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Equivalence of Tariffs and Quotas
Under Foreign Supply Monopoly
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Econ 567 Project 1
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3/18/2013
Fei Zhan & Can Huang
Table of Content
I. INTRODUCTION
This model examines the equivalence of tariffs and quotas in their protective effects with
monopolistic supply from abroad, in the development of practical commercial policies by
analyzing the "Voluntary Export Restrictions."
The paper based on the previous research of Jagdish Bhagwati, which concluded that an
import tariff and a corresponding quota produce identical discrepancy between foreign
and domestic prices. Hirofumi Shibata improved the model by introducing a monopoly
element into the foreign supply, this does not create different domestic prices whether a
given import level is permitted by a tariff or by a quota as concluded.
By constructing the model, we tested separately the two conditions: when an import tariff
is charged and when a quota is allocated. By setting the constraints and adopting the
“Solver” in Microsoft Excel, we achieved the same results for both conditions. The
import ratio set by government when a tariff is imposed equals the one when quota is
allocated.
II. MODEL
A. GENERAL ASSUMPTIONS
(a) Monopoly in foreign supply.
(b) Perfect competition in domestic production.
(c) A quota which was allocated so as to ensure perfect competition among the
quota holders.
(d) An import ratio is set by government
(e) Import market is in balance.
B. VARIABLES AND PARAMETERS
(a) Parameters
a
10
b
0.5
c
20
j
-0.5
e
3
f
0.25
g
5
(b) Variables for model with tariff
Endogenous
Definition
Initial values
Sd
domestic supply
14
Pd
domestic price
8
D
domestic demand
16
Df
demand for import
2
Sf
Foreign Supply
2
R
tax revenue collected by the government
0
t
tax
0
h
import ratio target set by the government
0.14
(c) Variables for model with quota
Endogenous
Definition
Initial values
Sdq
domestic supply
14
Dq
domestic demand
16
Dfq
demand for import
2
Pdq
domestic price
8
Sfq
Foreign supply
2
hq
import ratio target set by the government
0.14
C. BASIC EQUATIONS AND EXPLANATIONS
(a) Equations and explanations for model with tariff
Equations
Sd=a+bPd
D=c+jPd
Df=D-Sd=(c-a)+(j-b)Pd
Df=Sf
C=e+gSf+fSf^2
dC/dSf=(1/(1+t))(d(PdSf)/dSf)
Notes
domestic supply
domestic demand
demand for import equals domestic demand minus
domestic supply
import market clearance
cost function of foreign producer
marginal cost equals marginal revenue after tariff
g+2fSf=(1/(1+t))(Pd+ Sf/(j-b))
R=(t/1+t)PdSf
tax revenue collected by the government
h=Sf/Sd
import ratio target set by the government
Name the equations from top to bottom (1) to (8). Equation (1) and (2) state that the
domestic supply and domestic demand are each a function of domestic price; in equation
(3), the difference between total demand and domestic supply equals the net demand
available to the foreign monopolist and in equation (4) this difference clears market by
equalizing to foreign supply; equation (5) that total cost of foreign supply is a function of
the level of production; equation (6) that marginal revenue from foreign sale is equated
by the monopolist to his marginal cost; and equation (7) that imported tariff collected by
government equals the tariff revenue per unit multiplied by the foreign supply; equation
(8) shows that an import ration is set by proportion foreign supply to domestic supply.
We have eight equations and eight unknowns: SD, D, DF, SF, PD, R, h, and t. Set each
initial values and constraint the equations to zero, we can determine the remaining values
and target value of h by using solver. Accordingly, corresponding to every t, there will be
some level of imports, SF, and domestic price, PD.
(b) Equations and explanations for model with quota
Equations
Notes
Sdq=a+bPdq
domestic supply
Dq=c+jPdq
domestic demand
Dfq=Dq-Sdq=(c-a)+(j-b)Pdq
demand for import equals domestic demand minus
domestic supply
Dfq=Sfq
import market clearance
Cq=e+gSfq+fSfq^2
cost function of foreign producer
dCq/dSfq=(d(PdqSfq)/dSfq)
marginal cost equals/less than marginal revenue
OR
after tariff
dCq/dSfq<(d(PdqSfq)/dSfq)
ie: g+2fSfq=(Pdq+ Sfq/(j-b))
OR
effective quota: less than
ineffective quota: equal
g+2fSfq<(Pdq+ Sfq/(j-b))
hq=Sfq/Sdq
import ratio target set by the government
All the same, we name the equations from top to bottom (1) to (7). Except for (6), all
other equations are exactly the same and have the same meanings with their
corresponding ones in equations of model under tariff charges. This case with quota
states that the maximizing equilibrium condition for the monopolist when a quota is set;
the equality sign holds if the monopolist sells less than the quota (i.e., the quota becomes
ineffective), and the inequality if he sells the maximum amount set by the quota.
In this case, there are thus seven equations and six unknowns: SD, D, DF, SF, PD, and h.
The import level which will maximize the foreign monopolist's profits is thus determined.
After equations are set, we can begin set constraints and use solver to solve for the values
of h and examine if the import ratios in the above two cases will be equal or not.
III. MODELING RESULTS AND ANALYSIS
Constraining the equations and setting initial values for endogenous variables, we get the
value of government-set import ratios in both cases with the help of solver.
As can be seen below, the procedure of tariff case is:
Constraint to
zero
equation value
Endogenous
Final viable
Initial viable
values
values
0
0
Sd
14.63414634
14
0
0
Pd
9.268292683
8
0
0
D
15.36585366
16
0
0
Df
0.731707317
2
3.38891E-10
0
Sf
0.731707317
2
0
R
8.014709855
0
0
t
0.590909091
0
h
0.05
0.14
-4.94462E09
2.58994E-13
target h
0.05
And for the case with quota, it illustrated as follows:
Constraint to
equation
zero
value
Endogenous
Final viable
Initial viable
values
values
0
0
Sdq
14.63414725
14
0
0
Pdq
9.268294504
8
0
0
Dq
15.36585275
16
0
0
Dfq
0.731705496
2
1.27566E-07
0
Sfq
0.731705496
2
-3.170736261
<=0
0.05
0.14
hq
target hq
0.05
Hence, the target import ratio set by government under the case of imposing an import
tariff equals the target import ratio when quota is allocated. Therefore, an import tariff
and a corresponding quota produce identical divergence between foreign and domestic
prices is proved. Additionally, the domestic prices are kept the same in both cases since
tariff and quota permit same level of imports as can be seen from the result boxes.
Further more, the equilibriums in the two systems are illustrated in an dynamic form in
figure 1.
Source: A Note on the Equivalence of Tariffs and Quotas
Figure 1
In this figure we place first a tariff rate that generates an import level; then we set the
identical import level as a quota and illustrate that the same domestic price is generated
but higher price for the foreign monopolist.
In the tariff system, because tax rate is MK divided by KQ, it shifts the net demand for
the monopolist downwards to GH and marginal revenue of monopolist to GL.
Equilibrium exists at J where the marginal cost line intersects marginal revenue line for
the monopolist, so that export of monopolist totals OQ, the domestic price is at OA while
the monopolist's c.i.f. price is at OB.
In the quota system, we adopted the same import level OQ as the quota. EI, as the
corresponding marginal revenue, becomes discontinuous at I. Equilibrium exists where
the marginal cost schedule for the monopolist cuts the demand curve below I so that the
monopolist exports exactly the same volume set by the quota and the domestic price is at
OA which in turn becomes the monopolist's c.i.f. price.
In the case marginal cost line crosses the marginal revenue curve between E and I, the
monopolist cannot use all the quota allocated, which intern pushes the domestic price
higher than OA. However, the marginal cost line will never cut the marginal revenue
schedule between E and I, as long as the quota is set at the same import level under the
positive tariff system, because at the monopolist's equilibrium export level reached under
a positive tariff (OQ in Figure 1), the monopolist's marginal cost (QJ) definitely be
smaller than the monopolist's marginal revenue that would exist if there were no tariff
(QI).
Thus we have shown that conditions of foreign supply make no difference for the
equivalence of tariffs and quotas in protective effect, under the condition of perfect
competition in domestic production and among quota holders.
IV. IMPLICATION FOR POLICIES
The demonstration here has implication on the “Voluntary Export Restriction” policy.
The system was employed by Japan, Hong Kong, and South Korea in their exports,
chiefly of textile products, to the United States, Canada, and other European countries. In
this system, the exporting and importing country negotiate about the quantity of specific
commodities allowed to enter into the importing country. In one condition that they fail
to make an agreement, the importing country will impose a tariff on the commodities in
question. In other condition, if the two countries agree on the volume of imports, the
exporting country will promise to voluntarily administer the de facto import quota agreed
upon, while the importing country concedes the non-use of tariffs. This type of policy has
its own rationality based on our analysis above. Firstly, for protection purpose, the tariff
and quota are equally effective for the policy maker of the importing country. Secondly,
for the monopolist of the exporting country, quota is preferred to tariff if some kind of
trade restriction is inevitable. Facing the restriction by quota, they can manage to obtain
some part of the quota rent through the formation of cartel. Whereas in the restriction of
tariff, the same part of revenue will be collected by the government of importing country.
Therefore, from the perspective of both the importing country and the exporting country,
the Voluntary Export Restriction Policy is preferred to the explicit tariff restriction.
Reference
1. J. BHAGWATI, "On the Equivalence of Tariffs and Quotas," in R. E. Bald- win
and others, editors, Trade, Growth, and the Balance of Payments- Essays in Honor
of Gottfried Haberler, Chicago 1965.
2.
J. BHAGWATI, "More on the Equivalence of Tariffs and Quotas," Am. Econ.
Rev., this issue, 142-46