Transcript Theme 8-English

Exercice 1
(PRGE p394 #6)
6. Mexico Direct offers flights to Mexico.
D: Q = 500 – P
C(Q) = 30,000$ +100Q
a) What price maximizes profits? How many
passengers will fly? Profits?
Exercice 1
a) What price maximizes profits? How many
passengers will fly? Profits?
Max π = (P*Q)-C(Q)
D-1: P = 500 – Q → MR = 500 – 2Q
MR = MC → 500 – 2Q=100
2Q = 400 → QM = 400/2 = 200
PM = 500 – QM = 500 – 200 = 300$
πM = (P*Q)-C(Q)
= (300$*200) – 30,000$ - 100*200
= 60,000$ - 30,000$ - 20,000$ = 10,000$
Exercice 1
b) Fix costs rise to 41,000$ per flight. What
happens to the company’s profits?
Exercice 1
b) Fix costs rise to 41,000$ per flight. What
happens to the company’s profits?
The quantity that maximizes profits remains
the same as it is unaffected by fixed costs.
Revenues don not change so that profits fall
by the amount of the increase in fixed costs,
(-11,000$) to -1,000$.
Exercice 1
b) Fix costs rise to 41,000$ per flight. What happens to the
company’s profits? Graphically
P
PM
MC1
MC0
MC
Q
QM
MR
D
Exercice 1
c) The company fnds out that there are two types of
custumers and decides to price discriminate between
the two. As a result, business clients (Type A) and
students (Type B) pay different prices.
A: Business
DA : Q = 260 – 0,4P
B: Students
DB : Q = 240 – 0,6P
i) Plot the demand curve for each type of soncumer
as well as that of the whole market.
ii) How much will MD charge each type of client?
How many clients of each type will be onboard MD
flights?
Exercice 1
i) Plot the demand curve for each type of soncumer as well as that of the
whole market.
A: Business
DA : Q = 260 – 0,4P
→ P = 650 – 2.5Q
B: Students
DB : Q = 240 – 0,6P
→ P = 400 – 5/3Q
P
650
P
- Business
-Students-
400
MC
260
Q
240
Q
Exercice 1
i) Plot the demand curve for each type of soncumer as well as that of the
whole market.
Market: When the price is above 400$ (and bellow 650$), only Type A
consumers are purchasing tickets. Beloow 400$, the demand is the sum
of both types of consumers.
P > 400$,
D: Q = 260 – 0,4P
P < 400$,
D: Q = (260 – 0,4P) + (240 – 0,6P) = 500 - P
Exercice 1
i) Plot the demand curve for each type of soncumer as well as that of the
whole market.
P > 400$,
D: Q = 260 – 0,4P
P < 400$,
D: Q = (260 – 0,4P) + (240 – 0,6P) = 500 - P
P
650
400
Q=260-0,4(400)=100
100
500
Q
Exercice 1
c) ii) How much will MD charge each type of client? How
many clients of each type will be onboard MD flights?
A: Business
DA : Q = 260 – 0,4P → P = 650 – 2.5Q
Max πA → MRA= 650 – 5Q = MC = 100 → 5QA = 550
→ QA= 110
PA = 650 – 2.5 (110) = 375$
B: Students
DB : Q = 240 – 0,6P → P = 400 – 5/3Q
Max πB → MRB= 400 – 10/3 Q = MC = 100 → 10/3QA = 300
→ QB = 90
PB = 400 – 5/3 (90) = 250$
Exercice 1
d) i) Is MD making profits with this pricing scheme?
QA = 110
π
PA = 375$
QB = 90
PB = 250$
= (110 * 375$) + (90*250$) – 41,000$ - (100$* (110+90))
= 41,250$ + 22,500$ - 41,000$ - 20,000$ = 2,750$
ii) Compute consumer surplus for each type of consumers and compare
for the situation where the company doesn’t discriminate.
Exercice 1
d) ii) Compute consumer surplus for each type of consumers.
CSA = (650 – 375) *110/2 = 15,125
CSB = (400 – 250) *90/2 = 6,750
CSA + CSB = 21,875
P
650
P
-Business-
-Students400
375
250
110
260
Q
90
240
Q
Exercice 1
e) Compare with the situation where the monopoly charges a unique price.
(First, figure out how mant tickwts will be purchased by each type?)
PM = 300$
Q A?
QB?
QA = 260 – 0,4P = 260 – 0,4*300 = 140 (tickets pucharsed by Business)
QB = 240 – 0,6P = 240 – 0,6*300 = 60 (tickets pucharsed by Students)
P
650
P
-Business
-Students400
300
300
110
260
Q
60
240
Q
Exercice 1
e) Compare with the situation where the monopoly charges a unique price.
CSA = (650 – 300) *140/2 = 24,500
CSB = (400 – 300) *60/2 = 3,000
SCA + SCB = 28,500
When the firm does not discriminate, CS is higher (28,500 vs 21,875)
in part because business travellers benefit from the fact that there
are students in the market who are more price sensitive. The global
demand’s elacticity is thus higher and the price charged to them is
lower which gives them surplus.
Observe that eventhough the quantity of tickets purchased remained
the same (200) the overall surplus distribution changed.
15
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?
16
Type 1
Consumers
Chooses plan 2
b/c C > D
CS:
A+B+C-D
PS:
E+H+F+G+I+J
17
Type 2
Consumers
Chooses plan 1
b/c G > H
CS:
A-B
PS:
C+D+B+E+F
Monopoly pricing (no discr.)
18
Strategic
interaction
Introduction

Game theory: the prisonner’s dilemma

Consequences on the possibility of reaching
a social optimum

Cartel or oligopoly? ( = collusion or
competition?)
A story about criminals
Bonnie and Clyde are arrested by the police for car
theft. A dead body is found in the trunk of the car.
The police has enough evidence to convict them of
theft, but not for murder: they need a confession.
The sheriff interrogates B and C separately and offers
the following deal:

If you both denounce each other: each get 15 years in
prison
 If you both stay silent: 2 years each
 If one talks and the other silent: the one who talked walks
away while the other gets 30 years in prison
 I made the same deal to the other suspect
The prisonner’s dilemma
One
can represent
this situation in a
payoff matrix.
Fill
Clyde
Talk
Silence
out the matrix.
T
15,15
__,__
S
30,0
__,__
B.
What
do?
would you
Nash equilibrium (NE)
Def.: A Nash equilibrium (NE) is a situation where
each player is playing its best response
strategy against the other player’s strategy. I.e.
no single player is better off deviating
unilaterally.
What is the NE of the previous game?
Is the NE the optimal outcome of this interaction? Can
B and C do better together?
*You’re in jail now…
Divide the class into 2
groups: “Group Bonnie”
and “Group Clyde”.
Clyde
Talk
Silence
T
Warning!
The payoffs (and losses)
are % points of your
participation grade.
+0,+0
+20,-20
B.
S -20,+20 +10,+10
The dilemma in business
Two firms, AirCanada and AirFrance are competing on
the YUL-CDG leg. They simultaneously decide how
many flights to operate per month: 48 or 64 flights.
AF
qAF=48
qAF=64
48
46,46
38,51
64
51,38
41,41
Your predictions?
Comments?
AC
Oligopoly
Def.: Market with a small number of firms, so that
the behavior of one firm has an impact on that
of its competitors.
Two possible types of interaction:

Collusion (cartel): firms agree to reduce output so as to
keep prices high

Competition (oligopoly)
Note: An oligopoly with 2 firms is called a duopoly.
Collusion
In most countries, explicit collusion is illegal.
However, some cartels do exist, for example:
- _______________
- _______________
-…
The dilemma is back!
Each firm has an incentive to produce more to take
advantage of the high price.
AF’s reasoning: « If AC produces 48, I can produce
more and increase my profit.»
What is AF’s best response to qAC = 48?
Instability of cartels
For this reason (incentive to deviate) we
observe relatively few cartels.
Nevertheless, a few cartels (OPEC, illegal
drugs) thrive. Why, in your opinion?
Conclusions

We now have a tool to analyze strategic
interactions and predict their outcome
(Game Theory)

Tension between strategic
considerations and optimality

We saw why cartels are unstable

Next: Risk and uncertainty