© Pilot Publishing Company Ltd. 2005 Chapter 9 Price-taking Model.

© Pilot Publishing Company Ltd. 2005

Chapter 9Price-taking Model


• 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:


• Advanced Material 9.1• Advanced Material 9.2

Contents:


Market


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.


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.


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


Conditions of a Price-Taking Market


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


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)


Demand and Revenue Curves of a Price-taker


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)


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.


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


Equilibrium of

a Wealth-maximizing Firm


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


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


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.


Short-run Model


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


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


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


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


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.


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 …


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.


Long-run Model


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


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


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


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*


Long run market supply curve

In the long-run equilibrium,

P always equates the minimum LRAC.



• The long-run market supply curve (relating P to Q) is actually relating

the minimum LRAC to Q.



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


q

$

0

S2: Constant-cost industry

S3: Decreasing-cost industry

S1: Increasing-cost industry

Long-run market supply curve


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


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.


Efficiency &

Price-taking Market


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)


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).


Allocation of resources involves three basic economic problems:

1. what to produce?

2. how to produce?

3. for whom to produce?


Correspondingly, three efficiency conditions are defined:

1. production efficiency

2. consumption efficiency

3. allocative efficiency


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.


• 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?


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.


MUVs of all individuals consuming the same goods are equal.

• Conditions of consumption efficiency (consumption by individuals with the highest MUV):

Why?


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.


• Conditions to achieve allocative efficiency (allocated to the highest-valued uses):

MUV of each good is equal to its MC

Why?


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


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


Allocative efficiency is achieved.

Individuals consume the quantities where MUV = P.


Allocation of resources

Firms produce the quantities where MC = P.

As they face the same market price, MUV = P = MC.


• 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.


Conclusion:


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.


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.


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


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


2. State of technology

S’(=MC’)

Q

P

0

S(=MC) Technology improvement S

MC


3. Tax

S’(=MC’)

MC

S

q

P

0

S(=MC)

Imposition of a sales tax


4. Subsidy

S’(=MC’)MC

S

q

P

0

S(=MC)

Imposition of a subsidy


5. Price expectation

S’(=MC’)

S

q

P

0

S(=MC)

Supplier expect the future price

Present supply

Why?


6. Weather and climate

S’(=MC’)

S

q

P

0

S(=MC)

Bad weathere.g. a typhoon

S of vegetables


7. Price of related goods (joint supply)

Px2

X2

PY

Y0

Pork chopPx

X0

Px1

X1

Pork

SxSY1 SY2

Why?


Px

X0

Sx

Px1

X1

PY

Y0

SY1Px2

X2

SY2

8. Price of related goods (competitive supply)

Fruits Vegetables

Why?


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


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


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


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:


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


Q9.8:The supply of new residential flats is inelastic. List all possible reasons.


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


$

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


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


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


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


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


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.


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.



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.



Survival Kit in ExamQuestion 9.1 :Explain why the equilibrium of a price-taking industry is efficient. Use a demand-supply diagram to explain.

© Pilot Publishing Company Ltd. 2005 Chapter 9 Price-taking Model.

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Transcript of © Pilot Publishing Company Ltd. 2005 Chapter 9 Price-taking Model.