GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 297

Tariffs versus Production Subsidies as Industry Protection

Yoshitomo Ogawa and Yoshiyasu Ono

February 2013

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Tariﬀs versus Production Subsidies as Industry Protection

Yoshitomo Ogawa∗ and Yoshiyasu Ono†

February 2013

Abstract
This paper provides a welfare comparison of a tariﬀ with a combinationof a production subsidy to, and a commodity tax on, an import-competing
commodity in a two-country economy. We treat some plausible situationsof industry protection, including where the initial tariﬀ is above the optimal tariﬀ, where a certain output level of a tariﬀ-imposed commodity
must be maintained, and where there is positive externality of its domestic production. In those cases we explore the optimal combination of the
production subsidy and the commodity tax and show it to be superior to
the tariﬀ from the welfare viewpoint.

Keywords: Commodity Tax, Production Subsidy, Tariﬀ, Industry Protection
JEL Classification: F11, F13, H23∗

Faculty of Economics, Kinki University, 3-4-1 Kowakae, Higashiosaka, Osaka 577-8502,
JAPAN; E-mail: ogawa@eco.kindai.ac.jp†
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka
567-0047, JAPAN; E-mail: ono@iser.osaka-u.ac.jp.

11Introduction

A tariﬀ is a typical policy that is aimed to protect a particular industry fromforeign imports.1 For example, Japan currently imposes high tariﬀs on various
agricultural products for producer protection, e.g., 1705% on konjac, 1083% on
pea, 778% on rice, 593% on peanut and 482% on butter. However, it comesunder mounting pressure in the regime of the General Agreement on Tariﬀs andTrade (GATT) and the World Trade Organization (WTO). Recent conclusionsof various free trade agreements (FTAs) and economic partnership agreements(EPAs) have also accelerated tariﬀ reductions. An alternative policy of industry
protection is a production subsidy. For example, Korea implemented an agriculture compensation system when it concluded an FTA with the US. Production
subsidies to agricultural sectors in the US and the European Union (EU) amountto around 20 and 70 billion dollars per year, respectively. Noting the expanding
importance of such policy changes, we analyze the welfare eﬀect of a replacementof a protective tariﬀ by a production subsidy with a commodity tax. In particular, we compare the welfare eﬀect of a tariﬀ with that of a combination of a
production subsidy and a commodity tax when these policies are carried out forthe purpose of industry production, and explore the optimal protection policy.2
It is well known that a tariﬀ attains higher welfare than a production subsidy
when the country has monopoly power in trade (Bhagwati, 1971). However, if acertain degree of industry protection is required, the superiority of a tariﬀ over a
production subsidy may be ambiguous. This paper presents a welfare comparison
between a tariﬀ and a combination of a production subsidy and a commodity tax
in such likely cases as where in an import-competing sector a very high protective
tariﬀ is imposed, a certain production level must be maintained, or domestic
production of the sector yields some positive externality.
The literature on the optimal tariﬀ is substantial (see, for example, Kaldor,
1940; Graaﬀ, 1949—50; Johnson, 1951—1952; Kemp, 1967; Kennan and Riezman,
1988; Bond, 1990; Lahiri and Ono, 1999; Syropoulos, 2002). However, all of themlack the viewpoint of industry protection. Bhagwati and Ramaswami (1963) and
Bhagwati, Ramaswami and Srinivasan (1969) assume general domestic distortions
and point out the possibility that commodity and production tax-cum-subsidies
increase welfare but do not explicitly discuss their optimal levels. We fill thisvoid and analyze the optimal combination of the production subsidy to, andthe commodity tax on, the import-competing sector when the sector has to beprotected.
After confirming that a tariﬀ is equivalent to a combination of a production
1

Even now, a tariﬀ is a primary source of government revenue in many developing countries.
Corden (1957) intuitively discussed a production subsidy and a commodity tax as protection
policy using a graphical analysis.
22subsidy and a commodity tax with the same magnitude as the tariﬀ, we first explore the optimal commodity tax and the optimal production subsidy when they
can take diﬀerent magnitudes. We then examine the welfare eﬀect of replacing
the tariﬀ by the combination of the production subsidy and the commodity tax
that realizes the same degree of protection. This conversion is found to make thehome country better oﬀ when the preimposed tariﬀ is higher than the optimal
tariﬀ. It may apply to the case of the Japanese rice protection because the 778%
tariﬀ must exceed the optimal rate. Furthermore, we extend the analysis to suchcases as where the commodity tax and the production subsidy are chosen so thatthe tariﬀ-protected industry maintains a certain level of production and where
there is production externality, and show the same property to hold.

2

The Model

We consider a standard 2 × 2 × 2 general equilibrium competitive model. The
home country exports commodity 1 and imports commodity 2. There are two
production factors, labor L and capital K, which are fixed in supply and internationally immobile. The home country imposes a commodity tax (t) and a
production subsidy (s) on commodity 2, while the foreign country imposes neither
tariﬀs nor tax-cum-subsidies.
The production function of sector i (i = 1, 2) in the home country is
yi = fi (ki )Li , fi0 > 0 and fi00 < 0,i = 1, 2,(1)where yi is output of commodity i, Li and Ki are respectively labor and capital
inputs in sector i, and ki ≡ Ki /Li . The home firms’ optimization behavior leadstof10 (k1 ) = (s + p)f20 (k2 ) = r,
f1 (k1 ) − f10 (k1 )k1 = (s + p) [f2 (k2 ) − f20 (k2 )k2 ] = w,(2)

where p is the world price of commodity 2, r is the capital rent, w is the wage
rate and commodity 1 is taken as numeraire. From (2) we deriver = r(s + p), w = w(s + p), ki = ki (s + p),

i = 1, 2.

(3)

The factor market equilibrium conditions in the home country are
L1 + L2 = L and k1 L1 + k2 L2 = K,

(4)

where L and K are the home endowments of the two factors respectively. Equations (1), (3) and (4) give the two sectors’ labor demand and commodity supply:
Li = Li (s + p), yi = yi (s + p),
3

for i = 1, 2.

(5)A representative consumer in the home country has a well-behaved utility
function u(x1 , x2 ) where xi is demand for commodity i. Both commodities are
assumed to be normal and hence the home demand functions
xi = Di (t + p, Y ),i = 1, 2,(6)satisfy
DiY (≡ ∂Di /∂Y ) > 0 for i = 1, 2,

(7)

where
Y ≡ y1 + (s + p)y2 − T,T ≡ sy2 − tx2 .
Similarly, the foreign supply, demand and excess demand functions of commodityi(= 1, 2) are respectivelyyi∗ = yi∗ (p),x∗i = x∗i (p) = Di∗ (p, Y ∗ ) where Y ∗ ≡ y1∗ (p) + py2∗ (p),zi∗ = zi∗ (p) = x∗i (p) − yi∗ (p).

(8)

The international market-clearing condition for commodity 2 isD2 (t + p, Y ) + D2∗ (p, Y ∗ ) − y2 (s + p) − y2∗ (p) = 0.

(9)Note that with Walras’ law the market-clearing condition for commodity 1 necessarily holds if all the other markets are in equilibrium.
From (1)—(9) we obtaindy2 = y20 d(s + p),(1 − tD2Y )dx2 = D2p d(p + t) + D2Y · [(y10 + py20 )d(s + p) + y2 dp + x2 dt] ,
¶
µ
¶
µ
sD2Y
D2Y
D2p
+
x2 dt +
+ 1 y20 ds,(10)Ωdp = −
1 − tD2Y
1 − tD2Y
1 − tD2Y

where D2p ≡ ∂D2 /∂(p + t) and Ω satisfies.

D2Y
D2p
+
(y2 − sy20 ) + z2∗0 − y20 < 0,
1 − tD2Y
1 − tD2Y
∗
∗
∗
∗0
= D2p
+ D2Y
∗ y2 − y2 < 0,
> 0,
> 0.

Ω ≡
z2∗0
y20
y2∗0

(11)

The negativity of Ω implies the stability condition of the market of commodity
2, whereas the positivity of y20 and that of y2∗0 represent positively-inclined home4and foreign supply functions of commodity 2.3 z2∗0 is naturally assumed to be
negative since it represents the own-price eﬀect of z2∗ , the foreign excess demandfor commodity 2. Since the foreign country exports commodity 2, from (8) and(9) we findz2∗ = x∗2 − y2∗ = − (x2 − y2 ) < 0.
(12)
The optimal household behavior yields
u2= t + p,u1

(13)

where ui ≡ ∂u(x1 , x2 )/∂xi . From (1), (2) and (4), the optimal firm behavior gives(14)

dy1 + (s + p)dy2 = 0.
Total diﬀerentiation of the balance of payment equation provides
dx1 + pdx2 + x2 dp = dy1 + pdy2 + y2 dp.

(15)

Using these three equations and the total diﬀerentiation of u(x1 , x2 ) we finddu= − (x2 − y2 ) dp + tdx2 − sdy2 .
u1

(16)

Substituting dp, dx2 and dy2 given in (10) into (16) leads to(1 − tD2Y )du = (t − Λ)h2 dt + [(sD2Y + 1 − tD2Y )Λ − s] y20 ds,
u1

(17)

h2 ≡ D2p + D2Y x2 < 0,

(18)

where

Λ≡

−(x2 − y2 ) + th2 − sy20
(1 − tD2Y )Ω

.

(19)

Note that h2 in (18), which is the Hicksian own-price eﬀect, is naturally assumed
to be negative. By partially diﬀerentiating with respect to Y the home budget
constraint:
Y = D1 (t + p, Y ) + (t + p)D2 (t + p, Y ),and using (7), we find
1 − tD2Y = D1Y + pD2Y > 0.
3

(20)

>From (1), (3) and (5), y20 obtains as a function of k20 and L02 . Totally diﬀerentiating (2)yields k10 and k20 . Substituting them into the total diﬀerentiation of (4) gives L02 . By applying k20
and L02 thus obtained to the expression of y20 and using (2) we eventually find y20 to be positive.
The positivity of y2∗0 > 0 analogously obtains.

5

3

Optimal Commodity Tax and Production Subsidy

Having set up the model we now turn to analyze the properties of the optimalcommodity tax and the production subsidy.
From (17) and (19) we obtain the eﬀects of changes in s and t on utility u.
Applying the sign properties of (11), (12), (18) and (20) to the results yields
¯
µ ¶
µ ¶
1 du ¯¯1[(x2 − y2 ) + sy20 ] h2 > 0,=¯
u1 dt t=0, s=const.
Ω
¯
∙
µ ¶
¸
1
1 du ¯¯=[−(x2 − y2 ) + th2 ] y20 > 0.
u1 ds ¯s=0, t=const.
(1 − tD2Y )Ω
Therefore, we obtain the following proposition:

Proposition 1. (i) Oﬀering a low production subsidy to the import-competing
sector improves welfare when a non-negative commodity tax is imposed on the
sector, and (ii) imposing a low commodity tax on the sector improves welfare
when a non-negative production subsidy is oﬀered to the sector.
This proposition shows that oﬀering a low production subsidy to the importcompeting sector still improves welfare even if a commodity tax above the optimal
tariﬀ level has already been imposed on the sector, and that imposing a low
commodity tax on the sector still improves welfare even if a production subsidy
above the optimal tariﬀ level has already been oﬀered to the sector. Thus, theoptimal tariﬀ implication (namely, the positive eﬀect of an improvement in theterms of trade through an import restriction) still holds for a low production
subsidy irrespective of the level of the predetermined commodity tax, and fora low commodity tax irrespective of the level of the predetermined production
subsidy.
Let us next turn to the optimal combination of the commodity tax and the
production subsidy. From (17) they satisfy
t = Λ, s = (1 − tD2Y ) Λ/ (1 − D2Y Λ) ,and hence using (11), (12) and (19) we obtain
topt = sopt = Φ,Φ ≡ z2∗ /z2∗0 > 0,(21)

where z2∗0 and z2∗ are respectively given by (11) and (12) and Φ is equivalent to
the optimal tariﬀ.4 This property is formally restated as follows:4

Bhagwati (1971) intuitively discusses this property but does not give a formal proof.

6

Proposition 2. The optimal combination of the commodity tax and the production subsidy is equivalent to the optimal tariﬀ.
Noting that a tariﬀ is equivalent to the combination of production subsidys and commodity tax t that have the same magnitude as the tariﬀ, we next
consider the case where the tariﬀ is separated into the production subsidy andthe commodity tax and only the commodity tax is revised while the production
subsidy is maintained in order for the import-competing sector to be protected.
For example, Japan currently imposes a 778% tariﬀ rate on imported rice andmost likely the tariﬀ rate exceeds the optimal tariﬀ level. Replacing the tariﬀ by
the production subsidy is often discussed and in fact the Japanese government
has adopted an individual income support system in the agriculture sector. In
the following we will show that the separation benefits the country.
Suppose that initiallyt = s.
(22)
Then, Ω and z2∗0 in (11) and Λ in (19) satisfyµ ∗0 ¶zt − Λ = (t − Φ) 2 ,Ω(23)and hence (17) reduces toµ ∗0 ¶(1 − tD2Y )z
du = (t − Φ) 2 (h2 dt − y20 ds) .
u1Ω
From (11), (18), (20), (22) and (24), if s is fixed at a higher level than Φ,
¯
du ¯¯
< 0.
dt ¯t=s(>Φ)

(24)

(25)

Next, when t decreases from s and reaches Φ, using (11) and (19) we obtainµ 0¶yt − Λ = (s − Φ) 2 .
(26)Ω

Substituting this into t − Λ in (17) where s(> Φ) is kept constant yields¶µ(1 − tD2Y )h2 y20dt.
du = (s − Φ)u1ΩFrom (10), (11) and (20), the above expression shows
¯
du ¯¯
> 0.
dt ¯t=Φ(25) and (28) imply the following proposition.
7

(27)

(28)

Proposition 3. Suppose that a tariﬀ higher than the optimal tariﬀ is initially
imposed. If the tariﬀ is separated into a production subsidy and a commodity tax
and the production subsidy must take the same level as the tariﬀ, the optimalcommodity tax is between the initial level and the optimal tariﬀ level.

4

Production Support and Environmental Preservation

4.1

Production Support Policy

This section considers the case where the tariﬀ is replaced by the production
subsidy with the commodity tax adjusted so that production of commodity 2
is kept constant. The Japanese individual income support for farmers is indeed distributed according to the past crop average. It should be noted that a
production-keeping policy is equivalent to a price-keeping policy in the present
setting. The US Counter-Cyclical Payment (CCP), which compensates the difference between the market price and the target price, may be an example of theprice-keeping policy.
Let us start the analysis from the situation of (22) and obtain the welfare
eﬀect of the above-mentioned policy. If y2 is fixed and hence dy2 = 0, from (5)we obtain
0 = ds + dp.
Applying this property and (18) to (10) leads to
ds = θdt where θ ≡h2(1 − tD2Y ) Ω + y20

.

(29)

From (11) and (22), θ is rewritten asθ=h2,h2 − D2Y · (x2 − y2 ) + (1 − tD2Y ) z2∗0

and therefore using (7), the second property of (11), (12), (18) and (20), we find
0 < θ < 1.

(30)

From the second property of (11), (24) and (30), a small change in the commodity
tax with the production subsidy following (29) yields¯µ ¶1 du ¯¯= (t − Φ) z2∗0 θ < 0.
u1 dt ¯y2 =const.
This property implies the following:8

Proposition 4. Suppose that initially s = t > Φ. Then, a reduction in thecommodity tax t accompanied by a reduction in the production subsidy s thatkeeps production of commodity 2 constant improves welfare.
Intuitively, a decrease in the commodity tax stimulates demand for commodity
2, which increases its home producer price. Thus, in order to keep the home
production of commodity 2 constant the production subsidy must also be reduced.
(11), (20), (22) and (24) imply that when t is kept constant, du/ds satisfies
¯
du ¯¯
< 0,
ds ¯s=t(>Φ)
i.e., a reduction in the production subsidy increases home welfare. (25) showsthat a reduction in the commodity tax also increases home welfare. Therefore,
the decrease in the commodity tax and the subsequent decrease in the production
subsidy, mentioned in the proposition, makes the home country better oﬀ.
Moreover, from (29) and (30), the subsequent reduction in s that keeps y2
constant is smaller than the initial reduction in t. Therefore, the beneficial tax
reform is indeed a separation of the tariﬀ to the commodity tax and the production subsidy.

4.2

Environmental Preservation

This section considers the case with positive production externality, such as environmental preservation owing to agricultural production. The WTO agreement
on agriculture allows member countries to give a subsidy to agricultural sectors forenvironmental preservation or maintenance of areas under cultivation. It is paid
according to the past production level and hence is indeed a production subsidy.
In this section, we examine how an externality aﬀects the optimal commodity tax
and the optimal production subsidy.5
To do so, we modify the utility function asu(x1 , x2 ) + βy2 ,where β(> 0) shows such externality. For given β, totally diﬀerentiating theutility and applying (13), (14) and (15) to the result yields
du= dx1 + (t + p)dx2 + βdy2 = −(x2 − y2 )dp + tdx2 − (s − β)dy2 .
u1
5Markusen (1975, p.19) analyzes the optimal combination of a tariﬀ, instead of a commodity
tax, and a production tax in the presence of externality.

9

Using (10) and (11), we rewrite it as follows:¶µβy20(1 − tD2Y )h2 dt + [(sD2Y + 1 − tD2Y )Λ − s
du =
t−Λ−
u1
Ω
µ ¶¸
β
∗0
+ {D2p + D2Y y2 + (1 − tD2Y ) z2 }y20 ds. (31)ΩTherefore, the optimal tax and the optimal subsidy must satisfy
topt − Λ −
opt

opt

opt

(s D2Y + 1 − t D2Y )Λ − s

βy20
= 0,
Ω

£
¡
¢ ¤
+ D2p + D2Y y2 + 1 − topt D2Y z2∗0

µ ¶
β
= 0.
Ω

From these two equations in which Ω and Λ are respectively given by (11) and(19), we obtain the optimal tax and subsidy mentioned below.
Proposition 5. In the presence of production externality β the optimal tax andthe optimal subsidy are
topt = Φ, sopt = Φ + β,where Φ ≡ z2∗ (p)/z2∗0 (p).
By comparing the equations in proposition 5 with (21) we find that without
externality β the implication of proposition 5 is the same as that of proposition
2, that is, the optimal combination of the production subsidy and the commodity
tax is equivalent to the optimal tariﬀ Φ. In the presence of externality β, however,the production subsidy must be higher than the commodity tax by the magnitudeof the externality.
The existence of the externality strengthens the benefit of separating the tariﬀ
into the production subsidy and the commodity tax and lowering the commodity
tax only. In fact, from (23), (26) and (31) we obtain¯µ¶µ ∗0 ¶(1 − tD2Y ) du ¯¯
h2 y20
z2 h2
−β
,
(32)
= (t − Φ)u1dt ¯t=sΩΩ¯¶µ(1 − tD2Y ) du ¯¯
h2 y20.
(33)= [s − (Φ + β)]u1dt ¯t=ΦΩObviously, −βh2 y20 /Ω, which is negative from (11) and (18), represents the externality eﬀect, which enhances the benefit of a reduction in the commodity tax,
shown in proposition 3. By comparing them with (24) and (27) respectively, we
find that (32) is negative and that (33) is positive. Thus, if the production subsidy is higher than the first-best optimal level Φ + β, the optimal commodity tax
is between s and Φ —i.e., basically the same implication as proposition 3 holds.
10Proposition 6. If a country must oﬀer a higher production subsidy than thefirst-best optimal level, the optimal commodity tax is between the level of the
production subsidy and its own first-best optimal level.
Next, we examine the eﬀect of a change in β on sopt and topt . Noting that Φ
depends only on p, from the equations in proposition 5 we finddtopt = Φ0 dp, dsopt = dβ + Φ0 dp,(34)

where Φ0 = dΦ/dp. Applying the property that sopt − topt = β, stated in proposition 5, and the above equations to the last equation of (10) yields
dtopt(βD2Y + 1) y20 Φ0.
=dβ(1 − topt D2Y ) Ω + h2 Φ0 − (βD2Y + 1) y20 Φ0
From (11), (18), (20), (34) and the above equation, we obtain
dsopt
dtopt
< 0 and 0 << 1 if Φ0 > 0.
−1 <
dβ
dβ
Therefore, if Φ0 > 0, as externality β is larger, the optimal commodity tax decreases and the optimal production subsidy increases but the magnitudes of thechanges are less than the magnitude of the increase in the externality. Moreover,using (21) we find Φ0 to satisfy
Φ0 =(z2∗0 )2 − z2∗ z2∗00> 0 if (z2∗0 )2 > z2∗ z2∗00 .
(z2∗0 )2

Since z2∗ (= x∗2 − y2∗ ) < 0 as shown in (12), the above condition is valid if z2∗00 ≥ 0,that is, if the foreign excess demand for commodity 2 is non-convex with respect
to the price.
The above results are summarized as follows.
Proposition 7. Suppose that (z2∗0 )2 > z2∗ z2∗00 , which holds when the foreign excess
demand of commodity 2 is non-convex, and that production of commodity 2 yields
positive externality, e.g. environmental preservation. If the externality expands,
the optimal production subsidy increases and the magnitude of the increase is lessthan the expansion of the externality. The optimal commodity tax decreases andthe magnitude of the decrease is less than the expansion of the externality.

5

Conclusion

This paper examines the welfare eﬀects of separating a protective tariﬀ to a
production subsidy to, and a commodity tax on, the protected sector in various
11plausible situations, including the cases where (i) the initial tariﬀ is set above
the optimal tariﬀ, (ii) domestic production of the protected commodity must
be maintained, and (iii) there is positive externality of the sector’s domestic
production. We show that separating a protective tariﬀ to a commodity tax
and a production subsidy and lowering only the commodity tax makes the homecountry better oﬀ in these situations. Without any distortion of such, however,
the optimal combination of the subsidy and the tax is equivalent to the optimal
tariﬀ.
In Japan there are recently lively debates on the forms of protection policies
for several agricultural products on which very high protective tariﬀs are imposed.
EU and Switzerland have increased the amount of direct payment to agricultural
sectors while reducing tariﬀs (or market price supports) on agricultural products(OECD, 2010). The present results imply that a shift from a tariﬀ to the combination of a production subsidy and a commodity tax benefits the country if thesector must be protected.

6

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13