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This PDF is a selection from an out-of-print volume from the National Bureau
of Economic Research
Volume Title: The Regionalization of the World Economy
Volume Author/Editor: Jeffrey A. Frankel, editor
Volume Publisher: University of Chicago Press
Volume ISBN: 0-226-25995-
Volume URL: http://www.nber.org/books/fran98-
Publication Date: January 1998
Chapter Title: The Welfare Implications of Trading Blocs among Countries
with Different Endowments
Chapter Author: Antonio Spilimbergo, Ernesto Stein
Chapter URL: http://www.nber.org/chapters/c
Chapter pages in book: (p. 121 - 152)
5 The Welfare Implications of
Trading Blocs among Countries
with Different Endowments
Antonio Spilimbergo and Ernesto Stein
5.1 Introduction Over the last decade, a large number of bilateral trading arrangements have been created, strengthened, or proposed in nearly every region of the world. The North American Free Trade Agreement (NAFTA), the European Union, Asia-Pacific Economic Cooperation (APEC), and Mercosur are just a few ex- amples of this trend. Furthermore, empirical evidence on bilateral trade flows shows that this phenomenon has been accompanied by increased trade region- alization, at least in some regions (Frankel, Stein, and Wei, chap. 4 in this volume). Therefore, the study of the welfare implications of trading blocs has become very relevant. One important contributor to the debate has been Krugman ( 1991 a, 1991b). He uses a model of trade under monopolistic competition to study how welfare of the world depends on the number of blocs into which the world is divided. In Krugman’s model, the world is completely symmetrical, so all blocs are exactly the same size. He finds that the number of blocs associated with the lowest possible welfare is three. The fact that welfare declines starting from one bloc (free trade) requires no explanation. The reason for the increase in welfare beyond three blocs, however, is more subtle: the distortions associated with a given tariff level become smaller as the number of blocs becomes larger and consumers buy a larger proportion of the varieties they consume from outside the bloc. This happens because a smaller portion of the relative prices
Antonio Spilimbergo is a research economist at the Inter-American Development Bank. Ernesto Stein is a research economist at the Inter-American Development Bank. The authors thank Deborah Davis, Jeffrey Frankel, Luis Jorge Garay, Jon Haveman, Arvind Panagariya, Roberto Rigobbn, participants in the NBER conference, and participants at the semi- nar at the Federal Reserve Board for useful comments. The authors take responsibility for any errors. The opinions expressed in the paper are the authors’ and do not necessarily reflect those of the Inter-American Development Bank.
121
123 Trading Blocs among Countries with Different Endowments
effects depend on such costs, as well as on the geographical character of trad- ing blocs (natural versus unnatural). In addition, including transport costs makes the model more realistic regarding the extent of trade diversion, since now natural barriers appear that restrict trade between countries that are far apart, therefore reducing the amount of trade diversion when blocs are formed. In this paper, we go a step further in the direction of resolving the issue of the likely welfare effects of world regionalization in trade, by using a two- factor model where trade is explained both by product variety and by compara- tive advantage. In fact, by appropriately setting the values of some parameters, the model can be transformed into either a pure product differentiation model (as in Krugman or Stein and Frankel) or a comparative advantage model. In addition, introducing two factors of production will enable us to study the welfare implications of the formation of trading blocs among countries at different stages of development (north-south integration), as well as those formed among similar countries (north-north and south-south integration). Our framework allows us to evaluate the case of PTAs as well as that of free trade areas (FTAs), the effects of transport costs, and the effects of different countries having different tariff levels. After setting up the model for the closed economy in the next section, we allow for trade in section 5.3. In section 5.4 we study the welfare implications of different types of trade arrangements. Section 5.5 offers our conclusions.
5.2 The Model for the Closed Economy
We will work with a model where there are three sectors: agriculture (a), intermediate inputs (v), and manufactures (m); and two factors of production: capital ( K ) and labor (L).4 On the demand side, consumers share a Cobb- Douglas utility function given by
(1) u = M"c;-",
where 0 < a 5 1 , and M and c, are the consumptions of manufactures and
agriculture. The Cobb-Douglas specification results in consumers spending a fixed proportion of their income on each type of good. On the production side, we make the assumption that each factor of produc- tion is specific to the production of one good. Agriculture is a homogeneous good produced under constant returns to scale, and labor is the only factor used in its production. The production function is given by q, = L, which means
- Another model that incorporates both product variety and comparative advantage can be found in Bond and Syropoulos (1993). In their work, however, countries are completely symmetric except that each of them is particularly adept at producing a different variety. Therefore, the prob- lem of blocs when there are differently endowed countries cannot be tackled with their model. Levy (1993) has a two-factor model that combines comparative advantage and product variety with a specification that is different from the one used here. He assumes, as do Deardorff and Stem, that tariffs are either prohibitive or zero.
- The basic structure of our model is in the tradition of Dixit and Norman (1980).
(^124) Antonio Spilimbergo and Ernesto Stein
that each unit of labor is transformed into one unit of agriculture. Therefore, given perfect competition, p , = w, where pa is the price of the agriculture good and w is the wage. There is a very large number of potential varieties of intermediate inputs, which are produced under monopolistic competition and use only capital as^ a factor of production. Increasing returns to scale are introduced by assuming a fixed cost (y) and a constant marginal cost (p):
where x, is the production of the ith variety, and K z the amount of capital used in its production. Each intermediate input enters symmetrically into the pro- duction of the final manufactured good, produced under a Dixit-Stiglitz tech- nology with constant returns to scale:
(3) M^ =^ (Zxf)''8,
where 0 < 8 < 1. This production function results in preference for variety,
which becomes stronger as the parameter 8 becomes closer to 0. Note that we use M to denote both consumption and production per capita of the manufac- tured good, since in this model they are always equal.? We assume that each individual is endowed with one unit of labor and k units of capital. In this way, L represents population size as well as labor, and k is the capital-to-labor ratio. The total capital in the economy is, therefore, K = kL. Since every individual is equally endowed, we can set aside distribu- tive considerations and work with a representative agent. Equilibrium in the intermediate input market is given by (4) X I = Lc,. Equilibrium in the capital market is given by
K = 2 K t = 2 (px, + y). I= I , = I As consumers, the individual maximization problem is (6) max M"c!-" subject to Mp, + cap, = I, where I = rk + w is the per capita income. From the first-order conditions we can obtain the inverse demand function:
5. In fact, M could alternatively be interpreted as the utility derived from the consumption of the heterogeneous product in a two-good model. In that case, we would have a utility function that is Cobb-Douglas between goods, and Dixit-Stiglitz between varieties. Both specifications are equivalent.
126 Antonio Spilimbergo and Ernesto Stein
Plugging equation (14) into the inverse demand function (7), substituting for M and p m , and using w = p, and cn = L, we obtain the relative returns to the factors of production:
Note that the relative price of the factors of production depends only on the relative endowments ( L and K ) , while the relative price ( p , / p , ) has a scale effect that depends on the capital endowment of the economy: the bigger K is, the lower p, is, as can be verified by dividing the left-hand side of equation (14) by pa, and the right-hand side by w.
5.3 Allowing for Trade We assume that countries have similar tastes, technologies, and population size.6 We will proceed in steps. First, we allow for tariffs in a world formed by N countries, assuming for the moment that they have the same factor propor- tions. In this first step, gains from trade arise only due to increased variety. Next, we introduce capital-rich and capital-poor countries. In this case, there are gains due to both comparative advantage and product variety. Note that if the parameter (Y in the utility function (1) were equal to 1, all gains would come from increase in variety, as in Stein and Frankel (1994). On the other hand, if the parameter 8 were equal to 1, there would be no preference for variety, and all gains would arise from comparative advantage. Finally, we will allow, in turn, for the formation of trading blocs, and for transport costs.
5.3.1 Allowing for Tariffs in a World with N Identical Countries We introduce ad valorem tariffs, uniform across countries, and for the mo- ment nondiscriminatory. The tariff revenue is redistributed equally to all con- sumers as a lump-sum transfer.' Now, the producer of the manufactured good faces different prices for different varieties of the intermediate inputs, de- pending on whether they are produced at home or abroad. The price of a for- eign variety in terms of a domestic one is
(16)
The producer of the final good now faces the following problem:
P f = P h ( 1 + t ).
6. A recent model that addresses the consequences of trade between north and south when
- We assume that the number of consumers is sufficiently large that they view this transfer
preferences are different is Spilimbergo (1994).
as exogenous.
127 Trading Blocs among Countries with Different Endowments
(17) max M = z c e subject to z c h p h + &p, 5 Mp,. ( )'" The first-order conditions yield ii(i -8) 1 1/(1 - 8) c , = c h ( ; ) =.(-) l + t.
In equilibrium, the per capita production of the manufactured good will be
where
The zero-profit condition in the production of manufactures yields the price of final manufactured goods in terms of the intermediate home variety:
(8- i)/e
p r K(l - 6)^ (i-nvn
( i - w n
(21) p , = p h n ( - ( ; ) = .[
] );(
Ph We can interpret (l/'P)ci-e)/n as the price index of the intermediate inputs in terms of the price of the domestic variety. We can see that the price of manufac- tures is proportional to the price of the home varieties. As expected, it depends negatively on n, the number of varieties produced in each country, due to pref- erence for variety in the production function. We have solved the problem of the manufacturer of final goods, who takes
p , as given. Now we need to solve the problem of the consumer. We can ex-
press this problem as
(22) max M v - " subject to p,M + poco 5 rk + w + 7 ',
where T is the per capita tariff receipts that are handed back to consumers as a lump-sum transfer:
+- # o f foreign varielies consume^ per^ variety
The first-order conditions yield
129 Trading Blocs among Countries with Different Endowments
We can now write the prices of intermediate inputs faced by producers of man- ufactures in a rich country, in terms of the ones produced at home:
where the subscript f denotes foreign variety. Likewise, in a poor country, the
prices are
p. = ( l + t ) p. Ph I
The producers of manufactures facing these relative prices will demand the following relative quantities of intermediate inputs. In rich countries,
In poor countries,
We use these relative consumptions to write the equation for equilibrium in the market for a variety produced in a rich country:
where N , and N, are the number of rich and poor countries, respectively. Notice that the supply for each variety is constant, as given by equation (12); chr and
130 Antonio Spilimbergo and Ernest0 Stein
chp, on the other hand, depend on the respective prices of factors in rich and poor countrie~.~
Now we find the equilibrium condition in agriculture. Since agriculture is a
homogeneous good, the law of one price requires that the price at home be the same whether the good is imported or produced domestically. Therefore, we can write pa, = pap( 1 + t ). The relative wage in rich and poor countries, then, is
The equilibrium in the agriculture sector is given by
The system formed by equations (32), (34), and (33), together with the normal-
ization wp = 1, determines the prices of factors of production (r,,, wp, r r , w J. Since the equations in the system above are nonlinear, an analytical solution is not possible, so the model will be solved through simulations.
5.3.3 Introducing Trade Arrangements
The framework outlined in the previous section can be used to examine the welfare implications of different types of trading blocs. Their formation simply introduces changes in the set of relative prices faced in each type of country. For the case of a rich country, the set of relative prices faced by the producers of manufactures will now be
- The results are derived following the same procedure of the previous section. cilr is equal to
%L + k ( t + I )
0a r.
where
is analogous to equation (20). The detailed derivations are available upon request
132 Antonio Spilimbergo and Ernesto Stein
poor country, the relative price of a variety produced in a rich extracontinental country in the absence of blocs will be
( 1 + t)P
(1 - a)(l - b)’
Pi,,,
(37)^.^.^ -^ .-.^ ~
where the subscript x stands for extracontinental. The relative consumption will be
and the relative demand will be
The rest of the relative prices, consumptions, and demands are determined ac- cordingly. In particular, the relative wage between the rich and poor coun- try will be ] / [ ( I - a)(l - b)], if they belong to the same bloc, and (1 + t ) / [( 1 - a)( 1 - b)] otherwise.
Gf.. = ( ( 1 ,ai(:,p h))l-^1 dhv (1^ -^ a ) ( l^ -^ b)’
5.4 Welfare Implications of Trade Agreements
In this section, we use our model to analyze the welfare implications of different types of trade arrangements. First, we come back to the question of the welfare effects of the consolidation of the world trading system into a few trading blocs. By changing the substitution parameters in the model, we will be able to see how these effects change as we move from the case where trade is explained mostly by product-variety considerations to one where compara- tive advantages play a large role in explaining trade. Second, in a simple world of four countries (two rich and two poor), we ask what is the optimal type of arrangement for each type of country, and how the answer changes for different values of the parameters. Finally, we introduce the possibility of PTAs (rather than just FTAs), and study the optimal level of intrabloc tariffs when continen- tal trading blocs are formed.
5.4.1 Does Welfare Increase as the World Consolidates into Blocs?
We now address the Krugman versus Deardorff and Stern debate. As dis- cussed in the introduction, Krugman’s product-variety model finds that, in the absence of transport costs, a world of a few large blocs results in the lowest level of welfare. In contrast, Deardorff and Stern suggest, using a comparative- advantage model, that welfare increases monotonically as the number of blocs becomes smaller, reaching maximum welfare under free trade. In figure 5.1, we present the results of simulations using our model, which incorporates both product variety and comparative advantages as motives for trade.
133 Trading Blocs among Countries with Different Endowments
000
m mm (^0) 1 2 3 4 5 6 7 8 9 10 1 1 12 N u m b e r of B l o c s
Fig. 5.1 Product variety versus comparative advantages Notes: a = 0.5; t = 0.3; k = 3; a = b = 0 (except a = 0.3 where noted in key); C = 1, N = 60.
Each curve represents the welfare of the world under different parameter values, as a function of the number of symmetrical blocs into which the world is divided. We work with a world of sixty countries, thirty rich and thirty poor. World welfare is obtained simply by averaging the welfare in rich and poor countries. All countries are assumed to levy the same tariff level on imports from outside the bloc (we use 30 percent in our simulations). Tariffs within the bloc are completely eliminated, as in FTAs." We use a value of (Y = 0.5, which means that half of the consumer's income is spent in agriculture and the other half in manufactures, and a value of k = 3, meaning that each individual in the rich country is endowed with three units of capital. The highest curve corre- sponds to a value of 8 = 0.75. In this case, the elasticity of substitution among varieties is 4. The rest of the curves correspond to higher values of 8. As 8 increases in value, preference for variety decreases, increasing the relative im- portance of comparative advantage as a source of gains from trade. As 8 ap- proaches 1, preference for variety disappears, and only differences in factor proportions explain trade. Intraindustry trade is eliminated, and only interin- dustry trade remains. For 8 = 0.75, the number of blocs associated with minimum welfare is three. This suggests that adding different factor proportions to a model with product variety does not change the implications in any significant way. It is
11. Since the tariff for the case of trade with countries outside the bloc is uniform, we do not distinguish here between FTAs and customs unions.
0
Fig. 5.2 Which arrangement should the rich country seek? Notes: (Y = 0.9; t = 0.3; k = 3; a = b = 0; C = 1; N = 4.
" l 0 055 060 065 070 075 080 085 090 095 100 0
Fig. 5.3 Which arrangement should the rich country seek? Notes: (Y = 0.1; t = 0.3; k = 3; a = b = 0; C = 1; N = 4.
Z LL I
w^ /I x S
L
0 0 5 5 060 065 070 0 7 5 o a o 0 8 5 090 095 100
Fig. 5. Notes: (Y = 0.9; t = 0.3; k = 3; a = b = 0; C = 1; N = 4.
Which arrangement should the poor country seek?
Fig. 5.5 Which arrangement should the poor country seek? Notes: (Y = O. l ; t = 0. 3 ; k = 3 ; a = b = 0; C = I ; N = 4.
138 Antonio Spilirnbergo and Ernest0 Stein
.-^ c
/ /_ / /
~ MFN. RE PB
. l l l l l ~ ~ l.. ~ l"/SS. - NS/NS
- FT I I I 1 I I.... 004 0 0 8 0.12 0. 1 6 0. 2 0 0. 2 4 0 2 8 0.32 0. 3 6 0. T a r i f f in t h e r i c h c o u n t r y Fig. 5.6 Differentiated tariffs: the effects on the rich countries Notes: a = 0.5; 0 = 0.75; t,, = 0.3; k = 3 ; a = b = 0; C = I ; N = 4.
another rich country (figure 5.6); and, as figure 5.7 shows, the poor would rather integrate among themselves than join the rich!lh The key to these results is the effect of the formation of blocs on the terms of trade. These effects are very different when the countries start from different tariff levels. We will pres- ent a simple example to provide the intuition for this result. Take a world of three symmetric countries, A, B, and C, where tariffs are nondiscriminatory, and uniform across countries. What are the effects on the terms of trade of the formation of an FTA between A and B? As explained above, both countries deviate trade away from C, and in favor of their partners. As a result, relative world demand for goods produced in C declines, and so do its terms of trade, while those in A and B improve. In addition to the trade-
diversion effect, there is a trade-creation effect: both A and B will demand
more goods from each other, at the expense of the demand for home goods. In this symmetric setting, this trade creation effect has no consequences for the terms of trade of A and B, since the effects in both countries cancel out, leaving demand unchanged. However, this changes when tariffs in A and B are not the same. Take now the extreme example where tariffs in A are zero, while those in B
are positive. The following effects will take place if A forms an FTA with B:
country B will deviate trade away from C in favor of A; B will also shift de- mand from itself to A (trade-creation effect). However, A will neither create nor deviate trade, since its tariff structure has not changed at all. The resulting
- We performed simulations for different values oft,,. The results are qualitatively similar.
139 Trading Blocs among Countries with Different Endowments
0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0. T a r i f f in t h e r i c h c o u n t r y
Fig. 5.7 Differentiated tariffs: the effects on the poor countries Nofes: a = 0.5; 8 = 0.75; fP = 0.3; k = 3; a = b = 0; C = 1 ; N = 4.
effect is a fall in the demand for the goods produced in country B. Therefore, the terms of trade of country B may actually fall when it enters into a bloc with A. In contrast, the improvement in country A's terms of trade is even larger than in the case where the tariff levels in A and B are similar. We chose a tariff level in A of zero for simplicity, but the result goes through for any tariff in A sufficiently low. In the case where tariffs in the rich countries are sufficiently lower than those in the poor countries, this example helps us understand why both rich and poor countries might prefer to integrate with the p00r.l~ This type of analysis helps us understand some of the issues involved when a country like Chile has to decide whether to join NAFTA or Mercosur. We use this only as an illustrative example since our framework leaves out a number of other important considerations in making this decision. Under which conditions, then, will Chile prefer to join Mercosur rather than NAFTA?Is The passage above suggests that the larger the tariff in the rich country (NAFTA) relative to the poor (Mercosur and Chile), the more inclined Chile will be to join Mercosur.
**17. The results of our simulations involving different tariff rates are consistent with the conclu- sions reached by Panagariya (1995) using a three-country example. In his example, countries lose by granting preferential treatment to their partners, and gain when preferential treatment is ex- tended to them. In this sense, Panagariya claims that the mercantilist approach is valid for analyz- ing tYTAs.
- In what follows we treat Mercosur as a single poor country, and NAFTA as a single rich country.**
