Chapter Sixteen

Equilibrium

Market Equilibrium

A market clears or is in equilibrium when the total quantity demanded by buyers exactly equals the total quantity supplied by sellers.

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 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 price must rise towards p*.

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*

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*).That is, a bp c dp * *

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

Two special cases arewhen quantity supplied is fixed,

independent of the market price, and

when quantity supplied is extremely sensitive to the market price.

Market Equilibrium

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

p

q

p*

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

Marketdemand

q* = c

Market quantity supplied isfixed, independent of price.

Market Equilibrium

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

Market quantity supplied isfixed, independent of price.

Market Equilibrium

Two special cases arewhen quantity supplied is fixed,

independent of the market price, and

when quantity supplied is extremely sensitive to the market price.

Market EquilibriumMarket quantity supplied isextremely sensitive to price.

p

q

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 called an excise tax.

If the tax is levied on buyers then it is called 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 actually pays the tax?How is the market’s ability to

generate gains-to-trade altered?

Quantity Taxes

A tax makes the price paid by buyers, pb, different from the price received by sellers, ps.

In fact, the buyer and seller prices must differ by exactly the amount of the tax.

p p tb s

Quantity Taxes

Even with a tax present the market must still clear, so the quantity demanded by buyers facing the price pb and the quantity supplied by sellers facing the price ps must be equal.

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 two 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 sales tax levied at a rate of $thas exactly the same effect on acompetitive market’s equilibrium as anexcise tax levied at a rate of $t.

Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax

Quantity Taxes & Market Equilibrium

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

Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax

Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

An sales tax lowersthe market demandcurve by $t

$t

Quantity Taxes & Market Equilibrium

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

Quantity Taxes & Market Equilibrium

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

Quantity Taxes & Market Equilibrium

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

Quantity Taxes & Market Equilibrium

Who pays the tax of $t per unit traded?

The division of the $t between buyers and sellers is called the incidence of the tax.

Quantity Taxes & Market Equilibrium

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

pbpb

qt

pb

ps

Tax paid by buyers

Tax paid by sellers

Quantity Taxes & Market Equilibrium

An example of computing the effects of a quantity tax on a market equilibrium.

Again suppose the market demand and supply curves are linear.

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

Quantity Taxes & Market Equilibrium

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

( ) .

Quantity Taxes & Market Equilibrium

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

Quantity Taxes & Market Equilibrium

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

.

Deadweight Loss and Own-Price Elasticities

A quantity tax imposed on a competitive market reduces the quantity traded at equilibrium and so reduces the gains-to-trade; i.e. the sum of Consumers’ Surplus and Producers’ Surplus is reduced.

The loss in total surplus is called the deadweight loss, or excess burden, of the tax.

Deadweight Loss and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No tax

Deadweight Loss and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

No taxCS

PS

Deadweight Loss and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

CS

PS

The tax reducesboth CS and PS

Deadweight Loss and Own-Price Elasticities

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

Deadweight Loss and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

CS

PSTax

Deadweight loss

Deadweight Loss and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

Deadweight loss fallsas market demandbecomes less own-price elastic.

Deadweight Loss and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

p*

q*

$tpb

qt

ps

Deadweight loss fallsas market demandbecomes less own-price elastic.

Deadweight Loss and Own-Price Elasticities

p

D(p), S(p)

Marketdemand

Marketsupply

ps= p*

$tpb

qt = q*

Deadweight loss fallsas market demandbecomes less own-price elastic.

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

Deadweight Loss and Own-Price Elasticities

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.