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© Pilot Publishing Company Ltd. 2005
Chapter 9Price-taking Model
© Pilot Publishing Company Ltd. 2005
• 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
Contents:
© Pilot Publishing Company Ltd. 2005
• Advanced Material 9.1• Advanced Material 9.2
Contents:
© Pilot Publishing Company Ltd. 2005
Market
© Pilot Publishing Company Ltd. 2005
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.
© Pilot Publishing Company Ltd. 2005
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.
© Pilot Publishing Company Ltd. 2005
A price-searcher : is a participant who
can affect the market price
has to search for the wealth-maximizing price.
Price-searching markets
• 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 number of sellers
3. Perfect/Imperfect information
2. Homogeneous/Heterogeneous goods
4. Free/Restricted entry and exit
Large
Homogeneous
Perfect
Free
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Violation of conditions
The market with only one seller is a _________.
The market dominated by a few large sellers is an __________.
The market with a large number of small sellers but selling heterogeneous goods or having imperfect information is a ______________________.
monopoly
oligopoly
monopolistic competition
(Options: monopolistic competition / oligopoly / monopoly)
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Demand and Revenue Curves of a Price-taker
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q
$
0
d
The demand curve faced by a price-taker is ___________ at the prevailing market price.
Demand curveA 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?
horizontal
(Options: vertical / horizontal)
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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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q
$
0
= d
Its MR curve and AR curve are __________ at the prevailing market price.
MR = AR
MR and AR curveA price-taker cannot influence the market price. What will be the shape of its MR curve & AR curve?
They coincide with the demand curve. (Options: vertical / horizontal)
horizontal
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Equilibrium of
a Wealth-maximizing Firm
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MC
MR
q
$
0
Loss
Gain
q*q’
Output below q’:
MR < MC
Loss incurred
Derivation:Output between q’and q*:
MR > MC
Wealth in producing them
Output beyond q*:
MR < MC
Wealth in producing them Loss
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1. MR = MC1. MR = MCMC
MR
q
$
0
Loss
Gain
q*q’
Wealth-maximizing output
Equilibrium conditions
3. In the short run, AR AVC and in the long run, AR LRAC
3. In the short run, AR AVC and in the long run, AR LRAC
2. MC curve cuts MR curve from below
2. MC curve cuts MR curve from below
Loss
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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 wealth-maximizing.
(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
The loss if suspend production = TFC= AFC^ x q^= (ATC^ -AVC^) x q^
D^= MR^=AR^
q
$
0
MC
ATC
AVC
ATC^
AVC^
P^
q^
Suspend production
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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
ATC0
P0= AVC0
q0
d0 = MR0 = AR0
q
$
0
MC ATC
AVC
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q
$
0
d1 = MR1 =AR1
MCATC
AVC
ATC1
AVC1
q1
P1
Wealth-maximizing output level at a price above AVC but below ATC
Produce at q1
The loss if produce at q1 < TFC
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q
$
0
d2 = MR2 = AR2
MC
ATC
AVC
ATC2
AVC2
q2
P2
The net receipt if produce at q2
Produce at q2
Wealth-maximizing output level at a price above ATC
© Pilot Publishing Company Ltd. 2005
q
$
0
ATC
AVC
q0
P0
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
For P > min. AVC, the supply curve coincides with the MC curve.
© Pilot Publishing Company Ltd. 2005
P
qa0
sa
qa1
P1
Firm a
Short run market supply curve of a price-taking industry
…
P
Q0
S
Q1
Market
P1
++
P
qb0
sb
qb1
Firm b
P1 …
© Pilot Publishing Company Ltd. 2005
Determination of the equilibrium price
$
Q0
S
D
P*
Q*
The equilibrium price is determined by the intersection point of the market demand and the market supply curves.
The equilibrium price is determined by the intersection point of the market demand and the market supply curves.
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Long-run Model
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MR=AR
$
P
q0
LRMC
LRAC
Long run adjustment
1. Producing at the output where MR equates LRMC
MR = LRMC
q
LRMC curve cuts MR curve from below
AR LRAC
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At q’ (MR = LRMC)
AR’ > LRAC’
Positive net receipt
New firms enter S & P
q
$
0
MR’=AR’P’
q’
LRMC
LRAC
2. Entry and exit until zero net receipt and production at the optimum scale are attained
Positive Net Receipt
Positive Net Receipt
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At q’’ (MR = LRMC) AR’’ < LRAC’’
Negative net receipt
Some firms leave. S & P
P’’
q
$
0
MR’’=AR’’
q’’
LRMC
LRAC
Negative Net Receipt
Negative Net Receipt
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At q* (MR =
LRMC), AR* = LRAC*
Zero net receipt
No entry nor exit
Long run equilibrium Long run equilibrium Long run equilibrium Long run equilibrium
q
$
0
MR*=AR*P*
LRMCLRAC*
q*
© Pilot Publishing Company Ltd. 2005
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
three kinds of long-run market supply curves can be derived:
• According to the relationship between LRAC and Q,
1. constant-cost
2. decreasing-cost
3. increasing-cost
© Pilot Publishing Company Ltd. 2005
q
$
0
S2: Constant-cost industry
S3: Decreasing-cost industry
S1: Increasing-cost industry
Long-run market supply curve
© Pilot Publishing Company Ltd. 2005
Q
P
0
D
LRAC
P*
Qdqs
Number of firms in a price-taking market
Number of identical firms in the industry = Qd /qs
Number of identical firms in the industry = Qd /qs
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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
Production efficiency is attained when
– defining the criterion of “how to produce”
then, it will be impossible to raise the output of any good without reducing the outputs of others.
goods are produced at the minimum cost.
© Pilot Publishing Company Ltd. 2005
• 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
Consumption efficiency is attained when
– defining the criterion of “for whom to produce”
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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MUVs of all individuals consuming the same goods are equal.
• Conditions of consumption efficiency (consumption by individuals with the highest MUV):
Why?
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3. Allocative efficiency
Allocative efficiency is attained when
– defining the criterion of “what to produce”
resources are allocated to their highest-valued uses.
then, it will be impossible to raise the TUV of all the commodities produced.
© Pilot Publishing Company Ltd. 2005
• Conditions to achieve allocative efficiency (allocated to the highest-valued uses):
MUV of each good is equal to its MC
Why?
© Pilot Publishing Company Ltd. 2005
Situation in a price-taking industry:
• 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.
• To maximize wealth, firms have to minimize cost. So they must use the cost-minimizing production methods in their production.
Behaviours of producers
© Pilot Publishing Company Ltd. 2005
Consumption efficiency is also achieved.
To maximize utility, individuals consume the amount at which MUV = P.
Situation in price-taking industry:
As individuals face the same market price, MUVs of all individuals consuming the same good are equal.
Behaviours of consumers
© Pilot Publishing Company Ltd. 2005
Allocative efficiency is achieved.
Individuals consume the quantities where MUV = P.
Situation in price-taking industry:
Allocation of resources
Firms produce the quantities where MC = P.
As they face the same market price, MUV = P = MC.
© Pilot Publishing Company Ltd. 2005
• 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.
Situation in price-taking industry:
Conclusion:
© Pilot Publishing Company Ltd. 2005
Appendix I: “Perfect competition” is a misleading term (as if other markets are less competitive)
2. “Price-taking” is a more appropriate term
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.
since individual sellers cannot affect the price.
© Pilot Publishing Company Ltd. 2005
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.
© Pilot Publishing Company Ltd. 2005
Appendix II: SupplyA. 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 ________ if expressed in the form of a curve --- supply _______
schedule
curve
© Pilot Publishing Company Ltd. 2005
S’(=MC’)
Q
P
0
S(=MC)
1. Price of a variable factor
Q
P
0
S(=MC)
S’(=MC’)
MC
S
Price of variable factor Price of variable factor
MC
S
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2. State of technology
S’(=MC’)
Q
P
0
S(=MC) Technology improvement S
MC
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3. Tax
S’(=MC’)
MC
S
q
P
0
S(=MC)
Imposition of a sales tax
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4. Subsidy
S’(=MC’)MC
S
q
P
0
S(=MC)
Imposition of a subsidy
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5. Price expectation
S’(=MC’)
S
q
P
0
S(=MC)
Supplier expect the future price
Present supply
Why?
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6. Weather and climate
S’(=MC’)
S
q
P
0
S(=MC)
Bad weathere.g. a typhoon
S of vegetables
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7. Price of related goods (joint supply)
Px2
X2
PY
Y0
Pork chopPx
X0
Px1
X1
Pork
SxSY1 SY2
Why?
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Px
X0
Sx
Px1
X1
PY
Y0
SY1Px2
X2
SY2
8. Price of related goods (competitive supply)
Fruits Vegetables
Why?
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Price elasticity of supply (pEs)
A. What is elasticity of supply?
pricein %
suppliedquantity in %Esp
is a measure of the responsiveness of the quantity supplied of a good to a change in its price.
Appendix III: Elasticity of Supply
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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
Point elasticity of supply
Arc elasticity of supply
1. According to the formula adopted in calculation
applied when the % Δ is very small
applied when the % Δ is not very small
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Δ X
ΔPx
P
P1
O X1
X
A
B
CTangent at point A
S
Point elasticity of supply--- non-linear supply curve
pEs at point A:
Graphical measure:
OX
BX
CP
OP
AC
AB
1
1
1
1 OX
BX
CP
OP
AC
AB
1
1
1
1
1
1
X
P
P
X
1
1
X
P
P
X
Mathematical measure:
© Pilot Publishing Company Ltd. 2005
SP
P1
O X1
X
A
B
C
Δ X
ΔPx
Point elasticity of supply --- linear supply curve
1
1
X
P
P
X
1
1
X
P
P
X
Mathematical measure:
pEs at point A:
Graphical measure:
OXBX
CPOP
ACAB
1
1
1
1 OXBX
CPOP
ACAB
1
1
1
1
© Pilot Publishing Company Ltd. 2005
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
2. Time for adjustment
3. Ease of entry and exit
4. Size of stock
5. Ease of storage
Production method Mobility of factors Production time required
© Pilot Publishing Company Ltd. 2005
$
q0
TC TR
TFC
Short run Short run
Advanced Material 9.1
Equilibrium by TR curve and TC curve
Largest net receipt
Slope = MC
Slope = MR
Notice:
At q*, MR = MC where the distance between TR & TC (= net receipt) is the largest.
Notice:
At q*, MR = MC where the distance between TR & TC (= net receipt) is the largest.
q*Wealth-maximizing output
© Pilot Publishing Company Ltd. 2005
Long run Long run Long run Long run $
q0
TREquilibrium by TR and TC curves
Wealth-maximizing output
q*
MC2
MC*
MC1
MR
q1 q2
At q1, MR>MC1, production raises net receipt.
At q2, MR<MC2, production reduces net receipt.
At q*, MR=MC*, net receipt is the largest.
The largest net receipt
© Pilot Publishing Company Ltd. 2005
Original net receipt
Advanced Material 9.2Marginal firms and infra-marginal firms
LRAC’ (under competition, factor incomes of superior factors rise and absorb the original net receipt)
q0
$
q0
LRMC
LRACP
1. Absorption of net receipts by superior factors
An established firm with superior factors
© Pilot Publishing Company Ltd. 2005
2. Classification of firms according to their responses to a fall in price
_____________________ are firms that do not have superior factors and they leave the industry even if the market price falls by a very small amount.
______________________ are firms that have superior factors and they leave the industry only if the market price falls drastically.
(Options: Marginal firms / Infra-marginal firms)
Marginal firms
Infra-marginal firms
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3. When price falls, some firms instead of all will leave
1. If resources are ________________, marginal firms would be the first to leave.
2. If resources are _______________, which firm will leave first is by random selection.
(Options: homogeneous / heterogeneous)
heterogeneous
homogeneous
Price some firms leave supply price until it reaches the mini. LRAC remaining firms can stay
4. The first firm to leave
© Pilot Publishing Company Ltd. 2005
Correcting Misconceptions:
1. The market demand curve faced by a price-taking industry is horizontal.
2. The short-run supply curve of a price-taker is its MC curve.
3. The equilibrium condition of a wealth-maximizing firm is TR = TC.
© Pilot Publishing Company Ltd. 2005
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.
Correcting Misconceptions:
© Pilot Publishing Company Ltd. 2005
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.
Correcting Misconceptions:
© Pilot Publishing Company Ltd. 2005
Survival Kit in ExamQuestion 9.1 :Explain why the equilibrium of a price-taking industry is efficient. Use a demand-supply diagram to explain.