Download Ch 9 Price-taking model

Chapter 9
Price-taking Model
© Pilot Publishing Company Ltd. 2005
Contents:
• Market
• Conditions of a Price-taking Market
• Demand and Revenue Curves of a Price-taker
• Equilibrium of a Wealth-Maximizing Firm
• Short Run Model
• Long Run Model
• Efficiency and Price-taking Market
• Appendix I
• Appendix II
• Appendix III
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Contents:
• Advanced Material 9.1
• Advanced Material 9.2
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Market
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What is a market?
A market (市場) is a system governed by
a set of rules or customs under which
a well-defined good is exchanged.
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Price-taking markets
A price-taker: is a participant who
 cannot affect the market price
 has to take (accept) whatever price that the
market determines.
• To a price-taker,
the market is a price-taking market or
a perfectly competitive market.
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Price-searching markets
A price-searcher : is a participant who
 can affect the market price
 has to search for the wealth-maximizing price.
• To a price-searcher,
 the market is a price-searching market or an
imperfectly competitive market
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Conditions of a Price-Taking Market
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Conditions of a price-taking market
1. Large/Small
Large number of sellers
2. Homogeneous/Heterogeneous
Homogeneous
goods
3. Perfect/Imperfect
information
Perfect
4. Free/Restricted
entry and exit
Free
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Violation of conditions
The market with only one seller is a _________.
monopoly
The market dominated by a few large sellers is an
__________.
oligopoly
The market with a large number of small sellers but
selling heterogeneous goods or having imperfect
monopolistic competition
information is a ______________________.
(Options: monopolistic competition / oligopoly / monopoly)
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Demand and Revenue Curves
of a Price-taker
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Demand curve
A price-taker cannot influence the market price. The price is
a constant irrespective of its quantity supplied. What is the
shape of its demand curve?
$
d
The demand curve
faced by a price-taker is
___________
horizontal at the
prevailing market price.
(Options: vertical / horizontal)
0
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q
Q9.2:
“As the demand curve faced by a price-taker is horizontal,
the market demand curve, which is the horizontal sum of
all individual demand curves, must also be horizontal.”
Discuss.
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MR and AR curve
A price-taker cannot influence the market price.
What will be the shape of its MR curve & AR curve?
$
horizontal
Its MR curve and AR curve are __________
at the prevailing market price.
They coincide with the demand curve.
(Options: vertical / horizontal)
MR = AR = d
0
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q
Equilibrium
of
a Wealth-maximizing Firm
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Output between
q’and
Output
beyond
Output below q*:
q’:
Derivation:
q*:
MR
< <MC
MR
MC
MR > MC
$
Loss
Wealth
 inin
Loss incurred
Wealth

them
Loss MC producing
producing them
MR
Gain
0
q’
q*
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q
Equilibrium conditions
1. MR = MC
$
Loss
Loss MC
2. MC curve cuts
MR curve from
below
MR
Gain
0
q’
q*
Wealth-maximizing
output
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q
3. In the short run,
AR  AVC and
in the long run,
AR  LRAC
Q9.3:
(a) At q*, MR = MC. The marginal gain is zero.
Explain why it is wealth-maximizing.
(b) At q’, MR = MC. Explain why it is not wealthmaximizing.
(c) In the short run, if ATC > AR > AVC, explain
why the output is still worth to be produced.
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Short-run Model
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Wealth-maximizing output level
at a price below AVC
Suspend production
$
The loss if
ATC^
suspend
production =
AVC^
TFC
= AFC^ x q^
= (ATC^ P^
AVC^) x q^
0
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MC
ATC
AVC
q^
D^=
MR^=AR^
q
Wealth-maximizing output level
at a price equal to AVC
Produce at q0
$
The loss if
produce at q0
= TFC
= AFC0 x q0
= (ATC0 AVC0) x q0
MC
ATC
ATC0
AVC
P0=
AVC0
0
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d0 = MR0
= AR0
q0
q
Wealth-maximizing output level
at a price above AVC but below ATC
$
The loss if
produce at
q1 < TFC
MC
ATC
ATC1
P1
d1 = MR1
=AR1
AVC
AVC1
Produce at q1
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0
q1
q
Wealth-maximizing output level
at a price above ATC
$
The net receipt
if produce at q2
MC
d2 = MR2 = AR2
P2
ATC
ATC2
AVC
AVC2
Produce at q2
0
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q2
q
Short run supply curve of a price-taker
For P < min. AVC,
Qs = 0 units. The supply
curve coincides with the
y-axis.
$
Supply
Curve
ATC
AVC
For P > min. AVC, the P
0
supply curve coincides
with the MC curve.
0
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q0
q
Short run market supply curve of
a price-taking industry
P
P
P
sa
P1
0
S
sb
P1
…
+
qa1 qa
Firm a
0
qb1 qb
Firm b …
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P1
0
Q1
Market
Q
Determination of the equilibrium price
$
The equilibrium price
is determined by the
intersection point of
the market demand
and the market supply
curves.
S
P*
0
D
Q*
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Q
Long-run Model
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Long run adjustment
1. Producing at the output where MR equates LRMC
MR = LRMC
LRMC curve cuts
MR curve from
below
$
LRMC
LRAC
P
MR=AR
AR  LRAC
0
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q
q
2. Entry and exit until zero net receipt and
production at the optimum scale are attained
$
P’
At q’ (MR = LRMC)
AR’ > LRAC’
LRMC
Positive
Net Receipt
LRAC


MR’=AR’
Positive net receipt
New firms enter
S & P 
0
q’
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q
$
Negative
Net Receipt
At q’’ (MR = LRMC)
AR’’ < LRAC’’
LRMC
LRAC

P’’
0

MR’’=AR’’
q’’
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Negative net receipt
Some firms leave.
S  & P
q
At q* (MR = LRMC),
AR* = LRAC*
$
LRMC
LRAC*
P*
MR*=AR*
Zero net receipt
No entry nor exit
Long run equilibrium
0
q*
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q
Long run market supply curve
In the long-run equilibrium,
 P always equates the minimum LRAC.
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Long run market supply curve
• The long-run market supply curve
(relating P to Q) is actually relating
 the minimum LRAC to Q.
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Long run market supply curve
• According to the relationship between
LRAC and Q,
 three kinds of long-run market supply
curves can be derived:
1. constant-cost
2. decreasing-cost
3. increasing-cost
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Long-run market supply curve
$
S1: Increasing-cost industry
S2: Constant-cost industry
S3: Decreasing-cost industry
0
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q
Number of firms in a price-taking market
P
Number of identical firms
in the industry = Qd /qs
LRAC
P*
D
0
qs
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Qd
Q
Q9.6:
After an increase in market demand,
predict what would happen to a price-taking industry
in both the short run and the long run
– number of firms, price, quantity supplied and
net receipt.
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Efficiency
&
Price-taking Market
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Pareto efficiency
Pareto optimality or efficiency is attained if
 it is impossible to reallocate resources to make
an individual gain (better off)
 without making other individuals lose (worse off)
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Pareto efficiency
Inefficiency occurs if
 it is possible to reallocate resources to
make an individual gain (better off) without
making other individuals lose (worse off).
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Allocation of resources involves three basic
economic problems:
1. what to produce?
2. how to produce?
3. for whom to produce?
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Correspondingly, three efficiency conditions
are defined:
1. production efficiency
2. consumption efficiency
3. allocative efficiency
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1. Production efficiency
– defining the criterion of “how to produce”
Production efficiency is attained when
 goods are produced at the minimum cost.
 then, it will be impossible to raise the
output of any good without reducing the
outputs of others.
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• Conditions of production efficiency
(production at the minimum cost):
 All firms use cost-minimizing production
methods to produce.
 MCs of all firms producing the same good
are equal.
Why?
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2. Consumption efficiency
– defining the criterion of “for whom to produce”
Consumption efficiency is attained when
 goods are consumed by individuals with
the highest MUV.
 then, it will be impossible to raise TUV of
any individual without reducing TUVs of
others.
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• Conditions of consumption efficiency
(consumption by individuals with the highest MUV):
 MUVs of all individuals consuming the
same goods are equal.
Why?
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3. Allocative efficiency
– defining the criterion of “what to produce”
Allocative efficiency is attained when
 resources are allocated to their
highest-valued uses.
 then, it will be impossible to raise the
TUV of all the commodities produced.
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• Conditions to achieve allocative efficiency
(allocated to the highest-valued uses):
 MUV of each good is equal to its MC
Why?
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Situation in a price-taking industry:
Behaviours of producers
• To maximize wealth, firms have to minimize cost. So
they must use the cost-minimizing production methods in
their production.
• To maximize wealth, firms produce the output at
which MC = MR = P. As they face the same price,
MCs of all firms producing the same good are equal.
Production efficiency is achieved.
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Situation in price-taking industry:
Behaviours of consumers
 To maximize utility, individuals consume the amount
at which MUV = P.
 As individuals face the same market price,
MUVs of all individuals consuming the same good
are equal.
Consumption efficiency is also achieved.
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Situation in price-taking industry:
Allocation of resources
 Individuals consume the quantities where MUV = P.
 Firms produce the quantities where MC = P.
 As they face the same market price, MUV = P = MC.
Allocative efficiency is achieved.
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Situation in price-taking industry:
Conclusion:
• In price-taking markets, resource allocation is efficient.
• This is achieved without any government intervention
nor guidance from visible hands.
• Individuals & firms make their own decisions
according to the market price (the invisible hand)
adjusted under the market mechanism.
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Appendix I: “Perfect competition” is a misleading term
(as if other markets are less competitive)
1. Under scarcity & maximization
 “severe” competition exists in all kinds of markets
 e.g., monopoly --- compete for the monopoly right,
against potential entrants, against takeover, with producers
of substitutes, factor suppliers and consumers, etc.
2. “Price-taking” is a more appropriate term
 since individual sellers cannot affect the price.
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Appendix II: Supply
A. Quantity supplied and supply
• Quantity supplied
 is the amount that a supplier is willing and able to sell
at a certain price within a certain period of time.
 at different prices, the supplier is willing to sell
different quantities.
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Appendix II: Supply
A. Quantity supplied and supply
• Supply
 describes the relationship between the price and
the quantity supplied of a good.
 if expressed in the form of a table --- supply ________
schedule
curve
 if expressed in the form of a curve --- supply _______
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1. Price of a variable factor
Price of variable factor 
P
S’(=MC’)
Price of variable factor 
P
S(=MC)
MC 
S(=MC)
S S’(=MC’)
MC
S
0
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Q
0
Q
2. State of technology
P
Technology
improvement
S(=MC)
S
S’(=MC’)
MC
0
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Q
3. Tax
P
Imposition of a
sales tax
S’(=MC’)
MC
S(=MC)
S
0
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q
4. Subsidy
Imposition of
S(=MC) a subsidy
P
S
S’(=MC’)
MC
0
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q
5. Price expectation
P
 Supplier expect
the future price 
S’(=MC’)
S(=MC)
S
0
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
Present supply 
q
Why?
6. Weather and climate
P
 Bad weather
e.g. a typhoon
S’(=MC’)
S(=MC)
S
0
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q

S of vegetables 
7. Price of related goods (joint supply)
Px
Pork
PY
Sx
Px2
Pork chop
SY1
SY2
Px1
Why?
0
X1
X2
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X0
Y
8. Price of related goods (competitive supply)
Px
Fruits
PY
Sx
Px2
Vegetables
SY2
SY1
Px1
Why?
0
X1
X2
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X
0
Y
Appendix III: Elasticity of Supply
A. What is elasticity of supply?
Price elasticity of supply (pEs)
 is a measure of the responsiveness of the quantity supplied
of a good to a change in its price.
%  in quantity supplied
p Es 
%  in price
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2. According to the size of elasticity
Perfectly inelastic
Es = 0
%Δin quantity
supplied of X = 0
Inelastic
Es < 1
%Δin X < %  in P
Unitarily elastic
Es = 1
%Δin X = %  in P
Elastic
Es > 1
%Δin X > %  in P
Perfectly elastic
Es = infinity %Δin X = infinity
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B.Classification of price elasticities of supply
1. According to the formula adopted in calculation
 Point elasticity of supply
 applied when the % Δ is very small
 Arc elasticity of supply
 applied when the % Δ is not very small
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Point elasticity of supply--- non-linear supply curve
P
X
P1

P
X1
ΔPx
A
P1
 Mathematical measure:
S
ΔX
 Graphical measure:
C
pEs
Tangent at point A
B
O
X1
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X
at point A:
AB
P1O
X1B


AC
P1C
X1O
Point elasticity of supply --- linear supply curve
 Mathematical measure:
P
X
P1

P
X1
S
ΔPx
A
P1
ΔX
 Graphical measure:
C
B
pEs
O
X1
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X
at point A:
AB
P1O
X1B


AC
P1C
X1O
Q9.8:
The supply of new residential flats is inelastic.
List all possible reasons.
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Determinants of elasticity of supply
1. Flexibility of production
 Production method
 Mobility of factors
 Production time required
2. Time for adjustment
3. Ease of entry and exit
4. Size of stock
5. Ease of storage
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Advanced Material 9.1
Equilibrium by TR curve and TC curve
$
TC
Short run
Slope = MR
Largest net
receipt
Slope = MC
TFC
0
TR
Notice:
At q*, MR = MC
where the
distance between
TR & TC
(= net receipt)
is the largest.
q
q*
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Wealth-maximizing output
Equilibrium by TR and TC curves
$
TR
 At q1, MR>MC1,
Long run
production raises
MR
MC2
The largest
net receipt
MC*
0
MC1
q1
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q*
q2
q
net receipt.
 At q2, MR<MC2,
 production
reduces net receipt.
 At q*, MR=MC*,
net receipt is the
largest.
Wealth-maximizing output
Advanced Material 9.2
Marginal firms and infra-marginal firms
1. Absorption of net receipts by superior factors
$
Original LRMC LRAC’ (under competition,
factor incomes of superior
net receipt
factors rise and absorb the
original net receipt)
P
LRAC
0
q0
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q
An established firm with
superior factors
2. Classification of firms according to their responses to
a fall in price
Marginal firms
_____________________
are firms that do not have
superior factors and they leave the industry even if the
market price falls by a very small amount.
Infra-marginal firms are firms that have
______________________
superior factors and they leave the industry only if the
market price falls drastically.
(Options: Marginal firms / Infra-marginal firms)
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3. When price falls, some firms instead of all will leave
Price  some firms leave  supply  price until it
reaches the mini. LRAC  remaining firms can stay
4. The first firm to leave
1. If resources are ________________,
heterogeneous marginal firms would
be the first to leave.
homogeneous which firm will leave first
2. If resources are _______________,
is by random selection.
(Options: homogeneous / heterogeneous)
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Correcting Misconceptions:
1. The market demand curve faced by a pricetaking industry is horizontal.
2. The short-run supply curve of a price-taker
is its MC curve.
3. The equilibrium condition of a wealthmaximizing firm is TR = TC.
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Correcting Misconceptions:
4. If a firm earns zero net receipt (profit), it is
not worth to produce.
5. As infra-marginal firms have superior factors
and lower production costs, they have positive
net receipts even in the long run.
6. When market price falls, all existing firms
suffer losses and they will leave the industry.
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Correcting Misconceptions:
7. After the imposition of a lump-sum tax,
a price-taker will cut its output both in
the short run and the long run.
8. Efficiency is attained if it is impossible to
reallocate resources to make an individual gain.
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Survival Kit in Exam
Question 9.1 :
Explain why the equilibrium of a price-taking
industry is efficient. Use a demand-supply
diagram to explain.
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