Chapter 5

Imperfect competition

Outline. An introduction to the theory of games

Some oligopoly models

Monopolistic competition

Collusion between firms Collusion is difficult to achieve on a

competitive market. Might seem less difficult to achieve among oligopolists, that is in industries served by only a small number of firms. However, collusion usually appears extremely

difficult to sustain.

Because it is the interest of each firm individually is usually not in the interest of all firms taken as a whole.

Similar to the prisoner’s dilemma

Prisoner’s dilemma 2 prisoners

If one of the 2 confesses, the confessor will be freed while the other one will spend 20 years in jail.

If both confess, they both get an intermediate sentence (say 5 years).

Payoff matrix:

Dominant strategy = confess

Table 1

Prisoner Y Confess Remains silent

Confess 5 years for each 0 years for X 20 years for Y

Prisoner X

Remains silent 20 years for X 0 years for Y

1 year for each

The sustainability of collusion Consider 2 firms that are the sole providers of

mineral water on a given market.

Market demand curve is given by: P = 20 – Q MC = 0

Collusion: each firm will offer half of the monopoly output and sell it at the monopoly price.

Monopoly quantity: 20 – 2Q = 0 Q = 10 and P = 10.

If both firms abide by this agreement: Each will sell 5 units of output Profit: = 50 – 0 = 50.

The sustainability of collusion (ctd 1) Each firm actually has two options: it can

abide by the agreement or defect. Assume that defection means cutting the price from 10 to 9. If one firm abides by the agreement and the

other one defects. What happens? The defector will capture the entire market because

of its lower price. He will sell Q = 20 – 9 = 11 and make a profit of 99.

The other firm sells nothing and makes zero profit.

If both firms defect, they will end up splitting the 11 units of output sold at a price of 9 and will make an economic profit of 49.5

The sustainability of collusion (ctd 2) Payoff matrix:

Dominant strategy = defect As this example is set up firms do not do much worse

when they defect that when they cooperate.

However, if firms find it in their interest to defect once, they are likely to defect again.

Table 2

Firm 1 Cooperate

(P = 10) Defect (P = 9)

Cooperate (P = 10)

1 = 50 2 = 50

1 = 99 2 = 0

Firm 2

Defect (P = 9)

1 = 0 2 = 99

1 = 49.5 2 = 49.5

Advertising

Oligopolists compete on prices but also by advertising. When a firm advertises its product, its demand increases for 2 reasons. First people who never used that type of

product before learn about it, which leads some of them to buy it.

Second other people who already consumed a different brand of the product will switch brand because of advertising.

US cigarette industry: brand-switching effect of advertisement is very strong.

Advertising (ctd)

Payoff matrix:

Dominant strategy = advertise

Table 3

Firm 1 Don't advertise Advertise

Don't advertise 1 = 500 2 = 500

1 = 750 2 = 0

Firm 2

Advertise 1 = 0 2 = 750

1 = 250 2 = 250

Nash equilibrium

In many games, not every player has a dominant strategy.

The dominant strategy for Firm 1 is to advertise. But Firm 2 has no dominant strategy

is the Nash equilibrium of the game

Table 4

Firm 1 Don't advertise Advertise

Don't advertise 1 = 500 2 = 400

1 = 750 2 = 100

Firm 2

Advertise 1 = 200 2 = 0

1 = 300 2 = 200

Nash equilibrium: definition

A Nash equilibrium is a combination of strategies such that each player's strategy is the best he can choose given the strategy chosen by the other player.

At a Nash equilibrium, neither player has any incentive to deviate from his current strategy.

In a prisoner's dilemma, the equilibrium is a Nash equilibrium.

But a Nash equilibrium does not require both players to have a dominant strategy.

The maximin strategy

In the previous example, we have assumed that Firm 2 believes that Firm 1 will act rationally. However, Firm 2 may not be sure that Firm 1 will act

rationally.

When Firm 2 has no dominant strategy and is not sure of what Firm 1 will do, what should it do?

If firm 2 is extremely cautious, it may choose the maximin strategy: it will choose the strategy that maximises the lowest possible value of its own payoff.

In this situation, the maximin strategy is not to advertise.

Repeated play in prisoner's dilemma

Strategy to prevent defection: tit-for-tat How it works: the first time you interact with somebody,

you cooperate. In each subsequent interaction you do what the person did in the previous interaction.

Robert Axelrod (The Evolution of Cooperation, 1984): tit-for-tat performs very well against a large number of alternative strategies

Conditions for tit-for-tat to be successful: There must be a rather stable set of players each of

whom can remember what the others have done in previous interactions.

Players must allocate a sufficiently high value to the future.

Tit-for-tat These conditions are often met in human

populations. Many people interact repeatedly and keep track of what others did in the past. Examples World War I Business world

Additional condition: there is not a known fixed number of future interactions.

Does tit-for-tat generate widespread collusion? By no means: cartels tend to be highly unstable. Problem of selective punishment Risk of entry

Sequential games

In many games, one player moves first and the other one can choose his strategy with full knowledge of the first player's choice

Example: USA versus Soviet Union during much of the Cold War Given the assumed payoff, USA may threaten to

retaliate, but if the payoffs are as displayed above, this is not credible.

In order to be sure that there won't be any risk of nuclear war, the USA should install a "doomsday" machine

USA versus Soviet Union

Useless investments: Sears Tower Consider the example of the Sears Tower in

Chicago (the highest building). A company X considers whether to build a higher

building. Its concern is that Sears may react by building an even higher building.

Sears Tower: strategic entry deterrence Before Sears had originally built its tower: option

of building a platform at the top on which it could subsequently build an addition that would make the building taller.

Building the platform costs 10 units but reduces the cost of making the building taller by 20 units.

This platform is an example of strategic entry deterrence

Sears Tower (ctd)

Outline. Some oligopoly models

Monopolistic competition

The Cournot model The central assumption of the model is that each

firm treats the amount produced by the other firm as a fixed quantity that does not depend on its own production decisions.

Suppose the market demand curve for mineral water is given by:

and suppose MC = 0

The demand curve for firm 1's water is:

)QQ(baP 21

12 bQ)bQa(P

The Cournot duopoly (ctd 1)

The Cournot model (ctd2) Firm 1's demand curve is the portion of the

original demand curve that lies to the right of this vertical axis.

So, it is sometimes called the residual demand curve.

The rule for firm 1's profit maximisation is: MR = MC = 0.

Marginal revenue has twice the slope as demand so that:

121 bQ2)bQa(MR

The reaction functions The optimal output level is given by:

This is firm 1’s reaction function:

Firm 2’s reaction function is given by:

b2

)bQa(Q0MR 2*

11

)Q(RQ 21*1

b2

)bQa()Q(RQ 1

12*2

The reaction functions (ctd)

The Nash equilibrium of the Cournot model The intersect of both reaction functions is the

Nash equilibrium of the Cournot model:

2121 QQ

b2

)bQa(

b2

)bQa(

b3

aQQ

b2

)bQa(Q 21

11

How profitable are Cournot duopolists? Since their combined output is 2a/3b, the market

price will be:

At this price, each will have a total revenue equal to the economic profit given by:

3

a)QQ(baP 21

b9

aofitPrTR

2

The Bertrand model Each firm chooses its price on the assumption

that its rival's price remains fixed.

Suppose that the market demand and cost conditions are the same as in the Cournot example. Suppose firm 1 charges an initial price

Then firm 2 faces essentially 3 choices: It can charge more than firm 1 and sell nothing. It can charge the same as firm 1 in which case both

firms will split the market demand at that price. It can sell at a marginally lower price than firm 1 and

capture the entire market. This last option is always the most profitable.

01P

The Bertrand model (ctd) As in the Cournot model the situations of the

duopolists are completely symmetric in the Bertrand model.

So, the strategy of selling at a marginally lower price will be chosen by both firms.

In this case, there is no stable equilibrium: the price-cutting process will go on until the price reaches the marginal cost =0.

In this case, both duopolists will share the market equally.

The Stackelberg model What would a firm do if knowing that its rival is a

naïve Cournot duopolist? This firm would choose its own output level by taking

into account the effect of that choice upon the output level of its rival.

Returning to the Cournot model, assume that firm 1 knows that firm 2 will treat firm 1's output as given. Firm 2's reaction function is:

Knowing this, firm 1 can substitute R2(Q1) for Q2 in the

equation for the market demand curve.

b2

)bQa()Q(RQ 1

12*2

The Stackelberg model (ctd 1)

The demand curve addressed to firm 1

2

bQa

b2

bQaQba)]Q(RQ[baP 11

1121

The Stackelberg model (ctd 2) Firm 1 = Stackelberg leader

Firm 2 = Stackelberg follower

Comparison of outcomes

A monopoly with the same demand and cost curves as the Cournot duopolist would have produced:

The Cournot duopolists P = a/3 Q = 2a/3b.

The Bertrand duopolists P = MC = 0 Q = a/b, so that each of them produce a/2b. This is similar to the perfect competition situation.

bQa)QQ(baP 21

b2

aQ0bQ2aMR

2

aP and

Comparison of outcomes (ctd 1)

The Stackelberg model: P = a/4 Q = 3a/4b = a2/8b and = a2/16b In the Stackelberg model, the leader fares better than

the follower.

Table 5

Model Industry output Q Market price P Industry profit Shared monopoly Qm=a/2b Pm=a/2 m=a2/4b Cournot (4/3)Qm (2/3)Pm (8/9)m Stackelberg (3/2)Qm (1/2)Pm (3/4)m Bertrand 2Qm 0 0 Perfect competition 2Qm 0 0

Comparison of outcomes (ctd 2)

Contestable markets

William Baumol, John Panzer and Robert Willig, Contestable Markets and the Theory of Industry Structure, 1982. The idea is that monopolies sometimes behave just like

perfectly competitive firms. This will happen when entry and exit are perfectly free.

Costless entry: there are no sunk costs associated with entry and exit When sunk costs are high, new firms will not enter the

market even if the incumbent is making high profits

When sunk costs are almost zero, new competitors will enter the market with the idea that they will pull out if post-entry business proves non profitable.

Contestable markets (ctd)

The contestable market theory Cost conditions will determine how many firms

will end up serving the market. But there is no clear relationship between the

actual number of competitors in a market and the extent to which prices and quantities are similar to what we would see under perfect competition.

Critics: there are substantial sunk costs involved in all activities

Competition under increasing returns to scale

Suppose that there exists a duopoly in an industry where there are increasing returns to scale. 2 firms started at an early stage of development Should we expect that one firm will drive the other one

out of the market?

2 solutions Merge: problem of antitrust laws. Price war: none of the 2 firms has any interest in doing

that. without a threat of entry, a live-and-let-live strategy is very

likely to be adopted

Competition under increasing returns to scale (ctd) Suppose now that a firm has a monopoly

position and that potential entrants face substantial sunk costs. Potential entrants may be reluctant to enter

the industry and face a potentially ruinous price war with the incumbent

Last solution Buyers may be willing to approach a potential

entrant. Local authorities usually do that

Outline. Monopolistic competition

Monopolistic competition

Monopolistic competition occurs when: Many firms serve a market with free entry and

exit But in which the product of each firm is not a

perfect substitute to the product of the other firms on the market.

The degree of substitutability between products determines how closely the industry resembles perfect competition

The Chamberlin model Developed in the 1930s by Edward Chamberlin and

Joan Robinson. Assumption: there exists a clearly defined market

composed of many firms producing products that are close but imperfect substitutes for one another.

So, each firm faces a downward-sloping demand curve but behaves as if its price and quantity decisions should not affect the behaviour of the other firms in the industry

Firms are perfectly symmetric so if it makes sense for a firm to alter its price in one direction, it will make sense for the other firms to do the same

The individual firm’s demand curves Each firm faces 2 demand curves

Chamberlinian equilibrium in the short run

Chamberlinian equilibrium in the long run

Perfect competition generates allocative

efficiency whereas monopolistic competition does not.

The Chamberlin model is more realistic than the perfect competition model on, at least, one point. Perfect competition: the price is equal to the marginal

cost firms are indifferent to the opportunity of filling a new order.

Monopolistic competition: the price is higher than the marginal cost firms will be very keen on filling an additional order.

In both market structures, long-run profits are 0.

Perfect competition versus Chamberlinian monopolistic competition

The model considers a group of products which

are different in some unspecified way but that are likely to appeal to any given buyer. George Stigler: it is impossible to draw operational

boundaries between groups of products in this way.

The Chamberlinian industry group quickly expands to contain all possible consumption goods in the economy.

Complicates the perfect competition model without altering its most important predictions.

Does not depart sufficiently from the perfect competition model Assumption that each firm has an equal chance to

attract any of the buyers in an industry: not always true

Criticisms of the Chamberlin model

One concrete way of thinking about the lack of

substitutability is distance.

The seminal paper in this literature has been published by

Harold Hotelling in the Economic Journal in 1929

Consider a small island with a big lake in the middle. Business activities are necessarily located at the periphery of the island. Restaurants: meals are produced under increasing returns to scale. Circumference of the island is 1 mile. Initially: 4 restaurants,

evenly spaced. Min. distance = 0 and Max distance = 1/8 miles. L customers scattered uniformly around the circle and the

cost of travel is t€ per mile.

The spatial interpretation of monopo-listic competition

Total cost curve of the restaurant is:

TC = F + MQ

ATC = TC/Q = F/Q + M

The initial location of restaurants

If TC = 50 + 5Q where Q is the number of meals served

each day. If L = 100 and there are 4 restaurants, each restaurant will

serve 100/4 = 25 persons a day.

So, the total cost is TC = 50 + (5x25) = 175€ per day. Average total cost is TC/25 = 7€ per meal.

Clearly this is higher than if there are only 2 restaurants: each serve 50 meals per day with AC = [50+(5x50)]/50 = 6€.

What is the average cost of transportation if there are 4 restaurants? In this case the farthest someone can live from a restaurant is

1/8 miles so that he round trip is 1/4 miles.

If the travel cost is 24€ per mile the total travel cost will be 6€.

The average cost of a meal with 4 restaurants

The average cost of a meal with 4 restaurants(ctd)

Since people are uniformly scattered around the loop, straightforward calculation (!) show that the average round trip is 1/8 miles Trick: this is the average between maximum distance

(=1/4) and minimum distance which is 0

So, the average transportation cost is 3€.

The overall average cost per meal is 7€ + 3€ = 10€

Results from a trade-off between the fixed cost of

opening new locations and the savings from lower transportation costs

What is the best number of outlets to have? If we increase the number of restaurants from 4 to 5,

what happens to the average cost? Each restaurant serves 20 meals per day, with an

ATC = [50+(5x20)]/20 = 7.5€

The distance between 2 restaurants is now 1/5 miles. So the maximum round-trip distance is 1/5 miles. The minimum being 0, the average round-trip distance is

1/10 miles.

So, the average transportation cost is 24€ x 1/10 = 2,4€.

The optimal number of locations

The overall average cost is therefore: 7.5 + 2.4 = 9.9€.

So, adding a fifth restaurant reduces the average cost of the meal by 0.1€.

Adding a 6th restaurant, the overall AC goes up

The optimal number of restaurants is 5.

What is the best number of outlets to have? If we increase the number of restaurants from 4 to 5,

what happens to the average cost?

Each restaurant serves 20 meals per day, with an ATC = [50+(5x20)]/20 = 7.5€

The optimal number of locations (ctd 1)

The distance between 2 restaurants is now 1/5 miles. So

the maximum round-trip distance is 1/5 miles.

The minimum being 0, the average round-trip distance is 1/10 miles.

So, the average transportation cost is 24€ x 1/10 = 2,4€.

The overall average cost is therefore: AC = 7.5 + 2.4 = 9.9€.

So, adding a fifth restaurant reduces the average cost of the meal by 0.1€

The optimal number of locations (ctd 2)

Generalisation In order to generalise this result, let us assume

that there are N outlets around the loop. The distance between adjacent outlets is 1/N and the

maximum one-way trip length is half of that: 1/2N.

If people are uniformly distributed around the loop, the average one-way trip length is 1/4N and the average round-trip distance is 1/2N.

The average transportation cost is :

The total cost of meals is:

N2

tLC trans

NFLMCmeals

Generalisation (ctd 1)

Generalisation (ctd 2) The first order condition is:

Applying this to our example yields:

0N

)CC( mealstrans

F2

tLN0F

N2

tL *2

59.4502

10024N*

An example Why are there many so many fewer small food

stores than 30 years ago (and so much larger supermarkets)?

Food stores face strongly increasing returns to scale.

Transportation costs have decreased

The analogy to product characteristics Consider the various airline flights between two

cities on a given day. People have different preferences for travelling at different times of the day.

The analogy to product characteristics (ctd) Virtually, any consumer product can be

interpreted in the context of the spatial model.

On the automobile market, there exists a very large variety of options. Of course, it would be much cheaper if there were only a

couple of models. But people are willing to pay a little extra for variety as

they are willing to pay some more for a more conveniently located shop.

Car manufacturers are said to "locate" on the "product-space". Their aim is to make sure that few buyers are left without a choice that lies "close" to the car that best suits them.

Similar interpretations apply to cameras, vacations, bicycles, etc

Paying for variety Wastefully high levels of product variety?

In our model we have assumed that all customers face the same transportation costs. This is clearly not the case in reality. Demand for variety increases sharply with income: it is a

luxury.

So, firms usually set prices in a different way for their different products. Typically, they will price their basic products very close

to the marginal cost And the more fancy products several times the marginal

cost.

The Hotelling model 2 hot-dog vendors who can choose where to

settle along a beach. Suppose the beach is 1 mile long and is bounded by

natural obstacles.

Suppose the vendors charge the same price and customers are evenly distributed along the beach. They buy one hot-dog from the nearest vendor.

Where should vendors position themselves?

The Hotelling model (ctd) A and B are the locations that minimise average

travel distance for all customers. Yet, they are not optimal from the perspective of the

vendors.

The only stable outcome is for each to locate at C. Each gets half of the market as before, but now the average one-way distance is ¼ of miles, i.e. twice as much as before.

Having both vendors at the centre of the beach is optimal for vendors but not for customers. In this case, the "invisible hand" does not guide resource

allocation so as to produce the greatest good for all.

U.S. political parties

Conservative Liberal A A' C B B'

Republicans Democrats