metadata: authors: 0: author: Robinson,Sherman
1: author: De Melo,Jaime A. P.
count: World
docna: 0: docna: Product differentiation and foreign trade in
            CGE models of small economies
docty: Policy Research Working Paper
subtopic: Labor Markets,International Trade and Trade Rules,Macroeconomic Management
teratopic: Environment
abstracts: cdata!: In recent years, two classes of
            computable general equilibrium (CGE) trade models have been
            used to investigate external sector policies: single country
            and and multicountry trade models. The authors examine the
            treatment of exports and imports in recent single country
            CGE models of small economies. They present a simple, one
            sector analytical model that captures the major features of
            the multi sector counterpart used in applied models. They
            show that applying the same assumption about product
            differentiation to imports as to exports gives rise to a
            well behaved, price taking economy and normally shaped offer
            curves. They illustrate the one-sector model with a
            numerical example which shows the implications of the choice
            of weights used as a proxy for the domestic price index in
            computations of real exchange rate indices. The model also
            shows the role of foreign trade elasticities in the popular
            Australian model, with traded and nontraded goods. Trade
            substitution elasticities on the import side play a crucial
            role in determining the direction of change in real exchange
            rate during terms of trade perturbations.
repnme: repnme: Product differentiation and foreign trade
            in CGE models of small economies
display_title: Product differentiation and foreign
            trade in CGE models of small economies
listing_relative_url: /research/1989/02/700569/product-differentiation-foreign-trade-cge-models-small-economies
topicv3: Trade m1326924 698,Trade Balance m1327679 1136,Production Frontier m1503947 2688,Computable General Equilibrium Modeling
            and GTAP m1504535 3113,Single Country Models m1504540 3118
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Environment
origu: Policy Plan & Prog Review Dept
no_of_pages: 36
author_keys: 0: author_key: 452473
1: author_key: 91075
model_extractions: # **Plc,Planning, and Research**

7 ~~Trade Policy In recent years, two classes of computable general equilibrium (CGE) trade models have been used to investigate extemal sector policies: single-country and multicountry trade models.

The single-country models have been used to analyze such extemal sector issues as the impact of restrictions on foreign trade or the impact of changes in net foreign transfers or world prices on the equilibrium of the real exchange rate. The multicountry models are typically concemed with resource allocation and the welfare implications of tariff reductions.

The authors examine the treatment of - exports a.od imports and different assumptions about export demand and import supply behavior - in recent single-country CGE models of small economies. They present a simple, one-sector analytical model that captures the major features of the multisector counterpart used in applied models.

They show that applying the same assumption about product differentiation to imports as to exports gives r se to a well-behaved, pricetaking economy and normally shaped offer curves.

They illustrate the one-sector model with a - numerical example which shows using different trade substitution elasticities -- the implications of the choice of weights used as a proxy for the domestic price index in computations of real exchange rate indices.

The model also shows the role of foreign trade elasticities in the popular Australian model - with traded and nontraded goods. Trade substitution elasticities on the import side play a crucial role in determining the direction of change in the real exchange rate during termsof-trade perturbations.

This paper is forthcoming in the _Journal of International Economics._ This paper is a product of the Trade Policy Division, Country Economics Department. Copies are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Karla Cabana, room N8-065, extension 61539.

The PPR Working Paper Series disseminates the ftndings of work under way in the Bank's Policy, Planning, and Research Complex. An objective of the series is to get these findings out quickly, even if presentations are less than fully polished. The findings, interpretations, and conclusions in these papers do not necessarily represent official policy of the Bank.

Produced at the PPR Dissemination Center
Product Differentiation and the Treatment of Foreign Trade in Computable General Equilibrium Models of Small Economies by Jaime de Melo and Sherman Robinson

||TABLE OF CONTENTS||
|---|---|---|
|1.|Introduction|1|
|2.|A Small-Country Model with Differentiated Trade|5|
||2.1<br>Model Equations|5|
||2.2<br>A Graphical Presentation||
|3.|Terms of Trade and Transfers: A Graphical Analysis|11|
||3.1<br>Terms-of-Trade Change|11|
||3.2<br>An Increase in Foreign Transfers|14|
|4.|A Numerical Example|16|
|5.|Conclusions|22|
||Appendix|25|
||Footnotes|29|
||References|31|

Sherman Robinson is a member of the Department of Agricultural and Resource Economics, University of California, Berkeley. We thank David Roland-Holst for help with derivations in the appendix, Taeho Bark, T.N. Srinivasan for discussions, a referee for very incisive comments, and Gabriel Castillo and Jackson Magargee for research and logistic support. This paper is forthcoming in the Journal of International Economics, JEL classification 410.
1

# 1. Introduction

In recent years, two classes of computable general equilibrium (CGE) trade models have been used to investigate external sector policies: singlecountry and multi-country trade models. The multi-country trade models (e.g. Deardorff and Stern (1981) and Whalley (1985)) have typically been concerned with resource allocation and welfare implications of tariff reductions such as those of the Tokyo round. The single-country models have been used to analyze a variety of external sector issues ranging from the impact of restrictions on foreign trade (e.g. tariffs and QRs, with or without rent seeking) to the impact of changes in net foreign transfers or world prices on the equilibrium real exchange rate. 1/ For both types of models, the results from policy simulations depend on how export and import behavior are modelled. In a recent paper, Whalley and Yeung (1984) -- henceforth WY -- examine this issue for single country models using the term "external closure" to refer to the various assumptions about export demand and import supply behavior. After noting that most applied models are quite disaggregated and separate traded and non-traded goods, they review three external closure rules in single-country models. Among the issues they raise, WY choose a simple two commodity (import and export) formulation with no non-traded commodity to show that in these models, "... there is no currency exchange rate in the conventional use of the term as a financial magnitude determined from financial sector activity." 2/ In the second of their three external closures, WY assert that the imposition of a zero trade balance condition in a two-good CGE model that incorporates product differentiation (i.e. the Armington assumption) with price-taking behavior for imports along with a downward-sloping foreign export
2 demand curve with constant elasticity yields a model in which both domestic and foreign offer curves lie on top of one annother. 3/ They are dissatisfied with this specification and go on to propose a third external closure: a model with price taking behavfir and no product differentiation for tradables, plus the inclusion of non-tradables. In essence, this closure corresponds to a multi-sector version of the well-known dependent economy (Australian) trade theoretic model. They show that in this formulation, there is an exchange rate variable -- or "parameter," as they call it -- that measures the relative price between composites of traded and non-traded goods. Tibey show that, in this model, the foreign offer curve is a straight line, while the domestic offer curve has some elasticity (thereby following conventional trade theory). However, they feel that this price taking assumption will be unpalatable in empirical models of large countrieo. More generally, they note that this model will not allow two-way trade, or cross hauling, which is widely observed in trade statistics at the aggregation levels used in all CGE models, and so is not a desirable specification.

Several points about the WY analysis deserve comment. First, the role of the exchange rate in computable general equilibrium models has received attention for some time and we can find no case in which modelers interpret it as a "financial variable." 4/ Second, the two-good model with both goods traded that IY use in their first discussion of external-sector closure does not represent well arty of the applied CGE trade models, which invariably include some non-traded goods. 5/ Third, an external closure using a price-taking formulation for all tradables in a model with perfect substitution will be unpalatable for stronger reasons than those mentioned by WY. If the price-taking formulation is not accompanied by some product
3 differentiation, the model will generate extreme specialization whenever it is subjected to a policy simulation such as reduction in tariffs. The assumption of a downward-sloping foreign demand curve, while it will help (but not fix) the specialization problem, will lead to unrealistically strong termu-of-.rade effects that will dominate the welfare results of policy changes in single country models. 6/ The essence of the external sector specification of most recent single-country CGE trade models can be captured by a simple one sector model with symmetric product differentiation for imports and exports. This model embodies (and extends) well-understood results from neoclassical trade theory and provides a compact statement of the external closures found in most applied models. The model is also useful to illustrate the role of trade elasticities in the Australian (dependent economy) model with trLded and nontraded goods. We show that the "parameter" referred to by WY in the analysis of their third external closure still exists in this model. We indicate how its equilibrium value is influenced by the assumed values for trade substitution elasticities and by the choice of weights used as a proxy for the domestic price index in computations of real exchange rate indices.

With this framework, we provide a systematic exploration of the behavior of a small price taking economy characterized by product differentiation on both the export and import sides. We argue that reasons for introducing product differentiation on the export side are the same as those for introducing product differentiation on the import side; namely, that multi-sector models, even when they are disaggregated, do not disaggregate products sufficiently. This assumption has in fact been used by Dixon et al (1982) and by Deardorff and Stern (1986). In Dixon et al. (1982), the justification is based on producers engaging in joint production, as in the
4 original presentation by Powell and Gruen (1968). While plausible under certain circumstances, we think that a more general reason along the lines pointed out above is the more plausible rationale for introducing symmetric product differentiation. This said, it should be pointed out (see Anderson (1985)) that calculations of the costs of protection carried out in aggregate economy-wide models with product differentiation to overcome the problem of specialization may severely understate the costs of protection, at least with respect to partial liberalization. But our purpose here is to study the properties of economywide models, so this issue of bias in results from applied models can be left aside.

The remainder of the paper is organized as follows: In section 2, we present the model and use it in section 3 to show how equilibrium is affected by terms-of-trade shifts and by changes in net capital iflows, both common experiments in single country models. The model is also useful for illustrating the role of elasticities in popular trade-theoretic models that include traded and non-traded goods. In Section 4, we derive an expression for the elasticity of the domestic offer curve in our model with symmetric product differentiation and set up a numerical example. The expression and the numerical example show the role of initial conditions (i.e. openess to trade) and of values of trade substitution elasticities in determining the shape of the well-behaved domestic offer curve. We also illustrate the wellknown fact that -- once weights entering the relevant price indices are chosen -- the equilibrium value of the real exchange rate (defined as the relative price of traded to non-traded goods) is indeed independent of the choice of numeraire.
5

# 2. A Small-Country Model with Differentiated Trade

For many developing countries, it is reasonable to assume that the country is "small" on world markets and cannot affect its international terms of trade. However, it is also reasonable to assume that world prices in the tradable sectors do not dominate t'e domestic price system. We present below a simple analytic model which captures these stylized facts and discuss its theoretical structure.

Make the following assumptions: (1) domestically produced and imported goods are imperfect substitutes -- the Armington assumption; (2) domestically produced goods sold on the domestic market are imperfect substitutes for goods sold on the export market; (3) the economy can purchase or sell unlimited quantities of imports and exports at constant world prices -- the small-country assumption; (4) aggregate production is fixed; and (5) there is a balance of trade constraint.

# 2.1 Model Equations

In Table 1, equations 1 and 2 give the trade aggregation functions. In applied models, and in the numerical example of Section 4, equation 1 is a CES function, following Armington, and equation 2 is a CET (constant elasticity of transformation) function. 7/ For the analysis here, we only require that F(-) be convex to the origin, that G(-) be concave, and that both be homogenous of degree one in their arguments. Given the aasumption of fixed output, which is equivalent to assuming full employment, G(-) represents a production possibility frontier delineating the tradeoffn between exports and domestic supply.

Equations (3) and (4) translate foreign prices into domestic prices using a conversion factor, r, which we refer to as the "nominal" exchange
6

||Table 1<br>A One Sector Small-Countrv<br>Model with Differentiated<br>Trade|
|---|---|
|(1)|Q*F(M,Dd)<br>Impurt aggregation function|
|(2)|- G(E,D<sup>5</sup>)<br>Export transformation<br>function|
|(3)|pm<br>-r ;m<br>Import price|
|(4)|pemr we<br>Export price|
|(5)|Pq. f1(p¶ pd)<br>Consumer price|
|(6)|p<br>*_g(pe,pd_<br>)<br>Producer price|
|(7)|Md. f 2(pmpd)<br>Import demand equation<br>Dd|
|(8)|Es<br>g2 Pe=P<br>Export supply equation<br>D|
|(9)|-<br>M - w E =B<br>Balance of trade constraint|
|(10)<br>where:|Dd-<br>Ds=0<br>Domestic demand-<br>supply<br>equilibrium|
|M,E|=<br>imports, exports|
|Dd,Ds|=<br>demand and supply of the domestic good.|
|Q|=<br>composite consumer good|
|X|=<br>composite production|
|-m|world price of imports|
|we|world price of exports|
|r|Conversion factor; "nominal" exchange rate|
|pm|domestic price of imports, M|
|pe|=<br>domestic price of exports, E|
|pd|=<br>domestic price of domestic sales, D|
|pq|=<br>domestic price of composite consumer good,Q|
|px|=<br>domestic price of composite output, X|
|B|exogenous balance of trade, or net foreign capitaL inflow (or<br>outflow for negative B).|
7 rate. It should be clear, but is worth repeating (as has been pointed out by DMR and WY) that this conversion factor, r, is not a financial exchange rate variable. Though often referred to as "the" exchange rate, we refer to it as the "nominal" exchange rate so as not to confuse it with the real exchange rate -- the relative price of the domestic good in terms of the (fixed) traded goods -- which is determined by the model. Indeed, the model could be written without reference to r -- as is common in trade theory -- by implicitly choosing it as numeraire. We use this approach below in Section 2.2. However, since we wish to consider alternative choices of the numeraire, we maintain r in our formulation. 8/ We assume that producers maximize profits and that demanders minimize the cost of purchasing a given quantity of composite good Q. 9/ These assumptions lead to equations 5 to 8. Equations 5 and 6 define composite good prices and are effectively dual cost functions. They are homogeneous of degree one in input prices. Equations 7 and 8 give the demand for imports and supply of exports arising from the first-order conditions.

Since only relative prices matter, the functions describing the model are homogeneous of degree zero in prices. To set the absolute price level, select r as numeraire. Equation 9 gives the equilibrium condition for the balance of trade; that in foreign units (expressed in terms of the numeraire) the value of imports equals the value of exports plus B. Finally, equation 10 is the equilibrium condition for the supply and demand for the domestic good. Overall, the model has 10 equations and 10 endogenous variables: Q, M, Dd, Ds, E, pm, pe, pd, pq, and px. The homogeneity of equations 1 and 2 guarantee that the system satisfies Walras' Law. This can be easily seen by writing out the aggregate income and expenditure equations:
8 P + rB total income PXX - PeE+ PdDa the value of production or GDP PqQ - P'M + PdDd Total expenditure or absorption Given the equilibrium conditions In equations 9 and 10, it follows that income always equals expenditure. The variable, B, in equation 9, denominated in foreign units, can be thought of as representing an increase (or decrease) in real income measured in terms of imports, given the fixed world price of imports.

# 2.2. A Graphical Presentation

This model is simple enough so that its properties can be shown graphically. Figure 1 presents a four-quadrant diagram that captures the essential features. For convenience, choose units so that the exogenous world prices for both exports and imports equal one. Also, set r as numeraire and - initially assume B 0. In this case, the balance of trade equation defines the foreign offer curve and graphs as a 45-degree line in quadrant 1. The production possibility frontier, PP, (equation 2) is graphed in quadrant 4. Quadrant 3 has a 45-degree line which simply indicates that domestic goods, D, which are supplied to the domestic market, are available for demand, defining equilibrium in the domestic goods market. The concave curve, CC, in quadrant 2 is the consumption possibility frontier, which is the locus of points that simultaneously satisfy the balance of trade constraint in quadrant 1 and the production possibility frontier in 3-.drant 4. Given our choice of units and the assumption that the balance of trade equals zero, the consumption possibility frontier in quadrant 2 is a mirror image of the production possibility frontier, PP, in quadrant 4.
9 Figure _1_ EQUILIBRIUM IN THE SMALL COUNTRY CASE <!-- Start of picture text --> M<br>I M-PE-O<br>C<br>I I<br>I I<br>I ~ ~I I<br>Do ~ - I-A I I<br>I I<br>I I<br>i C I<br>3'I ALG(E.D) I<br>II<br>II<br>p<br>DI ,<br>wow l" - 4J-*:<br><!-- End of picture text -->
10 In quadrant 2, the import aggregation function, equation 1, generates a series of "iso-good" curves, II, analogous to indifference curves. 10/ Equilibrium is achieved at the point of tangency with the consumption possibility frontier. At this point, the equilibrium price ratios, pd/pm and pO/pe, equal the slope of the tangents in quadrants 2 and 4, and are derived from the first-order conditions in equations 7 and 8. 11/ Given our choice of units, the two ratios are equal, and the equilibrium value of pd is the equilibrium value of the relative price of non-tradables to tradables. Thus, selecting r as numeraire is convenient since it allows us to interpret Pd as the real exchange rate. In this model, the foreign offer curve is the **450** line in the M,E quadrant in figure 1. We derive in section 4 the elasticity of the domestic offer curve and show that it is a well-behaved curve which intersects the straight-line foreign offer curve.

Consider the limicing "Ricardian" case corresponding to an infinitely elastic supply of exports. Then PP becomes a straight line, which in turn implies a straight line censumption possibility curve. The real exchange rate is now fixed and, as in a Ricardian world, is determined by technology. Substitution possibilities in demand only determine the composition of production for domestic and for export sales.

Our graphical presentation can also be used to consider the closure criticized by WY; namely, a specification with product differentiation on the import side and with less than infinitely elastic foreign export demand. rn e =E -I/C this case, the model would include an extra equation, n = [ I , where E0 C > 1 is the constant price elasticity of foreign export demand and w e is now endogenous. Now the foreign offer curve is given by: 12/
11 e which is derived by substituting the above expression for se into the balance of trade constraint. This case is depicted in figure 2, where Eo is the equilibrium under the small country assumption (i.e. a = 1). With market power, the foreign offer curve becomes OC, and the corresponding consumption possibility curve is CoC1 with new equilibrium at E1. From the diagram, one can see that assuming market power leads to an optimum with less trade and a correspondingly lower real exchange rate.

Clearly this model, which is representative of many single-country CGE models, does not suffer from the problem of overlapping offer curves described by WY in their discussion of a similar model with constant price elasticities of foreign demand and import supply. As we have shown, the foreign offer curve in this model has the usual shape. As we analyze in some detail below, the shape of the domestic offer curve depends only on the parameters of the export transformation and import aggregation functions and also has the usual shape. Hence the two offer curves will intersect, but will certainly not coincide.

# 3. Terms-of-Trade and Transfers: A Graphical Analysis

Is the one sector model with differentiated trade well behaved? We examine two typical experiments conducted with single-country models: a termsof-trade shift and a change in foreign transfers.

# 3.1 Terms-of-Trade Change

Figure 3 shows the effect on equilibrium of an improvement in the e e terms-of-trade (TOT0 + TOT1) corresponding to an increase in ff, dir > 0. This terms-of-trade change shifts out the consumption possibility schedule to CoC1. Will the economy supply a larger volume of exports at this improved
12 FIgure 2 EQUILIBRIUM 'WTH CONSTANT FOREIGN DEMAND ELASTICITY <!-- Start of picture text --> M<br>Co~~~~~~~~~~C<br>DO CIO~ ~ ~ ~~~~~~- C<br>Ntr atuoeuupoocnaf dmd ><br>I X I 1 J<br>I I~~~~~~~~D<br>LZ~~~~~~~~~D<br><!-- End of picture text --> NatO' Poregn offe cufve dgn9ed under asmptwJ~ion of conhtOnt frgnl demand ekOfhcitV >1

> t 8n-4~3' ':,
13 <!-- Start of picture text --> FNgure 3<br>TERMS.OF-TRADE IMPROVEMEW<br>M<br>/TOT,<br>C,~~~~~~~hT<br>A~~~~~~~<br>/~~~~~~~~~~~~~~~ POT<br>Ds<br><!-- End of picture text --> WohCd Bank - 43
14 terms-of-trade? The result depends on the shape of the domestic offer curve. As drawn in figure 3, exports fall. The demand for the domestic good increases, which in turn implies that the domestic offer curve, FF, is inelastic. 13/ Also note that the real exchange rate will appreciate. -In the limiting "Ricardian" case considered above, the real exchange appreciation will d -e. be equal to the change in the terms of trade, i.e. dp d7

# 3.2 An Increase in Foreign Transfers

Figure 4 shows the effect on equilibrium of an increase in foreign transfers. The effect of a transfer, B, is an upward parallel shift of the external budget constraint to 0101 and the consumption possibility curve to C1Ci. Will the increase in transfers lead to a real exchange rate appreciation, as one would expect in a model where the domestic good is consumed? Yes, if the domestic goods are not inferior in c aumption, which is the case drawn in figure 4 and is guaranteed for the CES function used in practice. Domestic consumption of D increases, exports fall, and imports rise. The graphical apparatus developed here can also be used to examine the effects of a change in commercial policy. This is not done here since it does not lead to any new insights about the properties of the external closure under review. We conclude that the specified external closure gives rise to a well-defined real exchange rate whose variations to policy changes is in accord with the usual assumptions of neoclassical trade theory for small economies. The assumption of product differentiation thus leads to a much more realistic small-country model that can accommodate two-way trade and a degree of autonomy in the domestic price system, but retains all the desirable features of the standard neoclassical model.
is Figure 4 AN INCREASE INFOREIGN TRANSFERS <!-- Start of picture text --> M<br>CO<br>'A<br>I<br>DI<br><!-- End of picture text --> <!-- Start of picture text --> 01<br>woBn I _.<br><!-- End of picture text -->
16

# 4. A Numerical Example

We conclude with a simple numerical example to show the influence of different parameter values on computed equilibria for an increase in transfers and a terms-of-trade change. Assume, a* in typical applications, that the import aggregation function is CES and the export transformation is CET. Then equations (1) and (2) in Table 1 are given by: where a bar denotes an exogenous variable and a and Q are elasticities of substitution and transformation respectively. Following the calibration common in CGE models, we construct parameters for the CES and CET functions to produce the initial equilibrium formulated in table 2 such that all prices are unity, i.e. m --e s e e = **r** .p = **x** ~ = pm _ ~ pe =1 ***** 14// Table 3 shows th- effects on the welfare indicator, Q, (Col. 3) and on the real exchange rate (Col. 4) of setting transfers equal to 10 -- i.e. to 10% of initial GDP -- under different values of the elasticities of import substitution and export transformation. Note that, in the limit, the increase in welfare is equal to the transfer itself. This result occurs when the marginal rate of transformation of production between sales to the domestic and export markets is infinite, i.e. in the Ricardian case discussed above. As expected, the required real exchange rate adjustment to absorb the transfer is an increasing function of the curvature of the CES and CET functions.
17 Table 2 Base Solution Values Transfer (I) Exports (E) Imports (M) Domestic Demand (D) CDP (2) 0 25 25 75 100
18 In this example, the numeraire is pq = 1. Had we selected another numeraire such as fixing the value of the GDP deflator with base year quantity weights (i.e., to set px 1), then the equilibrium values of the "nominal" exchange rate (or conversion factor) in column S would have been replaced by d the values appearing in column 6. Likewise, with p 1 as numeraire, the equilibrium values for the "nominal" exchange rate would have been given by the values in column 4. And, with r _ 1 as numeraire, the equilibrium value of pd appearing in column 4 would have corresponded to the equilibrium value of the real exchange rate. Regardless of the choice of numeraire, the equilibrium values of the relative price indices appearing in columns 4 and 6 of table 3 remain unaltered.

In this one sector model, there is no ambiguity with respect to the appropriate definition of the real exchange rate, r/pd. In applied work, however, two problems arise. In multisector CGE applications, a choice must be made with respect to the weights entering the aggregator for the domestic price index. Even though the choice of weights will affect the computed values for the equilibrium r-al exchange rate, the equilibrating mechanism working through changes in the real exchange rate is the same, no matter what price is chosen as numeraire.

The other problem relates to the choice of weights used to proxy the domestic price index in computations of real exchange rate indices. Typically, the domestic price index is proxied by some published price index such as the CPI or the GDP deflator, both of which include traded goods. As shown by the values in the last two columns of Table 3, when values of a and Q are low, the choice of proxy for the domestic price index makes a great deal of difference in the computed value of the real exchange rate. For example, with
19 Table 3 Welfare and Real Exchange Rate Calculations for an Increase in Transfers al

|cn|....<br>/|Q|r/pd|r|r/p|
|---|---|---|---|---|---|
|(1)|(2)|(3)|(4)|(5)|(6)|
|.2|.2|106.9|.38|.46|.45|
|.5|.5|1.08.7|.68|.75|.74|
|2|2|109.6|.91|.93|,93|
|5|5|109.9|.96|.97|_.91_|
|5|X|110.0|1.00|1.00|1.00|

Transfer _(K)_ set equal to 10. _kI_ Elasticity of substitution in CES (eq.l, table 1 and eq.4.1). c/ Elasticity of transformation in CET (eq.2, table 2 and eq.4.2).
20 _a -_ a = 0.5, the real exchange rate index with CPI (or GDP) weights used as proxy has a value of 0.75 (0.74) whereas the correct value is 0.68.

Finally we come to the shape of the offer curve. It can be shown oc that the elasticity of the offer curve, e0, is given by the following expression: 15/ where From expression (4.3), it is clear that the offer curve will be vertical (£oc- - ) for a = 1, positively sloping (soc > 1) for a > 1 and negatively sloping (eoc < 0) for a < 1. For given values of Q , ec monotonically decreases for increasing values of a (with discontinuity at a = 1). For given values of a , the curvature of the offer curve is less (oec is lower), the higher is the value of a . Finally, for given values of a and a , the value of sc is larger, the more open is the economy. 16/ Figures 5(a) and 5(b) trace the elasticity of the domestic offer curve for different values of a , a * 1. Negative values of c correspond t3oc a backward bending offer curve. In this case, the income effect of al; improvement in the terms of trade dominates the substitution effect and less oc exports are supplied. Negative values of c imply that the real exchange rate must appreciate to insure a greater supply to the domestic market (this is the case drawn in Figure 3). Raising the elasticity of export supply lowers the offer curve elasticity, which in the limit is unity. This result follows directly from the relation between the two elasticities along the
21 Figure 5 OFFER CURVE ELASTICllY a) MEDIUM ECONOMY (EO=MO=25) Offer Cures With High and Low Omega <!-- Start of picture text --> 40 - ~ v gOmega(High)=2 0<br>- - a Omego(Low)= 02<br>30x<br>~20<br>10 -~__ _<br>10<br>-10<br>-20<br>-30<br>-40 A -L . , L , .-<br>0.2 0.4 O6 08 1 12 14 16 18 2<br>sigma Volues<br>b) CLOSED AND OPEN ECONOMY OFFER CURVES<br>With Omegn=1<br>20<br>16 i d(E 0 =M0 =10)<br>* 8 t-- Open (EJ=M0=40)<br>12<br>-8<br>-12<br>-14 ' ! * * .<br>0.2 04 06 08 1 12 14 16 18 2<br>Sgmao vatues<br><!-- End of picture text --> WoEd Bank - 43114:5
22 external budget constraint. Increasing the degree of openess raises the offer curve elasticity, a result also found in standard trade-theoretic models.

Finally, Figure 6 traces the equilibrium values obtained from solving the model with the initial conditions il Table 6 under a high and a low set of trade substitution elasticities. Figure 6 draws the equilibrium values of the welfare indicator, the real exchange rate, and the import share in absorption for different values of the terms-of-trade. The arrows indicate the path of the variables as the terms-of-trade improve. As expected, welfare gains measured here in terms of absorption, Q) are larger for the higher set of trade substitution elasticities. The higher gain attributable to greater specialization appears as a much larger variation in the share of imports in absorption for the high value of a . More importantly, Figure 6 confirms the critical role assumed by the value of o in determining whether the real exchange rate will appreciate or depreciate when the terms-of-trade varies.

The two numerical examples in figure 6 could be construed to represent a developing country with a low import substitution elasticity and a developed country with a higher elasticity. For the developing country, adjusting to the deterioration in its terms-of-trade requires a real devaluation to generate increased exports required to pay for more expensive crucial imports. For the developed country, adjustment requires a real revaluation and a decline in the volume of foreign trade.

# 5. Conclusions

In this paper, we have studied systematically the typical external closure of many single-country applied general equilibrium trade models. We
23

**Flgure** 6 WELFARE, REAL EXCHANGE RATE, AND TERMS OF TRADE

<!-- Start of picture text --> 114<br>112<br>3 10/ For Offtwt Value d S1gm-(K)<br>108 ~~~~~~~~~~~~~~~~~~~(a. 0)<br>ioo * 100 _(0.2. 1.0)<br>`1034 * _ _-(50. 1.0)<br>1 02*_<br>9I a<br>hi--<br>907<br>60 80 100 120 140 160 0 02 04<br>Teems d Trade (we/ om) Imoorts/Absovption(M/6Q)<br><!-- End of picture text --> <!-- Start of picture text --> 14-c - * * -<br><!-- End of picture text -->
24 have shown that the standard assumption of product differentiation on the import side can be naturally extended to the export side. An external closure with symmetric product differentiation for imports and exports is theoretically well-behaved and gives rise to normally shaped offer curves. We derive the elasticity of the domestic off,r curve for a one sector model and illustrate the model with a numerical example. The numerical example illustrates, under different trade substitution elasticities, the implications of the choice of weights used as a proxy for the domestic price index in computations of real exchange rate indices. The model is also useful to illustrate the role of foreign trade elasticities in the popular Australian model with traded and non-traded goods. In particular, we show the crucial role of trade substitution elasticities on the import side in determining the direction of change of the real exchange rate for terms-of-trade perturbations.