Equilibrium. Market Equilibrium A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers. An equilibrium

Equilibrium

Market Equilibrium

A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers.

An equilibrium situation is one where agents are choosing the best possible actions and the behaviors of all agents are mutually consistent.

Market Equilibrium It turns out that the equilibrium outcome

of a competitive market is Pareto efficient. At any amount of output less than the equilibrium level there is at least one producer willing to supply extra quantity of the good at a price that is less than the price at least one consumer is willing to pay. Therefore, we can improve the situation of at least two people without hurting anybody else.

Market EquilibriumThe equilibrium outcome of a

competitive market is the only Pareto efficient outcome.

Market Equilibrium

p

D(p)

q=D(p)

Marketdemand

Market Equilibrium

p

S(p)

Marketsupply

q=S(p)

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

q*

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

q*

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

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

S(p’)

D(p’) < S(p’); an excessof quantity supplied overquantity demanded.

p’

D(p’)

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

S(p’)

D(p’) < S(p’); an excessof quantity supplied overquantity demanded.

p’

D(p’)

Market price must fall towards p*.

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

D(p”)

D(p”) > S(p”); an excessof quantity demandedover quantity supplied.

p”

S(p”)

Market Equilibrium

p

D(p), S(p)

q=D(p)

Marketdemand

Marketsupply

q=S(p)

p*

D(p”)

D(p”) > S(p”); an excessof quantity demandedover quantity supplied.

p”

S(p”)

Market price must rise towards p*.

Market Equilibrium

The effects of setting a maximum price

The effects of setting a minimum price

Market EquilibriumDemand shifts and motives:

- income,- preferences,- prices of substitutes or complements

have changed,- expectations of future changes in

income or prices,- population,- taxes on consumption

Market EquilibriumSupply shifts and motives:

- production technology,- changes in the prices of

production factors (wages, prices of raw materials, interest rate, …),

- number of producers,- expectations of future price

changes,- taxes on production

Market Equilibrium The effects of elasticities on price and

quantity variations: when one curve is very inelastic, price accommodates; when one curve is very elastic, quantity accommodates

(“One of DeBeers’ main roles is to maintain the notion that diamonds are a scarce commodity. This they do by means of advertising and by purchasing excess supplies when that is needed to avoid price decreases: as a matter of principle, prices are never lowered by DeBeers.”)

Market Equilibrium

An example of calculating a market equilibrium when the market demand and supply curves are linear.

D p a bp( ) S p c dp( )

Market Equilibrium

p

D(p), S(p)

D(p) = a-bp

Marketdemand

Marketsupply

S(p) = c+dp

p*

q*

Market Equilibrium

p

D(p), S(p)

D(p) = a-bp

Marketdemand

Marketsupply

S(p) = c+dp

p*

q*

What are the valuesof p* and q*?

Market EquilibriumD p a bp( ) S p c dp( )

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


At the equilibrium price p*, D(p*) = S(p*).That is, a bp c dp * *



which gives pa cb d

*



which gives pa cb d

*

and q D p S pad bcb d

* * *( ) ( ) .

Market Equilibrium

p

D(p), S(p)

D(p) = a-bp

Marketdemand

Marketsupply

S(p) = c+dpp

a cb d

*

dbbcad

q*

Market Equilibrium

Can we calculate the market equilibrium using the inverse market demand and supply curves?

Yes, it is the same calculation.

Market Equilibrium

Two special cases:quantity supplied is fixed,

independent of the market price, and

quantity supplied is extremely sensitive to the market price.

Market Equilibrium

p

q

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

Marketdemand

q* = c

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

p* =(a-c)/b

Market quantity supplied isfixed, independent of price.

Market EquilibriumMarket quantity supplied isextremely sensitive to price.

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*

Quantity Taxes

A quantity tax levied at a rate of €t is a tax of €t paid on each unit traded.

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.

Quantity Taxes

What is the effect of a quantity tax on a market’s equilibrium?

How are prices affected?How is the quantity traded affected?Who pays the tax?How are gains-to-trade altered?

Quantity Taxes

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

Quantity Taxes

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( ) ( )

Quantity Taxes

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

describe the market’s equilibrium.Notice that these conditions apply nomatter if the tax is levied on sellers or onbuyers.

Quantity Taxes

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

describe the market’s equilibrium.Notice that these two conditions apply nomatter if the tax is levied on sellers or onbuyers.

Hence, a tax rate €t has thesame effect no matter the side of themarket on which it is levied.

Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax


p

D(p), S(p)

Marketdemand

Marketsupply

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


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

And sellers receive only ps = pb - t.

ps


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

A 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 andreduces the quantitytraded.€t

qt

ps


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

An sales tax lowersthe market demandcurve by €t, lowersthe sellers’ price andreduces 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 equilibriumas does an excise taxlevied at rate €t.€t

pbpb

qt

pb

ps

€t


Who pays the tax of €t per unit traded?

The division of the €t between buyers and sellers is the economic incidence of the tax.


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid by buyers


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

psTax paid by sellers


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid by buyers

Tax paid by sellers


E.g. suppose the market demand and supply curves are linear.

D p a bpb b( ) S p c dps s( )


andD p a bpb b( ) S p c dps s( ) .


and

With the tax, the market equilibrium satisfies

and so

and

D p a bpb b( ) S p c dps s( ) .

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

p p tb s a bp c dpb s .


D p a bpb b( ) S p c dps s( ) . and

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

( ) .


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

tb s

b

( ) ( )

.

pa c dt

b db


pa c bt

b ds

pa c dt

b db

qad bc bdt

b dt

As t 0, ps and pb theequilibrium price ifthere is no tax (t = 0) and qt the quantity traded at equilibriumwhen there is no tax.

ad bcb d

,

*,pdbca


pa c bt

b ds

pa c dt

b db

qad bc bdt

b dt

As t increases, ps falls,

pb rises,

and qt falls.


pa c bt

b ds

pa c dt

b db

qad bc bdt

b dt

The tax paid per unit by the buyer isp p

a c dtb d

a cb d

dtb db

* .


pa c bt

b ds

pa c dt

b db

qad bc bdt

b dt

The tax paid per unit by the buyer isp p

a c dtb d

a cb d

dtb db

* .

The tax paid per unit by the seller isp p

a cb d

a c btb d

btb ds

* .


pa c bt

b ds

pa c dt

b db

qad bc bdt

b dt

The total tax paid (by buyers and sellerscombined) is

T tq tad bc bdt

b dt

.

Tax Incidence and Own-Price Elasticities

The incidence of a quantity tax depends upon the own-price elasticities of demand and supply.


p

D(p), S(p)

Marketdemand

Marketsupply

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 q.

q


Around p = p* the own-price elasticityof demand is approximately

*

*

*

ppp

qq

bD


Around p = p* the own-price elasticityof demand is approximately

*

**

*

*

*

q

pqpp

ppp

qq

Db

bD


p

D(p), S(p)

Marketdemand

Marketsupply

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 q.

q


Around p = p* the own-price elasticityof supply is approximately

Ss

q

q

p p

p

*

*

*


Around p = p* the own-price elasticityof supply is approximately

Ss

sS

q

q

p p

p

p pq p

q

*

*

*

**

*.


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid by buyers

Tax paid by sellers


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid by buyers

Tax paid by sellers

Tax incidence = p p

p pb

s

*

*.


Tax incidence = p p

p pb

s

*

*.

.*

**

q

pqpp

Db

p p

q p

qs

S

*

*

*.


Tax incidence = p p

p pb

s

*

*.

.*

*

*

q

pqpp

Db

p p

q p

qs

S

*

*

*.

So

D

S

s

b

pp

pp

*

*


Tax incidence is

The fraction of a €t quantity tax paidby buyers rises as supply becomes moreown-price elastic or as demand becomesless own-price elastic.

D

S

s

b

pp

pp

*

*


p

D(p), S(p)

Marketdemand

Marketsupply

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



p

D(p), S(p)

Marketdemand

Marketsupply

ps= p*

€tpb

qt = q*


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


Similarly, the fraction of a €t quantitytax paid by sellers rises as supplybecomes less own-price elastic or asdemand becomes more own-price elastic.

Deadweight Loss and Own-Price Elasticities

A quantity tax imposed on a competitive market reduces the quantity traded and so reduces gains-to-trade (i.e. the sum of Consumers’ and Producers’ Surpluses).

The lost total surplus is the tax’s deadweight loss, or excess burden.


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No taxCS


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax

PS


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No taxCS

PS


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No taxCS

PS


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

€tpb

qt

ps

CS

PS

The tax reducesboth CS and PS


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

€tpb

qt

ps

CS

PS

The tax reducesboth CS and PS,transfers surplusto government

Tax


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

€tpb

qt

ps

CS

PS

The tax reducesboth CS and PS,transfers surplusto government

Tax


p

D(p), S(p)

Marketdemand

Marketsupply

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

PSTax

Deadweight loss


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

€tpb

qt

ps Deadweight loss


p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

€tpb

qt

ps

Deadweight loss fallsas market demandbecomes less own-price elastic.


p

D(p), S(p)

Marketdemand

Marketsupply

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.


Deadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic.

If either D = 0 or S = 0 then the deadweight loss is zero.

Fiscal Revenue

Fiscal revenue decreases for t sufficiently large, because market transactions are highly reduced: the Laffer curve.

Long-Run Implications of Taxation in a Competitive Market

In a short-run equilibrium, the burden of a tax is typically shared by both buyers and sellers, the tax incidence depending upon the own-price elasticities of demand and supply.

Q: Is this true in a long-run market equilibrium?


LR supply (no tax)

p

X,Y

Market demand

Qe

pe


LR supply (no tax)

p

X,Y

Market demand

Qe

ps=pe

LR supply (with tax)

Qt

pb = pe+t

t


LR supply (no tax)

p

X,Y

Market demand

Qe

ps=pe

LR supply (with tax)

Qt

pb = pe+t

t

In the long-run thebuyers pay all of asales or an excise tax.

Documents

Equilibrium. Market Equilibrium A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers. An equilibrium