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Chapter 5Imperfect 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 prisoners dilemma

Prisoners 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

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 P 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.

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

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

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

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

The reaction functions

- The optimal output level is given by
- This is firm 1s reaction function
- Firm 2s reaction function is given by

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

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

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.

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.

The Stackelberg model (ctd 1)

- The demand curve addressed to firm 1

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.

and

Comparison of outcomes (ctd 1)

- The Stackelberg model
- P a/4
- Q 3a/4b
- P1 a2/8b and P2 a2/16b
- ? In the Stackelberg model, the leader fares

better than the follower.

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 firms demand curves

- Each firm faces 2 demand curves

Chamberlinian equilibrium in the short run

Chamberlinian equilibrium in the long run

Perfect competition versus Chamberlinian

monopolistic competition

- 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.

Criticisms of the Chamberlin model

- 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

The spatial interpretation of monopo-listic

competition

- 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 initial location of restaurants

- Total cost curve of the restaurant is
- TC F MQ
- ? ATC TC/Q F/Q M

The average cost of a meal with 4 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(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

The optimal number of locations

- 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 (ctd 1)

- 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 2)

- 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

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

Generalisation (ctd 1)

Generalisation (ctd 2)

- The first order condition is
- Applying this to our example yields

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.

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