topic 8 chapter 13 - university of victoria - web.uvic.caweb.uvic.ca/~okhan/ch13.pdf¾an oligopoly...

Econ 203 Topic 8 page 1

Topic 8 Chapter 13

Oligopoly and Monopolistic Competition Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry’s output. Firms behave strategically -- Game Theory Focus on firm’s behaviour -- pricing choice or quantity choice ►Competition model 1: the Cournot theory ►Competition model 2: Van Stackelberg duopoly theory ►Competition model 3: the Bertrand Theory


Monopolistic Competition

Characterized by: ►The existence of numerous firms each producing a product that is a close, but imperfect substitute for the products of other firms ►free entry and exit of firms


Oligopoly: In Chapter 12: the situation with a single firm (monopoly). The Monopolist: ►set price (market power) ►maintain an economic profit in the long run ►no entry of new firms Oligopoly: ►more than one firm in the market ►each firm has some market power to set price ►awareness of its competition in decision making process


Ther are many theories on how firms behave in an oligopolistic market. Behaviour will be determined by pricing and quantity choices. Such choices depend on the firms in the market and on how they compete. Main focus of this chapter will be on the duopoly: two firms in the market.


►There is no single theory of oligopoly. In contrast to perfect competition or monopoly, where there is a single model, many types of oligopoly models exist. Depending on the circumstances each one of these theories may be appropriate.

An oligopoly is a market structure with a limited or small number of firms.


An example in Canada, of an oligopoly is the Chartered Banks. Each of the major firms takes account of the reaction of the others when it determines its price and output policy, since its policy will affect the others. That is, when a firm increases its price, it must anticipate the reaction of other firms in the industry. If its competition decides against a price increase, it is likely that the price increase will have to be rescinded; otherwise, its rival will pull away a large number of its customers.


In some industries, the number of firms tends to be small, because low costs cannot be achieved unless a firm is producing an output equal to a substantial percentage of the total available market: economies of scale. (Each firm must be large relative to the market.)


Collusive Agreements

Conditions in oligopolistic industries tend to encourage collusion. This is because: 1) the number of firms is small 2) firms are aware of their interdependence If firms collude they will:

1) achieve greater profits 2) decrease their uncertainty

3) have a stronger ability to prevent entry of new firms


Collusive arrangements are difficult to maintain and control, since the payoff from cheating on the agreement enables the cheating firm to attain even higher profits.

Cartel: is a formal collusive arrangement among firms within an industry.

What Price Will a Cartel Charge? If a cartel is established to set a uniform price for a particular homogeneous product, the cartel must estimate the marginal cost curve for the cartel as a whole. If we assume that input prices do not increase as the cartel expands, this marginal cost curve is the horizontal sum of the marginal cost curves of the individual firms.


Price MC (Cartel) P0 A MC=MR Demand MR Q0 Output

In the diagram, suppose the marginal cost curve for the cartel is shown.


If the demand curve for the industry’s product and MR curve are as above, the output that maximizes the total profit of the cartel members is Q0. That is, if the cartel maximizes profits, it will choose a price P0. This is the monopoly price! The cartel acts as a monopoly.

The cartel must distribute the industry’s total sales among the firms belonging to the cartel.


It will allocate sales to firms such that the marginal cost of all firms is equal, in order to maximize cartel profits. The cartel could make more money by reallocating output among firms so as to reduce the cost of producing the cartel’s total output. But this allocation of output is unlikely, since allocation decisions are the result of negotiation between firms with differing productive abilities. The process of negotiation between firms is very “political”, and the firms with the greatest influence, are likely to receive the largest sales quotas, even though this raises total cartel costs.


The Cournot Model: “An industry in which firms produce identical goods and each firm determines its profit-maximizing output level, taking its

rivals’ current output levels as given.” p. 398. ►firms maximize profits ►firms choose price and quantity assuming that the other firm(s) keeps their quantity fixed. Assume: ►two firms producing the same good. ►each duopolist treats the other’s quantity of output as fixed.


Cournot’s Water Example: MC =0 Let total market demand curve is given:

P a b Q Q= − +( )1 2 , where a an b are positive numbers and Q1 and Q2 are outputs of the two firms. The profit maximizing problem facing firm 1, given the assumption that firm 2’s output is fixed at the current level:

Max Q Q PQ C Q

Q11 2 1 1 1Π( , ) ( )= −

.


The demand curve for firm 1 is therefore given by:

P a bQ bQ1 2 1= − −( ) . (Q2 is assumed to be fixed.) We get the demand curve for firm 1 by subtracting bQ2 from the vertical intercept of the market demand curve. The idea is that firm 2 has already supplied the Q2 units of market demand, leaving firm 1 the rest to work with.


Firm 1’s demand curve lies to the right of this new vertical axis. Often referred to as a residual demand curve. The firm’s MR curve is labelled MR1.


Since the profit maximizing level of output for firm 1 is found where MR1=MC and MC=0 in this case, they should supply at a point where MR1=0.

( )P a bQ bQ price

TR PQ a bQ bQ Q

TR aQ bQ Q bQ

MR TRQ

a bQ bQ

1 2 1

1 1 1 2 1 1

1 1 2 1 12

11

2 12

= − − ←

= = − −

= − −

= = − −

( )

( )

( )∂∂

MR has twice the slope as demand so it intersects MC=0 at the half way point between Q1=0 on the horizontal intercept of the demand curve.


By symmetry, Q2=Q1. Set MR = MC and solve for the output of firm 1 in terms of the output of firm 2.

MR TRQ

a bQ bQ MC

a bQ bQQ Qa bQ bQa bQ

Q ab

Q

11

2 1

2 1

2 1

1 1

1

1 2

2 0

2 0

2 03

3

= = − − = =

− − ==

− − ==

= =

∂∂


MR TRQ

a bQ bQ MC

Q a bQb

11

2 1

12

2 0

2

= = − − = =

=−

∂∂

Reaction Function: a curve that tells the profit-maximizing level of output for one oligopolist for each amount to supplied by another. For the example where MC=0, the reaction function for firm 1 is :

Q a bQb1

2

2=

−.


The function tells how firm 1’s quantity will react to the quantity level offered by firm 2. Since the Cournot duopoly problem is completely symmetric, firm 2’s reaction function has the same structure:

Q a bQb2

1

2=

− .


The two reaction functions are illustrated above. There is a stable equilibrium at the intersection of the two reaction functions.


Here, both firms are producing ab3 units of output, and neither

firm has any incentive to change. Profit?

Combined output Q=Q1+Q2=ab3 +

ab3 =2

ab3 .

Market price will be P a b Q Q

P a b ab

a a a a a= − +

= − ⎛⎝⎜

⎞⎠⎟ = − ⎛⎝⎜

⎞⎠⎟ = − =

( )

.

1 2

23

23

33

23 3

Total revenue will equal:

TR PQ a ab

ab

= = × =3 3 9

2

.


With production cost being assumed to be zero, profit equals TR. Example: A duopolist faces a market demand curve given by P Q= −56 2 . Each firm can produce output at a constant MC of $20 per unit. Graph their reaction functions and find the equilibrium price and quantity. For firm 1: P Q Q Q

P Q Q

= − = − +

= − −

56 2 56 2

56 2 21 2

1 2 1

( )

( ) Produce an output where: MR=MC


( )TR PQ Q Q Q

TR Q Q Q QMR Q Q

1 1 1 2 1 1

1 1 1 2 12

1 2 1

56 2 2

56 2 256 2 4

= = − −

= − −= − −

( )

MCMR Q QMC MR

Q Q

== − −=

= − −

2056 2 4

20 56 2 4

1 2 1

1

2 1

4 36 236 2

49 0 5

36 24

9 0 5

1 2

12

2

21

1

Q Q

Q Q Q reaction function

Q Q Q reaction function

= −

=−

= − ←

=−

= − ←

.

.


Since each firm will produce the same amount at the point where the reaction functions intersect, substitute into the expression for Q2:

Q Q reaction functionQ Q reaction functionequate

Q Q

Q QQ Q

Q

Q

Q QQ units

1 2

2 1

2 1

1 1

1 1

1

1

1 2

9 0 59 0 5

9 0 5 9 0 5

9 0 5 9 0 5 9 0 59 4 5 0 25 9 0 5

4 5 0 754 50 75

6

66 6 12

= − ←= − ←

− = −

− − = −− + = −

− = −

= =

= == + =

..

:. .

. ( . ) .

. . .. .

..

Price is: P=56-2Q=56-2(12)=$32/unit.


The Bertrand Duopoly Model: “ An industry in which two firms produce identical goods and each firm chooses its price assuming that its rival’s price will

remain fixed.” p.401 According to the model, from the buyer’s perspective, what really counts is how the prices charged by the two firms compare. Buyers would want to purchase the good from the firm with the lowest price. Bertrand argued that each firm would choose a price on the assumption that its rival’s price would remain fixed.


Illustration: If the market demand and cost conditions are same as in the Cournot example, firm 1 could charge an initial price of denoted P1

0 . Firm 2 can either: (1) charge more than firm 1, (sell nothing in the market) (2) split the market demand equally at that price, or (3) sell at a marginally lower price than firm 1 (capture the entire market demand). ►Option 3 is the most profitable. However, each firm would desire this strategy and would undercut the other until price reaches marginal cost. ►With each firm charging a price equal to MC, it is assumed the duopolists will share the market equally.


Example: Bertrand duoplists face a market demand curve given by P= 56 – 2Q. Each can produce output at a constant marginal cost of $20 / unit. Find the equilibrium price and quantity. Both firm s price at marginal cost: P=MC = 20 Industry output is determined by market demand: 20=56-2Q Q=18. If the firms split the market equally, then each firm produces half of industry output: Q1=Q2=9 units.


The Stackelberg Model:

“An industry in which one firm (the Stackelberg leader) sets its

profit-maximizing level of output first, knowing that its rival (the Stackelberg follower) will behave as a Cournot duopolist.’ p. 402

In the Stackelberg model, a firm would want to choose its output level by taking into account the effect that choice would have on the output level of its rival. Suppose firm 1 knows that firm 2 will treat firm 1’s output as fixed. Can this knowledge be used to the advantage of firm 1?


Since firm 2’s reaction function is given by Q a bQ

breaction function2

1

2=

−← .

Knowing that firm 2’s output will depend on Q1 in this manner, firm 1 can then substitute the reaction function for Q2 into the equation for the market demand curve: P a b Q Q a b Q a bQ

ba bQ

= − + = − +−⎛

⎝⎜⎞⎠⎟ =

−( )1 2 11 1

2 2 . This demand curve and MR curve are shown in figure 13.4.


With MC assumed to be zero in this example, firm 1’s profit maximizing output level will be the one for MR1 is zero, at Q a

b1 2* = .

Firm 2 will produce: Q ab2 4

* .=

Price:

P a b Q Q a b ab

ab

P a a a a a a a

= − + = − +⎛⎝⎜

⎞⎠⎟

= − − = − − =

( )

.

* *1 2 2 4

2 444

24 4 4


Example: A Stackelberg leader (firm 1) and follower (firm 2) face a market demand curve given by P=56-2Q. Each can produce output as a constant marginal cost of $20/unit. Find the equilibrium price and quantity. By substituting firm 2’s reaction function: Q Q reaction function2 19 0 5= − ←. into the demand facing firm 1: P Q Q

P Q QP Q QP Q

1 2 1

1 1 1

1 1 1

1 1

56 2 2

56 2 9 0 5 256 18 238

= − −

= − − −= − + −= −

( )

( ( . )


To derive MR: TR PQ Q Q

TR Q Q

MR Q

1 1 1 1 1

1 1 12

1 1

38

38

38 2

= = −

= −

= −

( )

.

Setting MR=MC, determines firm 1’s output: MR QMC

QQ

Q units

1 1

1

1

1

38 220

20 38 22 38 20 18

18 2 9

= −=

= −= − =

= =/

Inserting Q1’s output of 9 units into the reaction function for firm 2 yields the output for firm 2:


Q Q reaction function

Q units2 1

2

9 0 5

9 0 5 9 9 4 5 4 5

= − ←

= − = − =

.

. ( ) . . Total industry output is 9 + 4.5=13.5 units. Price is: P=56 - 2Q = 56 - 2(13.5) =56-27 = $29 unit. Firm 1 is referred to as a Stackelberg leader. Firm 2 is the Stackelberg follower.


The best output choice is a/2b for firm 1 once it takes into account that firm 2 will respond to its choice according to the reaction function for firm 2. Once firm 1 produces a/2b, firm 2 will consult its reaction function and product a/4b.


If firm 1 believes that firm 2 will fix the amount produced at a/4b, it should consult its own reaction function and produce the corresponding quantity 3a/8b. Firm 1 would earn more. However, firm 1 knows that if it cuts back, this will elicit a reaction from firm2. The best option is for firm 1 to remain at a/2b. Firm 1 earns more profit than at the intersection of the reaction curves, but does not give firm 2 any incentive to increase output.


Stackelberg’s model is viewed as a superior model to compared to the other two models since it allowed one firm to act strategically. However, there is nothing stopping the rival firm to behave in the same way. For consumers this would be desirable with a large output and low price result! For owners of the firms, this strategic behaviour leads to the worst possible outcome.


Game Theory Managers who must analyse and participate in oligopolistic decision making, are very likely to use modern game theory. Since a basic feature of oligopoly is that each firm must take account of its rivals’ reactions to its own decision making, oligopolistic decision making has many of the characteristics of a game. Game theory attempts to study decision making where, like an oligopoly, there is a mixture of conflict and cooperation.


A game is a competitive situation in which two more opponents pursue their own interests, and no one can dictate the outcome. Each player of the game is a decision making entity with a certain amount of allocated resources. The rules of the game describe how resources can be used. A strategy specifies what a player will do under each situation while playing the game.

These are the actions that will be taken in response to a particular action taken by another player, or actions that reflect where the player wants to end up.


A player’s payoff varies from game to game. For two-player games, the possible outcomes are illustrated with the aid of a payoff matrix.

Possible Strategies for Firm B 1 2

Possible Strategies

3 A’s profit: $30 B’s profit: $40

A’s profit: $20 B’s profit: $30

for Firm A 4 A’s profit: $40 B’s profit: $30


Firm A can choose strategy 3 or 4 and Firm B can choose strategy 1 or 2.


The payoff, expressed in terms of profits for each firm, is shown above for each combination of strategies. In this game, there is a dominant strategy for each player. Regardless of whether Firm B chooses strategy 1 or 2, Firm A will make more profit if it chooses strategy 4 rather than 3. Strategy 4 is Firm A’s dominant strategy. Similarly, regardless of whether Firm A adopts strategy 3 or 4, firm B will make more profit if it chooses strategy 1 rather than 2. Hence, strategy 1 is Firm B’s dominant strategy. The solution to this game is that Firm A chooses strategy 4 and Firm B chooses strategy 1.


Nash Equilibrium Not all games have a dominant strategy for every player.


Possible Strategies





Suppose the pay off matrix for Firms A and B are as shown. Under these circumstances, Firm A still has a dominant strategy: 4. Regardless of which strategy firm B adopts, strategy 4 is firm A’s best strategy.


But firm B no longer has a dominant strategy. Its optimal strategy depends on what firm A decides to do.

If Firm A chooses strategy 3, firm B will make more profit if it chooses strategy 1 rather than strategy 2.

If Firm A adopts strategy 4, Firm B will make more profit if it chooses strategy 2 rather than strategy 1.

To determine what action should be taken, Firm B must try to anticipate what action Firm A will take. That is, Firm B must try to figure out what the best action it would take if it was Firm A.


Since we know from the table that Firm A’s dominant strategy is strategy 4, Firm B can surmise that this strategy will occur. Firm A will most likely choose strategy 4, and hence, Firm B will choose strategy 2 because it is more profitable than strategy 1 if Firm A adopts strategy 4. Thus, Firm A is expected to adopt Strategy 4 and Firm B is expected to adopt strategy 2. This is the Nash equilibrium for this game.


A Nash equilibrium is a set of strategies such that each player believes that it is doing the best it can given the strategy of the other player. Neither player regrets its own decision or has any incentive to change it. If each player has a dominant strategy, this strategy is its best choice regardless of what other players do. This is a Nash equilibrium too. The next table is an example of a payoff matrix for a game with two Nash equilibria.



Possible Strategies





If Firm A adopts strategy 3 and Firm B adopts strategy 1, each is doing the best it can given the other’s choice of strategy. If Firm A adopts strategy 4 and B adopts strategy 2, each is doing the best it can given the other’s choice of strategy. Hence, there are two Nash equilibria in this game.


Monopolistic Competition

With monopolistic competition all firms sell a somewhat different product. Product differentiation is the primary defining difference with this market structure compared to perfect competition. With perfect competition, the product produced by all firms in the industry is identical. With monopolistic competition, each product within the industry is just a bit different.


Such differences can be in the product’s physical make-up (Coke versus Pepsi), or in the amount of service each firm offers (Payless shoes versus Footlocker). Because of these differences, producers have a certain amount of control over the price of their product, although it is usually small because the products of other firms are very similar to their own.

In addition to product differentiation, there are four other conditions that must be met for an industry to be considered to be part of the market structure known as monopolistic competition:


1) There must be a large number of firms in the industry.

The good must be produced by at least 50 to 100 firms, with each firm’s product a close substitute for the products of the other firms in the industry.

2) The number of firms in the industry must be large enough that each firm expects its actions to be of no real concern or ignored by its rivals, and it is not concerned with possible retaliatory moves by its rivals.

With a large number of firms within the industry, this is usually met. The actions of the firm are not driven explicitly by the possible responses of its competitor.


3) There must be easy entry into the industry. No legal barriers.

4) There must be no collusion, such as price fixing or market sharing among firms in the industry.


Price and Output Decisions Under Monopolistic Competition

Because each firm produces a slightly different product, the demand curve facing each firm slopes downward to the right.

If the firm raises its price, the quantity demanded for its product will go down, but will no completely disappear. It will still retain some of its customers and not lose all of its customers to other firms. Conversely, if the firm decides to lower its price, it will gain some customers, but not all of its competitors’ customers. (Product loyality.)


Price MC P0 C AC A B MC=MR Demand (d0) MR q0 Output Firm (Short-Run)

profit


The diagram illustrates the short run equilibrium of a monopolistically competitive firm.

The firm will set its price at P0 and output rate at q0, due to the fact that it will maximize its profits where MC=MR.

Profit will be earned because P0 is higher than average total cost at this output of q0. (P0>A) Profit = AP0CB


Price MC P0 LAC P1 Demand (d1) MC=MR MR1 q1 Output The next diagram illustrates the long run equilibrium.

Profits are temporary since there are no barriers to entry. Other firms can enter and sell similar products.


As firms enter the industry, the firm’s demand function shifts inward. In the long run, each firm must be making no profit and maximizing its profits. The zero profit condition is met at the combination of price=P1 and output=q1, since the firm’s average cost at this output equals price P1. Profit maximization is met, since MC=MC at this output rate.


In monopolistically competitive industries, profits are competed away with entry of new firms, just like they are in competitive industries.

Unlike competitive industries, each monopolistically competitive firm is a price maker, and therefore price exceeds marginal cost. Marginal cost equals price in a competitive industry.

Under monopolistic competition each firm produces a

smaller quantity than a competitive firm. Long run average cost is higher than minimum average cost.


But, consumers benefit from the variety of products and the ability of the industry to cater to particular demands of some consumers.

topic 8 chapter 13 - university of victoria - web.uvic.caweb.uvic.ca/~okhan/ch13.pdf¾an oligopoly...

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