economics 102 lecture 10 market equilibrium rev

7/27/2019 Economics 102 Lecture 10 Market Equilibrium Rev

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Lecture 10: Equilibrium

Introduction

Market equilibrium

Comparative statics

The effects of taxes

Pareto efficiency



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Supply

Supply curve – measures how much a firm is

willing to supply of a good at each possible

market price, i.e., for each p, how much of

the good S(p) will be supplied

Market supply curve –it is just the sum of the

individual supply curves of suppliers of thegood

Assume a competitive market

Competitive market – individual consumers and

suppliers take prices as given, and determine their best

response given those market prices.

Rationale: the consumer or supplier is small relative tothe market and thus has a negligible effect on the market

price.

It is the actions of all the agents together that determine

the market price.



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Equilibrium price – price at which the supplyof the goods equal the demand.

Let:

market demand curve :

market supply curve:

, the equilibrium price is the pricethat solves the equation:

)( p D

)( pS * p

)()( ** pS p D

Demand and supply curves represent theoptimal choices of the agents involved andthe fact that they are equal at some price p*means that the behaviors of demandersand suppliers are compatible.

In equilibrium, all agents are choosing thebest action for themselves and eachperson’s behavior is consistent with that of others.



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Only when the amount that people want to buy at agiven price equals the amount that people want to sellat that price will the market be in equilibrium

Demand is greater than supply: Some suppliers realize that they can sell at a higher price to

some of the demanders, thus prices would be pushed up.

Supply is greater than demand: some suppliers will not be able to sell at the going price and the

only way they can sell more is if they lower the price.

*' p p

*' p p

p

D(p)

q=D(p)

Marketdemand



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p

S(p)

Marketsupply

q=S(p)

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)



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p

D(p), S(p)

q=D(p)

Market

demandMarketsupply

q=S(p)

p*

q*

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

q*

D(p*) = S(p*); the marketis in equilibrium.



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p

D(p), S(p)

q=D(p)

Market

demandMarketsupply

q=S(p)

p*

S(p’)

D(p’) < S(p’); an excess

of quantity supplied over quantity demanded.

p’

D(p’)

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

S(p’)

D(p’) < S(p’); an excess

of quantity supplied over quantity demanded.

p’

D(p’)

Market price must fall towards p*.



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p

D(p), S(p)

q=D(p)

Market

demandMarketsupply

q=S(p)

p*

D(p”)

D(p”) > S(p”); an excess

of quantity demandedover quantity supplied.

p”

S(p”)

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

D(p”)

D(p”) > S(p”); an excess

of quantity demandedover quantity supplied.

p”

S(p”)

Market price must rise towards p*.



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An example of calculating a market

equilibrium when the market demand and

supply curves are linear.

D p a bp( )

S p c dp( )

p

D(p), S(p)

D(p) = a-bp

Marketdemand

Marketsupply

S(p) = c+dp

p*

q*



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1

p

D(p), S(p)

D(p) = a-bp

Market

demandMarketsupply

S(p) = c+dp

p*

q*

What are the valuesof p* and q*?

D p a bp( )

S p c dp( )

At the equilibrium price p*, D(p*) = S(p*).That is,

a bp c dp * *

which givesp a c

b d

*

andq D p S p

ad bc

b d

* * *( ) ( ) .



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p

D(p), S(p)

D(p) = a-bp

Market

demandMarketsupply

S(p) = c+dp

p

a c

b d

*

dbbcadq*

Equilibrium via inverse demand and supply

curves

Inverse demand – price that someone is willing

to pay in order to acquire some given amount of the good

Inverse supply – price that must prevail in order

to generate a given amount of supply



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1

Equilibrium price - determined by finding that

quantity at which the amount the demanders are

willing to pay to consume that quantity is equal to

the price that suppliers must receive in order to

supply that quantity.

inverse supply:

inverse demand:

equilibrium is determined by the condition:

)( *q P S

)( *q P D

)()( ** q P q P DS

q D p a bp pa q

bD q

( ) ( ),1

q S p c dp pc q

d

S q

( ) ( ),1

the equation of the inverse marketdemand curve. And

the equation of the inverse marketsupply curve.



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1

q

D-1(q),S-1(q)

D-1(q) = (a-q)/b

Market

inversedemand

Market inverse supplyS-1(q) = (-c+q)/d

p*

q*

q

D-1(q),S-1(q)

D-1(q) = (a-q)/b

Marketdemand

S-1(q) = (-c+q)/d

p*

q*

At equilibrium,D-1(q*) = S-1(q*).

Market inverse supply



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1

p D qa q

b

1( ) p S q

c q

d

1( ) .and

At the equilibrium quantity q*, D-1(p*) = S-1(p*). That is,

d

qc

b

qa **

which gives qad bc

b d

*

and p D q S q a cb d

* * *( ) ( ) .

1 1

q

D-1(q),S-1(q)

D-1(q) = (a-q)/b

Marketdemand

Marketsupply

S-1(q) = (-c+q)/d

p

a c

b d

*

db

bcadq*



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1

In the general case, the equilibrium price

and equilibrium quantity are jointly

determined by demand and supply curves.

Special cases

Case of the fixed supply.

Amount supplied is some fixed number and is

independent of prices. Supply curve is vertical.

Equilibrium quantity is determined entirely by

supply conditions and the equilibrium price

by demand conditions

Market quantity supplied isfixed, independent of price.

p

qq*



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S(p) = c+dp, so d=0and S(p) c.

p

qq* = c



p

qq* = c

D-1(q) = (a-q)/b

Marketdemand




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1


p

q

p*

D-1(q) = (a-q)/b

Market

demand

q* = c



p

q

p* =(a-c)/b

D-1(q) = (a-q)/b

Marketdemand

q* = c

p* = D-1(q*); that is,p* = (a-c)/b.




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p

q

D-1(q) = (a-q)/b

Market

demand

q* = c

p* = D-1(q*); that is,p* = (a-c)/b.

p* =(a-c)/b


p a cb d

*

qad bc

b d

*


p

q

D-1(q) = (a-q)/b

Marketdemand

q* = c

p* = D-1(q*); that is,p* = (a-c)/b.

pa c

b d

*

qad bc

b d

*

with d = 0 give

pa c

b

*

q c* .

p* =(a-c)/b




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1

Case of perfectly horizontal supply curve

Industry will supply any amount of the

good at a constant price

Equilibrium price is determined by

supply conditions and the equilibrium

quantity is determined by the demand

curve.

Market quantity supplied isextremely sensitive to price.

p

q



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2


S-1(q) = p*.p

q

p*


S-1(q) = p*.

p

q

p*

D-1(q) = (a-q)/b

Marketdemand



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2


S-1(q) = p*.p

q

p*

D-1(q) = (a-q)/b

Market

demand

q*


S-1(q) = p*.

p

q

p*

D-1(q) = (a-q)/b

Marketdemand

q* =a-bp*

p* = D-1(q*) = (a-q*)/b soq* = a-bp*



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2

How will the equilibrium price and quantitieschange when demand and supply curveschange?

Demand increases ( decreases), equilibrium priceand quantity must increase (decrease)

Supply increases (decreases), equilibrium pricesfall (rise) and equilibrium quantity increases(decreases).

Simultaneous changes in demand and supply,results depend on the magnitudes and directions of the shifts.

p

D(p), S(p)

Marketdemand

Market supply

p*

q*



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2

With taxes, there are two prices of interest

that differ by the amount of the tax:

price that the demander pays (demand price)

price that the supplier gets (supply price)

Quantity taxes – tax levied per unit of quantity

bought or sold:

Ad valorem or value tax. Expressed in percentage

units:

t P P sb

sb P P )1(

If the tax is levied on sellers then it is an excise

tax.

If the tax is levied on buyers then it is a sales tax.

As far as the equilibrium price facingdemanders and suppliers is concerned, it

doesn’t really matter who is responsible for

paying the tax. It just matters that the tax must

be paid by someone.



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2

A tax rate t makes the price paid by buyers,

pb, higher by t from the price received by

sellers, ps.

p p tb s

Even with a tax the market must clear.

I.e. quantity demanded by buyers at price pb

must equal quantity supplied by sellers at

price ps.

D p S pb s( ) ( )



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2

p p tb s D p S pb s( ) ( )and

describe the market’s equilibrium. Notice theseconditions apply no matter if the tax is levied on sellersor on buyers.

Hence, a sales tax rate t has the same effect as an

excise tax rate t.

Effects of quantity taxes:

Case 1: Supplier required to pay the tax.

Amount supplied will depend on the supplyprice – the amount the supplier gets afterpaying the tax.

Amount demanded will depend on thedemand price – the amount that the demanderpays.

Amount supplier gets will be the amount that the demander pays minus the amount of thetax



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2

This gives us two equations:

Substituting the second equation into thefirst we have the equilibrium condition: .

Alternatively we can rearrange the secondequation to get:

To get:

t P P

P S P D

b s

sb

)()(

)()( t P S P D bb

t P P sb

)()( s s P S t P D

Case 2: Demander has to pay the tax

The amount paid by the demander minus the

tax equals the price received by the supplier:

Substituting into the demand and supply

condition results in:

This is the same equation as in the case where

the supplier pays the tax.

sb P t P

)()( t P S P D bb



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2

Utilizing inverse demand and supply

functions:

Equilibrium quantity is that quantity q* such that

the demand price at q* minus the tax being paid is

just equal to the supply price at q*:

If the tax is being imposed on suppliers, the

condition is that the supply price plus the amount of the tax must equal the demand price:

)()( ** q P t q P sb

t q P q P sb )()( **

Geometric representation: Using the

inverse demand and supply curves

Find the quantity where the curve

crosses the curve.

Shift the demand curve downwards by the amount of

the tax.

Alternatively, we can find the quantity where

crosses .

Simply shift the supply curve by the amount of the tax

t q P b )( *

)(*

q P s

)( *q P b

t q P s )(*



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2

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

No tax

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax



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2

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

t

An excise taxraises the marketsupply curve by t

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

An excise taxraises the marketsupply curve by t,raises the buyers’

price and lowers thequantity traded.

tpb

qt



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3

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

An excise taxraises the marketsupply curve by t,raises the buyers’

price and lowers thequantity traded.

tpb

qt

And sellers receive only ps = pb - t.

ps

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax



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3

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

An sales tax lowersthe market demandcurve by t

t

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

An sales tax lowersthe market demandcurve by t, lowersthe sellers’ price and

reduces the quantitytraded.t

qt

ps



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3

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

An sales tax lowersthe market demandcurve by t, lowersthe sellers’ price and

reduces the quantitytraded.t

pbpb

qt

pb

And buyers pay pb = ps + t.

ps

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

A sales tax levied atrate t has the sameeffects on themarket’s equilibrium

as does an excise taxlevied at rate t.t

pbpb

qt

pb

ps

t



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3

Another way to determine the impact of the

tax. Find the quantity q* such that when the

suppliers face ps and the demander faces

pb=ps+t, the quantity q* is demanded by

consumers and supplied by firms.

Represent the tax as a vertical segment and slide it

along the supply curve until it just touches the

demand curve.

This is the equilibrium quantity

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

t

pbpb

qt

pb

ps



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3

Effects of the tax:

Quantity sold must decrease.

Price paid by demanders must go up

Price received by suppliers must go down.

E.g. suppose the market demand and supply

curves are linear.

D p a bpb b( )

S p c dps s( )



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3

With the tax, the market equilibrium satisfies

and so

and

p p tb s D p S pb s( ) ( )

p p tb s a bp c dpb s .

With the tax, the market equilibrium satisfies

p p tb s D p S pb s( ) ( )and so

p p tb s a bp c dpb s .and

Substituting for pb gives

a b p t c dp pa c bt

b ds s s

( ) .



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pa c bt

b ds

and p p tb s give

The quantity traded at equilibrium is

q D p S p

a bpad bc bdt

b d

t

b s

b

( ) ( )

.

pa c dt

b db

Amount paid by the demander increases and

the price received by the supplier decreases.

Amount of the price change depends upon the

slope of the demand and supply curves.



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3

Tax incidence: Passing along a tax

In general, a tax will both raise the price paid

by consumers and the lower the price received

by suppliers.

The division of the t between the buyers and

the sellers is the incidence of the tax. How much of a tax gets passed along depends

on the characteristics of demand and supply.

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps



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3

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid bybuyers

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps Tax paid by

sellers



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3

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid bybuyers

Tax paid bysellers

pa c bt

b ds

pa c dt

b db

qad bc bdt

b d

t

As t 0, ps and pb

the

equilibrium price if there is no tax (t = 0)

and qt

the quantity traded at equilibrium when there is no tax.

,

d b

bcad

*,p

db

ca



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d b

bt ca p s

d b

dt ca pb

d b

bdt bcad q

t

The tax paid per unit by the buyer is

.*

d b

dt

d b

ca

d b

dt ca p pb

The tax paid per unit by the seller is

.*

d b

bt

d b

bt ca

d b

ca p p s

d b

bt ca p s

d b

dt ca p

b

d b

bdt bcad q

t

As t increases, ps falls, pb rises, and qt

falls.



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The total tax paid (by buyers and sellers combined) is

.

d b

bdt bcad t tqT t

The incidence of a quantity tax depends

upon the own-price elasticities of demand

and supply.



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p

D(p), S(p)

Market

demandMarketsupply

p*

q*

tpb

qt

ps

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

tpb

qt

ps

Change to buyers’

price is pb - p*.Change to quantitydemanded is Dq.

Dq



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Around p = p* the own-price elasticity of demand is approximately

Db

q

q

p p

p

D

*

*

*

Around p = p* the own-price elasticity of demand is approximately

D

bb

D

q

q

p p

p

p p

q p

q

D

D*

*

*

**

* .



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4

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

$tpb

qt

ps

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

tpb

qt

ps

Change to sellers’

price is ps - p*.Change to quantitydemanded is Dq.

Dq



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p

D(p), S(p)

Market

demandMarketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid bybuyers

Tax paid bysellers

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid bybuyers

Tax paid by

sellers

Tax incidence =p p

p p

b

s

*

*.



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4

Tax incidence =p p

p p

b

s

*

*.

p pq p

qb

D

**

*.

p pq p

qs

S

**

*.

So p p

p p

b

s

S

D

*

* .

p p

p p

b

s

S

D

*

*.

Tax incidence is =

The fraction of a t quantity tax paid by buyersrises as supply becomes more own-price elasticor as demand becomes less own-price elastic.



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Special cases of taxation: Perfectly elasticsupply the price is entirely determined by the supply curve and

the quantity sold is determined by demand

Imposing a tax is just like shifting the supply curve bythe amount of the tax.

The supply price is the same as before and demandersend up paying the entire tax.

Since the industry is willing to supply any amount at certain price p* and zero amounts at another price, then

if any good will be sold at all, then the price that suppliers receive must be p*.

This determines the equilibrium supply price and thedemand price is p* +t.

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

t

qt

As market supplybecomes more own-price elastic, taxincidence shifts more

to the buyers.

p*+ t



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4

Special case of taxation: Perfectly inelastic

supply

The quantity of the good is fixed and the equilibrium

price of a good is determined entirely by demand.

The supply curve just slides along itself and we still

have the same amount of the good supplied, with or

without the tax.

Demanders determine the equilibrium price of the good

and they are willing to pay p* for the supply of the goodthat is available, tax or no tax. Thus the demand price is

p* and the suppliers end up receiving p*-t.

The entire amount of the tax is paid by the suppliers.

p

D(p), S(p)

Marketdemand

Marketsupply

p*

t

qt = q*

As market supplybecomes less own-price elastic, taxincidence shifts more

to the sellers.p*- t



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Ordinary cases

Amount of the tax that gets passed along will

depend on the steepness of the demand curve

relative to the supply curve

If the supply curve is nearly horizontal, nearly all

of the tax gets passed along to the consumers.

If the supply curve is nearly vertical, almost none

of the tax gets passed along to the consumers.

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

tpb

qt

ps

As market demandbecomes less own-price elastic, taxincidence shifts more

to the buyers.



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p

D(p), S(p)

Market

demandMarketsupply

p*

q*

tpb

qt

ps

As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

tpb

qt

ps


to the buyers.



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5

p

D(p), S(p)

Market

demandMarketsupply

ps= p*

tpb

qt = q*

As market demandbecomes less own-price elastic, taxincidence shifts moreto the buyers.

p

D(p), S(p)

Marketdemand

Marketsupply

ps= p*

tpb

qt = q*


to the buyers.

When D = 0, buyers pay the entire tax, even though it is leviedon the sellers.



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Welfare effects of a tax From the society’s viewpoint, the real cost of a tax is lost

output.

Social cost of a tax can be explored utilizing consumers’ andproducers’ surplus.

the loss in consumers’ surplus is the area A+B

the loss in producers’ surplus is given by the area C+D.

Is there any party that gains what the producers and theconsumers lose? This party is the government and it gainspart of the loss in consumer and producer surplus in the

form of tax revenue. Suppose that tax revenues will be utilized to provide services

to consumers and producers, then the net benefit to thegovernment is the area A+C.

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax



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p

D(p), S(p)

Market

demandMarketsupply

p*

q*

No taxCS

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax

PS



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p

D(p), S(p)

Market

demandMarketsupply

p*

q*

No taxCS

PS

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No taxCS

PS



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5

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

tpb

qt

ps

CS

PS

The tax reducesboth CS and PS

A

C

B

D

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

tpb

qt

ps

CS

PS

The tax reducesboth CS and PS,transfers surplusto governmentTax



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p

D(p), S(p)

Market

demandMarketsupply

p*

q*

tpb

qt

ps

CS

PS


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

tpb

qt

ps

CS

PS




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5

p

D(p), S(p)

Market

demandMarketsupply

p*

q*

tpb

qt

ps

CS

PS

The tax reducesboth CS and PS,transfers surplusto government,and lowers total

surplus.

Tax

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

tpb

qt

ps

CS

PS

Tax

Deadweight loss = B + D



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p

D(p), S(p)

Market

demandMarketsupply

p*

q*

tpb

qt

psDeadweight loss

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

tpb

qt

ps

Deadweight loss fallsas market demandbecomes less own-price elastic.



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p

D(p), S(p)

Market

demandMarketsupply

p*

q*

tpb

qt

ps


p

D(p), S(p)

Marketdemand

Marketsupply

ps= p*

tpb

qt = q*


When D = 0, the tax causes no deadweight loss.



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The total net cost of the tax is the algebraic sum of the net benefits and the net costs: -(A+B) –(C+D) +(A+C)= –(B+D).

This area is know as the deadweight loss of the taxor the excess burden of the tax.

Source of excess burden – It is the lost value toconsumers and producers due to the reduction insales of the good.

We could also derive the deadweight loss directly byjust measuring the social value of the lost output. Demand price measures how much a consumer was willing

to pay for the good and the supply price measures the priceat which somebody was willing to supply. The difference isthe lost value on that unit of the good.

Is a competitive market Pareto efficient?

Competitive market determines how much is

produced based on how much people are willing

to pay to purchase the good as compared to how

much people must be paid to produce the good.

If a good were produced and exchanged between

these two people at any price between the

demand price and the supply price, they would

both be made better off.



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Competitive market produces a Pareto efficient amount of output.

In a competitive market, everyone pays the same priceof the good and this price is the marginal rate of substitution between the good and all other goods.

If the MRS is not the same, then there must be at least two people who value a unit of the good differently.Thus any allocation with different marginal rates of substitution cannot be Pareto efficient.

economics 102 lecture 10 market equilibrium rev

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