next Exam Wednesday
Is your Aplia average above 75%?
Can you answer nearly all the problems on the
first three Self-Grading Quizzes on Sakai?
If you cant answer both questions with yes,
you are at risk of underperforming in this class.
You need to:
Diagnose your problems quickly.
Use the Krugman-Wells Study Guide (on Aplia) to improve your
understanding in the problem areas you identify.
See me or a TA in our office hours.
Attend a review session.
Today: 4:30 to 5:50 p.m. Frelinghuysen A4
Tomorrow: 4:30 to 5:50 p.m. Scott 202
Todays agenda
Taxes
Who pays a tax?
When does taxation have an efficiency cost?
What makes a good tax base?
Cross price elasticity of demand
AB
% Q A
=
=
% P B
QA
QA
PB
PB
Income elasticity of demand
Y
% Q
=
=
% Y
Q
Q
Y
Y
Price elasticity of supply
S
% QS
=
%P
QS
QS
=
P
P
Who really pays a tax?
legal incidence
From whom is the tax is directly collected?
vs.
economic incidence
How is the economic burden of the tax shared?
Who really pays a tax?
Economic incidence is not the same as legal
incidence because taxes change prices.
These price changes can shift tax burdens
from buyers to sellers, or vice versa
upstream
downstream
Today: focus on buyers v. sellers
Supply curves:
the Marshallian view
Usual
interpretation
When P = c,
quantity
supplied is d.
$/Q
S
c
Another view
To be willing to
supply d, the
minimum price
suppliers must
receive is c.
d
Q
Demand curves viewed the same way
Usual
interpretation
$/Q
When P = c,
quantity
demanded is d.
Another view
The maximum
price at which
buyers would be
willing to
purchase the
quantity d
equals c.
c
D
d
Q
Market equilibrium, la Marshall
$/Q
Equilibrium occurs
at the quantity at
which:
D
S
the maximum
price buyers are
willing to pay
equals
P*
the minimum
price sellers
insist on
receiving
Q*
Q
$t per unit tax, collected from sellers
With no tax,
sellers must
receive $c per
unit in order to
be willing to
supply d.
$/Q
S
c
d
Q
$t per unit tax, collected from sellers
With no tax,
sellers must
receive $c per
unit in order to
be willing to
supply d.
Since sellers
must remit $t
to the tax
collector, the
gross price
they must
receive is $c+t.
$/Q
c+t
S
c
d
Q
$t per unit tax, collected from sellers
With no tax,
sellers must
receive $c per
unit in order to
be willing to
supply d.
Since sellers
must remit $t
to the tax
collector, the
price they must
receive is $c+t.
S+t
$/Q
c+t
a+t
S
c
a
d
Q
$t per unit tax, collected from sellers
Now add
the demand
curve.
$/Q
S+t
S
D
Q
$t per unit tax, collected from sellers
Now add
the demand
curve.
Equilibrium
without the
tax occurs
at (P0,Q0).
S+t
$/Q
S
P0
D
Q0
Q
$t per unit tax, collected from sellers
Equilibrium
with the tax
occurs at Qt.
Only at Qt is the
price buyers are
willing to pay
equal to the
(gross) price
sellers must get.
S+t
$/Q
S
P0
D
Qt Q0
Q
$t per unit tax, collected from sellers
Equilibrium
with the tax
occurs at Qt.
Only at Qt is the
price buyers are
willing to pay
equal to the
(gross) price
sellers must get.
S+t
$/Q
S
Pb
P0
Ps
Now 2 prices
D
Buyers price Pb
Sellers price Ps
P s = Pb - t
Qt Q0
Q
$t per unit tax, collected from sellers
Equilibrium
with the tax
occurs at Qt.
Only at Qt is the
price buyers are
willing to pay
equal to the
(gross) price
sellers must get.
S+t
$/Q
S
Pb
P0
Ps
Now 2 prices
D
Buyers price Pb
Sellers price Ps
P s = Pb - t
Qt Q0
Q
Does the buyer pay the whole tax?
Pb
P0
Ps
Does the buyer pay the whole tax?
Pb
t
P0
Ps
Does the buyer pay the whole tax?
Pb
t
P0
Ps
Tax per unit
Does the buyer pay the whole tax?
Pb
t
P0
Ps
Increase in price
paid by buyer
Does the buyer pay the whole tax?
Pb
t
P0
Ps
Decrease in price
received by seller
Does the buyer pay the whole tax?
No.
$t per unit tax, collected from sellers
Equilibrium
with the tax
occurs at Qt.
Only at Qt is the
price buyers are
willing to pay
equal to the
(gross) price
sellers must get.
S+t
$/Q
S
Pb
P0
Ps
Now 2 prices
Buyers price Pb
D
Sellers price Ps
P s = Pb - t
Qt Q0
Q
$t per unit tax, collected from sellers
Buyers share
of the tax =
S+t
$/Q
S
(Pb - P0)
t
Sellers share
of the tax =
Pb
P0
Ps
(P0 - Ps)
D
t
Qt Q0
Q
$t per unit tax, collected from buyers
With no tax, the $/Q
maximum price
at which buyers
are willing to
purchase the
quantity d is $c.
c
D
d
Q
$t per unit tax, collected from buyers
With no tax, the $/Q
maximum price
at which buyers
are willing to
purchase the
quantity d is $c.
c
If buyers must
remit $t to the
tax collector,
c-t
the most they
are willing to
pay to sellers is
$(c - t).
D-t
d
D
Q
$t per unit tax, collected from buyers
$/Q
Equilibrium
without a tax
occurs at (P0,Q0).
S
P0
D-t
Q0
D
Q
$t per unit tax, collected from buyers
$/Q
Equilibrium
without a tax
occurs at (P0,Q0).
Equilibrium with
the tax occurs at
Qt.
S
P0
Only at Qt is the net
price buyers are
willing to pay equal
to the (net) price
sellers must get.
D-t
Qt
Q0
D
Q
$t per unit tax, collected from buyers
Again, there are $/Q
2 prices
S
Buyers price Pb
Sellers price Ps
Pb = Ps + t
Relative tax
burdens of the
two sides are
determined as
before.
Pb
P0
Ps
D-t
Qt
Q0
D
Q
Does legal incidence matter?
$/Q
Now compare
the incidence of
S
a tax levied on
sellers
a tax levied on
buyers
Pb
P0
Ps
D-t
Qt
Q0
D
Q
Does legal incidence matter?
$/Q
Now compare
the incidence a of
S+t
S
tax levied on
sellers
a tax levied on
buyers
Qt, Pb, and Ps are
the same
regardless of the
legal incidence
of the tax!
Pb
P0
Ps
D-t
Qt
Q0
D
Q
Does legal incidence matter?
Significance
Can ignore the
legal incidence and
analyze economic
incidence by
whatever method
is convenient.
Pointless in
designing tax
policy to worry
about legal
incidence.
Example: Social
Security payroll
(FICA) taxes
$/Q
S+t
S
Pb
P0
Ps
D-t
Qt
Q0
D
Q
Algebraic analysis of tax incidence
To find P0 and Q0 without the tax, solve
simultaneously:
P = c + dQ
(supply equation)
P = a - bQ
(demand equation)
To find Pb and Qt with the tax, solve
simultaneously:
P = (c + t) + dQ
(shifted supply equation)
P = a - bQ
(demand equation)
Then compute Ps = Pb - t
Example: $10 per unit tax
PD = 100 .01 Q
PS = 20 + .03 Q
100 .01 Q = 20 + .03 Q
S+t
$/Q
S
Pb
P0
Ps
80 = .04 Q
2000 = Q 0
80 = P0
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 .01 Q
PS = 20 + .03 Q
100 .01 Q = 20 + .03 Q
S+t
$/Q
S
Pb
P0
Ps
80 = .04 Q
2000 = Q 0
80 = P0
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 .01 Q
PS = 20 + .03 Q
100 .01 Q = 20 + .03 Q
S+t
$/Q
S
Pb
P0
Ps
80 = .04 Q
2000 = Q 0
80 = P0
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 .01 Q
PS = 20 + .03 Q
100 .01 Q = 20 + .03 Q
S+t
$/Q
S
Pb
P0
Ps
80 = .04 Q
2000 = Q 0
80 = P0
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 .01 Q
PS = 20 + .03 Q
100 .01 Q = 20 + .03 Q
S+t
$/Q
S
Pb
P0
Ps
80 = .04 Q
2000 = Q 0
80 = P0
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 . 01 Q
S+t
$/Q
PS = 20 + 10 + . 03 Q
100 . 01 Q = 30 + . 03 Q
70 = . 04 Q
S
Pb
P0
Ps
1750 = Q *
Pb = 100 . 01 (1750 )
Pb = 82.50
Ps = 72.50
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 . 01 Q
S+t
$/Q
PS = 20 + 10 + . 03 Q
100 . 01 Q = 30 + . 03 Q
70 = . 04 Q
S
Pb
P0
Ps
1750 = Q *
Pb = 100 . 01 (1750 )
Pb = 82.50
Ps = 72.50
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 . 01 Q
S+t
$/Q
PS = 20 + 10 + . 03 Q
100 . 01 Q = 30 + . 03 Q
70 = . 04 Q
S
Pb
P0
Ps
1750 = Q *
Pb = 100 . 01 (1750 )
Pb = 82.50
Ps = 72.50
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 . 01 Q
S+t
$/Q
PS = 20 + 10 + . 03 Q
100 . 01 Q = 30 + . 03 Q
70 = . 04 Q
S
Pb
P0
Ps
1750 = Q t
Pb = 100 . 01 (1750 )
Pb = 82.50
Ps = 72.50
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 . 01 Q
S+t
$/Q
PS = 20 + 10 + . 03 Q
100 . 01 Q = 30 + . 03 Q
70 = . 04 Q
S
Pb
P0
Ps
1750 = Q t
Pb = 100 . 01 (1750 )
Pb = 82.50
Ps = 72.50
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 . 01 Q
S+t
$/Q
PS = 20 + 10 + . 03 Q
100 . 01 Q = 30 + . 03 Q
70 = . 04 Q
S
Pb
P0
Ps
1750 = Q t
Pb = 100 . 01 (1750 )
Pb = 82.50
Ps = 72.50
D
Qt Q0
Q
Example: $10 per unit tax
PD = 100 . 01 Q
S+t
$/Q
PS = 20 + 10 + . 03 Q
100 . 01 Q = 30 + . 03 Q
70 = . 04 Q
S
Pb
P0
Ps
1750 = Q *
Pb = 100 . 01 (1750 )
Pb = 82.50
Ps = 72.50
D
Qt Q0
Q
What determines
the incidence of a tax?
How the tax burden is shared between buyers
and sellers depends on the relative price
elasticities of supply and demand.
$t per unit tax, collected from sellers:
benchmark case
Buyers share
of the tax =
S+t
$/Q
S
(Pb - P0)
t
Sellers share
of the tax =
Pb
P0
Ps
(P0 - Ps)
D
t
Qt Q0
Q
Buyers bear a smaller share
of the tax if demand is more elastic
Buyers share
of the tax =
S+t
$/Q
S
(Pb - P0)
t
Sellers share
of the tax =
Pb
P0
D
Ps
(P0 - Ps)
t
Qt Q0
Q
Buyers bear a greater share
of the tax if demand is less elastic
Buyers share
of the tax =
(Pb - P0)
t
Sellers share
of the tax =
S+t
$/Q
S
Pb
P0
Ps
(P0 - Ps)
D
t
Qt Q0
Q
Benchmark case again
Buyers share
of the tax =
S+t
$/Q
S
(Pb - P0)
t
Sellers share
of the tax =
Pb
P0
Ps
(P0 - Ps)
D
t
Qt Q0
Q
Sellers bear a greater share
of the tax if supply is less elastic
Buyers share
of the tax =
$/Q
S+t
S
(Pb - P0)
t
Sellers share
of the tax =
Pb
P0
Ps
(P0 - Ps)
D
t
Qt Q0
Q
Sellers bear a smaller share
of the tax if supply is more elastic
Buyers share
of the tax =
$/Q
S+t
(Pb - P0)
t
Sellers share
of the tax =
S
Pb
P0
Ps
(P0 - Ps)
D
t
Qt
Q0
Q
Moral of the story...
How the tax is shared between buyers and
sellers depends on the relative elasticities of
demand and supply.
The less elastic side of the market bears a
larger share of the tax.
The economic incidence of a tax does not
depend on the legal incidence of the tax.
Cost of taxation in an efficient market
$t per unit tax
What is the
impact of this
tax on consumer
and producer
surplus?
S+t
$/Q
S
Pb
P0
Ps
How large is tax
revenue?
D
Qt Q0
Q
Cost of taxation in an efficient market
b
0
s
t
0
Cost of taxation in an efficient market
b
0
s
t
0
Cost of taxation in an efficient market
b
0
s
t
0
Cost of taxation in an efficient market
b
0
s
t
0
Cost of taxation in an efficient market
b
0
s
t
0
Cost of taxation in an efficient market
b
0
s
t
0
Does taxation always cause a
deadweight loss?
Does taxation always cause a
deadweight loss?
Does taxation always cause a
deadweight loss?
Does taxation always cause a
deadweight loss?
Different,
for example,
in cases of
pollution or
congestion
Does taxation always cause a
deadweight loss?
Does taxation always cause a
deadweight loss?
Does taxation always cause a
deadweight loss?
Does taxation always cause a
deadweight loss?
Todays agenda
Taxes
Who pays a tax?
When does taxation have an efficiency cost?
What makes a good tax base?