Chapter 10 THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL.

Chapter 10

THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL

Lee, Junqing Department of Economics , Nankai University

CONTENTS

Partial Equilibrium Analysis Market Demand Timing of the Supply Response Pricing in the Very Short Run Short-Run Price Determination Shifts in Supply and Demand Curves Mathematical Model of Supply and Demand Long-Run Analysis Shape of the Long-Run Supply Curve Comparative Statics Analysis of Long-Run

Equilibrium- industry structure Producer Surplus in the Long Run

Partial Equilibrium Analysis


General vs. Partial Equilibrium


When is Partial Equilibrium Appropriate?


When is Partial Equilibrium Not Appropriate?


The restriction of supply ?


The Four Types of Market Structure


Profit Maximization

Market Demand


Market Demand Assume that there are only two goods (x and

y)

An individual’s demand for x is

Quantity of x demanded = x(px,py,I)

If we use i to reflect each individual in the market, then the market demand curve is

1

Market demand for , ),( yx i

n

ii

x p pX

I

Same price

Different distribution


Market Demand

To construct the market demand curve, PX is allowed to vary while Py and the income of each individual and preferences are held constant

If each individual’s demand for x is downward sloping, the market demand curve will also be downward sloping


Market Demand

x xx

pxpxpx

x1* x2*

px*

To derive the market demand curve, we sum thequantities demanded at every price

x1

Individual 1’sdemand curve

x2

Individual 2’sdemand curve

Market demandcurve

X*

X

x1* + x2* = X*


Shifts in the MarketDemand Curve

The market demand summarizes the ceteris paribus relationship between X and px

changes in px result in movements along the

curve (change in quantity demanded)

changes in other determinants of the demand for

X cause the demand curve to shift to a new

position (change in demand)


Shifts in Market Demand individual 1’s demand for oranges is given by

x1 = 10 – 2px + 0.1I1 + 0.5py

and individual 2’s demand is

x2 = 17 – px + 0.05I2 + 0.5py

The market demand curve is

X = x1 + x2 = 27 – 3px + 0.1I1 + 0.05I2 + py

If py = 4, I1 = 40, and I2 = 20, the market demand curve becomes

X = 27 – 3px + 4 + 1 + 4 = 36 – 3px


Shifts in Market Demand

If py rises to 6, the market demand curve shifts outward to

X = 27 – 3px + 4 + 1 + 6 = 38 – 3px

note that X and Y are substitutes

If I1 fell to 30 while I2 rose to 30, the market

demand would shift inward to

X = 27 – 3px + 3 + 1.5 + 4 = 35.5 – 3px

note that X is a normal good for both buyers


Generalizations

Suppose that there are n goods (xi, i = 1,n) with prices pi, i = 1,n.

Assume that there are m individuals in the economy

The j th’s demand for the i th good will depend on all prices and on Ij

xij = xij(p1,…,pn, Ij)


Generalizations

The market demand function for xi is the sum of each individual’s demand for that good

11

( ,..., , )m

jij nj

i x p pX

I

The market demand function depends on the prices of all goods and the incomes and preferences of all buyers


Elasticity of Market Demand

The price elasticity of market demand is measured by

D

DPQ Q

P

P

PPQe

),',(

,

I

Market demand is characterized by whether demand is elastic (eQ,P <-1) or inelastic (0> eQ,P > -1)


Elasticity of Market Demand

The cross-price elasticity of market demand is measured by

D

DPQ Q

P

P

PPQe

'

'

),',(,

I

The income elasticity of market demand is measured by

D

DQ Q

PPQe

II

II

),',(

,


From Market Demand Curve to the demand curve faced by the firm

Timing of the Supply Response


Timing of the Supply Response In the analysis of competitive pricing, the time

period under consideration is important very short run

no supply response (quantity supplied is fixed) short run

existing firms can alter their quantity supplied, but no new firms can enter the industry

long runnew firms may enter an industry

Pricing in the Very Short Run



In the very short run (or the market period), there is no supply response to changing market conditions price acts only as a device to ration demand

price will adjust to clear the market the supply curve is a vertical line

Perishable goods and antiques



Quantity

Price

S

D

Q*

P1

D’

P2

When quantity is fixed in thevery short run, price will risefrom P1 to P2 when the demandrises from D to D’


A note

Increasing in quantity supplied need not come only from increased production

Short-Run Price Determination


Short-Run Price Determination

What’s short-run? The number of firms in an industry is fixed These firms are able to adjust the quantity

they are producingthey can do this by altering the levels of the

variable inputs they employ


Perfect Competition A perfectly competitive industry is one that

obeys the following assumptions: there are a large number of firms, each

producing the same homogeneous product, so, each firm is a price taker (its actions have no effect on the market price)

Freedom to entry and exit information is perfect transactions are costless


Short-Run Market Supply Curve

quantity Quantityquantity

PPP

q1A q1

B

P1

To derive the market supply curve, we sum thequantities supplied at every price

sA

Firm A’ssupply curve sB

Firm B’ssupply curve

Market supplycurve

Q1

S

q1A + q1

B = Q1


Short-Run Market Supply Function

The short-run market supply function shows total quantity supplied by each firm to a market

1

( , , ) ( , , )n

s ii

vv wQ wq PP

Firms are assumed to face the same

market price and the same prices for inputs


Short-Run Supply Elasticity

The short-run supply elasticity describes the responsiveness of quantity supplied to changes in market price

,

% change in supplied

% change in S

S P

S

S

S

QQ Pe

P P Q PQ

PQ

Because price and quantity supplied are positively related, eS,P > 0


Geometric Meaning of es,P


Classification of Elasticity of Supply


Equilibrium Price Determination

An equilibrium price is one at which quantity demanded is equal to quantity supplied neither suppliers nor demanders have an

incentive to alter their economic decisions An equilibrium price (P*) solves the equation:

( , )', * ,* ( , )D SQ QP PP v wI

( ( )* *)D SQ QP PThe equilibrium price depends on

many exogenous factors


Equilibrium Price Determination

Quantity

d

q’

q1

P1

Quantity

PriceS

D

Q1

P1

Q2

P2

D’

Price

output

PriceSMC

q1

P1

q

2

P2

SAC

q’d

A typical firm A typical individualThe market

q2 q’1

P2

profit

profit

The equilibrium price services two functions: first act to signal for firm to make output decision ; second ration demand for consumer

Shifts in Supply and Demand Curves


Shifts in Supply and Demand Curves

Demand curves shift because incomes change prices of substitutes or complements change preferences change

Supply curves shift because input prices change technology changes number of producers change


Shifts in Supply

Quantity Quantity

PricePriceS

S’S

S’

DD

PP

Q

P’

Q’

P’

QQ’

Elastic Demand Inelastic Demand

Small increase in price,large drop in quantity

Large increase in price,small drop in quantity


Shifts in Demand

Quantity Quantity

PricePrice

S

S

D D

P P

Q

P’

Q’

P’

Q Q’

Elastic Supply Inelastic Supply

Small increase in price,large rise in quantity

Large increase in price,small rise in quantity

D’ D’

Mathematical Model of Supply and Demand



Suppose that the demand function is represented by

QD = D(P,)

is a parameter that shifts the demand curveD/ = D can have any sign

D/P = DP < 0



The supply relationship can be shown as

QS = S(P,)

is a parameter that shifts the supply curve

S/ = S can have any sign

S/P = SP > 0

Equilibrium requires that QD = QS



To analyze the comparative statics of this model, we need to use the total differentials of the supply and demand functions:

dQD = DPdP + DddQS = SPdP + Sd

Maintenance of equilibrium requires that

dQD = dQS



Suppose that the demand parameter () changed while remains constant

The equilibrium condition requires thatDPdP + Dd = SPdP

P PS

P

D

D

Because SP - DP > 0, P/ will have the same sign as D



We can convert our analysis to elasticities

PDS

D

P

Pe

PPP

,

,

,,

,( ) S P Q

QP

PP P

ee

DQ

P e eS DQ

Long-Run Analysis


Long-Run Analysis

In the long run, a firm may adapt all of its inputs to fit market conditions profit-maximization for a price-taking firm

implies that price is equal to long-run MC Firms can also enter and exit an industry in

the long run perfect competition assumes that there are no

special costs of entering or exiting an industry


Long-Run Competitive Equilibrium conditions

Condition : A perfectly competitive industry is in long-run equilibrium zero-profit condition :

P= AC (passive):- no incentives for firms to enter or to leave the industry, ;

P = MC (active) - profit-maximizing each firm operates at minimum AC

Market clear

',( , ) ( , )* ,*D SP v wPQ QP I


Long-Run Competitive Equilibrium in constant-cost industry

We will assume that all firms in an industry have identical cost curves no firm controls any special resources or

technology

Assume that the entry of new firms in an industry has no effect on the cost of inputs constant-cost industry


Long-Run Equilibrium: Constant-Cost Case

A Typical Firm Total MarketQuantity Quantity

SMC MC

AC

S

D

q1

P1

Q1

Initial equilibrium:This is a long-run equilibrium for this industry

P = MC = ACPrice Price



A Typical Firm Total Market

q1 Quantity Quantity

SMC MC

AC

S

D

P1

Q1

P2

Market price rises to P2

Q2

Suppose that market demand rises to D’

D’

Price Price





SMC MC

AC

S

D

P1

Q1

D’

P2

Economic profit > 0

Q2

In the short run, each firm increases output to q2

Or in the long run for this firm ,this firm increase more than output of q2

q2

Price Price





SMC MC

AC

S

D

P1

Q1

D’

Economic profit will return to 0

Q3

In the long run, new firms will enter the industry

S’

PricePrice





SMC MC

AC

S

D

P1

Q1

D’

Q3

S’

The long-run supply curve will be a horizontal line (infinitely elastic) at p1

LS

Price Price

Shape of the Long-Run Supply Curve


Shape of the Long-Run Supply Curve

The zero-profit condition is the factor that determines the shape of the long-run cost curve if average costs are constant as firms enter, long-

run supply will be horizontal if average costs rise as firms enter, long-run

supply will have an upward slope if average costs fall as firms enter, long-run

supply will be negatively sloped


Long-Run Equilibrium: Increasing-Cost Industry

Reason :The entry of new firms may cause the average costs of all firms to rise prices of scarce inputs may rise new firms may impose “external” costs on

existing firms new firms may increase the demand for tax-

financed services



A Typical Firm (before entry) Total Market


SMC MC

AC

S

D

P1

Q1

Suppose that we are in long-run equilibrium in this industry

P = MC = ACPricePrice





SMC MC

AC

S

D

P1

Q1


D’

P2

Market price rises to P2 and firms increase output to q2

Q2q2

Price Price


SMC MC

AC


A Typical Firm (after entry) Total MarketQuantity Quantity

SMC’ MC’

AC’

S

D

P1

Q1

D’

q3

P3

Entry of firms causes costs for each firm to rise

Q3

Positive profits attract new firms and supply shifts out

S’

Price Price



A Typical Firm (after entry) Total Market


SMC’ MC’

AC’

S

D

p1

Q1

D’

p3

Q3

S’

The long-run supply curve will be upward-sloping

LS

Price Price


Long-Run Equilibrium: Decreasing-Cost Industry

Reason :The entry of new firms may cause the average costs of all firms to fall new firms may attract a larger pool of trained

labor entry of new firms may provide a “critical mass” of

industrializationpermits the development of more efficient

transportation and communications networks


Long-Run Equilibrium: Decreasing-Cost Case



SMC MC

AC

S

D

P1

Q1

Suppose that we are in long-run equilibrium in this industry

P = MC = ACPrice Price





SMC MC

AC

S

D

P1

Q1


D’

P2

Market price rises to P2 and firms increase output to q2

Q2q2

Price Price





SMC’MC’

AC’

S

D

P1

Q1

D’P3

Entry of firms causes costs for each firm to fall

Q3q3

Positive profits attract new firms and supply shifts out

S’

PricePriceSMC MC

AC





SMC’MC’

AC’

S

D

P1

Q1

The long-run industry supply curve will be downward-sloping

D’P3

Q3q3

S’

LS

Price Price


Classification of Long-Run Supply Curves

Constant Cost entry does not affect input costs the long-run supply curve is horizontal at the

long-run equilibrium price Increasing Cost

entry increases inputs costs the long-run supply curve is positively sloped


Classification of Long-Run Supply Curves

Decreasing Cost entry reduces input costs the long-run supply curve is negatively sloped


Long-Run Elasticity of Supply

The long-run elasticity of supply (eLS,P) records the proportionate change in long-run industry output to a proportionate change in price

LS

LSPLS Q

P

P

Q

P

Qe

in change %

in change %,

eLS,P can be positive or negative the sign depends on whether the industry

exhibits increasing or decreasing costs

Comparative Statics Analysis of Long-Run Equilibrium- industry structure


Comparative Statics Analysis of Long-Run Equilibrium- industry structure

Assume that we are examining a constant-cost industry

Suppose that the initial long-run equilibrium industry output is Q0 and the typical firm’s output is q* (where AC is minimized)

The equilibrium number of firms in the industry (n0) is Q0/q*


Comparative Statics Analysis of Long-Run Equilibrium

A shift in demand that changes the equilibrium industry output to Q1 will change the equilibrium number of firms to

n1 = Q1/q*

The change in the number of firms is

1 01 0 *

Qn n

q

Q

completely determined by the extent of the demand shift and the optimal output level for the typical firm



The effect of a change in input prices is more complicated

Q*0 Quantity

MC0

AC0

P1

Price

MC1

AC1

Q*1

*

* *

*

**

*

*

* 1

*0

output q :

( , , ) ( , , )

by v

>0 ?

q

optimal

AC v w q MC v w q

differentiating

AC q MC MC

v v v q

MC AC MC

q

AC

q

AC

q

v v

v

q

v



Therefore, the change in the number of firms becomes

**

0

0

1

101

q

Q

q

Qnn

Producer Surplus in the Long Run


Producer Surplus in the Long Run Short-run producer surplus represents the

return to a firm’s owners in excess of what would be earned if output was zero the sum of short-run profits and fixed costs

In the long-run, all profits are zero and there are no fixed costs owners are indifferent about whether they are in

a particular market Suppliers of inputs may not be indifferent

about the level of production in an industry



Long-run producer surplus represents the additional returns to the inputs in an industry in excess of what these inputs would earn if industry output was zero

For long-run surplus we must penetrate back into the chain of production in order to identify who the gainers from market transactions are



In the constant-cost case, input prices are assumed to be independent of the level of production inputs can earn the same amount in alternative

occupations

In the increasing-cost case, entry will bid up some input prices suppliers of these inputs will be made better off


Ricardian Rent

Long-run producer surplus can be most easily illustrated with a situation first described by economist David Ricardo assume that there are many parcels of land on

which a particular crop may be grownthe land ranges from very fertile land (low costs of

production) to very poor, dry land (high costs of production)


Ricardian Rent

Low-Cost Firm Total Marketq* Quantity Quantity

MC

AC

S

D

P*

Q*

The owners of low-cost firms will earn positive profits

Price Price


Ricardian Rent

Low-Cost Firm Total Marketq* Quantity Quantity

MC

AC

S

D

P*

Q*

The owners of medium-cost firms will earn positive profits

Price Price


Ricardian Rent

Marginal Firm Total Marketq* Quantity Quantity

MC

AC

S

D

P*

Q*

The owners of the marginal firm will earn zero profit

Price Price


Ricardian Rent

Firms with higher costs (than the marginal firm) will stay out of the market would incur losses at a price of P*

Profits earned by intramarginal firms can persist in the long run they reflect a return to a unique resource

The sum of these long-run profits constitutes long-run producer surplus


Ricardian Rent

For each firm, P – AC representsprofit per unit of output

Total MarketQuantity

S

D

P*

Q*

Each point on the supply curve represents minimum average cost for some firm

Total long-run profits can becomputed by summing over allunits of output

Price

* *

* *

*

*

* *

* *

0 0

* * *

0 0

* * * * *

0

* *

0

*

*

( )

profit:

= ( ) from lowest to highest cost

( )

)

( )

(

i i

n n

i

i i

n n

i

n

Q

p AC q

total

di p AC q di

p q di AC q di

p q n p iq q di

p Q p Q dQ

AC p iq p

Q iq


Ricardian Rent

It is the scarcity of low-cost inputs that creates the possibility of Ricardian rent

In industries with upward-sloping long-run supply curves, increases in output not only raise firms’ costs but also generate factor rents for inputs

It is inputs to the industry that actually receive this surplus


CONTENTS

Partial Equilibrium Analysis Market Demand Timing of the Supply Response Pricing in the Very Short Run Short-Run Price Determination Shifts in Supply and Demand Curves Mathematical Model of Supply and Demand Long-Run Analysis Shape of the Long-Run Supply Curve Comparative Statics Analysis of Long-Run

Equilibrium- industry structure Producer Surplus in the Long Run


Important Points to Note:

In the short run, equilibrium prices are established by the intersection of what demanders are willing to pay (as reflected by the demand curve) and what firms are willing to produce (as reflected by the short-run supply curve) these prices are treated as fixed in both

demanders’ and suppliers’ decision-making processes



A shift in either demand or supply will cause the equilibrium price to change the extent of such a change will depend on the

slopes of the various curves Firms may earn positive profits in the short

run because fixed costs must always be paid, firms

will choose a positive output as long as revenues exceed variable costs



In the long run, the number of firms is variable in response to profit opportunities the assumption of free entry and exit implies that

firms in a competitive industry will earn zero economic profits in the long run (P = AC)

because firms also seek maximum profits, the equality P = AC = MC implies that firms will operate at the low points of their long-run average cost curves



The shape of the long-run supply curve depends on how entry and exit affect firms’ input costs in the constant-cost case, input prices do not

change and the long-run supply curve is horizontal

if entry raises input costs, the long-run supply curve will have a positive slope



Changes in long-run market equilibrium will also change the number of firms precise predictions about the extent of these

changes is made difficult by the possibility that the minimum average cost level of output may be affected by changes in input costs or by technical progress



If changes in the long-run equilibrium in a market change the prices of inputs to that market, the welfare of the suppliers of these inputs will be affected such changes can be measured by changes in

the value of long-run producer surplus

Chapter 10

THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL

END

Chapter 10 THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL.

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Transcript of Chapter 10 THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL.