Download Monopolistic Competition Until now, we have studied two extreme

Two broad cases are noteworthy:
Monopolistic Competition
Until now, we have studied two extreme cases
of competition: perfect competition and
monopoly.
Yet, reality is often in between: often, a firm’s
residual demand curve is downward sloping.
This is the case when fixed costs in an industry
are large compared to market demand, but not
as big as to create a natural monopoly.
•
Oligopoly: The good in question is
relatively homogenous, but entry is
limited because of (quasi-)fixed costs (or
possibly regulation).
•
Monopolistic competition: The good of
one supplier is unique, but there exist
close substitutes for the good.
In practice, the distinction between these
two market forms is sometimes difficult to
draw precisely.
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Monopolistic competition is characterized by
the following features:
1. A firm produces a specific variety of a good,
which consumers perceive as different from
that offered by competitors ( = product
differentiation, e.g. geographic location,
quality, taste, …)
→ Monopolistically competitive firm has market
power; firm’s residual demand curve is downward sloping, because consumers only
gradually shift away when firm raises its price.
Firm’s MR curve is downward sloping.
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2. The firm must pay high quasi-fixed costs to
maintain its brand name (remember: quasifixed costs are paid independently of the
quantity sold, if the quantity is positive).
→ ACs decline over a large range, and the
industry’s minimum efficient scale is large.
3. Entry is possible in principle.
→ firms in a monopolistically competitive
industry make (approximately) zero profits.
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These features together imply that firm
behaviour in monopolistic competition is given
by two simple rules:
p, $ per unit
AC
MC
p = AC
p
1. Marginal revenue equals marginal cost
2. Price equals average cost.
MR r =MC
In particular, the firm’s residual demand curve
and its average cost curve are tangent at the
firm’s optimal operating decision.
MR r
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Three points to note:
• Monopolistically competitive equilibrium is
inefficient: price is above marginal cost.
• In monopolistically competitive industries,
there is excess capacity: if there were fewer
firms, each firm could slide down its average
cost curve by expanding output (but careful:
less variety).
• Firms’ profits are driven to zero because of
potential entry. But because quasi-fixed costs
are large, not all profits need to be eroded.
Hence, profits are only approximately zero. 7
Dr
q, Units per year
q
p
300
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Example: The Swiss coated cornflakes
market (hypothetical numbers). 2 firms
with quasi-fixed cost of SFr. 2.3 million:
275
π = $1.8 million
211
183
AC
MC
147
D r for 2 firms
MR r for 2 firms
0
64
137.5
275
q, Thousand tons per year
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2
With 3 firms, the individual firm’s residual demand
curve shifts inward. All 3 firms make zero profits.
p
Note: if fixed cost is larger than SFr. 2.3 million,
the third firm does not enter, and both firms make
positive profits (smaller than SFr. 1.8 million).
300
243
195
An example of product differentiation:
geographic location (Hotelling)
Imagine the beach of a sea-side resort.
Suppose the beach is one kilometer long, and
families are distributed equally along the
beach.
AC
MC
147
D
MR
0
48
r
r
for 3 firms
for 3 firms
121.5
q , Thousand tons per year
243
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Answer:
At x = 0.25 and x = 0.75. The vendors have a
clientele of [0, 0.5) and (0.5, 1], respectively.
The average walking distance of all the
people on the beach is minimized if the
vendor sets up his shop at:
x = 0.5
But if the two vendors are acting competitively,
where do they locate? (To simplify assume
that they charge the same price.)
(where x = 0 represents the left end-point
and x = 1 the right end-point of the beach).
Now assume that there are two ice-cream
vendors. Where should the two optimally
locate?
If there is one vendor who sells ice-cream,
where should the vendor be located?
The vendor at x = 0.25 has an incentive to
move to the right: by doing this, she keeps all
her old customers, but captures some new
customers in the middle.
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Another application:
Circular City (Salop)
Similarly, the vendor at
x = 0.75 has an incentive to move to the left.
Result:
- Both vendors locate at x = 0.5.
- The monopolistically competitive
equilibrium is inefficient (too little variety).
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Oligopoly
We now turn to markets in which the good in
question is relatively homogenous, but there
are only few suppliers in the market
because of high fixed costs or other entry
barriers. In such markets (oligopolies), the
production choice of each producer has a
strategic impact on all other producers.
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Reminder:
The distinction between oligopoly and
monopolistic competition is not always clear
cut. On the one hand, homogenous goods
offered by different firms are rarely exactly
identical, on the other hand, even if a
producer sells a differentiated product that
protects her somewhat from market
pressure, the other producers’ strategic
choices will matter for her.
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We study the simplest form of oligopoly:
duopoly (“two sellers”)
The strategic interaction in such a market
can and does take many forms. In particular,
one should ask:
Assumptions:
• Is the relevant choice variable price or
quantity?
• Is one firm dominant (leads in the decision
making)?
• (Both these questions are irrelevant in
monopoly or in perfect competition)
• Market with one homogenous product,
market demand D(p)
• Two firms in the market, no entry
• Firm i has cost function C i (q ) .
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The Cournot model
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2
In this model (Augustin Cournot, 1838),
neither firm is dominant (in the sense that it
can directly influence the other’s decision
making), and both firms choose quantities.
The important point: Each firm’s optimal behaviour depends on what the other firm does.
If, for example, firm 2 chooses quantity q ,
firm 1 faces a residual demand curve of
D r ( p) = D( p ) − q 2. Firm 1 will, therefore,
maximise its returns from pricing on this
residual demand curve.
If p(Q) = D −1(Q ) is the inverse market
demand curve, this means that firm 1
chooses q1 to maximize
p(q1 + q 2 )q1 − C 1(q1)
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Assuming constant marginal cost:
This argument gives an optimal quantity
q1 = R1(q 2 ) for firm 1 as a function of what firm
2 produces.
p
Similarly, we can derive the optimal quantity
of firm 2 as a function of what firm 1 does:
q 2 = R 2 (q1) .
MC
The R i are called best-response functions or
reaction functions.
q 2
MR r
0
Dr
D
q1
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The Cournot equilibrium is defined as the
pair (q1, q 2 ) such that q1 = R1(q 2 ) and
q 2 = R 2 (q1) .
In words: firm 1’s behaviour is the best
response to firm 2’s behaviour, and firm 2’s
behaviour is the best response to firm 1’s
behaviour.
In other words: each firm chooses an output
based on a belief about the other firm’s
choice, and no firm has an incentive to
change its behaviour, once it learns the
competitor’s choice.
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The Cournot equilibrium is the intersection
point of the two best-response curves:
q2
Firm 1’s best-response curve
Cournot equilibrium
Firm 2’s best-response curve
0
q1M
q1
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Application: Competition in the airline market
On many air-traffic routes, there are very few
direct flights. In Europe these flights are often
limited to the national carriers.
Example: Geneva – Berlin, where only Swiss
and Lufthansa offer direct flights.
The “production function” of air travel is
characterized by
• constant and relatively low marginal costs
• high fixed costs
We study competition between Swiss and
Lufthansa on the Geneva - Berlin route by
using a simple Cournot model, using rough
estimates of cost and demand.
Variables (expressed as one-way flight):
• price p (in SFr)
L
S
• quantity Q = q + q (1000 passengers/year)
• Demand: D(p) = 300 – 0.3 p
• Cost: VC(q) = 300q (identical for both
L
S
carriers) and F = 13,000,000; F = 8,000,000)
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The Cournot equilibrium is given by the
intersection of these two reaction functions:
The Swiss perspective:
maximize pq S − 300 q S
= (1000 − 3.33(q S + q L )) q S − 300q S
q S = 105 − 0.5q L = 105 − 0.5(105 − 0.5q S )
= 70
By symmetry, also q L = 70 .
This gives a total quantity of Q = 140 and a
price of p = 533.33.
At this price, each airline makes a profit of
LH: (533.33 – 300)70,000 – 8,000,000 =
8.33 million/year)
SWISS: (533.33 – 300)70,000 –
13,000,000 = 3.33 million/year
The optimum is at q = 105 − 0.5q .
L
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S
The Lufthansa perspective:
maximize (1000 − 3.33( q S + q L ))q L − 300q L
S
L
which yields q = 105 − 0.5q
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Generalisation of Cournot model
Consider n firms, all with identical cost
structures, C(q) = cq.
Remark:
The model is simplified in several respects.
One is the lack of price discrimination:
airlines charge at least two prices for the
same flight in the same class, one
discounted for weekend travels and one
marked up for within-week travel.
Linear market demand:
p = a - bQ (for Q < a/b).
The individual firm maximizes profits:
(a − b( q1 + ...q n ) − c)q i
which gives the reaction function:
qi =
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a − c − b(q 2 + ... + q n ) − 2bq1 = 0
M
• For n = 1, this is just the monopoly output
(determined by a- 2bQ = c).
n
j
Summing all these equations, using ∑ q = Q ,
j =1
yields
n(a − c) − nbQ = bQ
which means
Q=
n a−c
n +1 b
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This simple formula is very useful and
reasonable:
The n reaction functions form a system of n
equations in n variables:
a − c − b(q1 + ... + q n −1 ) − 2bq n = 0
1
(a − c − b∑ q j )
2b
j ≠i
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• As n increases, Q increases.
• As n becomes large, Q tends to (a – c)/b.
But this is just the competitive output (given
by c = a – bQ)
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Summary Table
Hence, the Cournot model provides a model
that fits in between the monopoly outcome
and the competitive outcome, and the
number of firms indicates a “degree of
competitiveness”.
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