Revenue-Constrained Combination of an Optimal Tariff and Duty Drawback

Transcription

1 Revenue-Constraned Combnaton of an Optmal Tarff and Duty Drawback Tatsuo Hatta Presdent, Asan Growth Research Insttute Workng Paper Seres Vol December 05 The vews expressed n ths publcaton are those of the author(s) and do not necessarly reflect those of the Insttute. No part of ths artcle may be used reproduced n any manner whatsoever wthout wrtten permsson except n the case of bref quotatons emboded n artcles and revews. For nformaton, please wrte to the Insttute. Asan Growth Research Insttute

2 Revenue-Constraned Combnaton of an Optmal Tarff and Duty Drawback Tatsuo Hatta Presdent, Asan Growth Research Insttute December, 05 Abstract A duty drawback s an export subsdy determned as a percentage of the tarffs pad on the mported nputs used n ts producton. Ths paper examnes the revenue-constraned optmal tarff structure n a small open economy ncludng a duty drawback as a trade polcy tool. Ths paper has two man ams. Frst, we show that the revenue-constraned optmal combnaton of tarff and duty drawback for a gven revenue level s not unque. Second, we show that f the optmal mport tarff rates are all postve when the duty drawback rate s zero, then the optmal mport tarff rates are always postve when the duty drawback s postve. Keywords: Revenue-Constraned Optmal Tarff, Duty Drawback, Export Subsdy, Unformty JEL classfcaton: F, F3, H. Introducton Many countres contnue to use mport tarffs as a major nstrument for collectng Ths paper s a by-product of earler work n Hatta and Ogawa (007), for whch the author gratefully acknowledges the detaled comments generously provded by Professor Ogawa. The usual dsclamer apples.

3 revenue as well as for protectng domestc ndustres. Ths s especally because some developng countres fnd t dffcult to manage broad-based taxes, such as commodty, value-added, or ncome taxes, because ther admnstratve and poltcal costs are relatvely hgh. In contrast, tarffs can be easly mposed and as a result are the man source of revenue n several countres, as shown by Greenaway and Morrssey (996) and Ebrll, Keen, Bodn and Summers (00). A duty drawback s an export subsdy determned as a percentage of the tarffs pad on the mported nputs used n ts producton. As wth an export subsdy, a duty drawback wll stmulate exports by offsettng the export-restranng effects of tarffs on the mported nputs. Indeed, f provded, a full duty drawback would allow export ndustres to obtan mported nputs at world prces. Thus, the World Bank permts export duty drawbacks as an allowable trade polcy (see Krueger and Rajapatrana (999)), wth the result that they now preval n many developng countres. 3 Nevertheless, just a few studes to date have analyzed the effects of duty drawbacks. Of these, Panagarya (99) examned the welfare effects of revenue-constraned tarff reforms under duty drawbacks and characterzed some welfare-mprovng tarff reform programs, whch are partcularly useful for actual tarff reform n developng countres. 4 More recently, Ianchovchna (007) analyzed the welfare effects of tarff and duty drawback reform by extendng the analytcal framework n Panagarya (99). However, for the most part, ths lterature has not addressed the goal of revenue-constraned tarff reforms under a duty drawback,.e., the structure of reference revenue-constraned optmal tarffs under duty drawbacks has not been analyzed. Moreover, ths lterature has not consdered the key queston of precsely how duty drawbacks affect the revenue-constraned optmal mport tarff structure. In ths paper, we examne the optmal combnaton of mport tarffs and duty drawbacks on the export good under a revenue constrant. Ths serves as an extenson of For example, the revenue obtaned from mport dutes as a proporton of total tax revenue was 44.8% for Madagascar n 000, 54.7% for Swazland n 000, 50.% for the Bahamas n 00, and 49.3% for Uganda n 000 (IMF, 00). Especally n many other Afrcan countres, t can exceed 30%. 3 Mchalopoulos (999) showed that many developng countres mpose at least some form of duty drawback on exports. 4 Mchael, Hatzpanayotou and Mller (99), Neary (998), and Keen and Lgthart (00) theoretcally analyzed tarff and tax reform as a revenue problem, but dd not allow for duty drawbacks.

4 the theory of a revenue-constraned optmal tarff that has been well developed n the tradton of optmal commodty tax theory by Dasgupta and Stgltz (974), Heady and Mtra (987), Mtra (99, p. 46), Dahl, Devarajan and van Wjnbergen (986), Panagarya (994), Hatta (994) and Hatta and Ogawa (007). These studes characterze the tarff combnaton that maxmzes utlty when a fxed level of the revenue has to be collected only from tarffs 5 n the stuaton where prce dstortons arsng from the tarffs are nevtable. 6 Thus, the revenue-constraned optmal tarff problem, whch can arse even n a small country, entrely dffers from the more famlar optmal tarff problem n a large economy. In the present analyss, we ntroduce a duty drawback nto the theory of the revenue-constraned optmal tarff. 7 We consder a small open economy wth three tradable goods (one mport good, one export good, and one mported nput), where a fxed level of revenue s collected from the combnaton of tarffs and the duty drawback. 8 We show the followng. Frst, an equlbrum supported by a combnaton of tarffs and a duty drawback can also be supported by nfntely many other combnatons of tarffs and duty drawbacks yeldng dentcal revenue. Ths mples that the revenue-constraned optmal combnaton of of tarffs and duty drawback, we requre at least one tarff or the duty drawback fxed at a gven level. Second, we show that as the duty drawback ncreases, the assocated optmal mport tarff rates of all goods monotoncally ncrease. The remander of the paper s organzed as follows. Secton analyzes the structure of optmal mport tarff rates and an export subsdy rate. Ths analyss s useful for examnng the effect of a duty drawback as a condtoned export subsdy. Secton 3 5 In an optmal commodty tax model, labor supply s endogenous and there s a dstorton generated between goods and lesure. Commodty taxes and wage subsdes at a unform rate would remove ths dstorton. However, tax revenue would then be zero. At ths pont, the optmal commodty tax problem for postve revenue becomes a concern. See, for example, Auerbach (985) for a detaled descrpton of optmal tax models. In the optmal tarff model, we assume a fxed labor supply, and hence can dsregard ths dstorton. 6 If there s a subsdy for the export good at the same rate as the mport tarff rate, there s no prce dstorton on tradable goods. However, under ths tarff structure, all revenues collected from mport tarffs are spent on the export subsdy,.e., tarff revenue s zero. Consequently, to collect revenue from tarffs, prce dstorton s nevtable. 7 Cadot, de Melo and Olarreaga (003) emprcally examned the mplcatons of a duty drawback n a poltcal economy framework, but dd not mpose a revenue constrant. Ianchovchna (007) and Chao, Yu and Yu (006) showed va smulaton analyss that duty drawbacks mprove the level of welfare n Chna. 8 Note that a duty drawback yelds negatve revenue.

5 presents the model employng a duty drawback as trade polcy and studes the structure of optmal combnaton of mport tarff rates and the duty drawback. Secton 4 derves qualtatve relatonshp between the duty drawback and the optmal mport tarff rate. Fnally, Secton 5 presents the exact formula of the mport tarff rates as functons of the duty drawback, wthout assumng the Leontef type technology wth rgd proportons of nputs and outputs.. The general tarff economy a. Nonunqueness of the equlbrum prce vector In ths secton, we consder an economy wth mport tarffs and an export subsdy. Ths prepares us for the followng secton, where we ntroduce a duty drawback by extendng the model n ths secton. More concretely, we revew the model of the General Tarff Economy (hereafter, GTE) ntroduced by Hatta and Ogawa (007). The GTE s a small open economy wth a revenue constrant arsng from tarffs and subsdy. Ths economy has three tradable goods: good 0 s an export good and goods and are mport goods. All of our notatons follow Hatta and Ogawa (007), such that q = q, q, ) s ( 0 q the domestc prce vector, p = p, p, ) s the world prce vector, t = t, t, ) s the ( 0 p ( 0 t specfc tarff vector, x = x, x, ) s the demand vector, y = y, y, ) s the supply ( 0 x vector, and r s the tarff revenue. In the GTE, the followng holds: ( 0 y q = p + t, () x = x ( q, u), = 0,,, y = y (q), = 0,,, z ( q, u) = x ( q, u) y ( q), z q, u) = ( z ( ), z ( ), z ( )), ( 0 p z( q, u) + r = 0, () q z( q, u) = 0, (3) where x ( q, u) s the compensated demand functon, y (q) s the supply functon, and z ( q, u) s the compensated excess demand functon for the -th good. Equatons () and (3) ndcate the nternatonal balance of payments and the prvate sector budget equaton, respectvely. As the GTE s a small open economy, the world prce vector p s constant. 3

6 We assume p 0 =. When Equatons (), (), and (3) are all satsfed, we say that the GTE s n equlbrum. When the vector ( q, x, y, u ) satsfes (), (), and (3), we refer to t as y an equlbrum vector of the GTE, to ( x, ) as ts equlbrum allocaton, and to q as ts equlbrum prce vector. Further, f two equlbrum vectors share the same equlbrum allocaton, we say that these equlbrum vectors are equvalent, and that ther equlbrum prce vectors are equvalent. Thus, f vectors ( q, x, y, u ) and ( q, x, y, u ) are both equlbrum vectors of the GTE, then they are equvalent equlbrum vectors, and q and q are equvalent equlbrum prce vectors. We should note that the levels of welfare and tarff revenue are both constant under equvalent prce vectors because the equlbrum allocatons assocated wth them are dentcal. Gven x ( q, u) and y (q) are homogeneous of degree zero wth respect to q, a proportonal ncrease n q does not affect the values of x ( q, u) and y (q), keepng the equlbrum allocaton of the GTE ntact. Therefore, when vector of the GTE, the vector for any postve number κ. Ths mples that q s an equlbrum prce κ q s also an equlbrum prce vector of the same model κ q and q are equvalent equlbrum prce vectors of the GTE (4) b. Nonunqueness of the equlbrum tarff vector The ad valorem tarff rate τ of the -th good may be defned by = t t, = q 0,,. (5) Then the ad valorem tarff vector τ, τ, ) correspondng to the prce vector ( 0 q q, q, ) can be expressed as ( 0 τ p p ( τ = 0, τ, τ ),,. (6) q0 q q 4

7 When ( q, x, y, u ) s an equlbrum vector of the GTE, so s ( κ q, x, y, u ) from (4). Hence the tarff vectors = p p ( τ 0, τ, τ ),, and q 0 q q κ κ κ = p p ( τ 0, τ, τ ),, κq 0 κq κq (7) are equvalent. Thus, the tarff mposton at any choce of κ n (7) does not affect the y κ equlbrum allocaton ( x, ). Therefore, when τ 0 s chosen, Equaton (7) determnes κ κ κ ( 0 ( 0 the vector τ, τ, τ ) equvalent to τ, τ, τ ), and we have the followng: Proposton. The tarff vector that supports a partcular equlbrum allocaton of the GTE for a gven tarff revenue s not unque. Ths proposton s an extenson of the Lerner Symmetry Theorem establshed by Lerner (936), whch states that there s always an equvalent rate of export tarff for any mport tarff rate. The Lerner Symmetry Theorem straghtforwardly mples many possble combnatons of mport and export tarffs that yeld the same revenue and support the same domestc prce vector. c. Nonunqueness of the revenue-constraned optmal tarff vector of the GTE In ths secton, we consder the optmal tarff rate of the GTE. We can say that the tarff structure τ, τ, ) s a revenue-constraned optmal tarff vector f ths structure ( 0 τ maxmzes u n the GTE model for a gven revenue level. It s obvous that Proposton contnues to hold even when the tarff vector s optmal. Thus, we have the followng: Proposton. The optmal tarff vector of the GTE for gven revenue s not unque. 3. The duty drawback economy a. Nonunqueness of the equlbrum prce vector of the duty drawback economy Ths secton ntroduces a duty drawback on the export good nto the GTE by ntroducng some structure to the GTE model. Thus x ( q, u) 0 holds. 5

8 Assumpton. Good s an mported nput used to produce both goods 0 and. It s not a consumpton good and not produced at home. The mported nput enters the output as a negatve element, that s, y < 0 and hence z = y 0. > Assumpton. A duty drawback s gven to an exportable good as a percentage of the tarff pad on the mported nputs used n that export. No other tarffs or subsdes are gven. The duty drawback β s defned by β = t t, (8) 0 a where a s the amount of the mported nput used n one unt of the export,.e., where ( 0) a y y, 0 ( 0) y denotes the amount of the mported nput used n the producton of the export good. Because the factor demand and supply functons depend only on the domestc prces of the goods n equlbrum, we express the mported nput rato functon of the export good by a = a(q). (9) If there s no duty drawback, then from (8) β = 0 and t 0. Conversely, f ββ =, the duty drawback s full and export ndustres can access mported nputs at the world prce. Indeed, t follows from (8) that t and the domestc prce on the exportable s gven by q = t When t > 0 and > 0 β, (8) mples that t 0 0 = 0 = t a. The relatonshp between the world prce 0 >. Ths shows that a postve duty drawback plays the same role as an export subsdy. The duty drawback, lke an ordnary export subsdy, rases the prce of the exportable good and thereby protects the export 6

9 ndustry. The GTE ncludng Assumptons and s regulated to as the duty drawback economy (DDE). The DDE model conssts of Equatons (), (), (3), (8), and (9). When the vector ( q, x, y, u ) satsfes Equatons (), (), and (3) for the DDE model, we say that the DDE s n equlbrum, and the vector ( q, x, y, u ) s an equlbrum vector of the DDE. Equatons (8) and (9) yeld the correspondng level of the duty drawback n ths DDE. Therefore, the DDE s smply a GTE wth the defnton of β added. When ( q, x, y, u ) s an equlbrum vector of the DDE, ( x, ) s ts equlbrum allocaton and q s the equlbrum prce vector of the DDE. y If two equlbrum vectors of a DDE share the same equlbrum allocaton, we can say that these equlbrum vectors are equvalent and that ther equlbrum prce vectors are equvalent. Thus, f vectors ( q, x, y, u ) and ( q, x, y, u ) are both equlbrum vectors of the DDE, then they are equvalent equlbrum vectors, and q and q are equvalent equlbrum prce vectors of the DDE. We should note that the levels of welfare and tarff revenue are both equal under the equvalent prce vectors because the equlbrum allocatons assocated wth them are dentcal. When ( q, x, y, u ) satsfes Equatons (), (), (3), (8), and (9) for some β, t s called an equlbrum vector of the DDE for the gven β. Note that a (q) n (9) s homogeneous of degree zero wth respect to q. Hence, Statement (4), establshed for the GTE, s vald even for the DDE gven (4) was derved from (), (), and (3). Thus, we have κ q and q are the equvalent equlbrum prce vectors of the DDE (0) b. Nonunqueness of the equlbrum tarff duty drawback vector of the DDE We may rewrte Equaton (8) n terms of the ad valorem tarff rates: τ 0 = αβτ and a = aq q0, () where α s the payment for the mported nput used n one dollar of the exported good. Assumpton, whch states that the mported nput produces both goods 0 and 7

10 mples that 0 < α <. Gven the varable a s homogeneous of degree zero wth respect to the domestc prces, α s constant under a proportonal change n domestc prces. From (5), (), and Statement (0), we have the followng: Proposton 4. The duty drawback tarff vector β, τ, τ ) that supports a partcular ( equlbrum of the DDE for a gven revenue s not unque. c. Nonunqueness of the revenue-constraned optmal duty drawback tarff vector of the DDE We say that ( β, τ, τ ) s the revenue-constraned optmal duty drawback tarff vector of the DDE f ths structure maxmzes u n the model of the DDE for a gven revenue level. It s obvous that Proposton 4 contnues to hold even when the tarff vector s optmal. Thus, we have the followng: Proposton 5. The optmal duty drawback tarff vector β, τ, τ ) of the DDE for a gven revenue level s not unque. ( Ths proposton mples that a polcy prescrpton vald n an economy wth a lump-sum tax does not necessarly apply n the DDE, where the total revenue from tarffs s fxed. For example, Proposton 3 n Panagarya (99) showed that n a three-commodty model smlar to the DDE model, rasng the duty drawback rate from zero accompaned by an ncrease of the tarff rate on the mported nput wll necessarly mprove the welfare of the economy, f the lump-sum tax s adjusted behnd the scenes. However, ths proposton does not necessarly hold n our fxed revenue economy. From Proposton 5, we can choose an optmal duty drawback tarff vector n such a way that β s zero. Thus suppose that the ntal level of β n the optmal duty drawback tarff vector s zero gven. Then an ncrease n β from zero, whle s adjusted to keep revenue constant and fxed, wll necessarly reduce welfare f the startng duty drawback tarff structure was optmal. Another mplcaton of the proposton s that the level of a duty drawback tself can be set at a poltcally or admnstratvely convenent level as long as the mport tarff rates are 8

11 optmally adjusted. In other words, t s possble to keep the tarffs on the mported nput hgh as long as t s possble to rase the duty drawback poltcally. On the other hand, f a nonzero duty drawback s poltcally or admnstratvely nfeasble, then the mport tarffs can be selected optmally to sut the zero level of a duty drawback. 4. Import tarff rates as a functon of the duty drawback rate a. Import tarff rates as a functon of the export tarff rate n the GTE From equaton (7), we can express two mport tarff rates as functons of an export tax rate so as to keep the equlbrum resource allocaton ntact. Let q, q, q ) be an equlbrum prce vector and ( x, ) be the equlbrum ( 0 allocaton acheved at q, q, q ). Then, the equlbrum ( x, ) can be attaned by the ( 0 κ κ κ tarff vector τ, τ, τ ) defned by (7) for any gven. For smplcty, we wrte the ( 0 κ κ κ equlbrum tarff vector τ, τ, τ ) correspondng to ( x, ) as τ, τ, ) hereafter. ( 0 y y y ( 0 τ y Lemma. Then, for any value τ 0, the equlbrum ( x, ) can be attaned by the tarff vector τ, τ, ) = τ, f ( τ ), f ( )), where ( 0 τ f ( 0 0 τ 0 q0 p q0 p ( τ 0) ( τ 0), f ( τ 0) ( τ 0). () q q Proof. By lettng τ 0 = τ κ 0, the frst equaton n (7) yelds the mplct level ofκ for τ 0, whch s κ = (( τ ) q ). Substtutng ths for κ of the second and thrd equatons n 0 0 (7) yelds (). Q.E.D. From Proposton, the tarff vector τ, τ, ) that supports a partcular equlbrum ( 0 τ allocaton of the GTE for a gven tarff revenue s not unque. However, when one of the three tarff rates s fxed at a gven level, the levels of the other two tarff rates are determned. As a specal case of the GTE, consder an economy satsfyng τ 0. Then, from (7), 0 = 9

12 the correspondng tarff vector s gven by (0, q 0 p q0 p f (0), f (0)) 0,,. (3) q q The followng lemma s used n subsequent analyss. ( τ 0 ( τ 0 Lemma. Then functons f ) and f ) defned n Lemma can be alternatvely expressed as f ( τ 0) ( τ 0) f (0) + τ 0, ( τ 0) ( τ 0) f (0) + τ 0 f. (4) Proof. From () we have. Applyng ths to (), we obtan f τ ) ( τ )( f (0)) = ( τ 0 ) f (0) + τ 0, =,. Q.E.D. ( 0 0 b. Import tarff rates as a functon of the duty drawback rate β n the DDE Defne the tarff vector τ, τ, ) of the DDE by (6) and the duty-draw-back-tarff vector β, τ, τ ) by (). ( ( 0 τ Snce Lemma s satsfed n the DDE, we have the followng: Lemma 3. Let q, q, q ) be an equlbrum prce vector and ( x, ) be the ( 0 equlbrum allocaton acheved at q, q, q ) of the DDE. If β, τ, τ ) s an ( 0 y ( equlbrum duty-draw-back-tarff vector that supports ths equlbrum. The mport tarff rates τ,τ can be rewrtten as functons of β and n terms of the functons of defned n Lemma as, (5) 0

13 Proof. Substtutng () for τ 0 n (4), we mmedately obtan the lemma. Q.E.D. c. Optmal mport tarff rates as a functon of the duty drawback rate β n the DDE When one element of β, τ, τ ) s fxed at a level, the optmal levels of the remanng ( elements (polcy varables) are unquely determned. Let us now examne the relatonshp between β and the optmal mport tarffs. Let ξ and be the optmal tarff of the DDE when β = 0. Substtutng ξ for n (5), and solvng for τ and τ yelds the followng: Proposton 6. The optmal mport tarffs, τ and τ n the DDE for a value of β can be expressed as τ ( β ) ( αβ ) ξ + αβξ =, ( αβ ) + αβξ Proposton 6 mples the followng: τ ( β ) ξ = ( αβ ) + αβξ. (6) Proposton 7. Assume that ξ > 0 and ξ > 0.9 Then the followng holds n the DDE. () The optmal mport tarffs τ and τ are always postve for any value of β. () As β ncreases, the optmal tarff rates on goods and ncrease. Proof. Gven 0 < α < and 0 β, we have 0 αβ <. Ths and (6) mmedately prove (). Next, we prove (). Gven ξ and ξ are constant, (6) yelds dτ αξ( ξ) = dβ [ + αβ ( ξ )], dτ αξ( ξ) = dβ [ + αβ ( ξ )]. (7) As 0 ξ < from the assumpton and defnton of the tarff rate, dτ dβ > 0. Q.E.D. < 9 Secton 5 shows that the optmal tarffs on the mported good and the mported nput are both postve f all goods (ncludng the mported nput) are substtutable. Note that Lopez and Panagarya (99) consdered three stuatons where the mported nput s always complementary wth one fnal good. In contrast, Hatta and Ogawa (003) provded the stuatons where all goods ncludng the mported nput are substtutable.

14 Fgure depcts the graphs of (6) n the case of ξ > ξ for a gven α, gven values of ξ and ξ, and for varous values of β satsfyng (6). 0 Because α < holds, a full duty drawback ( β = ) s allowed. If β exceeds one and approaches α, the optmal tarff rates on goods and approach one. Substtutng β = α nto (6) yelds τ =τ. = However, the optmal tarff rates are never equal to one from the defnton of the ad valorem tarff rate. Fgure shows that the optmal tarff on good s always postve n the range of β < α and that β s negatve when τ <. ξ 5. Optmal tarff of the DDE when In Proposton 6, we expressed the optmal mport tarffs of the DDE as functons of ξ and, the optmal tarffs when β = 0. In the present secton, we n turn express ξ and as functons of the elastctes of excess demand functons as follows: Proposton 8. β = 0 are gven by The optmal tarff rates for the two mports of the DDE when ξ = η + η η ) θ, (8a) ( 0 + ξ = η + η η ) θ, (8b) ( 0 + where η = z q ) ( q z ) s the elastcty of the excess demand for the - th j ( j j good wth respect to the j - th good and θ s a postve scalar. Proof. The duty-draw-back-tarff combnaton of a DDE can be expressed by the tarff 0 From (6), we have ( d τ ) d β = {αξ( ξ)( ξ)[ αβ ( ξ)]} [ + αβ ( ξ )] > 0, 4 ( d τ ) d β = {α ξ ( ξ ) [ αβ ( ξ )] } [ + αβ ( ξ )] 0, > where ξ > 0 and αβ ( ξ ) > 0 are used. The nequalty αβ ( ξ ) > 0 s derved from 0 αβ < and 0 < ξ <. The above four nequaltes characterze the graph of (7) n Fgure. Substtutng τ = τ nto (6), we obtan β = α. Ths mples that the graph of (6) never ntersects n the range of β < α. From (6), we have τ ( αβ )( ξ ξ ) τ =, ( αβ ) + αβξ whch shows that τ > ( =, < ) τ f ξ > ( =, < ) ξ. 4

15 vector of the correspondng GTE. Thus the optmal mport tarff rates and of the GTE wth are equal to the optmal mport tarff rates ξ and correspondng DDE wth β = 0. Thus we have of the, =,. (9) Lemma () n Hatta and Ogawa (003, p. ) provded the formula of the optmal mport tarff rates of the GTE when. In terms of ths formula and (9), we have Proposton 8. Q.E.D. If all three goods of the DDE are substtutable for each other,.e., f the excess demand elastctes n (0) are all postve, therefore, the optmal tarffs on the mport good and mported nput are both postve, and the premse of Proposton 7 s satsfed. There are two cases where ths premse s not satsfed. The frst case s when the mported nput s complementary wth the export good. Then η 0 holds, and equaton (9a) mples that optmal tarff on the mported fnal 0 < good ξ can be negatve. However, equatons (9b) mples that the optmal tarff on the mported nput ξ s necessarly postve then, snce the mported nput cannot then be complementary wth the mported fnal good and η > 0 holds. The second case s when the mported nput s complementary wth the mported fnal good. Then, η +η 0 holds and ether ξ or ξ can be negatve from (8). 3 In that < case, the mported nput needs be subsdzed even when there s no duty drawback. Note that by substtutng (8) for ξ or ξ n (6), we obtan precse formula for mport tarffs for any non-zero value of. Note that from the assumpton (9), the elastctes related to the mported nput can now be expressed by η 0 = y 0 y, η = q y y and η = q y z. Snce the DDE s a three-good economy, when the mported nput s complementary wth the export good, t must be substtutable for the mported fnal good. 3 Lopez and Panagarya (99) analyzeded the three stuatons where the mported nput s always complementary wth one fnal good because of the Leontef type technology. On the other hand, Hatta and Ogawa (003) studed the stuatons where all goods ncludng the mported nput are substtutable for each other. 3

16 6. Concluson We analyzed revenue-constraned optmal tarffs n the presence of a duty drawback on the export good. Our fndngs are as follows. Frst, the combnaton of an mport tarff and duty drawback can be at a level that s most sutable poltcally because the optmal combnaton s not unque. Second, f optmal mport tarffs are postve when the duty drawback s zero, then the mport tarffs are postve for all postve values of the duty drawback. 4

17 References Auerbach, A. J. (985), The Theory of Excess Burden and Optmal Taxaton, n A. J. Auerbach and M. Feldsten (eds.), Handbook of Publc Economcs, Vol I. Amsterdam: North Holland, pp Cadot, O., J. de Melo and M. Olarreaga (003), The Protectonst Bas of Duty Drawbacks: Evdence from Mercosur, Journal of Internatonal Economcs 59, pp Chao, C. C., E. S. H. Yu and W. Yu (006), Chna s Import Duty Drawback and VAT Rebate Polces: A General Equlbrum Analyss, Chna Economc Revew 7, pp Dahl, H., S. Devarajan and S. van Wjnbergen (986), Revenue-Neutral Tarff Reform: Theory and an Applcaton to Cameroon, Economc Studes Quarterly 45, pp Dasgupta, P. and J. Stgltz, (974) Beneft Cost Analyss and Trade Polces Journal of Poltcal Economy 8, pp. 33. Ebrll, L. P., M. J. Keen, J.-P. Bodn and V. Summers (00), The Modern VAT, Internatonal Monetary Fund, Washngton, DC. Greenaway, D. and O. Morrssey (996), Trade Lberalzaton and Multlateral Insttutons n V. N. Balasubramayan and D. Greenaway (eds.), Trade and Development: Essays n Honor of Jagdsh Bhagwat. MacMllan Press, London, pp. 3. Hatta, T. (994), Why Not Set Tarffs Unformly Rather Than Optmally, Economc Studes Quarterly 45, pp. 96. Hatta, T. and Y. Ogawa (007), Optmal Tarffs under a Revenue Constrant, Revew of Internatonal Economcs 5, pp Heady, C. J. and P. K. Mtra (987), Dstrbutonal and Resource Rasng Arguments for Tarffs Journal of Development Economcs 0, pp Ianchovchna, E. (007), Are Duty Drawbacks on Exports Worth the Hassle?, Canadan Journal of Economcs 40, pp Internatonal Monetary Fund (IMF) (00), Government Fnance Statstcs Yearbook, 5

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19 Fgure τ, τ τ = τ( β ) ξ τ = τ ) ξ ( β 0 α β Full duty drawback 7