discrimination is everywhere! Look for
more examples around you.

Next: Competition and strategic interactions