Chapter 12 The Partial Equilibrium Competitive Model Nicholson and Snyder, Copyright ©2008 by...

Chapter 12

The Partial Equilibrium Competitive Model

Nicholson and Snyder, Copyright ©2008 by Thomson South-Western. All rights reserved.

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

n

iiyxi ppxX

1

),,( for demand Market I

Market Demand

• To construct the market demand curve, pX is allowed to vary while py and the income of each individual 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 Market Demand 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

• Suppose that 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


• To graph the demand curve, we must assume values for py, I1, and I2

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

X = 27 – 3px + 4 + 1 + 4 = 36 – 3px


• 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

jn

m

jiji ppxX 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

),',(

,

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 run• new 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

Pricing in the Very Short Run

Quantity per period

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’

Short-Run Price Determination

• The number of firms in an industry is fixed

• These firms are able to adjust the quantity they are producing– they 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– each firm attempts to maximize profits– each firm is a price taker

• its actions have no effect on the market price

– information is perfect– transactions are costless

Short-Run Market Supply• The quantity of output supplied to the

entire market in the short run is the sum of the quantities supplied by each firm– the amount supplied by each firm depends

on price

• The short-run market supply curve will be upward-sloping because each firm’s short-run supply curve has a positive slope

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

n

iis wvPqwvPQ

1

),,(),,(

• 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

S

SPS Q

P

P

Q

P

Qe

in change %

supplied in change %,

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

A Short-Run Supply Function

• Suppose that there are 100 identical firms each with the following short-run supply curve

qi (P,v,w) = 10P/3 (i = 1,2,…,100)

• This means that the market supply function is given by

3

1000

3

10100

1

100

1

PPqQ

i iis

A Short-Run Supply Function

• In this case, computation of the elasticity of supply shows that it is unit elastic

13/10003

1000),,(,

P

P

Q

P

P

wvPQe

S

SPS

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:

),*,(),'*,( wvPQPPQ SD I


• The equilibrium price depends on many exogenous factors– changes in any of these factors will likely

result in a new equilibrium price


Total output per period

Price

S

D

Q1

P1

The interaction betweenmarket demand and marketsupply determines theequilibrium price

Market Reaction to a Shift in Demand

Price

S

D

Q1

P1

Q2

P2 Equilibrium price andequilibrium quantity willboth rise

If many buyers experiencean increase in their demands,the market demand curvewill shift to the right

D’

Total output per period

Market Reaction to a Shift in Demand

PriceSMC

q1

P1

This is the short-runsupply response to anincrease in market price

q2

P2

If the market price rises, firms will increase their level of output

SAC

Output per period

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 and Demand Curves

• When either a supply curve or a demand curve shift, equilibrium price and quantity will change

• The relative magnitudes of these changes depends on the shapes of the supply and demand curves

Shifts in Supply

Q perperiod

Q perperiod

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

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’

Q perperiod

Q perperiod

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 + Dd

dQS = SPdP + Sd

• Maintenance of equilibrium requires that

dQD = dQS


• Suppose that the demand parameter () changed while remains constant

• The equilibrium condition requires that

DPdP + Dd = SPdP

PP DS

DP

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


• We can convert our analysis to elasticities

PDS

D

P

Pe

PPP

,

PQPS

Q

PPP ee

e

QPDSQD

e,,

,, )(

Equilibria with Constant Elasticity Functions

• Suppose the demand for automobiles is given by

32.11.0),( II

PPQD

• The supply for automobiles is

5.0400,6),(

PwPQS w


• If I = $20,000 and w = $25

2.111)108(),(

PPQD I

PPQS 280,1),( w

• Equilibrium occurs where P* = 9,957 and Q* = 12,745,000


• If I increases by 10 percent

2.112)1006.1(),(

PPQD I

PPQS 280,1),( w



• If instead w increases to $30 per hour

PPQS 2168,1),( w


2.111)108(),(

PPQD I

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– perfect competition assumes that there are

no special costs of entering or exiting an industry

Long-Run Analysis• New firms will be lured into any market

where economic profits are greater than zero– the short-run industry supply curve will shift

outward– market price and profits will fall– the process will continue until economic

profits are zero

Long-Run Analysis• Existing firms will leave any industry

where economic profits are negative– the short-run industry supply curve will shift

inward– market price will rise and losses will fall– the process will continue until economic

profits are zero

Long-Run Competitive Equilibrium

• A perfectly competitive industry is in long-run equilibrium if there are no incentives for profit-maximizing firms to enter or to leave the industry– this will occur when the number of firms is

such that P = MC = AC and each firm operates at minimum AC

Long-Run Competitive Equilibrium

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

technology

• The equilibrium long-run position requires that each firm earn zero economic profit

Long-Run Equilibrium: Constant-Cost Case

• Assume that the entry of new firms in an industry has no effect on the cost of inputs– no matter how many firms enter or leave

an industry, a firm’s cost curves will remain unchanged

• This is referred to as a constant-cost industry


A Typical Firm Total MarketQuantityper period

Quantityper period

SMC MC

AC

S

D

q1

P1

Q1

This is a long-run equilibrium for this industry

P = MC = ACPrice Price


A Typical Firm Total Market

q1

SMC MC

AC

S

D

P1

Q1

P2

Market price rises to P2

Q2

Suppose that market demand rises to D’

D’

Price Price

Quantityper period

Quantityper period



q1

SMC MC

AC

S

D

P1

Q1

D’

P2

Economic profit > 0

Q2

In the short run, each firm increases output to q2

q2

Price Price

Quantityper period

Quantityper period



q1

SMCMC

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

Quantityper period

Quantityper period



q1

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

Quantityper period

Quantityper period

Infinitely Elastic Long-Run Supply

• Suppose that the total cost curve for a typical firm in the bicycle industry is

C(q) = q3 – 20q2 + 100q + 8,000

• Demand for bicycles is given by

QD = 2,500 – 3P

Infinitely Elastic Long-Run Supply• To find long-run equilibrium, we must

find the minimum point on the typical firm’s average cost curve– where AC = MC

AC = q2 – 20q + 100 + 8,000/q

MC = 3q2 – 40q + 100– this occurs where q = 20

• If q = 20, AC = MC = $500– this will be the long-run equilibrium price

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

• 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

q1

SMC MC

AC

S

D

P1

Q1

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

P = MC = ACPricePrice

Quantityper period

Quantityper period



q1

SMCMC

AC

S

D

P1

Q1


D’

P2

Market price rises to P2 and firms increase output to q2

Q2q2

Price Price

Quantityper period

Quantityper period


A Typical Firm (after entry) Total Market

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

Total MarketQuantityper period

Quantityper period


A Typical Firm (after entry) Total Market

q3

SMC’ MC’

AC’

S

D

p1

Q1

D’

p3

Q3

S’

The long-run supply curve will be upward-sloping

LS

Price Price

Quantityper period

Quantityper period

Long-Run Equilibrium: Decreasing-Cost Industry

• 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 industrialization• permits the development of more efficient

transportation and communications networks

Long-Run Equilibrium: Decreasing-Cost Case


q1

SMCMC

AC

S

D

P1

Q1

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

P = MC = ACPrice Price

Quantityper period

Quantityper period



q1

SMC MC

AC

S

D

P1

Q1


D’

P2

Market price rises to P2 and firms increase output to q2

Q2q2

Price Price

Quantityper period

Quantityper period



q1

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’

PricePrice

Quantityper period

Quantityper periodA Typical Firm (before entry)

Q1



q1

SMC’MC’

AC’

S

D

P1

Q1

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

D’P3

Q3q3

S’

LS

Price Price

Quantityper period

Quantityper period

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

• Comparative statics analysis of long-run equilibria can be conducted using estimates of long-run elasticities of supply and demand

• In the long run, the number of firms in the industry will vary from one long-run equilibrium to another

Comparative Statics Analysis• 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• 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

*q

QQnn 01

01

– determined by demand shift and the optimal output level for the typical firm


• The effect of a change in input prices is more complicated– we need to know how much minimum

average cost is affected– we need to know how an increase in long-

run equilibrium price will affect quantity demanded


• The optimal level of output for each firm may also be affected

• Therefore, the change in the number of firms becomes

**

0

0

1

101

q

Q

q

Qnn

Rising Input Costs and Industry Structure

• Suppose that the total cost curve for a typical firm in the bicycle industry is

C(q) = q3 – 20q2 + 100q + 8,000

and then rises to

C(q) = q3 – 20q2 + 100q + 11,616

• The optimal scale of each firm rises from 20 to 22 (where MC = AC)

Rising Input Costs and Industry Structure

• At q = 22, MC = AC = $672 so the long-run equilibrium price will be $672

• If demand can be represented byQD = 2,500 – 3P

then QD = 484

• This means that the industry will have 22 firms (484 22)

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• they could earn identical returns on their

investments elsewhere

• Suppliers of inputs may not be indifferent about the level of production in an industry


• 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


• Long-run producer surplus is the extra return that producers make by making transactions at the market price over and above what they would earn if nothing were produced– the area above the long-run supply curve

and below the market price

Ricardian Rent• Assume that there are many parcels of

land on which a particular crop may be grown– the land ranges from very fertile land (low

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

Ricardian Rent• At low prices only the best land is used

• Higher prices lead to an increase in output through the use of higher-cost land– the long-run supply curve is upward-sloping

because of the increased costs of using less fertile land

Ricardian Rent

Low-Cost Firm Total Marketq*

MC

AC

S

D

P*

Q*

The owners of low-cost firms will earn positive profits

Price Price

Quantityper period

Quantityper period

Ricardian Rent

Marginal Firm Total Marketq*

MC

AC

S

D

P*

Q*

The owners of the marginal firm will earn zero profit

Price Price

Quantityper period

Quantityper period

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

Ricardian Rent• The long-run profits for the low-cost firms

may be reflected in the prices of the unique resources owned by those firms– the more fertile the land is, the higher its

price

• Thus, profits are said to be capitalized into inputs’ prices– reflect the present value of all future profits

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

Economic Efficiency and Welfare Analysis

• The area between the demand and the supply curve represents the sum of consumer and producer surplus– measures the total additional value

obtained by market participants by being able to make market transactions

• This area is maximized at the competitive market equilibrium


Quantity per period

Price

P *

Q *

S

D

Consumer surplus is thearea above price and belowdemand

Producer surplus is thearea below price andabove supply

At output Q1, total surpluswill be smaller


Quantity per period

Price

P *

Q *

S

D

Q1

At outputs between Q1 andQ*, demanders would valuean additional unit more thanit would cost suppliers toproduce


• Mathematically, we wish to maximize

consumer surplus + producer surplus =

Q Q

dQQPQUdQQPPQPQQU0 0

)()(])([])([

• In long-run equilibria along the long-run supply curve, P(Q) = AC = MC


• Maximizing total surplus with respect to Q yields

U’(Q) = P(Q) = AC = MC

– maximization occurs where the marginal value of Q to the representative consumer is equal to market price

• the market equilibrium

Welfare Loss Computations

• Use of consumer and producer surplus makes it possible to calculate welfare losses caused by restrictions on voluntary transactions– in the case of linear demand and supply

curves, the calculation is simple because the areas of loss are often triangular


• Suppose that the demand is given by

QD = 10 - P

and supply is given by

QS = P - 2

• Market equilibrium occurs where P* = 6 and Q* = 4


• Restriction of output to Q0 = 3 would create a gap between what demanders are willing to pay (PD) and what suppliers require (PS)

PD = 10 - 3 = 7

PS = 2 + 3 = 5

The welfare loss from restricting outputto 3 is the area of a triangle


Quantity per period

Price

S

D

6

4

7

5

3

The loss = (0.5)(2)(1) = 1


• The welfare loss will be shared by producers and consumers– it will depend on the price elasticity of

demand and the price elasticity of supply to determine who bears the larger portion of the loss

• the side of the market with the smallest price elasticity (in absolute value)

Price Controls and Shortages

• Sometimes governments may seek to control prices at below equilibrium levels– this will lead to a shortage

• The changes in producer and consumer surplus from this policy show its impact on welfare


Quantity per period

PriceSS

D

LS

P1

Q1

Initially, the market isin long-run equilibriumat P1, Q1

Demand increases to D’

D’


Quantity per period

PriceSS

D

LS

P1

Q1

D’

Firms would begin toenter the industry

In the short run, pricerises to P2

P2

The price would endup at P3

P3


Quantity

Price SS

D

LS

P1

Q1

D’

P3

There will be a shortage equal toQ2 - Q1

Q2

Suppose that thegovernment imposesa price ceiling at P1

This gain in consumersurplus is the shadedrectangle


Quantity per period

PriceSS

D

LS

P1

Q1

D’

P3

Q2

Some buyers will gain because they can purchase the good for a lower price

The shaded rectangletherefore represents apure transfer fromproducers to consumers


Quantity per period

Price

D

P1

Q1

D’

SS

LSP3

Q2

The gain to consumers is also a loss to producers who now receive a lower price

No welfare loss there

This shaded trianglerepresents the value of additional consumer surplus that would have been attained without the price control


Quantity per period

PriceSS

D

LS

P1

Q1

D’

P3

Q2

This shaded trianglerepresents the value of additional producer surplus that would have been attained without the price control


Quantity

PriceSS

D

LS

P1

Q1

D’

P3

Q2

This shaded arearepresents the total value of mutually beneficial transactions that are prevented by the government


Quantity

Price SS

D

LS

P1

Q1

D’

P3

Q2

This is a measure of the pure welfare costs of this policy

Disequilibrium Behavior• Assuming that observed market

outcomes are generated by

Q(P1) = min [QD(P1),QS(P1)],

suppliers will be content with the outcome but demanders will not

• This could lead to a black market

Tax Incidence• To discuss the effects of a per-unit tax

(t), we need to make a distinction between the price paid by buyers (PD) and the price received by sellers (PS)

PD - PS = t

• In terms of small price changes, we wish to examine

dPD - dPS = dt

Tax Incidence• Maintenance of equilibrium in the

market requires

dQD = dQS

or

DPdPD = SPdPS

• Substituting, we get

DPdPD = SPdPS = SP(dPD - dt)

Tax Incidence

• We can now solve for the effect of the tax on PD:

DS

S

PP

PD

ee

e

DS

S

dt

dP

• Similarly,

DS

D

PP

PS

ee

e

DS

D

dt

dP

Tax Incidence

• Because eD 0 and eS 0, dPD /dt 0 and dPS /dt 0

• If demand is perfectly inelastic (eD = 0), the per-unit tax is completely paid by demanders

• If demand is perfectly elastic (eD = ), the per-unit tax is completely paid by suppliers

Tax Incidence

• In general, the actor with the less elastic responses will experience most of the price change caused by the tax

S

D

D

S

e

e

dtdP

dtdP

/

/

Tax Incidence

Quantity per period

PriceS

D

P*

Q*

PD

PS

A per-unit tax creates awedge between the pricethat buyers pay (PD) andthe price that sellers receive (PS)

t

Q**

Buyers incur a welfare lossequal to the shaded area

Tax Incidence

Quantity per period

PriceS

D

P*

Q*

PD

PS

Q**

But some of this loss goesto the government in theform of tax revenue

Sellers also incur a welfareloss equal to the shaded area

Tax Incidence

Quantity per period

PriceS

D

P*

Q*

PD

PS

Q**

But some of this loss goesto the government in theform of tax revenue

Therefore, this is the dead-weight loss from the tax

Tax Incidence

Quantity per period

PriceS

D

P*

Q*

PD

PS

Q**

Deadweight Loss and Elasticity

• All nonlump-sum taxes involve deadweight losses– the size of the losses will depend on the

elasticities of supply and demand

• A linear approximation to the deadweight loss accompanying a small tax, dt, is given by

DW = -0.5(dt)(dQ)


• From the definition of elasticity, we know that

dQ = eDdPD Q0/P0

• This implies that

dQ = eD [eS /(eS - eD)] dt Q0/P0

• Substituting, we get

00

2

0

50 QPeeeeP

dtDW DSSD )]/([.


• Deadweight losses are zero if either eD or eS are zero

– the tax does not alter the quantity of the good that is traded

• Deadweight losses are smaller in situations where eD or eS are small

Transactions Costs• Transactions costs can also create a

wedge between the price the buyer pays and the price the seller receives– real estate agent fees– broker fees for the sale of stocks

• If the transactions costs are on a per-unit basis, these costs will be shared by the buyer and seller– depends on the specific elasticities involved

Gains from International Trade

Quantity per period

Price

S

D

Q*

P*

In the absence ofinternational trade,the domesticequilibrium price would be P* andthe domesticequilibrium quantitywould be Q*

Gains from International TradePrice

Q*

P*

S

D

Quantity demanded willrise to Q1 and quantitysupplied will fall to Q2

Q1Q2

If the world price (PW)is less than the domesticprice, the price will fallto PW

PW

Imports = Q1 - Q2

imports

Quantity per period

Consumer surplus rises

Producer surplus falls

There is an unambiguouswelfare gain

Gains from International TradePrice

Q*

P*

S

D

Q2Q1

PW

Quantity per period

Effects of a TariffPrice

S

D

Q1Q2

PW

Quantity demanded fallsto Q3 and quantity suppliedrises to Q4

Q4 Q3

Suppose that the governmentcreates a tariff that raisesthe price to PR

PR

Imports are now Q3 - Q4

imports

Quantity per period

Consumer surplus falls

Producer surplus rises

These two triangles represent deadweight loss

The government getstariff revenue

Effects of a TariffPrice

S

D

Q1Q2

PW

Q4 Q3

PR

Quantity per period

Quantitative Estimates of Deadweight Losses

• Estimates of the sizes of the welfare loss triangle can be calculated

• Because PR = (1+t)PW, the proportional change in quantity demanded is

DDW

WR teeP

PP

Q

QQ

1

13

The areas of these twotriangles are

Quantitative Estimates of Deadweight Losses Price

S

D

Q1Q2

PW

Q4 Q3

PR

))((. 311 50 QQPPDW WR

12

1 50 QPetDW WD.

))((. 242 50 QQPPDW WR

22

2 50 QPetDW WS.

Quantity per period

Other Trade Restrictions• A quota that limits imports to Q3 - Q4

would have effects that are similar to those for the tariff– same decline in consumer surplus– same increase in producer surplus

• One big difference is that the quota does not give the government any tariff revenue– the deadweight loss will be larger

Trade and Tariffs• If the market demand curve is

QD = 200P-1.2

and the market supply curve is

QS = 1.3P,

the domestic long-run equilibrium will occur where P* = 9.87 and Q* = 12.8

Trade and Tariffs

• If the world price was PW = 9, QD would be 14.3 and QS would be 11.7

– imports will be 2.6

• If the government placed a tariff of 0.5 on each unit sold, the world price will be PW = 9.5

– imports will fall to 1.0

Trade and Tariffs• The welfare effect of the tariff can be

calculated

DW1 = 0.5(0.5)(14.3 - 13.4) = 0.225

DW2 = 0.5(0.5)(12.4 - 11.7) = 0.175

• Thus, total deadweight loss from the tariff is 0.225 + 0.175 = 0.4

Important Points to Note:• Short-run equilibrium prices are

determined by the intersection of what demanders are willing to pay (demand) and what firms are willing to produce (supply)– both demanders and suppliers act as price

takers

Important Points to Note:

• In the long run, the number of firms may vary 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)

Important Points to Note:• The shape of the long-run supply curve

depends on how entry affects input prices– 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


• If shifts in long-run equilibrium affect input prices, 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

Important Points to Note:• The concepts of consumer and producer

surplus provide useful ways of measuring the welfare impact of economic changes– changes in consumer surplus represent

changes in utility– changes in producer surplus represent

changes in the monetary returns that inputs receive


• The competitive model can be used to study the impact of various economic policies– it can be used to measure the transfers

and welfare losses associated with price controls


• The competitive model can also be applied to study taxation– the model illustrates tax incidence and the

welfare losses associated with taxation– similar conclusions can be derived by using

the competitive model to study transactions costs


• A final, important application uses the competitive model to study international trading relationships– it can help us identify those who win and

those who lose with the opening of trade– it can also be used to study the welfare

implications of trade restrictions

Chapter 12 The Partial Equilibrium Competitive Model Nicholson and Snyder, Copyright ©2008 by...

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Transcript of Chapter 12 The Partial Equilibrium Competitive Model Nicholson and Snyder, Copyright ©2008 by...