multilateral policy reforms and quantity restrictions on trade

Journal of International Economics 52 (2000) 153–168www.elsevier.nl / locate /econbase

Multilateral policy reforms and quantity restrictions ontrade

a b ,*Arja H. Turunen-Red , Alan D. WoodlandaDepartment of Economics and Finance, University of New Orleans, New Orleans, LA 70148, USA

bDepartment of Econometrics, University of Sydney, Sydney, N.S.W. 2006, Australia

Received 6 May 1996; received in revised form 2 February 1999; accepted 10 April 1999

Abstract

We specify a many-nation, many-commodity model of international trade involving tariffand quota distortions. We derive conditions for the existence of strict Pareto improvingmultilateral reforms of quotas, and obtain recommendations for specific directions of suchquota reforms. Given a mild rank condition on the world trade matrix, all directions ofquota reform that attain a strict Pareto improvement using international lump sumcompensation remain strict Pareto improving even without lump sum compensation,provided that the quota reform is accompanied by a multilateral reform of tariffs. Theprecise nature of the tariff reform that accomplishes the redistribution task is determined. 2000 Elsevier Science B.V. All rights reserved.

Keywords: Quotas; Policy reform; Pareto improvements; Tariffs

JEL classification: F13

1. Introduction

Several studies have analyzed the effects of unilateral reforms of quotas in smallopen economies but, surprisingly, no work exists on the multilateral aspects ofthese trade restrictions. The present paper specifies a many-nation, many-com-modity model in which economic distortions arise from both tariffs and quotas. We

*Corresponding author. Tel.: 11-61-2-9351-6825; fax: 11-61-2-9351-6049.E-mail address: [email protected] (A.D. Woodland).

0022-1996/00/$ – see front matter 2000 Elsevier Science B.V. All rights reserved.PI I : S0022-1996( 99 )00025-2

154 A.H. Turunen-Red, A.D. Woodland / Journal of International Economics 52 (2000) 153 –168

examine the feasibility of strict Pareto improving quota reforms and derive specific1recommendations as to the directions of such reforms.

It makes a great deal of difference whether or not international transfers ofincome are available as multilateral policy instruments. If we adopt the standardassumption that such transfers are available, reforms of trade policy (e.g. quotas)can be directed solely toward generating efficiency gains for the world economywhile redistribution of the gains is relegated to (unspecified) internationaltransfers. If, however, transfer compensation cannot be combined with other policyreforms, changes in other policy variables must be directed both toward generatingglobal efficiency gains and toward redistributing these gains among participatingcountries. Due to the difficulty of the resulting problem, very few decisive results

2have been obtained in this more restrictive framework.In Section 3 below, we show that the redistribution task previously assigned to

international income transfers can be taken on by multilateral reforms of tariffs.Specifically, we argue that all directions of quota reform that are strict Paretoimproving given international lump sum compensation remain strict Paretoimproving even without such compensation, assuming that the quota reform can beaccompanied by a suitable perturbation of world tariffs. We characterize thecomplete set of possible tariff reforms that perform this task and, as a special case,explicitly derive one family of reforms that are common to all countries. Inpractical terms, these observations should emphasize the importance of continuingmultilateral negotiations on tariffs despite the fact that absolute levels of tariffs inthe world are, by now, generally low.

Section 4 of the paper offers some suggestions for particular directions of quotareforms. We derive a condition that characterizes all Pareto improving directionsand generalizes Falvey’s (1988) condition for successful unilateral quota reform ina small open economy. We also investigate special quota reforms, including,among others, proportional relaxations of quotas and unilateral reductions ofextreme quotas.

The literature on quota reforms is relatively sparse. As already mentioned,Falvey (1988) has considered quota reform in the context of a single smallcountry. Neary (1995) has recently extended Falvey’s results to the case of a largecountry, while Anderson and Neary (1992) and Lahiri and Raimondos (1996) haveconsidered the possibility that quota rents may not be fully appropriated by theconsumers in the domestic economy. In contrast to these studies, which deal with a

1Tariffs and quotas are equivalent in a static sense in a competitive economy, excluding incomedistribution considerations. However, there are differences in the consequences of changes in tariffs andquotas (termed ‘‘dynamic nonequivalence’’ by Vousden (1990: Ch. 9)) that necessitate a separatetreatment of tariff and quota reform.

2See Turunen-Red and Woodland (1993) for the (complex) conditions under which multilateral tariffreforms are welfare improving without accompanying transfer compensation.

A.H. Turunen-Red, A.D. Woodland / Journal of International Economics 52 (2000) 153 –168 155

single country, our model and analyses are focused on quota reform from a3multilateral viewpoint.

2. The model

We assume that K countries trade in N commodities. All markets are perfectlycompetitive but national governments are allowed to impose taxes and/orsubsidies (‘‘tariffs’’) or quantity restrictions (‘‘quotas’’) on international trade.Governments may undertake domestic transfers to and from the consumer sector;international lump-sum transfers between national governments, however, are notpermitted unless stated otherwise.

Nations and internationally traded commodities are divided into two groups.1One subgroup of countries, denoted by K , is allowed to impose tariffs on all

traded goods but does not employ quotas. The other group of countries, denoted by2K , may employ both tariffs and quotas but the tariffs and quotas are imposed on

tseparate groups of goods. Thus, one subset of commodities, N , is subject only toqtariff distortions, while the commodities in the group N are subject to tariff

1 2 4distortions by the countries in K and to quotas by the countries in K . The pricesT T T T T Tof traded goods are denoted by p ; ( p , p ) 5 (1, r , r ) 5 (1, r ), where thet q t q

tfirst commodity in N serves as the numeraire and the superscript ‘‘T ’’ refers to thektranspose of a (column) vector. The symbol t refers to trade tariffs for countries

1 tin K , and to tariffs on goods in N and quota premia (price increases due toq 2quantity restrictions on trade) on goods in N for countries in K . The domestic

k kprice vector for traded goods is p ; p 1 t in every country k [ K.1The economies of the countries in K are described by the maximal net revenue

functions

k k k k k k k k k 1S ( p 1 t , p 1 t , u ) ; G ( p ) 2 E ( p , u ), k [ K , (1)t t q q

k kwhere G and E are the countries’ GNP and expenditure functions, respectively,k 5and the variables u denote the welfare of each country. The gradients of

k k k k k kfunctions S with respect to prices, S ( p , u ) ; ≠S /≠p , yield the net exportp1 k k kTfunctions of all countries in K . Accordingly, the Hessian matrices S ; ≠S /≠ppp p

3Guesnerie and Roberts (1984) have analyzed welfare implications of personalized consumptionquotas in a closed economy context. The quotas considered by us are quantity limits on countries’ netimports or net exports of traded goods. Differences in these analyses arise since countries (consumers)in our model face different prices due to trade tariffs, whereas consumers in the model of Guesnerieand Roberts necessarily face the same prices.

4At the cost of more complex notation, the model can be generalized to allow each country to choosethe subsets of tariffed and quota protected goods.

5See, e.g., Woodland (1982: pp. 169–172) for details of the maximal net revenue function.


describe the pure substitution effects of changes in prices and are referred to as the1 k k knet substitution matrices of countries in K . The vectors 2 S ; 2 ≠S /≠u 5pu p

k k≠E /≠u may be interpreted as the income derivatives of the (Marshallian) demandp

k kfunctions under the normalizing assumption (which we make) that E ; ≠E /uk 6

≠u 5 1 at the initial equilibrium.2For nations in K , it is convenient to follow Anderson and Neary (1992) and

apply the variable maximal net revenue functions

k k k k k k k k kT k 2S ( p 1 t , x , u ) ;min S ( p , p , u ) 2 p x , k [ K . (2)h jt t q t q q qkpq

kˆThe functions S yield the values (at domestic prices) of the countries’ netkexports of tariffed goods, keeping the quantity restrictions on trade, x , and theq

k kutilities, u , constant. As in the case of the maximal revenue functions S , thek k k t 2ˆ ˆvectors S ; ≠S /≠p yield the net exports of goods in N for countries in K andt t

k k kTˆ ˆthe matrices S ; ≠S /≠p describe the pure substitution effects upon net exportstt t t

of tariffed goods of changes in their prices.k k kˆ ˆThe matrices S ; ≠S /≠x indicate the spill-over effects of changes in thetq t q

kquotas x upon the net exports of tariffed goods; these effects play an importantq

role in the welfare evaluation of quota reforms. Also important are the incomekˆeffects in the presence of quotas, captured by the vectors S , which indicate thetu

effect of an increase in consumer income upon the net exports of tariffed goods.kk k ˆThe direct effects of changes in quotas upon domestic prices p 5 p 1 t 5 2 S ,q q q q

k k2 kTˆ ˆk [ K , of quota restricted goods are given by 2 S ; 2 ≠S /≠x , whileqq q qk k k kk kTˆ ˆ ˆ ˆ2 S ; 2 ≠S /≠u and 2 S ; 2 ≠S /≠p indicate the effects upon thesequ q qt q t

prices of an increase in income and of a change in the domestic prices of othergoods.

Given our definitions, the equilibrium conditions for the world economy areexpressed as follows:

kk k k k k k kˆO S ( p 1 t , p 1 t , u ) 1 O S ( p 1 t , x , u ) 5 0, (3)t t t q q t t t q1 2k[K k[K

k k k k kO S ( p 1 t , p 1 t , u ) 1 O x 5 0, (4)q t t q q q1 2k[K k[K

T k T k k 1p S 1 p S 5 b , k [ K ,t t q q(5)T k T k k 2ˆp S 1 p x 5 b , k [ K ,t t q q

kO b 5 0. (6)k[K

6See Diewert (1978: p. 146).


Eqs. (3) and (4) are the world market equilibrium conditions for the tariffed andquota protected goods, respectively, while Eqs. (5) define the national tradebalances. If any of the trade balances are nonzero, they are interpreted asinternational transfers from the country k to the rest of the world (which we allowin some situations) and, as such, they must satisfy the international balance

7 kcondition (6). Eqs. (3)–(5) endogenously determine the utilities (u , k [ K) andk 1 kthe world prices of the non-numeraire goods, r, given the tariffs (t , k [ K ;t , kt

2 k 2[ K ), the quotas (x , k [ K ), and the trade balances (international incomeqktransfers) (b , k [ K).

Near the initial equilibrium, the differential comparative statics system con-sistent with the model (3)–(6) is

k kˆ ˆS Sk k k ktt tqO S (dp 1 dt ) 1 O (dp 1 dt ) 1 O dxF G F Gpp t t q1 2 20 Ik[K k[K k[K

kS 0k k ktu1 O S du 1 O du 5 , (7)F G F Gpu1 2 0 0k[K k[K

T k k T k k kT k 1p S du 1 p S (dp 1 dt ) 1 S dp 5 db , k [ Kpu pp p

T k k T k k kT kT T k T k kˆ ˆ ˆ ˆp S du 1 p S (dp 1 dt ) 1 S dp 1 x dp 1 ( p S 1 p ) dx 5 db ,t tu t tt t t t t q q t tq q q

2k [ K , (8)

kO db 5 0. (9)k[K

T T T 8In (7)–(9), dp 5 (dp , dp ) gives the endogenous changes in world prices andt q

k k kˆO S O S O Stt tq tt 0S S S Stt tq 1 1 2 11 1rk[K k[K k[KS 5 5 1 5pp

k k3 4 3 4 3 4 3 4S S O S O S 0 0 S Sqt qq qt qq r1 rr1 1k[K k[K

S S5 , (10)p1 prf g

is the world net substitution matrix for all traded commodities.Eqs. (8) indicate the various partial (direct, spillover, income and terms of

trade) effects of tariff and quota reforms upon utilities. The consequences of anypolicy reform, be it unilateral or multilateral, must balance these partial effects.

7 k 2Given this interpretation of b , Eqs. (5) for the countries in K specify that these countries retain allquota rents.

8The first element of the vector dp is zero, i.e. dp 5 0, since the first good is the numeraire for the1

price system.


3. Quota reform and redistribution of gains

In this section, we show that the conditions for multinational quota reforms tobe welfare improving do not depend on the mode of the accompanying internation-al compensation. In particular, the conditions are exactly the same whethercompensation is achieved by international income transfers or by a multilateralagreement on a reform of tariffs.

A mild restriction on the world net trade matrix is required.

kTk 1 kT TˆFRank Condition. rank X 5 K 2 1 ( # N 2 1), where X ; S , k [ K ; (S , x ) ,p t q2Gk [ K .

According to the Rank Condition, the N 3 K world trade matrix X, whose columnscomprise the countries’ net exports vectors of all tradable goods, must have rank

9equal to the number of countries minus one. This implies that the number ofcountries (K) must be less than or equal to the number of traded goods (N), andthe net export vectors must be linearly independent in the subspace defined by theworld market equilibrium conditions. Applying this rank condition, we obtain ourmain result.

Theorem 1. Let the Rank Condition hold at the initial equilibrium. If there exists a0 0quota and transfer reform (dx , db ) such that a strict Pareto improvement in

0 0welfare is attained (du 4 0), then there exists a quota and tariff reform (dx ,1 0dt ) yielding the same welfare improvement du 4 0. The direction of tariff

1reform, which is common to all countries, is any solution s to the linear equationT 1 0system X s 5 db .

Proof. We denote a solution to the differential equation system (7)–(9) as (du, dp,10dt, dx, db), using obvious vector notation, and consider two separate solutions.

0 0First, under the quota and transfer reform (dx , db ) with no changes to tariffs, let0 0 0(du , dp ) be the solution to the differential system (7)–(9) with du 4 0.

0 1 1 0Second, consider a potential solution to (7)–(9) of the form (du , dp , dt , dx ,0). This solution involves identical quota reforms and welfare outcomes as theprevious solution, but the vector of changes in international lump sum transfers is

1set to zero. This new solution automatically satisfies Eq. (9) since db 5 0 byassumption. For this new solution to hold, Eqs. (7) and (8) further imply that

kSk 1 1k 0 1 1k 0ttO S sdp 1 dt 2 dp d 1 O dp 1 dt 2 dp 5 0, (11)s dF Gpp t t t1 2 0k[K k[K

9The world trade matrix cannot have rank greater than K 2 1, since the market equilibriumconditions require the columns of X to sum to the zero vector.

10For example, dt and dx are vectors consisting of the changes in all explicit tariffs and quotas.


T k 1 1k 0 kT 1 0 0k 1p S sdp 1 dt 2 dp d 1 S sdp 2 dp d 1 db 5 0, k [ K ,pp p

T k 1 1k 0 kT 1 0 kT 1 0 0kˆ ˆp S dp 1 dt 2 dp 1 S dp 2 dp 1 x dp 2 dp 1 db 5 0,s d s d s dt tt t t t t t t q q q

2k [ K . (12)

If the tariff reform is chosen so that

1 1k 0 1 1 1k 0 2dp 1 dt 5 dp , k [ K and dp 1 dt 5 dp , k [ K , (13)t t t

equation system (11) is automatically satisfied. Clearly, this requirement impliesthat each country’s domestic prices for tariffed commodities are the same in thetwo policy scenarios and further implies that the tariff reform must be common toall countries.

Under this requirement on the tariff changes, the equations in (12) will besatisfied if

T 0 1 0X (dp 2 dp ) 5 db , (14)

where X is the world trade matrix. Recognizing that one equation in (14) isredundant due to the market equilibrium condition and Eq. (9), the rank conditionon the world trade matrix ensures the existence of a solution to these K linearequations of the form

1 0 1 21 0 1s ; dp 2 dp 5 Y db 2 Y s , (15)f gR R R RR R RS S

where

Y YRR RSY 5F GY YSR SS

is the transpose of the world trade matrix X, partitioned so that the K 2 10 1dimensional square matrix Y is of full rank, and the vectors db and s areRR

1similarly partitioned. The sub-vector s may be arbitrarily chosen (as the nullS1 0 1vector, for example). Finally, vector s ; dp 2 dp is interpreted via (13) as the

11common tariff reform direction. h

Theorem 1 has some interesting implications. Most importantly, it demonstratesthat tariff and quota policy instruments can be sufficient in number and effective-ness to perform both the efficiency-creating and redistribution tasks required toachieve a strict Pareto gain in welfare. Consequently, policy suggestions formultilateral welfare improvements do not need to rely on the unrealistic assump-tion of multilateral financial compensation. Nevertheless, the considerable simplifi-

11 1 1 0Since good 1 is the numeraire, its tariff will be zero (s 5 dp 2 dp 5 0) and will be included in1 1 12 1sub-vector s . Also, for countries in K the tariff reform involves the sub-vector of s corresponding toS

tariffed goods only.


cation of analysis obtained if the assumption of international lump sum compensa-tion is invoked can still be taken advantage of in deriving suggestions for policyreform (as in Section 4 below).

Specifically, Theorem 1 demonstrates that a suitably chosen multilateral reformof tariffs can be a perfect substitute for income transfers in that both policyscenarios (involving identical quota reforms) yield identical welfare outcomes. Theprecise nature of one family of tariff reforms that succeeds in this task isestablished (others may, of course, exist). The tariff reform is common for allcountries and is therefore inherently multilateral. It is constructed by ensuring thatdomestic prices of all traded goods remain the same under the two policyscenarios; the multilateral tariff change therefore neutralizes the welfare impactarising from domestic sources. However, the tariff reform still allows for pureterms of trade effects in the world economy and these can, by the Rank Condition,

12be induced to yield a strict welfare gain.The tariff reform solution in Theorem 1 is unique if the number of traded goods

is equal to the number of countries (N 5 K). If the number of traded commoditiesexceeds the number of countries, there is an infinity of solutions that involvealtering N 2 K tariff rates arbitrarily (for example, leaving them unchanged).Therefore, the compensating reform does not require altering all world tariffs;considerable freedom of choice is allowed, based, for example, on political

13calculations. According to (15), the compensating tariff reform depends on the0world trade matrix and the structure of the transfers db . Of these, the trade matrix

0is readily observable, while the determination of the vector db requires econo-metric estimation of various substitution and income effects.

There are two important extensions of Theorem 1. The first extension concernsthe question of whether the proposition in Theorem 1 can be reversed. It turns outthat an arbitrary quota and tariff reform might not be able to be replicated (i.e.yield identical welfare effects) by a quota and transfer reform. However, it can beshown that an arbitrary quota and common tariff reform may be replicated (same

14welfare effects) by a quota and transfer reform. Thus, Theorem 1 can be extendedto show the equivalence between a quota and transfer reform and a quota andcommon tariff reform.

The second, more significant, extension is to characterize all tariff reforms thatcan accompany the quota reform in place of international income transfers asredistribution instruments. In order to achieve the same welfare outcome with thesame quota reforms as under the quota-transfers scenario, it is necessary and

12The Rank Condition guarantees that a change in international terms of trade can yield a welfaregain to all countries. See Weymark (1979) and Diewert et al. (1989) for analogous conditions in othercontexts.

13Theorem 1 can be generalized by requiring the compensating tariff reform to involve only alteringq 1tariffs on goods N in countries K . Details are available from the authors.

14Details are available from the authors.


sufficient for the world price and tariff changes to satisfy Eqs. (11) and (12) (asshown in the proof of Theorem 1). These N 1 K linear equations may be solved

0 0for the required changes in world prices and tariffs, given (dp , db ). The set ofsolutions to these equations constitutes the complete characterization of tariffreforms that yield identical welfare outcomes as transfers when quotas areperturbed. Recognizing that one equation is redundant, the price of the numeraireis fixed and each country’s tariff vector can be normalized to have the numeraire

1 t 2untaxed, there are N 2 1 K 1sN 2 1dK 2 K degrees of freedom in the choice ofs dthe tariff change. This implies that, given the appropriate rank condition, changesin only K tariffs are needed for a strict Pareto improvement to be attained. Such achange can involve, for example, the change of the tariff on one good in everycountry. Our solution in Theorem 1, which involves a common tariff reform, is a

15special case of this more general solution.

4. Directions of quota reforms

In this section, we characterize all strict Pareto improving directions ofmultilateral quota reforms, irrespective of whether lump sum compensation ormultilateral tariff reform serves as the international redistribution mechanism. Wealso offer specific reform recommendations. These include changes in quotasproportional to their shadow values, to distortions arising from quotas and to thequota levels, as well as a relaxation of the most extreme quotas.

4.1. Welfare improving quota reforms

In order to identify the strict Pareto improving directions of quota reforms, it isconvenient to utilize a set of shadow prices for traded commodities.

Definition. The world shadow prices for internationally traded commodities equalT T T 21p ; p 1 0, 2 p S S .s dpr rr

According to this definition, the shadow prices we use to evaluate tradedT T T˜ ˜commodities differ from world prices by the vector t 5 p 2 p 5 0,s

T 212 p S S . This vector of world ‘‘shadow tariffs’’ reflects the changes in thedpr rr

countries’ tariff revenues and terms of trade arising from a change in the worldexcess supply of traded goods, and is non-zero provided there are some explicit

16tariff distortions.

15We are grateful to an anonymous referee for pointing out this generalization.16See Turunen-Red and Woodland (1991) for further discussion of an analogous shadow price

concept.


17The following theorem characterizes welfare improving quota reforms.

Theorem 2. Let the world net substitution matrix, S , be invertible; let the Rankrr

Condition hold; and let all countries satisfy the normality conditions

kT kkT T k 1 T 2ˆ ˆ˜ ˜b ; 2 p S . 0, k [ K ; b ; 2 p S . 0, k [ K , (16)pu tu

at the initial equilibrium. Then, irrespective of whether international incomek ktransfers or tariffs are available, a change of quotas of the form dx 5 c da,q

2da . 0, k [ K , is strict Pareto improving if and only if

k kT T k k T k T kˆ ˆS ˜ ˜ D F ˜ ˜ Gu ; O p S 1 p c 5 O t 2 t S 1 t 2 t c . 0. (17)s d s dt tq q t t tq q q2 2k[K k[K

Condition (17) guarantees that the quota reform yields an aggregate efficiency18gain. The efficiency improvement u is defined as the sum, across all countries in

2K , of the effect of the reform on the value of net exports, evaluated using theworld shadow prices (keeping utility levels constant). This measure consists of the

kT k T kˆ˜ ˜sum of the direct (o p c ) and indirect or spillover (o p S c ) effects2 2k[K q k[K t tq

of the reform. The second expression for u in (17) evaluates the direct and indirectconsequences of the quota reform using the country-specific price distortions

˜defined with respect to the world shadow tariffs, t. These diversions of eachcountry’s tariffs and quota premia from the world shadow tariffs create room forPareto improving quota reforms.

Using (17) we may formulate a condition that characterizes circumstances inwhich a Pareto improving quota reform will involve a ‘‘relaxation’’ of the existingquantity restrictions on trade.

Condition S (Substitutability and Policy Stringency Condition). The quotakˆprotected and tariffed commodities are net substitutes, i.e., S , 0; the quantitytq

k˜restrictions on trade are relatively stringent, i.e., t , t ; and the trade tariffs areq qk˜relatively low, i.e., t . t .t t

2If Condition S holds for countries k [ K , the second expression for u in (17)kimplies that the directions of efficiency improving quota reforms, c , are negative

for all commodities (i.e. a relaxation of binding import quotas is required). GivenCondition S, such a relaxation of the relatively stringent quotas provides large

17The proofs of Theorem 2 and its corollaries are provided in the Appendix, which is available fromthe authors upon request.

18Conditions (16) guarantee that an income transfer from abroad to any country will result in awelfare gain even when the subsequent changes in the terms of trade and tariff revenues are taken intoaccount. These normality conditions ensure that a worldwide efficiency improvement is necessary for amultilateral welfare gain to be attained.


primary efficiency gains in quota protected markets at the cost of small spillovertlosses in tariff revenues on goods in the set N .

In a small open economy, Falvey (1988) has shown that the effects of a quotareform should be evaluated using the expression (in our notation)

k kT T k kT kT kˆ ˆS D S Dp S 1 p c 5 2 t S 1 t c , (18)t tq q t tq q

kwhich must be positive for the reform direction c to be welfare improving. Thisformula uses world market prices to evaluate the direct and indirect effects of

19quota reform; in contrast, (17) applies world shadow prices for this purpose. Inthe special case of no explicit tariffs, the shadow and market prices of all goodscoincide and our condition (17) reduces to

kT T k kT kˆS ˜ ˜ DO p S 1 p c 5 2 O t c . 0. (19)t tq q q2 2k[K k[K

2This condition is satisfied if at least one nation k [ K imposes binding quantitykrestrictions on trade (implying that t ± 0). Hence, the Falvey conclusion that aq

relaxation of a binding quota constraint is welfare improving in a small openeconomy that does not impose explicit tariffs also applies in a trading world withno explicit tariffs: any relaxation of a binding quota by any country will be Pareto

20improving if no country imposes tariffs.

4.2. Specific directions of quota reforms

The following corollaries of Theorem 2 provide some recommendations formultilateral quota reforms that are strict Pareto improving in welfare.

4.2.1. Reforms proportional to shadow valuesWe first examine reforms of quotas that are proportional to their shadow values

as expressed in Eq. (17).

Corollary 2.1. Let A be any (conformable) positive definite matrix. Then, thefollowing two directions of quota reform are strict Pareto improving:

k kk k k 2ˆ ˆ˜ ˜ ˜ ˜c 5 A[S p 1 p ] 5 A[S (t 2 t ) 1 (t 2 t )], ;k [ K , (20)qt t q qt t t q q

19The two conditions can be reconciled by observing that in a small country (which does notexperience changes in its terms of trade or the subsequent changes in its tariff revenue), the appropriateshadow prices of traded goods are the world market prices.

20This assumes that the countries are able to either undertake a lump sum redistribution of the worldefficiency gain or that they choose a Pareto improving reform of tariffs. In the latter case, a multilateraltariff reform would (possibly) involve introducing nonzero tariffs in a world that previously employedno trade tariffs.


j jk j jˆ ˆ˜ ˜ ˜ ˜c 5 A O [S p 1 p ] 5 A O [S (t 2 t ) 1 (t 2 t )],qt t q qt t t q q2 2j[K j[K

2;k [ K . (21)

Since A is an arbitrary positive definite matrix, these two families of quotareforms are very general. If A is set equal to an identity matrix, we obtain from(20) a country-specific reform proportional to the efficiency consequences ofchanges in quotas and, from (21), a reform proportional to the aggregate impactof quotas; the latter reform direction is common to all countries with quotarestrictions. The country-specific reform (20) recommends a relaxation of quotasin countries that satisfy Condition S. According to (21) on the other hand, a

2common relaxation of quotas is efficiency improving if the countries k [ Ksatisfy the less demanding multilateral version of Condition S, which is that

kk k ˆ˜ ˜o (t 2 t ) , 0 (i.e. quotas are relatively stringent) and o (t 2 t )S , 02 2k[K q q k[K t t tq

(i.e. goods with relatively low trade tariffs tend to be net substitutes for quotaprotected goods).

4.2.2. Reforms proportional to distortionsQuota reforms proportional to the market distortions as defined in (17) are strict

Pareto improving under a special condition, as the following corollary dem-onstrates.

Corollary 2.2. Multilateral reforms of quantity restrictions on trade in thedirections

kk kˆ ˜ ˜c 5 S (t 2 t ) (22)qt t t

k k˜ ˜c 5 (t 2 t ), (23)q q

are strict Pareto improving if

kk kˆ˜ ˜O (t 2 t )S (t 2 t ) . 0. (24)t t tq q q2k[K

Condition (24) is a correlation condition on the relative distortions in tariff and2quota protected markets in countries K . If tariff and quota protected goods are net

kˆsubstitutes (i.e. S , 0), then (24) holds if relatively stringent (soft) quotas are, ontq2average, combined with relatively low (high) tariffs in K . This will be the case if,

2for example, all countries in K satisfy Condition S. However, condition (24) isless demanding than Condition S, as quota protected commodities need not be netsubstitutes for (24) to hold.

The quota reform (23) is of interest since it recommends that countriesharmonize the country-specific shadow premia for quota protected goods (towards

˜the world shadow premia, t ). Given (24), such a reform reallocates net exportsq


from countries with high market distortions to countries in which marketdistortions on the net substitutes of these goods are low, thus yielding amultilateral efficiency gain. An analogous interpretation applies to reform (22).

4.2.3. Proportional quota reductionsProportional perturbations of existing distortions are among the standard

reforms considered in literature and are therefore of particular interest.

Corollary 2.3. If quantity restrictions on trade are only imposed on importedk 2 2commodities, i.e., x , 0 for all k [ K , and countries in K satisfy Condition S, aq

k k 2proportional relaxation of all quotas ( given by c 5 x , for all k [ K ) is strictq

Pareto improving.

In the special case of no explicit tariffs, the shadow tariffs are zero andCondition S is satisfied if the quota premia are positive, i.e., the import quotas arebinding. Thus, Corollary 2.3 becomes a many country generalization of Falvey’s(1988) theorem for unilateral reforms in a small country: a proportional relaxationof binding import quotas is strict Pareto improving. More generally, withoutinvoking Condition S and allowing for quantity restrictions on exports, it can beshown that proportional changes of all quotas are welfare improving if the quota

k k 21rents, o x (2t ), are positive.2k[K q q

4.2.4. Unilateral reductions of extreme quotasThe preceding reforms may also be successfully applied unilaterally by any

country for which an efficiency improving quota perturbation exists. An alternativeunilateral quota reform is obtained by considering the relaxation of quantityrestrictions on goods with high quota premia. This yields a version of the so-called‘‘concertina theorem’’.

t qCorollary 2.4. Let the goods in N be net substitutes for the goods in N in2country k [ K . Assume further that there is a good j in country k such that

k k k k t˜ ˜t 2 t . t 2 t for all i [ N , (25)j j i i

k k k k k˜ ˜where t ; t /p is the ad valorem quota premium and t ; t /p is the shadowi i i i i i

ad valorem quota premium on good i in country k. Then, a unilateral relaxation ofqthe quota on commodity j [ N in country k is strict Pareto improving.

21Quota rents are guaranteed to be positive if quotas are binding with non-zero quota premia; abinding maximum quota on imports yields a positive quota premium by raising the domestic price,while a binding maximum quota on exports reduces the domestic price yielding a negative quotapremium. In each case, the quota rents accruing to importers and exporters are positive.


Corollary 2.4 prescribes a relaxation of quotas the tariff equivalents of whichexceed the corresponding shadow tariff equivalents, in ad valorem terms, by morethan the tariffs of all tariffed goods exceed their shadow tariffs. Corollary 2.4applies to all quota protected commodities for which the quota premia satisfy theinequality. In contrast, when multilateral tariff reforms are considered, thecommodity with the highest (shadow) distortion is special — a multilateral Paretoimprovement may be attained by a unilateral reduction of a country’s highest tariffrate but not necessarily by a reduction of other tariffs (Turunen-Red and Woodland(1991)). This wider scope of the quota reform theorem is due to the lack ofsubstitution effects among the quota goods: since we only need to take intoaccount the possible substitution effects between the tariffed and quota protectedcommodities, there is no need to restrict the quota relaxation only to the good withthe worst quota distortion.

Some special cases of Corollary 2.4 have been derived by Falvey (1988) for asmall open economy and by Neary (1995) for a large country. Falvey’s case canbe obtained from Corollary 2.4 by recognizing that the world shadow tariffs for a

k ksmall open economy are zero, whereby the selection of good j now requires t . tj itfor all i [ N . Accordingly, a small country benefits if it reduces the quota on any

good whose ad valorem quota premium is greater than all explicit tariff rates. Ourgeneralization of Falvey’s ‘‘concertina theorem’’ emphasizes the importance of theshadow tariffs and quota premia in the evaluation of a policy of reducing a singlequota when world prices adjust to the policy reform.

5. Summary and conclusions

We have demonstrated that international income transfers are not needed forsuccessful co-operative trade reform. Specifically, quota reforms that are welfareimproving when accompanied by compensatory international income transfersremain welfare improving in the absence of income transfers, provided that thequota perturbations are accompanied by suitable multilateral reforms of tariffs (afamily of tariff reforms that accomplish the redistribution task is specified). It canbe shown, moreover, that tariff reform remains an effective tool of internationalredistribution when combined with reforms of any additional policy instruments(not necessarily quota restrictions) that we may wish to add to the model.

We evaluate the effectiveness of quota reforms in terms of world shadow prices,which take into account the world market equilibrium conditions for traded goodsand reflect the tariff distortions of all countries. The world shadow prices are theappropriate prices to evaluate policy reforms and, in general, will differ frommarket prices. They depend upon the structure of the world substitution matrixwhich, in principle, can be econometrically estimated, thus providing an empiricalbase for implementation of the policy recommendations that have been made.

Our results may suggest avenues for future research. First, our results establish


that particular directions of quota reform are strict Pareto improving whenaccompanied by suitable tariff reforms (and no transfers), and we have identifiedone family of reforms that serves the purpose. While we have also characterizedthe complete set of tariff reforms performing this task as solutions to a set of linearequations, it would be desirable to determine other special cases that are ofparticular interest and have clear economic interpretations. Determining theseconstitutes an important research objective. Secondly, quantity restrictions on tradeare not always quotas on specific goods. Value quotas are a possibility, as arequotas involving heterogeneous or differentiated goods. In each case, a weightedsum of imports and/or exports is formed and this aggregate is subject to a groupquota. The policy reform literature has not analyzed reforms that involvecommodity group quotas. However, it is likely that a reduction or reallocation ofcommodity group quotas will yield welfare gains.

Acknowledgements

We thank Bijit Bora, Guy Laroque, Peter Neary, Pascalis Raimondos-Møllerand the referees for helpful comments on earlier drafts of this paper. The authorsgratefully acknowledge financial support of the University of Sydney, theUniversity of Texas at Austin and the University of New Orleans. Woodlandgratefully acknowledges the support of the Fulbright Foundation, the American-Australian Education Foundation and the Australian Research Council.

References

Anderson, J.E., Neary, P.J., 1992. Trade reform with quotas, partial rent retention and tariffs.Econometrica 60, 57–76.

Diewert, W.E., 1978. Optimal tax perturbations. Journal of Public Economics 10, 139–177.Diewert, W.E., Turunen-Red, A.H., Woodland, A.D., 1989. Productivity and Pareto improving changes

in taxes and tariffs. Review of Economic Studies 56, 199–216.Falvey, R.E., 1988. Tariffs, quotas and piecemeal policy reforms. Journal of International Economics

25, 177–183.Guesnerie, R., Roberts, K., 1984. Effective policy tools and quantity controls. Econometrica 52, 59–88.Lahiri, S., Raimondos, P., 1996. Correcting trade distortions in a small open economy. Review of

International Economics 4, 287–299.Neary, J.P., 1995. Trade liberalization and shadow prices in the presence of tariffs and quotas.

International Economic Review 36, 531–554.Turunen-Red, A.H., Woodland, A.D., 1991. Strict Pareto improving reforms of tariffs. Econometrica

59, 1127–1152.Turunen-Red, A.H., Woodland, A.D., 1993. Multilateral reforms of tariffs without transfer compensa-

tion. In: Long, N.V., Herberg, H. (Eds.), Trade, Welfare and Economic Policies: Essays in Honor ofMurray Kemp. University of Michigan Press, Ann Arbor, pp. 145–166.


Vousden, N., 1990. The Economics of Trade Protection. Cambridge University Press, New York.Weymark, J.A., 1979. A reconciliation of recent results in optimal taxation theory. Journal of Public

Economics 12, 171–189.Woodland, A.D., 1982. International Trade and Resource Allocation. North-Holland, Amsterdam.

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