Appunti di Industrial economics and policy

C P

Method 1: Calculus

●

Profit of Coke: π = (P – 4.96)(63.42 – 3.98P + 2.25P )

C C C P

Profit of Pepsi: π = (P – 3.96)(49.52 – 5.48P + 1.40P )

P P P C

Differentiate with respect to P for Coke and P for Pepsi respectively.

C P

Method 2: R’ = C’

●

Reorganise the demand functions:

P = (15.93 + 0.57P ) – 0.25Q

C P C

P = (9.04 + 0.26P ) – 0.18Q

P C P

Calculate marginal revenue, equate to marginal cost, solve for Q and Q and

C P

substitute in the demand functions.

Spatial Model

An alternative approach for product differentiation: the spatial model of Hotelling.

- There is a main street over which N consumers are distributed.

- They are supplied by two shops located at opposite ends of the street. The

shops are competitors.

- Each consumer buys exactly one unit of the good but its full price must be less

than V (maximum willingness to pay).

- A consumer buys from the shop offering the lower full price.

Consumers incur in transport costs of t per unit distance in travelling to a shop.

What prices will the two shops charge?

Graph:

Street has a length of 1 unit.

Both shops set a price for the goods sold: p and p .

1 2

The prices increase as the distance of the customers from the shop increases,

because of the transportation costs both lines measure the full price of the goods.

⇒

The customers located between 0 and x are going to buy from shop1, while x and 1

m m

are going to buy from shop 2. In x customers would be indifferent from buying

m

from shop 1 or 2.

Which is the best price that shops set in order to maximise the profit?

To do this the equilibrium prices for product 1 and 2 we need a demand function (for

each shop).

If product 1 increases the price, there would be customers that will prefer buying

from shop 2 x’ - x are those who will buy from shop 2.

→ m m

But which is the demand function? For the 1st shop, it is equal to x while for the

m

2nd shop it will be equal to the difference between 1 and x .

m

Where t is the transportation cost.

When there are N customers it will be multiplied by N:

While for shop 2 you multiply it by (1 - N).

Explain this model. Build the theoretical framework, graph, say in words how

★ you would find the BRFs.

Profit to firm 1:

1

π = (p - c)D = N(p - c)(p - p + t)/2t

1 1 1 2 1

12

π = N(p p - p + tp + cp - cp - ct)/2t

1 2 1 1 1 2

Differentiate with respect to p :

1

dπ /dp = (N/2t)(p - 2p + t + c) = 0

1 1 2 1

Solve this for p :

1

1*

p = (p + t + c)/2 Best response function of

→

2

firm 1

What about firm 2? By symmetry, it has a similar

best response function:

2*

p = (p + t + c)/2 Best response function of

→

1

firm 2

By putting BRF = BRF we find the equilibrium

1 2

price for firm 1 and 2:

p * = t + c

2

p * = t + c

1

These firms make a profit equal to t for each unit.

When the shops are in the same place, t is the price the customers are willing to pay

because of the customers’ preferences.

Conclusion:

t is a measure of transport costs but it is also a measure of the value consumers

place on getting their most preferred variety.

- When t is large, competition is softened and profit is increased.

- When t is small, competition is tougher and profit is decreased.

Locations have been taken as fixed but in the real world, product design can be set

by the firms.

Comparison Cournot and Bertrand:

Best response functions are very different with Cournot and Bertrand:

- They have opposite slopes.

- Reflect very different forms of competition.

- Firms react differently, e.g., to an increase in costs.

Suppose firm 2’s costs increase:

- In Cournot

This causes firm 2’s Cournot best response function to fall:

At any output for firm 1, firm 2 now wants to produce less. Firm 1’s output

increases and firm 2’s falls.

Aggressive response of firm 1.

- In Bertrand:

Firm 2’s Bertrand best response function rises:

At any price for firm 1, firm 2 now wants to raise its price. Firm 1’s price

increases as does firm 2’s.

Passive response of firm 1 (because they behave in the same way).

When best response functions are upward sloping (es. Bertrand): Strategic

complements.

When best response functions are downward sloping (es. Cournot): Strategic

substitutes.

It is difficult to determine the strategic choice variable (price or quantity):

in some sectors, the output choice is made before sale probably quantity.

→ ⇒

in some sectors, production schedules easily changed and intense competition

→

for customers probably price.

⇒

4.3. Stackelberg model

Differently from Cournot and Bertrand models, where firms compete

simultaneously, in a wide variety of markets firms compete sequentially.

One firm is the first mover: the introduction of new products or the investment in

advertising expenditures. A second firm sees this move and responds.

These are dynamic games:

- May create a first-mover advantage or may give a second-mover advantage.

- May also allow early mover to preempt the market.

- Second firm sees this move and responds.

Can generate very different equilibria from simultaneous move games.

The first case we are going to see is the one in terms of the Cournot model.

Here the firms choose output sequentially:

1) The leader sets output first, and visibly.

2) The follower then sets output.

The firm moving first has a leadership advantage:

Can anticipate the follower’s actions.

● Can therefore manipulate the follower.

●

For this to work the leader must be able to commit to its choice of output. Strategic

commitment has value.

We assume there are two rational firms (N = 2) with identical products, competing à

la Cournot; with the following demand function: P = A – BQ = A – B(q + q ). Their

1 2

marginal cost is the same and equal to c. The firms have to choose their output level

q, so the competition is on quantities.

Observations:

The quantity produced by the leader is the monopoly output, but firm 2 is not

● excluded from the market.

The aggregate quantity here is larger than when the game is simultaneous:

● S C

Q > Q

The equilibrium price in Stackelberg is lower than the equilibrium price in

● S C

Cournot: P < P

In comparison to the cournot model:

● 1sc 1cour sc 1cour 1sc 1cour

q > q , p < p , and π > π leadership benefits firm 1 and

⇒

consumers (for the prices).

2sc 2cour sc 2cour 2sc 2cour

q < q and with p < p and π < π this harms firm 2.

⇒

1sc 2sc

q > q

Aggregate profit in Stackelberg is lower than aggregate profit in Cournot. The

● leader has higher profit in Stackelberg while the follower has higher profit in

Cournot.

With price competition things are different; Bertrand model.

The first-mover does not have an advantage.

⇒

Suppose products are identical:

the first-mover commits to a price greater than marginal cost C’, while the

second-mover will undercut this price and take the market. So the only equilibrium

is: P = C’, identical to the simultaneous game.

Now suppose that products are differentiated (perhaps as in the spatial model):

firm 1 sets and commits to its price first;

This defines the Stackelberg equilibrium. 1SB 2SB

Prices are higher than in the simultaneous game: p , p > p* = c + t

● 1SB 2SB 1B 2B

and p , p > p , p .

Firm 1 sets a higher price than firm 2, and so has lower market share:

● 1SB 2SB 1SB 2SB

p > p so q < q and D < D

1 2

m m m

c + 3t/2 + tx = c + 5t/4 + t(1 – x ) x = ⅜

⇒

m

Firm 2: 1 – x = ⅝

Profits:

● π = 18Nt/32

1

π = 25Nt/32

2

π < π

1 2

Price competition gives a second mover advantage.

Dynamic games and credibility

The dynamic games above require that firms move in sequence and that they can

commit to the moves; and also the strategy of the first mover has to be credible:

- It is with quantity.

- But it is less obvious with prices these strategies are more volatile.

→

With no credible commitment, the solution of a dynamic game becomes very

different.

- Cournot first-mover cannot maintain output.

- Bertrand firm cannot maintain price.

Consider a market entry game: Can a market be preempted by a first-mover?

Example:

Take two companies: Megasoft (incumbent) and Novasoft (entrant).

Novasoft makes its decision first: Enter or stay out of Megasoft’s market.

Megasoft then chooses: Accommodate or fight.

Pay-off matrix is as follows:

- Fight, enter - is not an equilibrium;

- Stay out, accommodate - is not an equilibrium;

There appear to be 2 equilibria in this game:

- Stay out, fight - not credible to fight the entrance because it decides to stay

out.

- Enter, accommodate.

We need a new representation of the game in an extensive way.

The options listed are strategies not actions:

Megasoft’s option to Fight is not an action, it is a strategy.

➔ Megasoft will fight if Novasoft enters but otherwise remains placid.

➔ Similarly, accommodation is a strategy.

➔

They are actions to take depending on Novasoft’s strategic choice.

Are the actions called for by a particular strategy credible? Is the promise to Fight if

Novasoft enters believable? If not, then the associated equilibrium is suspect.

The matrix-form ignores timing.

Represent the game in its extensive form to highlight sequences of moves.

Nova is the first mover and will decide to enter because the payoff is higher;

Megasoft will accommodate because if it fights the entry the payoff will be equal to

0.

Exercises

1) The global aircraft industry, with capacity exceeding 400 passengers, is

dominated by two major manufacturers: Airbus (A) and Boeing (B). Suppose that

each firm's total cost functions are: TCi = 5q + 100, where i = A, B. The world demand

i

for aircraft of this type is given by: P = 185 - 3/2 Q, where Q = q + q . The two firms

A B

compete on quantity (à la Cournot).

a. Calculate the quantity and the equilibrium price in that market.

b. Calculate the profits that firms make in equilibrium.

c. Suppose that the European Union wants to support the European company A,

guaranteeing a production subsidy equal to "θ" for each aircraft produced.

Now calculate the equilibrium quantities produced by the two firms.

2) Suppose that the Italian steel industry is composed of three companies, indicated

with 1, 2 and 3, which compete à la Cournot. Indicate the total output with Q, and

imagine that the demand curve is given b