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 1a) 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 1b) Fix costs rise to 41,000$ per flight. What

happens to the company’s profits?

Exercice 1b) 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 1b) Fix costs rise to 41,000$ per flight. What happens to the

company’s profits? Graphically

QD

MR

MCMC0

MC1

P

PM

QM

Exercice 1c) 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 1i) 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

Q

MC

P- Business

Q

P-Students-

400

650

240260

Exercice 1i) 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 1i) 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

Q

P650

400

100Q=260-0,4(400)=100

500

Exercice 1c) 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 1d) i) Is MD making profits with this pricing scheme?

QA = 110 PA = 375$ QB = 90 PB = 250$

π = (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

Q

P-Business-

Q

P-Students-

400

240260

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

650

375

110

250

90

Exercice 1

Q

P-Business

Q

P-Students-

400

240260

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$ QA? 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)

650

300

110

300

60

Exercice 1e) 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

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?

Implicit market segmentation (cont.)

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

18

Monopoly pricing (no discr.)

Strategic interactionStrategic

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 out the matrix.

What would you do?

Clyde

Talk Silence

B.

T 15,15 __,__

S 30,0 __,__

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”.

Warning!

The payoffs (and losses) are % points of your participation grade.

Clyde

Talk Silence

B.

T +0,+0 +20,-20

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

AC

48 46,46 38,51

64 51,38 41,41

Your predictions?

Comments?

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 highCompetition (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