Transcript Firm A`s best

Chapter 14
Imperfect
Competition
© 2006 Thomson Learning/South-Western
Imperfect Competition
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Pricing in these markets falls between
perfect competition and monopoly.
Three topics considered:
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Pricing of homogeneous goods in markets
with few firms.
Product differentiation in these markets.
How entry and exit affect long-run outcomes
in imperfectly competitive markets.
表 14.1 台灣的領導性寡佔產業
產業經濟學—陳正倉、林惠玲、陳忠榮、莊春發著
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表 14.2 台灣的油品供應市場
單位:KL/日
資料來源：亞證投顧91年6月底資料。
產業經濟學—陳正倉、林惠玲、陳忠榮、莊春發著
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Pricing of Homogeneous Goods
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Market where a relatively few firms
produce a single homogeneous good.
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Assume demanders are price takers.
Assume there are no transactions or
informational costs.
These assumptions result in a single
equilibrium price for the good.
Initially, assume a fixed, small number
of identical firms.
Competitive Outcome
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In Figure 14-1, the equilibrium of the
Bertrand game occurs at point C.
This equilibrium also corresponds to
the perfectly competitive outcome.
FIGURE 14-1: Pricing under
Imperfect Competition
Price
P
C
C
MC
D
MR
0
7
Q
C
Quantity
per week
Perfect Cartel Outcome
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A model of pricing in which firms coordinate
their decisions to act as a multiplant
monopoly is the cartel model.
Assuming marginal costs are constant and
equal across firms, the cartel output is point
M (the monopoly output) in Figure 14-1.
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The plan would require a certain output by each firm
and how to share the monopoly profits.
FIGURE 14-1: Pricing under
Imperfect Competition
Price
P
P
P
M
M
A
A
C
C
MC
D
MR
0
9
Q
M
Q
A
Q
C
Quantity
per week
The Cournot Model
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The Cournot model of duopoly is one in
which each firm assumes the other firm’s
output will not change if it changes its own
output level.
Assume
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A single owner of a costless spring.
A market demand curve for water has the
equation Q = 120 - P.
Nash Equilibrium in the Cournot
Model
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For a pair of quantities, qA and qB, to be a
Nash equilibrium, qA must be a best
response to qB and vice versa.
A’s total revenue equals:
14.3
qA (120  qA  qB )
A’s marginal revenue equals
120  2qA  qB
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14.4
FIGURE 14-2: Cournot BestResponse Functions
Firm B’s 120
price(qB)
Firm A’s bestresponse function
0
12
60
120
Firm A’s
price(qA)
Nash Equilibrium in the Cournot
Model
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Equating marginal revenue with the marginal
cost of 0, and solving for qA gives A’s bestresponse function
120  q B
14.5
qA 
2
B’s best-response function would then be
120  q A
14.6
qB 
2
Nash Equilibrium in the Cournot
Model
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In this Nash equilibrium each firm
produces 40 units of output.
q A  40
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qB  40.
Total output is 80, and the market price is
$40.
Total industry profit is $3,200, $1600 for
each firm.
FIGURE 14-2: Cournot BestResponse Functions
120
Firm B’s
price(qB)
Firm A’s bestresponse function
60
Nash
equilibrium
40
0
15
40
60
Firm B’s bestresponse function
120
Firm A’s
price(qA)
Comparisons and Antitrust
Considerations
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As shown in Figure 14-2, the Nash
equilibrium is somewhere between perfect
competition and monopoly.
Perfectly competitive firms would set P = 0
and Q = 120 with profit = 0.
On the other hand, the monpoly would
maximize profit by producing Q = 60 with a
price = $60 and profits (revenue) = $3600.
The Bertrand Model
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Bertrand Model: An oligopoly model in
which firms simultaneously choose
prices for a homogeneous product.
Bertrand Paradox: result that the Nash
equilibrium in the Bertrand model is the
same as in perfect competition.
FIGURE 14-3: Bertrand Model with
Differentiated Product
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Figure 14-3 shows what the graphical solution
tends to look like in the typical Bertrand game
with differentiated products.
Best-response functions show the profitmaximizing price for each firm given a price
charged by its competitor.
The upward-sloping best-response functions are
in contrast to the Cournot case.
FIGURE 14-3: Bertrand Model with
Differentiated Product
Firm B’s
price (PB)
Firm A’s
best-response
function
Firm B’s
best-response
function
P*B
Nash
equilibrium
0
19
P*A
Firm A’s
price (PA)
FIGURE 14-4: Increase in Product
Differentiation Softens Price Competition
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In Figure 14-4 two firms produce
moderately differentiated products.
If the differentiation between the firms’
products increases, the best-response
functions shift out to BR’A and BR’B.
The Nash equilibrium shifts to one
involving higher prices.
FIGURE 14-4: Increase in Product
Differentiation Softens Price Competition
BRA
Firm B’s
price (PB)
BR’A
BR’B
P**B
BRB
P*B
Shift in
Nash
equilibrium
0
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P*A
P**A
Firm A’s
price (PA)
Product Selection
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There are two offsetting effects at work in the first-stage
product-characteristics game.
One effect is that firms prefer to locate near the greatest
concentration of consumers because that is where
demand is greatest.
There is an offsetting strategic effect. Firms realize that
if their products are close substitutes, they will compete
aggressively in the second-stage price game.
An increase in product differentiation between the two
firms shifts their best-response functions out and leads
to a Nash equilibrium with higher prices for both.
Search Costs
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Prices may differ across goods if products are
differentiated.
Prices may differ even across homogeneous
products if consumers are not fully informed
about price.
A search cost is the cost to the consumer in
terms of time, effort, telephone or Internet tolls,
and/or fuel costs to contact a store to learn the
price it changes for the good.
There are many possible outcomes, depending
on exactly how search costs are specified.
Advertising
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Advertising can be classified into two types.
A first type, informative advertising, provides
“hard” information about prices, product
attributes, and perhaps store locations and
hours of operation.
A second type of advertising, persuasive
advertising, attempts to convince consumers to
buy one product rather than another close－
perhaps perfect－substitute.
公平交易法
第十四條(聯合行為之禁止、例外許可及其核駁期限 )
事業不得為聯合行為。但有左列情形之一，而有益於整體經濟與公共利益，經申
請中央主管機關許可者，不在此限：
一、為降低成本、改良品質或增進效率，而統一商品規 格或型式者。
二、為提高技術、改良品質、降低成本或增進效率，而 共同研究開發商品或市場
者。
三、為促進事業合理經營，而分別作專業發展者。
四、為確保或促進輸出，而專就國外市場之競爭予以約 定者。
五、為加強貿易效能，而就國外商品之輸入採取共同行 為者。
六、經濟不景氣期間，商品市場價格低於平均生產成本， 致該行業之事業，難以
繼續維持或生產過剩，為有 計畫適應需求而限制產銷數量、設備或價格之共
同 行為者。
七、為增進中小企業之經營效率，或加強其競爭能力所 為之共同行為者。
中央主管機關收受前項之申請，應於三個月內為核駁之決定；必要時得延長一次。
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Tacit Collusion with Indefinite
Time Horizon
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If firm A continues with collusive equilibrium, it
earns its share of monopoly profit (M/2) forever.
Because the present value of the stream of
profits in the collusive equilibrium is given by:
M 1
14.12

2 r
Cheating will be unprofitab le if
M 1
14.13
M 

2 r
Generalizations and Limitations
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Extending the analysis to allow for any number of
firms, N, the profit from deviating would be the
same as before M.
The present profit from continuing with the
collusive equilibrium becomes:
M
1
14.14

N r
The new condition for cheating to be unprofitab le becomes
M
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M
1


N r
14.15
First-Mover Advantages
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Using the Cournot model where market demand is given
by Q = 120 – P and using backward induction solves for
B’s best-response function:
120  q A
qB 
.
2
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And solving for P allows A to compute the net demand
for its own product:
qA
P  60  .
2
28
[14.16]
[14.18]
FIGURE 14-5: Stackelberg
Equilibrium and Entry Deterrence
120
Firm B’s
price(qB)
Firm A’s bestresponse function
Firm B’s bestresponse function
60
Nash equilibrium of Cournot game
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Stackelberg equilibrium
Entry-deterring output
0
29
40
60
120
Firm A’s
price(qA)
Figure 14-6: Entry Game with
Incomplete Information
.
Nature
Probability ½
A high cost
.
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Probability ½
A low cost
.
B
No entry
Entry
No entry
4, 0
1, 3
6, 0
B
Entry
3, -1
個案研究---掠奪性定價
民國69年時，景泰玻璃公司進入台灣壓花玻璃市
場，帶給台灣玻璃公司與新竹玻璃公司兩家主要
玻璃廠商很大的壓力。為了保有市場，台玻與新
玻與景泰從民國70年開始了價格戰，每箱壓花玻
璃由約新台幣800元降至約700元。結果迫使新進
的景泰玻璃公司停工，最後於72年台玻及新玻以
新台幣1億5千萬元收購景泰玻璃公司。而在景泰
玻璃公司退出市場後，壓花玻璃的價格每箱即暴
漲至新台幣900餘元。
資料來源：產業經濟學，蕭峰雄著。
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Price Leadership Model
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A model in which one dominant firm takes
reactions of all other firms into account in
its output and pricing decisions is the
price leadership model.
A formal model assumes the industry is
composed of a single price-setting leader
and a competitive fringe which is a group
of firms that act as price takers.
表 14.3 91年1月至92年2月中油與台塑
調整油價情形
產業經濟學—陳正倉、林惠玲、陳忠榮、莊春發著
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Price Leadership Model
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This model is shown in Figure 14-7.
The demand curve D represents the total
demand curve for the industry’s product.
The supply curve SC represents the
supply decisions of all the firms in the
competitive fringe.
Price Leadership Model
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The demand curve (D’) for the dominant
firm is derived as follows:
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For a price of P1 or above the competitive
fringe will supply the entire market.
For a price of P2 or below, the dominant
firm will supply the entire market.
Between P2 and P1 the curve D’ is
constructed by subtracting what the fringe
will supply from the total market demand.
FIGURE 14-7: Formal Model of
Price-Leadership Behavior
Price
SC
P1
D’
P
2
D
0
36
Quantity
per week
Price Leadership Model
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Given D’, the leader’s marginal revenue
curve is MR’ which equals the leader’s
marginal cost (MC) at the profit
maximizing level QL.
Market price is PL and equilibrium output is
QT (= QC + QL).
The model does not explain how the
leader is chosen.
FIGURE 14-7: Formal Model of
Price-Leadership Behavior
Price
SC
P1
D’
P
P
L
2
MC
MR’
0
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Q
C
Q Q
L
T
D
Quantity
per week
Monopolistic Competition
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Monopolistic competition is a market in
which each firm faces a negatively sloped
demand curve and there are no barriers to
entry.
This type of market is illustrated in Figure
14-8.
FIGURE 14-8: Monopolistic
Competition
Price,
costs
d
mr
MC
AC
P*
0
40
q*
Quantity
per week
Monopolistic Competition
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Initially the demand curve is d, marginal
revenue is mr, and q* is the profitmaximizing output level.
If entry is costless, the entry shifts the
firm’s demand curve inward to d’ where
profits are zero.
At output level q’, average costs are not
minimum, and qm - q’ is excess capacity.
FIGURE 14-8: Monopolistic
Competition
Price,
costs
d
mr
MC
AC
d’
P*
P’
mr’
0
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q’
q* qm
Quantity
per week
Barriers to Entry
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The existence of barriers to entry change
the type of analysis.
In addition to those previously discussed,
barriers include brand loyalty and
strategic pricing.
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Firms may drive out potential entrants with
low prices followed later by price increases or
they may buy up smaller firms.