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Exercice 1

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(PRGE p394 #6)

6. Mexico Direct offers flights to Mexico.

D: Q = 500 – PC(Q) = 30,000$ +100Q

a) What price maximizes profits? How many passengers will fly? Profits?

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$

b) Fix costs rise to 41,000$ per flight. What happens to the company’s profits?

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$) to -1,000$.

b) Fix costs rise to 41,000$ per flight. What happens to the company’s profits? Graphically

P

PM

MC1

MC0

MC

Q

QM

D

MR

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: BusinessDA : 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?

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

P

- Business

-Students-

650

400

MC

Q

Q

260

240

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

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

Q

100

500

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$

d) 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.

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

P

-Business-

-Students-

650

400

375

250

Q

Q

110

260

90

240

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)

P

P

-Business

-Students-

650

400

300

300

Q

Q

110

260

60

240

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.

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

Strategic interaction

- Game theory: the prisonner’s dilemma
- Consequences on the possibility of reaching a social optimum
- Cartel or oligopoly? ( = collusion or competition?)

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

- One can represent this situation in a payoff matrix.
- Fill out the matrix.
- What would you do?

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?

Divide the class into 2 groups: “Group Bonnie” and “Group Clyde”.

Warning!

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

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.

Your predictions?

Comments?

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.

In most countries, explicit collusion is illegal.

However, some cartels do exist, for example:

- _______________

- _______________

- …

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?

For this reason (incentive to deviate) we observe relatively few cartels.

Nevertheless, a few cartels (OPEC, illegal drugs) thrive. Why, in your opinion?

- 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