The Gains from Trade and Policy Reform Revisited * W. Erwin Diewert Alan D. Woodland. Abstract

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1 Te Gains from Trade and Policy Reform Revisited * W. Erwin Diewert Alan D. Woodland Abstract Te rimary urose of te aer is to rovide caracterizations of te conditions for welfare imrovements in several situations tat ave received very little attention in te existing literature. Te first aim is to exibit te gains tat can accrue to a country from te elimination of excess sulies as a result of a olicy move from autary to free trade. Te second contribution of te aer is to caracterize te conditions under wic te introduction of new goods into te economy will generate welfare gains. Te tird main area discussed is te extension of our metodology to a large oen economy tat can influence its terms of trade. Te tecniques tat we use to illustrate te gains from eliminating excess sulies and from te introduction of new goods ave a muc wider alicability; tey may be used to obtain and syntesize several welfare results from te literature. *Diewert: Deartment of Economics, University of Britis Columbia, # East Mall, Vancouver, B.C. V6T Z, Canada. Tel: , Fax: , diewert@econ.ubc.ca. Woodland: Econometrics and Business Statistics, Scool of Economics & Political Science, University of Sydney, Sydney, N.S.W. 26, Australia. Tel: , Fax: , A.Woodland@econ.usyd.edu.au. We tan, witout imlicating, Kala Krisna, Miciiro Oyama and te referees of tis journal for valuable comments on a revious draft. Financial suort from te Australian Researc Council, te Social Sciences and Humanities Researc Council of Canada and te University of Sydney Modeling of Economic and Financial Beaviour Researc Cluster Fund is gratefully acnowledged. JEL Classifications: F3, D6 Date: 3 Marc, 23 Address of Contact Autor: Alan D. Woodland: Econometrics and Business Statistics, Scool of Economics & Political Science, University of Sydney, Sydney, N.S.W. 26, Australia. Tel: , Fax: , A.Woodland@econ.usyd.edu.au. Fortcoming in Review of International Economics

2 . Introduction In tis aer, we consider questions tat are related to a very old question: wat are te gains to a country of oening u its borders to international trade? We also consider te more modern and general question: wat are te welfare effects of some tax olicy cange or of some oter exogenous soc to te economy? Te rimary urose of te aer is to rovide caracterizations of te conditions for welfare imrovements in several situations tat ave received very little attention in te existing literature. Te first of tese is to exibit te gains tat can accrue to a country from te elimination of excess sulies as a result of a olicy move from autary to free trade. Tis is a source of gain tat as been overlooed in te recent literature, wit te excetion of Oyama 972,. 49 and Neary and Scweinberger 986,. 428, but as its origins in te vent for surlus idea develoed by Myint 958. Tis source of gains accrues to te country were te autary equilibrium as some free goods, i.e., goods tat are in excess suly, and te oening u of trade eliminates tese excess sulies. Tese gains, wic are not te usual consumtion and roduction gains tat are discussed by Dixit and Norman 98,. 78 and Woodland 982,. 267, are illustrated in section 4 below using te general metods develoed in section 3. Te second contribution of te aer is to caracterize te conditions under wic te introduction of new goods into te economy will generate welfare gains. Wile te aearance of new goods is a fundamental feature of te modern economy and as been te subject of analysis in various endogenous growt models, tere as been little attention aid to teir role in te gains from trade and olicy reform literature. Accordingly, our analysis of te gains from te introduction of new goods in section 5 below is offered as a ste in te direction of redressing tis deficiency in te literature, as discussed by Romer 994. Our analysis of tis source of welfare gain requires a formulation of te model to allow consumer secific and roducer secific taxes and so te traditional formulation of trade gains is not sufficient for our uroses. Te tird main area discussed is te extension of our metodology to a large oen economy tat can influence its terms of trade. Our measure of welfare imrovement now includes terms reflecting a sift in te foreign offer set and te otimality or oterwise of tariff and tax olicies. We develo, in section 6, a new sufficiency condition for a welfare imrovement tat alies if te country imoses otimal tariffs in te new situation.

3 Te tecniques tat we use to illustrate te gains from eliminating excess sulies and from te introduction of new goods ave a muc wider alicability. Tus, in sections 2 and 3 below, we set out a general equilibrium model of an oen economy tat can be adoted to study a wide range of roblems involving te welfare consequences of discrete canges in te economy. Our main tas in tese sections is te derivation of alternative exressions for te decomosition of a measure of welfare cange, wic we call te aggregate quasi variation. Tis variation gives cardinal measures of canges in consumers' welfare between two eriods and is evaluated at an arbitrarily given vector of reference rices. Our main secial cases of tis general exression are te identities for te aggregate quasi-comensating variation and for te aggregate quasi-equivalent variation, evaluated at te initial and second eriod world maret rices resectively. Tese quasi variations reduce to te usual comensating and equivalent variations originally defined by Hics 942, rovided tat tere are no consumer commodity tax distortions in te economy. Our formulae for tese quasi variations bear some similarities to identities derived by Grinols and Wong 99, wo, as in te early welfare analysis of Oyama 972, decomosed aggregate canges in real income into various endowment growt, roduction growt, tax revenue growt and canges in te terms of trade comonents. Our analysis is similar to tese autors in tat we also rovide decomosition. However, te focus of our aer is te alication of our welfare identities to te treatment of new goods and goods in excess suly. 2. A Model of a Small Oen Economy We assume tat tere are N internationally traded goods and domestic goods and/or resources in te economy. Tere are H ouseolds or consumers, K firms and one consolidated government sector in te economy. It is furter assumed tat te economy is small in te usual sense tat all agents ouseolds, firms and te government tae world rices as exogenously given. Te rimary aim of te aer is to comare welfare in two situations or eriods, wic are distinguised by suerscrit t T {, }. For eriod t T {, } and ouseold H, let te consumtion vector for all goods bot internationally traded and domestic be t c, were factor sulies are indexed wit negative signs. 2 Let t y denote te observed eriod t net suly vector for firm inut demands are indexed wit negative signs. Te net exort vector for te economy in eriod t T is denoted as t t x if x i <, ten te i-t 2

4 good is imorted into te economy in eriod t. Te vector v t reresents te sum of te economy's endowments of goods less te government's fixed net demand vector for goods. In eriod t te maret balance conditions for te economy for goods are given by H c t = K y t x t + v t t e, t T. Te vector e t is te eriod t excess suly vector. We assume, consistent wit maret equilibrium, tat tese vectors are non-negative; i.e., e t for t T, 2 and tat e t i can only be ositive if all demanders of te i-t good face zero rices for tis good. Turning now to te rice side of te economy, we assume tat te eriod t rice t vector for goods is. Since te economy as been assumed to be a small oen economy, te rices for internationally traded goods are given exogenously, wile te maret rices for domestic goods are endogenously determined to clear domestic marets. 3 In eriod t T, ouseold faces te rice vector t + t t were t t sould usually be interreted as a vector of commodity tax distortions faced by ouseold in eriod t, but oter interretations are ossible as we sall see later. In eriod t T, firm faces te rice vector t + t t τ, were τ sould usually be interreted as a vector of commodity tax distortions faced by firm in eriod t. In te usual case considered in international trade teory, tere are no domestic tax distortions and a common tariff vector is faced by all consumers and roducers in eriod t. However, our general formulation allows us to deal wit ouseold and industry secific taxes and subsidies. Cometitive otimizing beaviour on te art of consumers and roducers is assumed in bot eriods. Tus, we assume tat ouseold 's references over various combinations of goods can be reresented by means of te utility function f. Te utility level attained in t t eriod t by ouseold is u f c, were c t is te observed eriod t consumtion vector for ouseold. Exenditure minimizing beaviour for ouseold in eac eriod is assumed, wence { } m u, + t min + t c: f c u t t t t t r c t t t + t c t T, H, 3 3

5 were t c denotes te inner roduct of te vectors function for ouseold. 4 vectors, Turning now to roducers, we assume tat firm t and c, and m is te exenditure K as a feasible set of net outut t S, in eriod t T. Te assumtion of rofit maximizing beaviour for firm in eriod t may be reresented as { } π t + τ t ; S t max t + τ t y: y S t t + τ t y t t T, K, 4 were 4 defines te rofit function outut vector Welfare Identities y π for firm and t y is te firm observed eriod t net Producer and Consumer Substitution Functions Before we define our main welfare identities, it is useful to detour briefly and define various consumer and roducer substitution functions. Tese functions caracterize te gains from substitution tat consumers and roducers exerience as a result of rice canges in te economy. Tese functions are ten used to el decomose aggregate welfare canges into easily interreted comonents. Tey are evaluated at an arbitrarily given reference rice vector, secific coices of wic will be considered furter below. Consider te roblem of minimizing te exenditure required for ouseold to attain its eriod r utility level, rices faced by ouseold, r u, but using te rice vector instead of te actual eriod r r r + t. Define te ouseold substitution function s r r refers to te utility level attained by ouseold in eriod r by s r r c m u, r, r T H, 5 r were te inequality follows since c is feasible for te minimization roblem 3 but is not necessarily otimal. Tis exression gives te cost, at te reference rice vector, of te consumtion vector actually consumed in eriod r minus te minimum exenditure needed to attain eriod r utility at tis reference rice vector. It terefore reresents a measure of te gains from substitution around te eriod r indifference curve. 6 Turning to te roducer side of te model, consider a yotetical sector rofit maximization roblem were firm faces te rice vectors and as available te eriod r tecnology set r S. Define te firm substitution function σ r refers to te firm r tecnology set in eriod r, r S by 4

6 r r σ π ; S y r T, K, 6 r were te inequality follows since r y is feasible for te maximization roblem but is not necessarily otimal. Tis exression is te rofit attained in eriod r at reference rice minus te rofit at tis same reference rice vector attained using te actual eriod r roduction oint. It terefore reresents a measure of te gains from substitution around te eriod r transformation frontier for firm. Tere is one additional set of definitions tat we require in subsequent sections. We first relate te firm roduction ossibilities set in eriod, S, to te firm roduction ossibilities set in eriod, S, by defining te firm tecnological cange function α, using te reference rices, by α π ; S π ; S, K. 7 It can be seen tat α is a measure of te exansion if ositive or contraction if negative in firm 's roduction ossibilities set going from eriod to. In general, te firms roduction ossibilities sets may be quite different in te two eriods under consideration and so te sign of te function α is ambiguous. However, as a secial case of some interest, it may be assumed tat tere is no tecnological regress, i.e., tat S is a subset of Using tis assumtion, it is easy to see tat π { } y{ } S, K. 8 ; S max y y: y S max y: y S π ; S 9 and, ence, tat te firm tecnological rogress function is non-negative, α. In tis secial case, it can be seen tat α is a measure of te exansion in firm 's roduction ossibilities set going from eriod to. It is useful to record te situations were te various functions defined above tae zero values. For future reference, we note tat: s c m u, = if = + t ; H, r T σ π ; S y = if = + τ ; K, r T α π π r r r r r r C r r r r r r S ; S ; S = if S = S ; K. Tus, te consumer substitution function is zero if it is evaluated at te eriod r rice vector facing tat consumer, wile te roducer substitution function is zero if it is evaluated at te eriod r rice vector facing tat roducer. If te tecnology does not cange ten te tecnology rogress function is zero for any reference rice vector. 5

7 Now we are ready to derive our main results. Te Basic Identities Define te money metric cange in utility 7 for ouseold going from eriod to using te reference rices,, by V m u, m u,, H. If we coose = + t ten becomes Hics' 942,. 28 comensating C variation for ouseold, and if we coose = + t ten reduces to Hics' C 942,. 28 equivalent variation for ouseold. Eac of tese money metric measures is a valid measure of individual welfare cange. More generally, it is straigtforward to sow tat, under suitable regularity conditions, a necessary and sufficient condition for tat V > for some. u > u is To andle an economy consisting of many ouseolds, we consider an aggregation of ouseold variation measures. Tus, te aggregate variation V is defined by H { m u, m u, } V V, 2 H wic is te sum of ouseolds money metric canges in utility. If all consumers face te same rice vector, =, te functions V and V are te aggregate equivalent t C variation and te aggregate comensating variation, resectively. Tis aggregate measure of welfare cange is valid in a multi-ouseold economy if lum sum transfers between te government and consumers are ermitted and if rices of goods tat enter ouseolds utility functions do not cange as a result of te transfers tat tae lace. 8 In our small oen economy context, in wic te rices of internationally traded goods are exogenously given, tis latter condition will be satisfied if te rices of nontraded goods are determined solely by international rices and te tecnology and not by ouseold references or te income distribution. Tis roerty occurs in a final-goods roduction model wen te number of roduced goods is at least as great as te number of fully used fixed factors Woodland, 982, Tis assumtion, commonly emloyed in te literature, as been used, for examle, by Wong 99,. 5 in is analysis of welfare comarisons. Te exression for te aggregate variation may be rewritten in several different ways tat allow for interesting economic interretations. Using, te aggregate variation may be exressed as te identity: C C 6

8 H s s + V V = c c. 3 H H H If we now relace te aggregate consumtion vectors by equivalent vectors using te material balance equations in for eriods t = and t =, we obtain te following identity: V s s + y y H H K x x + v v e e. 4 Now eliminate te roduction vector t y from using definition. We tus obtain te tird identity: V = s s + σ σ + α H H K K K x x + v v e e. 5 Exressions 3-5 rovide tree interesting identities for te aggregate variation. Te first identity 3 sows tat te aggregate variation equals a difference of non-negative consumer substitution functions lus an index of consumtion growt, using as weigts te reference rices. Te second identity 4 relaces te index of consumtion growt by indices of growt in its various comonents: outut, net imorts te negative of net exorts, endowments and excess demands negative of excess sulies. In te tird identity 5, te aggregate variation of outut growt on te rigt and side of 4 as been relaced by te following tree sets of terms: i a non-negative sum of roducer substitution functions, K σ ; ii a non-ositive sum of roducer substitution functions, σ ; and iii a K sum of tecnical cange effects, α, tat are non-negative if tere is no tecnical K regress. Te identity 5 is one of te main results in te aer. In a one consumer economy, it decomoses an exact index of welfare cange into various consumer and roducer substitution functions and additional comonents tat are sources of growt, including tecnical rogress, growt in real imorts, growt in endowments and reductions in excess sulies. Tis identity is similar in some resects to one derived by Oyama 972, However, Oyama deals exclusively wit consumer rices and does not exlicitly define te consumer and roducer substitution functions. Our identity is also similar to an exression derived by Grinols and Wong 99, as an exact measure of welfare cange. Wile Grinols and Wong also define consumer and roducer substitution functions, tey use domestic maret rices for evaluation. As will be seen below, it is convenient to deal wit te 7

9 general identity above, and ten consider articular coices of reference rices to establis articular results. 4. Te Gains from Eliminating Excess Sulies In tis section, we use te welfare decomosition develoed above to caracterize te gains from trade tat can arise from te elimination of excess sulies. Some goods tat may be in excess suly, and ence ave zero rices, in te autary equilibrium may command ositive rices in a free trade situation due to strong foreign demand. Te result is tat tere is a welfare gain arising from tis elimination of te excess suly. Assume tat autary equilibrium occurs in eriod t = and tat free trade occurs in eriod t =. Furtermore, assume for simlicity tat tere are no taxes before or after trade, no tecnical cange and no endowment canges. We now consider te case were some goods are free in te autary equilibrium, so tat tere are excess sulies of some commodities in te eriod t = equilibrium, but tat tere are no excess sulies in te free trade equilibrium, so tat e =. Under tese conditions, we ave e = and te aggregate quasi-equivalent variation may be exressed as. 6 V = s + σ + e H K We see tat te traditional consumer and roducer gains, given by te first two non-negative terms, are now augmented by an additional term tat reflects te disaearance of free goods. If te vector of excess sulies in autary, e, contains ositive elements and te corresonding elements of te free trade rice vector,, are ositive ten te last term in 6 will be ositive, ence roviding a sufficient condition for a welfare imrovement. Tus we ave te following roosition. Proosition : Assume tat a small oen economy moves from autary to free trade and tat tere are no taxes before or after trade, no tecnical cange and no endowment canges. A sufficient condition for a welfare gain is tat tere is some good tat is in excess suly in autary, but trades at a ositive rice under free trade. Tis can be an imortant source of gains tat seems to ave been overlooed in te traditional trade literature, wit te excetion of te aers by Oyama 972,. 49 and Neary and Scweinberger 986, Neary and Scweinberger oint out te otential gains from trade due to reviously free factors being ositively riced in free trade. However, as exected, our formulation alies equally to te elimination of surluses in eiter factors or goods., It also alies to any cange in circumstance or olicy, not just to te move 8

10 from autary to free trade. Accordingly, it rovides a formalization and generalization of at least one asect of te idea of a vent for surlus gain from trade as initially conceived by Adam Smit and furter develoed by Myint 958 and Findlay 97, Te gains from trade identity is illustrated using Figure for te secial case were tere are two traded goods, one ouseold and one firm N = 2, H = and K = and were non-traded goods do not enter te utility function and ence are in fixed suly or demand. Te economy's roduction ossibilities set for traded goods is reresented by te curve D D. Te autary consumtion vector is c and te autary roduction vector is y. It can be seen tat good is in excess suly in te autary equilibrium and its rice is zero. Wen te region is oened u to trade at ositive rices, te roduction vector becomes y and te consumtion vector becomes c. Te measure of trading gains, V, uses te international rices under free trade,, as reference rices. If we measure te gains in terms of good, we ave tat V = AE. Tis consists of s, te consumtion substitution gain AB, lus σ, te roduction substitution gain CE, lus e, te elimination of excess suly gain BC. Turning to te equivalent variation measure of trading gains reresented by, evaluated at te autary rices, we find tat we can no longer measure gains and losses in terms of good because good is a free good in te autary equilibrium. However, if we measure te gains in terms of good 2, we find tat V = DE = x. Tis consists of te net imort vector valued at autary rices given by te distance CF, less consumer substitution function E F, less s, te σ, te roducer substitution function CD. Note tat te excess suly elimination gain does not exlicitly sow u in tis decomosition of te gains from trade. 5. Te Gains from te Introduction of New Goods Nowadays goods are being introduced into most economies at an increasingly raid ace. Desite tis emirical fact, te literature on te role of new goods in international trade is rater sarse. A discussion of wy tis may be so, and of te imortance of develoing te teoretical analysis of new goods in te analysis of trade and trade olicy, as been rovided recently by Romer 994. In addition, Feenstra 994 rovides an analysis of te role tat new goods lay in emirical researc in international trade, secifically in te measurement 9

11 of rice indices. In tis section, we indicate ow our gains from trade framewor may be adated to deal wit te introduction of a new good into an oen economy. Wile we do not exlain te creation of new goods, we model teir introduction as a result of rofit and utility maximizing coices: new goods are introduced wen current rices yield ositive roduction, wile revious rices did not. Our caracterization of te gains from te introduction of new goods in terms of te aggregate quasi variation develoed above tus requires us to determine sadow rices for new goods before tey were introduced. Tese sadow rices are constructed using te concet of restricted rofit and exenditure functions and, since tey are firm and consumer secific, our general formulation, involving firm and consumer secific taxes, is required for te analysis to roceed. In eriod, a new internationally traded good, say good, is introduced into te world economy. We assume for simlicity tat tere are no commodity tax distortions in eiter eriod so tat, in articular, we ave t =, τ =, H; K. 7 Te vector of eriod equilibrium rices is,, were 2,..., N is defined as te vector of eriod rices excluding te new good. Te vector of eriod equilibrium rices is 2,..., N. We assume tat consumers ave references over te new good even before it is introduced but tey are restricted to consume zero units of it in eriod. 2 We now loo for a sadow or virtual rice for good tat will just induce ouseold to consume zero units of te new good in eriod. 3 How can we find tese sadow rices? For H, define te restricted exenditure function for ouseold as 4 m ~ u { ~ c ~ : f c, c ~ u },c, ~, 8 minc~ were f is te ouseold utility function, ~ and c ~ are vectors of rices and quantities, c is consumtion of te new good and observed eriod consumtion vector u ~ = = u, c =, ; i.e., we ave m ~ ~ u,, ~ = u is a reference utility level. We assume tat te ~ c~ c~ for ouseold solves wen, H. 9 Assuming tat te derivative from te rigt exists, te aroriate ouseold sadow rice for good in eriod may be defined as 5 m ~ u,, ~ / c, H. 2

12 Using exression for te aroriate ouseold sadow rice for good in eriod, te ouseold secific distortion vectors are defined by coosing te reference rice te new good, and taxes according to for t, ti, i, i N, H. 2 On te roducers side of te economy, we assume tat te tecnology includes te new good even before it is introduced but roducers are restricted to roduce zero units of it in eriod. Accordingly, we loo for a eriod sadow rice for good tat would induce firm to suly a zero quantity of te new good. To do tis we define te restricted rofit function for firm K, as 6 ~ π y, ~, S max { ~ y~ : y, y~ S }, 22 y~ were y ~ is a vector of quantities excluding te first good. We assume tat te observed eriod roduction vector y~ for firm solves wen and y = = ; i.e., we ave ~ y, ~, S π = ~ y~, K. 23 Assuming tat te derivative from te rigt exists, te aroriate firm sadow or virtual rice for good in eriod may be defined as 7 π,, S / y, K. 24 Using te sadow rices defined by, te firm secific distortion vectors are defined by using te reference rice for te new good, and taxes according to τ i τ,, i, i N, K. 25 Wit tese ouseold and firm secific distortions defined, te reference rices determine te welfare effects in te usual way, as is now illustrated. To focus exclusively on te introduction of a new good we assume no tecnical rogress, so tat S = S for eac, no endowment cange and no excess suly of goods in eac eriod. Ten exression for te aggregate variation, evaluated at eriod world rices, reduces to, 26 V = s + σ x x H K since s =, σ = and α = for all ouseolds and firms, v = v and e = e. By a similar argument, exression for te aggregate variation, evaluated at eriod world rices, reduces to V = s s + σ σ x x H H K K

13 In te following, it is assumed, for simlicity of exosition, tat international rices are constant =. In tis case, te substitution terms s and σ vanis from 27 and te two aggregate variation measures above are seen to be identical. If, furter, tere t t is a zero trade balance in te two eriods x = ten te terms x x and x x equal. Under tese conditions, 26 sows tat te country will unambiguously gain from te introduction of te new good from abroad if any of te roducer or consumer substitution functions are ositive. Accordingly, we ave establised te following roosition: Proosition 2: Assume tat a new good is introduced into small oen economy from abroad and tat tere are no taxes, no tecnical cange, no excess sulies, zero trade balances in eac eriod and no canges in te terms of trade. Te ositivity of any roducer or consumer substitution function in te aggregate quasi-comensating variation 26 is sufficient for a welfare imrovement as a result of te introduction of te new good from abroad. Te secial case were tere are two traded goods, one ouseold, one firm, no rice canges and zero balances of trade is illustrated in Figure 2. Te initial consumtion vector is c = y at C, were no units of good are consumed or roduced. Wen te new good is introduced, roduction moves to y and consumtion moves to c. Te constant world rices are = and = and te lines CC, DD and BB ave sloes equal to 2 2 / 2. Te sloe of te line CA equals and te sloe of te line CE equals / 2 /. Under our simlifying assumtions, te aggregate variation 26 becomes 2 V = s +σ = BC + CD = BD. 28 were te substitution terms are s c m u = BC and, σ π =. Due to te simlicity of te model and our ; S y BD assumtion tat te terms of trade are constant, our two measures of gain coincide in tis case and aggregate variation 27 is readily sown to yield te same outcome. Te above model assumed tat te tecnology was caable of roducing te new good in eriod but roducers were constrained to suly zero units of it; te introduction of te new good involved no tecnical cange. An alternative model assumtion is tat te introduction of te new good involves a cange in te tecnology ossibly affecting te 2

14 roducer s ability to roduce all goods. 9 Under tis assumtion, roducers are simly unable to roduce te new good in eriod but tecnological cange occurs just before eriod, allowing roducers to roduce and utilize te new commodity in eriod. Tis new set of assumtions concerning te nature of te tecnological cange can be accommodated using our existing notation by adding te following restriction to te eriod tecnology sets S : y, y S imlies y =, K. 29 It can also be seen tat te reviously defined firm substitution terms continue to satisfy te inequalities in 6, secifically tat ; σ π S y if y S. We also mae te assumtion tat tere is no tecnological regress as a result of te introduction of te new commodity and te associated new tecnology in eriod. Tat is, we assume tat S S, K, as given by 8. Assumtions 29 and 8 on tecnological cange imly tat te introduction of te new good is costless. In addition to te above assumtions, assume constant endowments, no excess sulies in eac eriod, constant world rices = and balanced trade in eac eriod. Under tese assumtions, exression 5 for te aggregate variation, evaluated at te constant world rices, reduces to. 3 V = s + σ + α H K K Under tese conditions, 3 sows tat te country will unambiguously gain from te combined effects of tecnological cange and te introduction of te new commodity if any of te consumer substitution terms, roducer substitution terms or te tecnical cange terms are ositive. Accordingly, we ave establised te following roosition. Proosition 3: Assume tat tere is costless tecnological cange between two eriods tat allows for te roduction of new commodities from abroad. In addition, assume no canges in endowments, constant world rices, no excess sulies, no taxes and a zero balance of trade in eac eriod. Ten te ositivity of any roducer, consumer or tecnical rogress terms in te aggregate quasi-comensating variation is sufficient for a welfare imrovement. Figure 3 illustrates tis roosition by extending te examle illustrated in Figure 2 were tere are two traded goods, one ouseold, one firm, no rice canges and zero balances of trade. In eriod, te roduction ossibilities set is given by te line segment OC. Te eriod consumtion and roduction oints satisfy c = y, were no units of 3

15 good are consumed or roduced. Wen te new good and associated tecnology are introduced, te roduction ossibilities set becomes OEF. Production moves to y and consumtion moves to c. Te constant world rices are = and = and te lines 2 2 BB, CC, DD and E E ave sloes equal to assumtions, te aggregate variation becomes / 2 V = s + σ + α = BC + + CD = BD,. Under our simlifying were te consumer substitution, roducer substitution and tecnical cange terms are s c m u = BC,, 3 ; σ π S y = and α π ; S π ; S = CD. Tus, te gain in welfare is measured as te sum of te consumer substitution term BC and te tecnical cange term CD. Te latter term embodies te inextricably lined introduction of te new good and te associated cange in tecnology. Te above analysis essentially assumed tat te tecnology for roducing te new commodity can be costlessly imorted from abroad; tat is, resident roducers did not ave to incur any researc and develoment costs in order to roduce te new commodity. In te case were te tecnology to roduce te new good requires te exenditure of domestic resources, te introduction of te new goods will no longer necessarily increase welfare. For examle, consider te case were tere are only two oututs in te economy in eriod and te new commodity is not roducible in eriod. In tis case, te outut roduction ossibilities sets in eriod would simly be line segments along te y 2 axis emanating from te origin; i.e., no units of y would be roducible in eriod. In tis case, we simly set y = in definitions and. Since te derivatives defined by would not exist in tis case, we simly relace te defined in by te reference rice. Wit tese alternative definitions, te firm secific taxes τ defined by all become zero. Tis is as it sould be, since, under te assumtion tat te tecnology for roducing te new good in eriod did not exist, tere are no roducer substitution effects in eriod. However, it is no longer te case tat te tecnological cange functions, α, are necessarily zero, since te existence of researc and develoment costs means tat we cannot assume tat S is a 4

16 subset of S for eac. Tus, te exression for te aggregate variation, evaluated at eriod rices, now reduces to V = s + σ + α x x. 32 H K K Again consider te simlified model tat was described in Figure 2 but now assume tat te eriod roduction ossibilities sets is te line segment OA in Figure 4. If te ratio of international rices in eriod is suc tat te sloe of te line segment AD is equal to /, ten te tecnological cange function α will equal zero and our revious 2 analysis carries troug. If / increases, ten it can be seen tat te domestic 2 roduction oint in eriod will be somewere along DC and α will be strictly ositive. Again, our revious analysis goes troug. However, if / 2 decreases, so tat te tangent line AD rotates towards te y 2 axis, ten α becomes negative and te welfare effects of te new good are indeterminate. If te consumer substitution effects are strong enoug, ten tis negative tecnological cange effect can be overcome, for a net welfare gain, but tis ay outcome is not guaranteed. Tus, it is ossible to over-invest in te develoment of new goods. Tus, we ave te following roosition. Proosition 4: Assume tat new goods are introduced into a small oen economy and tat tey incur researc and develoment costs. Assume furter tat tere are no taxes, no tecnical cange and no excess sulies. Te introduction of new goods will be welfareimroving if V > ; welfare may fall if te roducer and consumer substitution effects are not sufficiently strong to outweig any negative welfare effects due to researc and develoment costs. 6. Extension to a Large Oen Economy We now extend te ideas develoed above to a large oen economy tat can influence its terms of trade by its tariff and tax olicies. First, we add terms to our exressions for welfare gains to deal wit canges in te world trade environment and wit te otimality of te tariff olicy. Second, we use tese exressions to develo a new sufficiency condition for a welfare imrovement. To tis end, we define te net trade value function { z z X } β, X max z :, 33 5

17 6 wic is te maximum value of net imorts foreign country net exorts, z, tat can be attained at reference rice vector,, wen te country faces te foreign country s offer set X. Tis function is analogous to a rofit function, recognizing tat X may be interreted as te roduction ossibilities set from trade. Using tis function, we define,, X X β β δ 34 as te difference in te maximum values arising from a sift in te foreign offer set. Tis function will be zero if tere is no cange in te foreign offer set, and will be non-negative if te offer set is enlarged. Finally, we define, r r r z X β γ. 35 Function r γ is te maximum value of attainable net imorts minus te cost, at te reference rices, of te actual net imort vector r z in eriod r. It terefore measures te gains from substitution around te foreign offer set and is called te trade substitution function. If tere are no consumer-secific taxes, otimality of te ome country s tariff vector imlies tat te common consumer rice vector, r C, satisfies te equation = r r C γ, wic is te usual first-order caracterization of otimal tariffs. Using tese definitions, te aggregate variation may be exressed alternatively as e e v v y y s s V H H K δ γ γ = 36 and. e e v v s s V K H H K K δ γ γ α σ σ = 37 Tese two exressions for te aggregate variation differ from teir counterarts 4 and 5 in tat te term x x as been relaced by te term γ γ δ +. Tis new term describes welfare gains from movements around, and sifts of, te foreign offer curve. Assuming for simlicity tat tere is no cange in tecnologies, endowments, excess sulies or in te foreign offer set, exression 36 reduces to y y s s V H H K γ +γ + =. 38 If, in addition, it is assumed tat tariffs are otimal in eriod and tat tere are no consumer-secific domestic taxes, a furter interesting simlification may be establised. To obtain tis simlification, we coose consumer rices as reference rices for te evaluation of

18 te aggregate variation. Ten, since te otimality of tariffs in eriod imlies tat γ = C, were C is te consumer rice vector in eriod, exression reduces to V C = s + y y + γ. 39 H C K Since te first and tird terms on te rigt and side of tis exression are non-negative, a sufficient condition for a welfare imrovement is tat K C y y >. 4 C Tis result aears to be new. It establises te following roosition. Proosition 5: Assume tat an oen economy imoses otimal tariffs following some exogenous cange and tat tere is no tecnical cange, no canges in endowments and no excess sulies. A sufficient condition for a welfare imrovement following some exogenous cange suc as a cange in consumer taxes is tat te value of roduction, at te eriod consumer rice vector, increases. Te assumtions beind te scenes are imortant. Te crucial one is tat te country imoses otimal tariffs against te rest of te world in eriod. If tariffs are not otimal, ten γ and ence te result does not follow. Notice, also, tat if consumer and roducer C > rices are equal in eriod, sufficiency condition for a welfare imrovement automatically olds. 7. Conclusions Te basic welfare identities develoed above ave been sown to be useful in measuring not only te gains from trade and from olicy reform, but also te gains or losses from oter sources of economic cange. Our aer considered some of tese, including, for examle, te gains from reducing excess sulies and from introducing a new internationally traded roduct. However, te welfare measures and identities we ave resented ave muc wider alicability and can, in rincile, be used to measure te welfare effects of a discrete cange in any olicy instrument or oter exogenous variable in our model. Moreover, tey are useful in syntesizing wat may aear to be disarate results on welfare and trade tat ave aeared in te literature. 2 However, our model and analysis are subject to a number of limitations, wic must be et in mind in evaluating our aroac to discrete welfare cange. In articular, i we are limited to an analysis of ex ost data, ii te same ouseolds are assumed to exist in bot eriods, 2 iii constancy of tastes is assumed, iv cometitive rice taing beaviour is C 7

19 assumed and v te model is static. 22 Finally, in te context of many consumers, it sould be noted tat our aggregate variation measures migt not be good measures of aggregate welfare cange if welfare of te economy deends uon te distribution of income. 8

20 References Diewert, W. Erwin, Functional Forms for Profit and Transformation Functions, Journal of Economic Teory 6 973: , Duality Aroaces to Microeconomic Teory, in Kennet J. Arrow and Micael D. Intriligator eds.handboo of Matematical Economics, Vol. II, Amsterdam: Nort-Holland, 982., Te Measurement of te Economic Benefits of Infrastructure Services, Berlin: Sringer-Verlag, 986., Te Gains from Trade Revisited, Discussion Paer No. 87-9, Deartment of Economics, University of Britis Columbia, 987. Dixit, Avinas and Victor Norman, Teory of International Trade, New Yor: Cambridge University Press, 98. Feenstra, Robert C., New Product Varieties and te Measurement of International Prices, American Economic Review : Findlay, Ronald, Trade and Secialization, London: Penguin, 97. Gorman, Terence W.M., Measuring te Quantities of Fixed Factors,.4-72 in James N Wolfe ed., Value, Caital and Growt: Paers in Honour of Sir Jon Hics, Cicago: Aldine, 968. Grinols, Earl L., Transfers and te Generalized Teory of Distortions and Welfare, Economica : Grinols, Earl L. and Kar-Yiu Wong, An Exact Measure of Welfare Cange, Canadian Journal of Economics 24 99: Hics, Jon R., Te Valuation of te Social Income, Economica 7 94: 5-24., Consumers' Surlus and Index-Numbers, Te Review of Economic Studies 9 942: , Value and Caital, second edition, Oxford: Clarendon Press, 946. Jonson, Harry G., Otimal Trade Intervention in te Presence of Domestic Distortions", in Ricard E. Caves, Peter B. Kenen and Harry G. Jonson eds, Trade, Growt and te Balance of Payments, Amsterdam: Nort-Holland, 965. Kem, Murray C., Te Gains from International Trade, Economic Journal : 33-9., Te Pure Teory of International Trade and Investment, Englewood Cliffs, N.J.: Prentice-Hall, 969. Kem, Murray C. and Henry Y. Wan, Te Gains from Free Trade, International Economic Review 3 972: Krisna, Kala, Concetually Based Measures of Structural Adatability", NBER Woring Paer, No. w439, 992. McFadden, Daniel, Cost, Revenue and Profit Functions,. 3-9 in Melvyn Fuss and Daniel McFadden eds., Production Economics: A Dual Aroac to Teory and Alications, Vol., Amsterdam: Nort Holland,

21 Myint, H, Te Classical Teory of International Trade and te Underdeveloed Countries, Economic Journal : Neary, J. Peter and Albert G. Scweinberger, Factor Content Functions and te Teory of International Trade, Review of Economic Studies : Neary, J. Peter and Kevin W.S. Roberts, Te Teory of Houseold Beaviour Under Rationing, Euroean Economic Review 3 98: Oyama, Miciiro, Trade and Welfare in General Equilibrium, Keio Economic Studies 9 972: Romer, Paul, New Goods, Old Teory, and te Welfare Costs of Trade Restrictions, Journal of Develoment Economics : Samuelson, Paul A., Te Gains from International Trade, Canadian Journal of Economics and Political Science 5 939: , Comlementarity - An Essay on te 4 t Anniversary of te Hics-Allen Revolution in Demand Teory", Journal of Economic Literature 2 974: Smit, Alasdair, Some Simle Results on te Gains from Trade, from Growt and from Public Production, Journal of International Economics 3 982: Wong, Kar-yiu, Welfare Comarison of Trade Situations, Journal of International Economics 3 99: Woodland, Alan D., International Trade and Resource Allocation, Amsterdam: Nort- Holland,

22 Endnotes. Te modern literature on tis subject begins wit Samuelson 939 and includes Kem 962, Jonson 965, Oyama 972, Kem and Wan 972, and Smit 982. For textboo accounts, see Kem 969, Dixit and Norman 98, and Woodland 982, We let te number of ouseolds and te set of ouseolds to be identified by te same notation. Firms and goods are similarly treated. 3. Wile non-traded goods rices adjust to clear te domestic marets, it is assumed furter below tat te domestic rices are solely determined by te traded goods rices and te tecnology and not by ouseold references or te income distribution. 4. Tis function was introduced to te economics literature by Hics 946,. 33. Te matematical roerties of exenditure functions are discussed in Diewert 982, We assume tat te minima in 3 exist. 5. Hics 946, , Gorman 968, McFadden 978 and Diewert 973 discuss roerties of rofit functions. We assume tat te maxima in 4 exist. 6. Te concet of a ouseold substitution function, and tat of a firm substitution function introduced below, is due to Grinols 987. See, also, te unublised aer by Diewert 987. Similar ideas lie beind Krisna s 992 concet of indices of structural adjustment. 7. Te term is due to Samuelson Secifically, if V > for some rice vector ten tere is sufficient income to be reallocated in a lum sum fasion to allow every ouseold to consume its initial consumtion vector wit some extra income left over. Provided tat tis rice vector,, is faced by ouseolds and does not cange as a result of te transfers, tis extra income can be redistributed to acieve a strict Pareto imrovement in welfare. Tis argument is no longer valid if rices alter; additional argument is needed to establis weter a Pareto imrovement as occurred or can be generated. Alternatively, a reresentative consumer model, wic is isomoric to a one ouseold model, could be assumed. 9. Our identity as no yotetical tax revenue terms. However, tax distortions do lay a role in 5 via te definitions of te roducer and consumer substitution terms.. Tin of transortation imrovement tat allows te natural resources of a reviously isolated region to be exloited.. Oyama s 972 Proosition 2 on te gains from self-financing trade covers te vent for surlus argument for commodities. 2. Tus, it is assumed tat te introduction of new goods is not associated wit a cange in ouseold references. Te analysis of canges in references due to te new good or to advertising introduces new issues tat go beyond te scoe of tis aer. 3. Te basic idea is due to Hics 94. Also see Neary and Roberts 98, wo introduced te term virtual rice for te sadow rice tat induces zero consumtion. 4. For te roerties of restricted exenditure functions, see Diewert 986, and Neary and Roberts To see wy te sadow rices defined by 2 do te job, consider te following eriod exenditure minimization roblem for ouseold : 2

23 { } { c c m u c } m u,, min c + c : f c, c u c, c = min +,, = c + c = c wic uses te definition of te restricted exenditure function, 8. It sould be evident tat te first order necessary condition for a solution to tis roblem is satisfied by c =. 6. For te roerties of restricted rofit functions, see Gorman 968, Diewert 973 and McFadden To see wy te sadow rices defined by 24 do te job, consider te following eriod rofit maximization roblem for firm : { } y { w y π y S } π w,, S max w y + y: y, y S y = max +,, = w y + y = y using te definition of te restricted rofit function, 22. It sould be evident tat te first order necessary condition for a solution to tis roblem is satisfied by y =. 8. In equation 27, te terms s and σ do not vanis as tey are evaluated at world rices, wic differ from te eriod ouseold and firm secific rices tat include te sadow rice for te new good. 9. We are indebted to an anonymous referee for ointing out tis extension of te model. 2. A syntesis of te results establised by Oyama 972 and Wong 99 is rovided in an earlier version of tis aer. 2. If a ouseold existed in only one of te two eriods under consideration, we would ave to absorb its non-zero consumtion vectors into te aroriate net endowment vectors. 22. Accordingly, tere is no modeling of saving and investment beaviour, no exectations about future rices are formed, and so on. Our results do aly, of course, if tere exists a full set of futures marets in a finite orizon model.,, 22

24 c2, y2 F c E u D c y u C y A B C D E c, y Figure. Te Gains from Elimination of Excess Sulies

25 c, y 2 2 D c C B c = y u y u A B C D E c, y Figure 2. Te Gains from New Goods

26 c, y 2 2 D E c C B c = y u y u BC F D c, y Figure 3. Te Gains from a New Goods Tecnology

27 c2, y2 A B E u D C c, y Figure 4. New Goods wit R&D Costs