Chapter Sixteen
Equilibrium
Market Equilibrium
A market is in equilibrium when total
quantity demanded by buyers equals
total quantity supplied by sellers.
Market Equilibrium
p
D(p),S(p)
q=D(p)
Market
demand
Market
supply
q=S(p)
p*
q*
D(p*) = S(p*); the market
is in equilibrium.
An Example
D p a bp( )
S p c dp( )
At the equilibrium price p*,D(p*) = S(p*).
That is,a bp c dp* *
which gives p a c
b d
*
and q D p S p ad bcb d* * *( ) ( ),
Market Equilibrium
Can we calculate the market
equilibrium using the inverse market
demand and supply curves?
Yes,it is the same calculation.
Market Equilibrium
q D p a bp p a qb D q( ) ( ),1
q S p c dp p c qd S q( ) ( ),1
the equation of the inverse market
demand curve,And
the equation of the inverse market
supply curve.
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
S(p) = c+dp,so d=0
and S(p)? c.
p
qq* = c
D-1(q) = (a-q)/b
Market
demand
Market quantity supplied is
fixed,independent of price.
Market Equilibrium
Market quantity supplied is
extremely sensitive to price.
S-1(q) = p*.
p
q
p*
D-1(q) = (a-q)/b
Market
demand
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 these conditions apply no
matter if the tax is levied on sellers or on
buyers.
Quantity Taxes
p p tb s D p S pb s( ) ( )?and
describe the market’s equilibrium.
Notice that these two conditions apply no
matter if the tax is levied on sellers or on
buyers.
Hence,a sales tax rate $t has the
same effect as an excise tax rate $t.
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
No tax
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$t
An excise tax
raises the market
supply curve by $t
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An excise tax
raises the market
supply curve by $t,
raises the buyers’
price and lowers the
quantity traded.
$tpb
qt
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An excise tax
raises the market
supply curve by $t,
raises the buyers’
price and lowers the
quantity traded.
$tpb
qt
And sellers receive only ps = pb - t.
ps
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An sales tax lowers
the market demand
curve by $t
$t
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An sales tax lowers
the market demand
curve by $t,lowers
the sellers’ price and
reduces the quantity
traded.$t
qt
ps
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An sales tax lowers
the market demand
curve by $t,lowers
the sellers’ price and
reduces the quantity
traded.$t
pb
qt
And buyers pay pb = ps + t.
ps
Quantity Taxes & Market Equilibrium
Who pays the tax of $t per unit
traded?
The division of the $t between buyers
and sellers is the incidence of the
tax.
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
pb
qt
ps
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
pb
qt
ps
Tax paid by
buyers
Tax paid by
sellers
Quantity Taxes & Market Equilibrium
E.g,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 sD p S pb s( ) ( )?and so
p p tb sa bp c dpb s,and
Substituting for pb gives
a b p t c dp p a c btb ds s s( ),
Quantity Taxes & Market Equilibrium
p a c btb dsand p p tb sgive
The quantity traded at equilibrium is
q D p S p
a bp
ad bc bdt
b d
t
b s
b
( ) ( )
.
p a c dtb db
Quantity Taxes & Market Equilibrium
p a c btb ds
p a c dtb db
q ad bc bdtb dt
As t increases,ps falls,
pb rises,
and qt falls.
Quantity Taxes & Market Equilibrium
p a c btb ds
p a c dtb db
q ad bc bdtb dt
The tax paid per unit by the buyer is
p p a c dtb d a cb d dtb db*,
The tax paid per unit by the seller is
p p a cb d a c btb d btb ds*,
Quantity Taxes & Market Equilibrium
p a c btb ds
p a c dtb db
q ad bc bdtb dt
The total tax paid (by buyers and sellers
combined) is
T tq t ad bc bdtb dt,
What Determines Tax Incidence?
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Change to buyers’
price is pb - p*.
Change to quantity
demanded is Dq.
Dq
Tax Incidence and Own-Price
Elasticities
Around p = p* the own-price elasticity
of demand is approximately
D
b
b
D
q
q
p p
p
p p
q p
q
D
D
*
*
*
*
*
*
.
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Change to sellers’
price is ps - p*.
Change to quantity
demanded is Dq.
Dq
Tax Incidence and Own-Price
Elasticities
Around p = p* the own-price elasticity
of supply is approximately
S
s
s
S
q
q
p p
p
p p
q p
q
D
D
*
*
*
*
*
*
.
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
pb
qt
ps
Tax paid by
buyers
Tax paid by
sellers
Tax incidence =
p p
p p
b
s
*
*
.
Tax Incidence and Own-Price
Elasticities
Tax incidence =
p p
p p
b
s
*
*
.
p p
q p
q
b
D
*
*
*
.
D
p p
q p
q
s
S
*
*
*
.
D
So
p p
p p
b
s
S
D
*
*
.
Tax Incidence and Own-Price
Elasticities
p p
p p
b
s
S
D
*
*
.
Tax incidence is
The fraction of a $t quantity tax paid
by buyers rises as supply becomes more
own-price elastic or as demand becomes
less own-price elastic.
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
ps= p*
$tpb
qt = q*
As market demand
becomes less own-
price elastic,tax
incidence shifts more
to the buyers.
When?D = 0,buyers pay the entire tax,even
though it is levied on the sellers.
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.
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
No tax
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
No tax
CS
PS
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
CS
PS
The tax reduces
both CS and PS,
transfers surplus
to government
Tax
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
CS
PS
The tax reduces
both CS and PS,
transfers surplus
to government
Tax
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
CS
PS
The tax reduces
both CS and PS,
transfers surplus
to government,
and lowers total
surplus.
Tax
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
CS
PS
Tax
Deadweight loss
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Deadweight loss falls
as market demand
becomes less own-
price elastic.
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Deadweight loss falls
as market demand
becomes less own-
price elastic.
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
ps= p*
$tpb
qt = q*
Deadweight loss falls
as market demand
becomes 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.
Equilibrium
Market Equilibrium
A market is in equilibrium when total
quantity demanded by buyers equals
total quantity supplied by sellers.
Market Equilibrium
p
D(p),S(p)
q=D(p)
Market
demand
Market
supply
q=S(p)
p*
q*
D(p*) = S(p*); the market
is in equilibrium.
An Example
D p a bp( )
S p c dp( )
At the equilibrium price p*,D(p*) = S(p*).
That is,a bp c dp* *
which gives p a c
b d
*
and q D p S p ad bcb d* * *( ) ( ),
Market Equilibrium
Can we calculate the market
equilibrium using the inverse market
demand and supply curves?
Yes,it is the same calculation.
Market Equilibrium
q D p a bp p a qb D q( ) ( ),1
q S p c dp p c qd S q( ) ( ),1
the equation of the inverse market
demand curve,And
the equation of the inverse market
supply curve.
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
S(p) = c+dp,so d=0
and S(p)? c.
p
qq* = c
D-1(q) = (a-q)/b
Market
demand
Market quantity supplied is
fixed,independent of price.
Market Equilibrium
Market quantity supplied is
extremely sensitive to price.
S-1(q) = p*.
p
q
p*
D-1(q) = (a-q)/b
Market
demand
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 these conditions apply no
matter if the tax is levied on sellers or on
buyers.
Quantity Taxes
p p tb s D p S pb s( ) ( )?and
describe the market’s equilibrium.
Notice that these two conditions apply no
matter if the tax is levied on sellers or on
buyers.
Hence,a sales tax rate $t has the
same effect as an excise tax rate $t.
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
No tax
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$t
An excise tax
raises the market
supply curve by $t
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An excise tax
raises the market
supply curve by $t,
raises the buyers’
price and lowers the
quantity traded.
$tpb
qt
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An excise tax
raises the market
supply curve by $t,
raises the buyers’
price and lowers the
quantity traded.
$tpb
qt
And sellers receive only ps = pb - t.
ps
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An sales tax lowers
the market demand
curve by $t
$t
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An sales tax lowers
the market demand
curve by $t,lowers
the sellers’ price and
reduces the quantity
traded.$t
qt
ps
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
An sales tax lowers
the market demand
curve by $t,lowers
the sellers’ price and
reduces the quantity
traded.$t
pb
qt
And buyers pay pb = ps + t.
ps
Quantity Taxes & Market Equilibrium
Who pays the tax of $t per unit
traded?
The division of the $t between buyers
and sellers is the incidence of the
tax.
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
pb
qt
ps
Quantity Taxes & Market Equilibrium
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
pb
qt
ps
Tax paid by
buyers
Tax paid by
sellers
Quantity Taxes & Market Equilibrium
E.g,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 sD p S pb s( ) ( )?and so
p p tb sa bp c dpb s,and
Substituting for pb gives
a b p t c dp p a c btb ds s s( ),
Quantity Taxes & Market Equilibrium
p a c btb dsand p p tb sgive
The quantity traded at equilibrium is
q D p S p
a bp
ad bc bdt
b d
t
b s
b
( ) ( )
.
p a c dtb db
Quantity Taxes & Market Equilibrium
p a c btb ds
p a c dtb db
q ad bc bdtb dt
As t increases,ps falls,
pb rises,
and qt falls.
Quantity Taxes & Market Equilibrium
p a c btb ds
p a c dtb db
q ad bc bdtb dt
The tax paid per unit by the buyer is
p p a c dtb d a cb d dtb db*,
The tax paid per unit by the seller is
p p a cb d a c btb d btb ds*,
Quantity Taxes & Market Equilibrium
p a c btb ds
p a c dtb db
q ad bc bdtb dt
The total tax paid (by buyers and sellers
combined) is
T tq t ad bc bdtb dt,
What Determines Tax Incidence?
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Change to buyers’
price is pb - p*.
Change to quantity
demanded is Dq.
Dq
Tax Incidence and Own-Price
Elasticities
Around p = p* the own-price elasticity
of demand is approximately
D
b
b
D
q
q
p p
p
p p
q p
q
D
D
*
*
*
*
*
*
.
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Change to sellers’
price is ps - p*.
Change to quantity
demanded is Dq.
Dq
Tax Incidence and Own-Price
Elasticities
Around p = p* the own-price elasticity
of supply is approximately
S
s
s
S
q
q
p p
p
p p
q p
q
D
D
*
*
*
*
*
*
.
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
pb
qt
ps
Tax paid by
buyers
Tax paid by
sellers
Tax incidence =
p p
p p
b
s
*
*
.
Tax Incidence and Own-Price
Elasticities
Tax incidence =
p p
p p
b
s
*
*
.
p p
q p
q
b
D
*
*
*
.
D
p p
q p
q
s
S
*
*
*
.
D
So
p p
p p
b
s
S
D
*
*
.
Tax Incidence and Own-Price
Elasticities
p p
p p
b
s
S
D
*
*
.
Tax incidence is
The fraction of a $t quantity tax paid
by buyers rises as supply becomes more
own-price elastic or as demand becomes
less own-price elastic.
Tax Incidence and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
ps= p*
$tpb
qt = q*
As market demand
becomes less own-
price elastic,tax
incidence shifts more
to the buyers.
When?D = 0,buyers pay the entire tax,even
though it is levied on the sellers.
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.
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
No tax
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
No tax
CS
PS
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
CS
PS
The tax reduces
both CS and PS,
transfers surplus
to government
Tax
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
CS
PS
The tax reduces
both CS and PS,
transfers surplus
to government
Tax
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
CS
PS
The tax reduces
both CS and PS,
transfers surplus
to government,
and lowers total
surplus.
Tax
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
CS
PS
Tax
Deadweight loss
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Deadweight loss falls
as market demand
becomes less own-
price elastic.
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
p*
q*
$tpb
qt
ps
Deadweight loss falls
as market demand
becomes less own-
price elastic.
Deadweight Loss and Own-Price
Elasticities
p
D(p),S(p)
Market
demand
Market
supply
ps= p*
$tpb
qt = q*
Deadweight loss falls
as market demand
becomes 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.
