PubPol/Econ 541
Tariff Analysis
Partial Equilibrium
by
Alan V. Deardorff
University of Michigan
2016
Outline
• Small country
• Large country
2
Small country
• Assumptions throughout
– Markets perfectly competitive
– Product homogeneous
– There are no “distortions” (externalities, etc.)
– Supply and demand curves linear
• Just for simplicity
• Special assumption for small country case
– World price is given (country too small to
influence it)
3
Small country, Import Industry
P
• Effects of move from
autarky to free trade
S
Paut
–
–
–
–
a
b
Price falls
Quantity supplied falls
Quantity demanded rises
Imports rise
• Welfare effects:
P0=PW
D
S0
M
0
D0
Q
– Suppliers lose −a
– Demanders gain +(a+b)
– Country gains
+b
Free trade
4
Small country tariff
P
• Effects of a tariff, starting from
free trade
S
Paut
–
–
–
–
–
P1=PW+t
t
P0=PW
Price rises
Quantity supplied rises
Quantity demanded falls
Quantity of imports falls
Tariff revenue rises from zero
D
M
1
S0 S
1
M
0
D1 D0
Q
Specific Tariff t
5
Small country tariff
P
• Welfare effects of a tariff,
starting from free trade
S
Paut
P1=PW+t
t
P0=PW
a
b
c
–
–
–
–
Suppliers gain
+a
Demanders Lose −(a+b+c+d)
Government gains +c
Country loses
−(b+d)
d
D
M
1
S0 S
1
M
0
D1 D0
Q
Specific Tariff t
6
Small country, larger tariff
P
• Effects of doubling the tariff
S
– Price rises by twice as much
– Imports fall by twice as much
– Deadweight loss is 4-times as
large!
Paut
P2=PW+2t
P1=PW+t
t
P0=PW
• (Efficiency loss rises with the
square of the tariff)
M
2
D
M
1
S0 S
1
M
D1 D0
Q
0
Specific Tariffs, t, then 2t
7
Small country, prohibitive tariff
P
PW+tP≠P1
• Welfare effects of a prohibitive
tariff, starting from free trade
S
P1= Paut
–
–
–
–
tP
a
b
d
Suppliers gain
+a
Demanders Lose −(a+b+d)
Government gains 0
Country loses
−(b+d)
P0=PW
D
S0 S
1
D1
M
( M01=0 )
D0
Q
Specific Tariff tP > Paut − PW
8
Outline
• Small country
• Large country
9
Large country
(i.e., Two Countries)
Home
P
Foreign (*)
P*
S
S*
Paut
D*
P*aut
D
Q
Q*
Autarky
10
Large country
(i.e., Two Countries)
Home
P
World
Foreign
P
S
P*
XS*
Paut
S*
D*
PW0
P0=PW0
P*0=PW0
D
S0 M D0
0
Q
MD
M0=X*
0
P*aut
M,X*
D*0 X* S*0
0
Q*
Free trade
11
Large country
(i.e., Two Countries)
Home
P
World
Foreign
P
S
P*
XS*
S*
D*
P1
P1
P0=PW0
t
P*1
M1
S0 M D0
0
S1 D
1
D
Q
P*1
M1=X*1
M0=X*
0
MD
M,X*
X*1
D*0 X* S*0
0
D*1 S*
1
Tariff, t
Requires: P=P*+t, MD=XS*
Q*
12
Large country (i.e., Two Countries)
Home
P
World
Foreign
P
S
P*
XS*
P1
t
P0=PW0
P*1
D*
P1
a
b
c
e
t
d
P*1
c
e
f
g
h
S0
D0
S1 D1
Q
MD
M0=X*
Suppliers
+a
Demanders –(a+b+c+d)
Government +(c+e)
Country
+e−(b+d) = e−f
M,X*
0
Welfare effects of Tariff, t:
• Home
i e j
P*1
D
–
–
–
–
S*
D*0
S*0
D*1 S*1
Q*
• Foreign
– Suppliers −(h+i+e+j)
– Demanders +h
– Country
−(i+e+j) = −(e+g)
• World: −(f+g) = −(b+d+i+j)
Large country, World Market
World Market
Home is Importer
Foreign (*) is Exporter
P
XS*
P1
t
a
c
Welfare effects of a largecountry tariff, starting from free
trade
• Home:
Private sector (S&D) loses −(a+b)
Government gains
+(a+c)
Country may gain or lose: +c−b
b
d
P*1
MD
• Foreign
Private sector (S&D) loses −(c+d)
M1=X*
M0=X*
1
0
M,X*
• World loses
−(b+d)
Large country, World Market
World Market
Home is Importer
Foreign (*) is Exporter
P
XS*
P1
t
a
c
b
d
P*1
MD
M1=X*
M0=X*
1
0
M,X*
Thus large country will gain from
tariff if c>b
• What is area c?
– The portion of the tariff paid by
foreign exporters, who get a
lower price
– A transfer from foreign producers
to the home government
– The result of improving the home
country’s “terms of trade”
Large country, “Optimal” tariff
Welfare
P
Paut
P1
t
XS*
a
c
b
d
b
c
topt
P*1
MD
Paut*
M1=X*
M0=X*
1
0
M,X*
t
c–b
Paut–Paut*
How Sizes and Slopes Matter
Home
P
World
Foreign
P
S
P*
XS*
Paut
S*
D*
PW0
P0=PW0
P*0=PW0
D
S0 M D0
0
Q
MD
M0=X*
0
P*aut
M,X*
D*0 X* S*0
0
Q*
Free trade
17
How Sizes and Slopes Matter
Home
P
Paut
World
Foreign
P
S
P*
XS*
PW0
P0=PW0
D*
S*
P*0=PW0
P*aut
D
MD
S0 M D0
0
Q
M0=X*
0
M,X*
D*0 X* S*0
0
Q*
Free trade
18