Econ 203 Topic 8
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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
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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
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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
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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.
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►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.
¾An oligopoly is a market structure with a limited or small
number of firms.
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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increase will have to be rescinded; otherwise, its rival will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.
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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.)
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Collusive Agreements
¾Conditions 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
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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.
¾What 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.
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Price
MC (Cartel)
P0
A
MC=MR
Demand
MR
Q0
Output
In the diagram, suppose the marginal cost curve for the cartel
is shown.
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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.
¾The cartel must distribute the industry’s total sales among
the firms belonging to the cartel.
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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.
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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.
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Cournot’s Water Example: MC =0
Let total market demand curve is given:
P = a − b( Q1 + Q2 ) ,
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 Π( Q1 , Q2 ) = PQ1 − C1( Q1 )
Q1
.
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The demand curve for firm 1 is therefore given by:
P1 = ( a − bQ2 ) − bQ1 .
(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.
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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.
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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.
P1 = ( a − bQ2 ) − bQ1 ← price
TR1 = PQ
1 1 = (( a − bQ2 ) − bQ1 )Q1
TR1 = ( aQ1 − bQ2 Q1 − bQ12 )
∂TR
MR1 =
= a − bQ2 − 2bQ1
∂Q1
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.
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By symmetry, Q2=Q1.
Set MR = MC and solve for the output of firm 1 in terms of
the output of firm 2.
∂TR
MR1 =
= a − bQ2 − 2bQ1 = MC = 0
∂Q1
a − bQ2 − 2bQ1 = 0
Q2 = Q1
a − bQ1 − 2bQ1 = 0
a = 3bQ1
a
Q1 =
= Q2
3b
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∂TR
MR1 =
= a − bQ2 − 2bQ1 = MC = 0
∂Q1
a − bQ2
Q1 =
2b
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 :
a − bQ2
Q1 =
2b .
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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:
a − bQ1
Q2 =
.
2b
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The two reaction functions are illustrated above.
There is a stable equilibrium at the intersection of the two
reaction functions.
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a
Here, both firms are producing 3b units of output, and neither
firm has any incentive to change.
Profit?
a
a
a
Combined output Q=Q1+Q2= 3b + 3b =2 3b .
Market price will be
P = a − b( Q1 + Q2 )
3a 2a a
a
a
−
= .
P = a − b⎛⎜ 2 ⎞⎟ = a − ⎛⎜ 2 ⎞⎟ =
⎝ 3b ⎠
⎝ 3⎠
3
3
3
Total revenue will equal:
a a
a2
TR = PQ = ×
=
.
3 3b 9b
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With production cost being assumed to be zero, profit equals
TR.
Example: A duopolist faces a market demand curve given by
P = 56 − 2Q . 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 = 56 − 2Q = 56 − 2( Q1 + Q2 )
P1 = ( 56 − 2Q2 ) − 2Q1
Produce an output where: MR=MC
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TR1 = PQ
1 1 = (( 56 − 2Q2 ) − 2Q1 )Q1
TR1 = 56Q1 − 2Q1Q2 − 2Q12
MR1 = 56 − 2Q2 − 4Q1
MC = 20
MR1 = 56 − 2Q2 − 4Q1
MC = MR1
20 = 56 − 2Q2 − 4Q1
4Q1 = 36 − 2Q2
36 − 2Q2
Q1 =
= 9 − 0.5Q2 ← reaction function
4
36 − 2Q1
Q2 =
= 9 − 0.5Q1 ← reaction function
4
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Since each firm will produce the same amount at the point
where the reaction functions intersect, substitute into the
expression for Q2:
Q1 = 9 − 0.5Q2 ← reaction function
Q2 = 9 − 0.5Q1 ← reaction function
equate:
9 − 0.5Q2 = 9 − 0.5Q1
9 − 0.5( 9 − 0.5Q1 ) = 9 − 0.5Q1
9 − 4.5 + 0.25Q1 = 9 − 0.5Q1
−4.5 = −0.75Q1
4.5
Q1 =
= 6
0.75
Q1 = Q2 = 6
Q = 6 + 6 = 12 units
Price is: P=56-2Q=56-2(12)=$32/unit.
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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.
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Illustration: If the market demand and cost conditions are
same as in the Cournot example, firm 1 could charge an
0
initial price of denoted P1 .
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.
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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.
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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?
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Since firm 2’s reaction function is given by
a − bQ1
Q2 =
← reaction function .
2b
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:
a − bQ1 ⎞ a − bQ1
⎛
P = a − b( Q1 + Q2 ) = a − b⎜ Q1 +
⎟ =
.
⎝
2b ⎠
2
This demand curve and MR curve are shown in figure 13.4.
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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
Q1* =
a
2b .
*
2
Firm 2 will produce: Q
a
=
.
4b
a
a⎞
⎛
P = a − b( Q + Q ) = a − b⎜
+ ⎟
⎝ 2b 4b ⎠
Price: P = a − a − a = 4a − 2a − a = a .
2 4
4
4
4 4
*
1
*
2
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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:
Q2 = 9 − 0.5Q1 ← reaction function
into the demand facing firm 1:
P1 = ( 56 − 2Q2 ) − 2Q1
P1 = ( 56 − 2( 9 − 0.5Q1 ) − 2Q1
P1 = 56 − 18 + Q1 − 2Q1
P1 = 38 − Q1
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To derive MR:
TR1 = PQ
1 1 = ( 38 − Q1 ) Q1
TR1 = 38Q1 − Q12
MR1 = 38 − 2Q1 .
Setting MR=MC, determines firm 1’s output:
MR1 = 38 − 2Q1
MC = 20
20 = 38 − 2Q1
2Q1 = 38 − 20 = 18
Q1 = 18 / 2 = 9 units
Inserting Q1’s output of 9 units into the reaction function for
firm 2 yields the output for firm 2:
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Q2 = 9 − 0.5Q1 ← reaction function
Q2 = 9 − 0.5( 9) = 9 − 4.5 = 4.5 units
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.
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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.
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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.
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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.
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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.
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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.
¾These 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.
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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
1
Possible
Strategies
for Firm A
3
4
A’s profit: $30
B’s profit: $40
A’s profit: $40
B’s profit: $30
Firm B
2
A’s profit: $20
B’s profit: $30
A’s profit: $30
B’s profit: $20
¾Firm A can choose strategy 3 or 4 and Firm B can choose
strategy 1
or 2.
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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.
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Nash Equilibrium
Not all games have a dominant strategy for every player.
Possible Strategies for
1
Possible
Strategies
for Firm A
3
4
A’s profit: $30
B’s profit: $40
A’s profit: $40
B’s profit: $30
Firm B
2
A’s profit: $20
B’s profit: $30
A’s profit: $30
B’s profit: $40
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.
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But firm B no longer has a dominant strategy. Its optimal
strategy depends on what firm A decides to do.
¾If Firm A chooses strategy 3, firm B will make more profit
if it chooses strategy 1 rather than strategy 2.
¾If 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.
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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.
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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.
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Possible
Strategies
for Firm A
3
4
Possible Strategies for
1
Firm B
2
A’s profit: $50
B’s profit: $50
A’s profit: $0
B’s profit: $0
A’s profit: $0
B’s profit: $0
A’s profit: $50
B’s profit: $50
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.
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Monopolistic Competition
¾With 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.
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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.
¾In 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:
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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.
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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.
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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.
¾If 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.)
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Price
profit
MC
P0
C
AC
A
B
MC=MR
Demand
(d0)
MR
q0
Firm (Short-Run)
Output
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The diagram illustrates the short run equilibrium of a
monopolistically competitive firm.
¾The 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
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Price
MC
P0
LAC
P1
Demand (d1)
MC=MR
MR1
q1
Output
The next diagram illustrates the long run equilibrium.
¾Profits are temporary since there are no barriers to entry.
¾Other firms can enter and sell similar products.
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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.
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¾In monopolistically competitive industries, profits are
competed away with entry of new firms, just like they are in
competitive industries.
¾Unlike competitive industries, each monopolistically
competitive firm is a price maker, and therefore price
exceeds marginal cost. ¾ Marginal cost equals price in a
competitive industry.
¾Under monopolistic competition each firm produces a
smaller quantity than a competitive firm. Long run average
cost is higher than minimum average cost.
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But, consumers benefit from the variety of products and the
ability of the industry to cater to particular demands of some
consumers.