Comparative Advantage, Trade, and Payments in a Ricardian Model with a Continuum of Goods

Comparative Advantage, Trade, and Payments in a Ricardian Model with a Continuum of Goods -

By R. DORNBUSCH, S. FISCHER, AND P. A. SAMUELSON*

This paper discusses Ricardian trade and I. The Real Model payments theory in the case of a continuum of goods. The analysis thus extends the de- In this section we develop the basic real velopment of many-commodity, two-coun- model and determine the equilibrium rela- try comparative advantage analysis as pre- tive wage and price structure along with the sented, for example, in Gottfried Haberler efficient geographic pattern of specializa- (1937), Frank Graham (1923), Paul Samuel- tion. Assumptions about technology are son (1964), and Frank W. Taussig (1927). specified in Section IA. Section IB deals with The literature is historically reviewed by demand. In Section Ic the equilibrium is John Chipman (1965). Perhaps surprisingly, constructed and some of its properties are the continuum assumption simplifies the explored. Throughout this section we as- analysis neatly in comparison with the dis- sume zero transport costs and no other im- crete many-commodity case. The distin- pediments to trade. guishing feature of the Ricardian approach emphasized in this paper is the determina- A. Technology and Efficient tion of the competitive margin in produc- Geographic Specialization tion between imported and exported goods. The analysis advances the existing literature The many-commodity Ricardian model by formally showing precisely how tariffs assumes constant unit labor requirements and transport costs establish a range of (a,,..., a,) and (al*,..., a*) for the n com- commodities that are not traded, and how modities that can be produced in the home the price-specie flow mechanism does or and foreign countries, respectively. The does not give rise to movements in relative commodities are conveniently indexed so cost and price levels. that relative unit labor requirements are The formal real model is introduced in ranked in order of diminishing home coun- Section 1. Its equilibrium determines the try comparative advantage, relative wage and price structure and the al*1a, > ... > ... > Ol*ai > ... > an*la, efficient international specialization pattern. Section II considers standard comparative where an asterisk denotes the foreign coun- static questions of growth, demand shifts, try. technological change, and transfers. Exten- In working with a continuum of goods, sions of the model to nontraded goods, we similarly index commodities on an inter- tariffs, and transport costs are then studied val, say [0, 1], in accordance with diminish- in Section III. Monetary considerations are ing home country comparative advantage. introduced in Section IV, which examines A commodity z is associated with each the price-specie mechanism under stable point on the interval, and for each com- parities, floating exchange rate regimes, and modity there are unit labor requirements in also questions of unemployment under the two countries, a(z) and a*(z), with rela- sticky money wages. tive unit labor requirement given by

* Massachusetts Institute of Technology. Helpful - *(z) (1) A(z) A a a (z) A'(z) < 0 comments from Ronald W. Jones are gratefully acknowledged. Financial support was provided by a Ford Foundation grant to Dornbusch, NSF GS-41428 The relative unit labor requirement function to Fischer, and NSF 75-04053 to Samuelson. in (1) is by strong assumption continuous

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This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms 824 THE AMERICAN ECONOMIC REVIEW DECEMBER 1977 and by construction (ranking or indexing of The relative price of home produced z in goods), decreasing in z. The function A (z) terms of a commodity z" produced abroad is shown in Figure 1 as the downward slop- is by contrast ing schedule. (7) P(z)/P(z") = wa(z)/w*a*(zP") Consider now the range of commodities produced domestically and those produced = wa(z)1a*(z''); abroad, as well as the relative price struc- z < z < z" ture associated with given wages. For that purpose we define as w and w* the domestic In summarizing the supply part of the and foreign wages measured in any (com- model we note that any specified relative mon!) unit. The home country will effi- real wage is associated with an efficient geo- ciently produce all those commodities for graphic specialization pattern characterized which domestic unit labor costs are less by the borderline commodity z(w) as well as than or equal to foreign unit labor costs. by a relative price structure. (The pattern is Accordingly, any commodity z will be pro- "efficient" in the sense that the world is out duced at home if on, and not inside, its production-possibility frontier.) (2) a(z)w < a*(z)w* B. Demand Thus On the demand side, the simplest Mill- (2') w < A (z) Ricardo analysis imposes a strong homo- where (3) defines the parameter w, funda- thetic structure in the form of J. S. Mill or mental to Ricardian analysis, Cobb-Douglas demand functions that asso- ciate with each ith commodity a constant (3) w/w* expenditure share, bi. It further assumes This is the ratio of our real wage to theirs identical tastes for the two countries or uni- (our "double-factoral terms of trade"). It form homothetic demand. follows that for a given relative wage w the By analogy with the many-commodity home country will efficiently produce the case, which involves budget shares range of commodities bi= PiCi/Y bi= bi* (4) 0 < z < (w) n

where taking (2') with equality defines the Z bi = I borderline commodity z, for which We therefore prescribe for the continuum (5) Z = A-I(w) case a given b(z) profile: A-'( ) being the inverse function of A( ). (8) b(z) = P(z)C(z)/Y > 0 By the same argument the foreign country will specialize in the production of com- b(z) = b*(z) modities in the range fb(z) dz I (4') (w) < z <

The minimum cost condition determines where Y denotes total income, C demand the structure of relative prices. The relative for and P the price of commodity z. price of a commodity z in terms of any Next we define the fraction of income other commodity z', when both goods are spent (anywhere) on those goods in which produced in the home country, is equal to the home country has a comparative advan- the ratio of home unit labor costs: tage:

(6) P(z)/P(z') = wa(z)/wa(z') z (9) 0(z) b b(z)fdz > 0 = a(z)/a(z'); z < z, z' < z 0 (z)= b(z) > 0

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms VOL. 67 NO. 5 - DORNBUSCH ET AL.: RICARDIAN MODEL 825 where again (0, 2) denotes the range of commodities for which the home country enjoys B(Z; L*/L) a comparative advantage. With a fraction t of each country's income, and therefore of world income, spent on home produced goods, it follows that the fraction of income spent on foreign produced commodities is

(9' 1 - 9(z) J b(z) dz

0 < ?<(z) < 1 A(z)

C. Equilibrium Relative Wages 0 . I and Specialization FIGURE 1

To derive the equilibrium relative wage and price structure and the associated pat- labor (goods) would decline.' A rise in the tern of efficient geographic specialization, domestic relative wage would then be re- we turn next to the condition of market quired to equate the demand for domestic equilibrium. Consider the home country's labor to the existing supply. labor market, or equivalently the market An alternative interpretation of the B( ) for domestically produced commodities. schedule as the locus of trade balance equi- With z denoting the hypothetical dividing libria uses the fact that (10) can be written line between domestically and foreign pro- in the balance-of-trade form: duced commodities, equilibrium in the mar- (10") [1 - 0(2)]wL = 0(2)w*L* ket for home produced goods requires that domestic labor income wL equals world This states that equilibrium in the trade bal- spending on domestically produced goods: ance means imports are equal in value to exports. On this interpretation, the B( ) (10) wL = 0(2)(wL + w*L*) schedule is upward sloping because an increase in the range of commodities hypo- Equation (10) associates with each z a value thetically produced at home at constant of the relative wage -w/w* such that market relative wages lowers our imports and raises equilibrium obtains. This schedule is drawn our exports. The resulting trade imbalance in Figure 1 as the upward sloping locus and would have to be corrected by an increase is obtained from (10) by rewriting the equa- in our relative wage that would raise our tion in the form: import demand for goods and reduce our exports, and thus restore balance. (10') I = l - D(@)( (L*/L) - B(z;L*/L) The next step is to combine the demand side of the economy with the condition of where it is apparent from (9) that the sched- efficient specialization as represented in ule starts at zero and approaches infinity as equation (5), which specifies the competitive z approaches unity. margin as a function of the relative wage. To interpret the B( ) schedule we note Substituting (5) in (10') yields as a solution that it is entirely a representation of the the unique relative wage 5, at which the demand side; and in that respect it shows world is efficiently specialized, is in bal- that if the range of domestically produced goods were increased at constant relative 'Throughout this paper we refer to "domestic" wages, demand for domestic labor (goods) goods as commodities produced in the home country would increase as the dividing line is shifted rather than to commodities that are nontraded. The -at the same time that demand for foreign latter we call "nontraded" goods.

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms 826 THE AMERICAN ECONOMIC REVIEW DECEMBER 1977 anced trade, and is at full employment with being of the representative person-laborer all markets clearing: at home relative to the well-being of the representative foreign laborer. (11) z = A(z) = B(-;L*/L)

The equilibrium relative wage defined in II. Comparative Statics (11) is represented in Figure 1 at the intersection of the A( ) and B( ) schedules.2 The unique real equilibrium in Figure 1 Commodity z denotes the equilibrium bor- is determined jointly by tastes, technology, derline of comparative advantage between and relative size, L*/L. We can now exploit commodities produced and exported by the Figure 1 to examine simple comparative home country (O < z < z), and those com- static questions. modities produced and exported by the foreign country (z < z < 1). A. Relative Size Among the characteristics of the equilibrium we note that the equilibrium relative Consider first the effect of an increase in wages and specialization pattern are deter- the relative size of the rest of the world. An mined by technology, tastes, and relative increase in L*/L by (10) shifts the B( ) size (as measured by the relative labor trade balance equilibrium schedule upward force).3 The relative price structure asso- in proportion to the change in relative size ciated with the equilibrium at point E is and must, therefore, raise the equilibrium defined by equations (6) and (7) once (11) relative wage at home and reduce the range has defined the relative wage z and the of commodities produced domestically. It equilibrium specialization pattern z(Z). is apparent from Figure 2 that the domestic The equilibrium levels of production relative wage increases proportionally less Q(z) and Q*(z), and employment in each than the decline in domestic relative size. industry L(z) and L*(z), can be recovered The rise in equilibrium relative wages due from the demand structure and unit labor to a change in relative size can be thought requirements once the comparative advan- of in the following manner. At the initial tage pattern has been determined. equilibrium, the increase in the foreign rela- We note that with identical homothetic tive labor force would create an excess sup- tastes across countries and no distortions, ply of labor abroad and an excess demand the relative wage Z- is a measure of the well- for labor at home-or, correspondingly, a trade surplus for the home country. The resulting increase in domestic relative wages 2See the Appendix for the relation of the diagram serves to eliminate the trade surplus while to previous analyses. 3The construction of the B( ) schedule relies heavily on the Cobb-Douglas demand structure. If, instead, demand functions were identical across countries and B(z; L*/L) homothetic, an analogous schedule could be con- LU\/ structed. In the general homothetic case, however, a set B(z; L*/L)O of relative prices is required at each z to calculate the equivalent of the B( ) schedule; the relative prices are those that apply on the A (z) schedule for that value of z. In this case the independence of the A ( ) and B( ) schedules is obviously lost. In the general homothetic case there is still a unique intersection of the A ( ) and B( ) schedules. For more general nonhomothetic demand structures, it is known that an equilibrium exists; but even in the case of two Ricardian goods there may be no unique equilibrium even though there will almost always be a finite number of equi- I ~~~~A (z) libria. See Gerard Debreu and Stephen Smale. Exten-

sions of our analysis with respect to the demand struc- Go 0 A ture and the number of countries are developed in un- published work by Charles Wilson. FIGURE 2

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms VOL. 67 NO. S DORNBUSCH ET AL.: RICARDIAN MODEL 827 at the same time raising relative unit labor (13) P(z) - P(z") = co - d*(z") > 0 costs at home. The increase in domestic relative unit labor costs in turn implies a where a "hat" denotes a proportional loss of comparative advantage in marginal change. Domestic real income increases, as industries and thus a needed reduction in does foreign real income.4 The range of the range of commodities produced domes- goods produced domestically declines since tically. domestic labor, in efficiency units, is now The welfare implications of the change in relatively more scarce. relative size take the form of an unambigu- An alternative form of technical progress ous improvement in the home country's real that can be studied is the international income and (under Cobb-Douglas demand) transfer of the least cost technology. Such a reduction in real income per head abroad. transfers reduce the discrepancies in relative We observe, too, that from the definition unit labor requirements-by lowering them of the home country's share in world in- for each z in the relatively less efficient come and (10), we have country-and therefore flatten the A (z) schedule in Figure 1. It can be shown that (12) wL/(wL + w*L*) = -() such harmonization of technology must It is apparent, as noted above, that a reduc- benefit the innovating low-wage country, tion in domestic relative size in raising the and that it may reduce real income in the domestic relative wage (thereby reducing high-wage country whose technology comes the range of commodities produced domes- to be adopted. In fact, the high-wage coun- tically) must under our Cobb-Douglas de- try must lose if harmonization is complete mand assumptions lower the home country's so that relative unit labor requirements now share in total world income and spending- become identical across countries and all even though our per capita income rises. our consumer's surplus from international trade vanishes.5 B. Technical Progress

To begin with, we are concerned with the C. Demand Shifts effects of uniform technical progress. By equation (1), a uniform proportional reduc- The case with a continuum of commodi- tion in foreign unit labor requirements im- ties requires a careful definition of a demand plies a reduction in a*(z) and therefore a shift. For our purposes it is sufficient to proportional downward shift of the A (z) ask: What is the effect of a shift from high z schedule in Figure 1. At the initial relative commodities toward low z commodities? It wage a, the loss of our comparative advan- is apparent from Figure 2 that such a shift tage due to a reduction in foreign unit labor will cause the trade balance equilibrium costs will imply a loss of some industries schedule B( ) to shift up and to the left. It in the home country and a corresponding follows that the equilibrium domestic rela- trade deficit. The resulting induced decline

in the equilibrium relative wage serves to 4The purchasing power of foreign labor income in restore trade balance equilibrium, and to terms of domestically produced goods is w* L*/wa(z) = offset in part our decline in comparative L*/a(z)z and in terms of foreign goods L*/a*(z). advantage. The fact that foreigners' real income per head rises is guaranteed by our Cobb-Douglas demand assumption. .The net effect is therefore a reduction in In the general homothetic case, a balanced reduction domestic relative wages, which must fall in a* (z) can be immiserizing abroad if the real wage rproportionally short of the decline in rela- falls strongly in terms of all previously imported tive unit labor requirements abroad. The goods; however, the balanced drop in a* (z) in the general homothetic case always increases our real wage. home country's terms of trade therefore im- 5Complete equilization of unit labor requirements prove as can be noted by using (7) for any implies that the A( ) schedule is horizontal at the two commodities z and z", respectively, level w = A (z) = 1. In this case geographic specializa- produced at home and abroad: tion becomes indeterminate and inessential.

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms 828 THE AMERICAN ECONOMIC REVIEW DECEMBER 1977 tive wage will rise while the range of com- relative price structure and the range of modities produced by the home country de- goods traded. clines. Domestic labor is allocated to a narrower range of commodities that are A. Nontraded Goods consumed with higher density while foreign labor is spread more thinly across a larger To introduce nontraded goods into the range of goods. analysis we assume that a fraction k of in- Welfare changes cannot be identified in come is everywhere spent on internationally this instance because tastes themselves have traded goods, and a fraction (1 - k) is changed. It is true that domestic relative spent in each country on nontraded com- income rises along with the relative wage. modities. With b(z) continuing to denote Further we note that since Zi rises, the rela- expenditure densities for traded goods, we tive well-being of home labor to foreign have accordingly labor (reckoned at the new tastes) is greater than was our laborers' relative well-being (14) k b a (z) dz < 1 (reckoned at the old tastes). where z denotes traded goods.6 As before D. Unilateral Transfers the fraction of income spent on domestically exportable commodities is O(z), except Suppose foreigners make a continual uni- that t now reaches a maximum value of lateral transfer to us. With uniform homo- (1)= k. thetic tastes 'and no impediments to trade, Equation (1) remains valid for traded neither curve is shifted by the transfer since goods, but the trade balance equilibrium we spend the transfer exactly as foreigners condition in (10 ") must now be modified to: would have spent it but for the transfer. The new equilibrium involves a recurring trade (15) [1 - 0(z) - (1 - k)]wL deficit for us, equal to the transfer, but there = O(Z)W*L* is no change in the terms of trade. As Bertil Ohlin argued against John Maynard since domestic spending on imports is equal Keynes, here is a case where full equilibra- to income less spending on all domestically tion takes place solely as a result of the produced goods including nontraded com- spending transfers. When we introduce non- modities. Equation (15) can be rewritten as traded goods below, Ohlin's presumption will be found to require detailed qualifica- (15') W = k (!) (L*/L) tions, as it also would if tastes differed geo- graphically. where k is a constant and therefore independent of the relative wage structure. III. Extensions of the Real Model We note that (15') together with (5) determines the equilibrium relative wage and Extensions of the real model taken up in efficient geographic specialization, (Co, z). this section concern nontraded goods, Further it is apparent that (15') has exactly tariffs, and transport costs. The purpose of the same properties as (10') and that ac- this section is twofold. First we establish cordingly a construction of equilibrium like how the exogenous introduction of non- that in Figure 1 remains appropriate. The traded goods qualifies the preceding analy- equilibrium relative wage again depends on sis. Next we turn to a particular specifica- tion of tariffs and transport costs to establish 6We can think of the range of nontraded goods as an equilibrium range of endogenously de- another [0, 1] interval with commodities denoted by x termined nontraded goods as part of the and expenditure fractions on those goods given by equilibrium solution of the model. Trans- c(x). With these definitions we have f c(x) dx- fers are then shown to affect the equilibrium I - k, a positive fraction.

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms VOL. 67 NO. 5 DORNBUSCH ET AL.: RICARDIAN MODEL 829 relative size, technology, and demand con- tive wage increases and the range of com- ditions. In this case demand conditions modities produced domestically is reduced. explicitly include the fraction of income The steps in achieving this result are, first, spent on traded goods: that at the initial relative wage only a fraction of the transfer is spent on imports in k- - -= A(z) k T- (z) L the home country, while foreign demand for domestic goods similarly declines only by a This nicely generalizes our previous equilib- fraction of their reduced income. The re- rium of (11) to handle exogenously given sulting surplus for the home country has to nontraded goods.7 be eliminated by, second, an increase in the Two applications of the extended model domestic relative wage and a corresponding highlight the special aspects newly intro- improvement in the home country's terms duced by nontraded goods. First consider a of trade.8 shift in demand (in each country) toward The analysis of nontraded goods there- nontraded goods. To determine the effects fore confirms in a Ricardian model the on the equilibrium relative wage we have to "orthodox" presumption with respect to the establish whether this shift is at the expense terms of trade effects of transfers.9 of high or low z commodities. In the former case the home country's relative wage in- B. Transport Costs: Endogenous creases while in the latter case it declines. Equilibrium for Nontraded Goods If the shift in demand in each country is uniform so that b(z) is reduced in the same The notion that transport costs give rise proportion for all z in both countries, then to a range of commodities that are non- the relative wage remains unchanged. traded is established in the literature and is Consider next a transfer received by the particularly well stated by Haberler (1937). home country in the amount T measured in In contrast with the previous section we terms of foreign labor. As is well known, shall now endogenously determine the and already shown, with identical homo- range of nontraded commodities as part of thetic tastes and no nontraded goods, a the equilibrium. We assume, following the transfer leaves the terms of trade unaf- "iceberg" model of Samuelson (1954), that fected. In the present case, however, the transport costs take the form of "shrink- condition for balanced trade, inclusive of age" in transit so that a fraction g(z) of transfers, becomes: commodity z shipped actually arrives. We further impose the assumption that g = g(z) (16) T= (k - )[wL + T] is identical for all commodities and the [L - T] same for shipments in either direction. or, in equilibrium, The home country will produce commodities for which domestic unit labor cost (16') falls short of foreign unit labor costs ad- =k = I (TIL) + k ( ) (L*/L) justed for shrinkage, and we modify (2') accordingly: It is apparent from (16') that a transfer (17) wa(z) < (1/g)w*a*(z) receipt by the home country causes the trade balance equilibrium schedule in Fig- or w < A(z)/g ure 1 to shift upward at each level of z. Accordingly, the equilibrium domestic rela- 8At constant relative wages the current account worsens by [(1 - k -. tY) + 0IJdT = (1 - k)dT which is less than the transfer, since it is equal to the fraction 7Diagrams much like Figures of income 1 spent and onI nontraded 2 again goods. apply: the descending A (z) schedule is as before; and now the 9The pre-Ohlin orthodox view of Keynes, Taussig, new rising schedule looks much as before. As before, a Jacob Viner and other writers is discussed in Viner rise in L*/L and a balanced drop in a* (z) will raise Z (1937) and Samuelson (1952, 1954). A recent treatment and lower z. with nontraded goods is Ronald Jones (1975).

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms 830 THE AMERICAN ECONOMIC REVIEW DECEMBER 1977

w (20) X(gw) f b(z)dz X'(gw) < 0 A(z)/g

A(z)g X*(W/g) j b(z)dz X*'(W/g) > 0

The dependence of X( ) and X*( ) on the variables specified in (20) and the respective U~~~~ I derivatives follow from (21) below. The limits of integration z and z* are derived from the conditions for efficient i I \ production in (17) and (18) by imposing equalities and so defining the borderline exportobles z nontroded z importobles I commodities. Thus, in Figure 3, z is the

FIGURE 3 borderline between domestic nontraded goods and imports for the home country, and z* denotes the borderline between Similarly the foreign country produces foreign nontraded goods and the home commodities for which foreign unit labor country's exports: cost falls short of adjusted unit labor costs (21) z* = A-'(w/g) di*/d(w/g) < 0 of delivered imports: z = A-1(gw) df/d(gw) < 0 (18) w*a*(z) < (l/g)wa(z) Of course, equilibrium z and z* are yet to or A(z)g < w be determined by the interaction of tech- In Figure 3 we show the adjusted relative nology and demand conditions. unit labor requirement schedules A (z)/g From (21) an increase in the relative wage and A (z)g. It is apparent from (17) and (18) reduces the range of commodities domesti- that for any given relative wage the home cally produced and therefore raises the frac- country produces and exports commodities tion of income spent on imports. Abroad to the left of the A (z)g schedule, both the converse holds. An increase in the do- countries produce as nontraded goods com- mestic relative wage increases the range of modities in the intermediate range, and the goods produced abroad and therefore re- foreign country produces and exports com- duces the fraction of income spent on im- modities in the range to the right of A (z)/g. ports. It follows that we can solve: To determine the equilibrium relative wage we turn to the trade balance equilib- (19') = - 1 - X*(&/g) (L*/L) rium condition in (19)-together with (20) and (21)-which is modified to take account 1- X(;L*IL,g) d

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms VOL. 67 NO. 5 DORNBUSCH ET AL.: RICARDIAN MODEL 831 goods z* < z < z depends in this formula- The implicit relations (25) can be solved for tion on the equilibrium relative wage, it is the equilibrium relative wage as a function obvious that shifts in given parameters will of relative size and the tariff structure: shift the range of nontraded commodities. (26) Z) = Co(L*/L, t, t*) Thus, a transfer that raises the equilibrium relative wage at home causes previously ex- From (26) and (23) it is apparent now ported commodities to become nontraded, that the range of nontraded goods will be a and previously nontraded commodities to function of both tariff rates. It is readily become importables. shown that an increase in the tariff im- proves the imposing country's relative wage C. Tariffs and terms of trade. Furthermore, as is well We consider next the case of zero trans- known, when all countries but one are free port cost but where each country levies a traders, then one country can always im- uniform tariff on imports at respective rates prove its own welfare by imposing a tariff t and t*, with proceeds rebated in lump sum that is not too large. form. This case, too, leads to cost barriers A further question suggested by (26) con- to importing, and to a range of commodi- cerns the effect of a uniform increase in ties that are not traded, with the boundaries world tariffs. Starting from zero, a small defined by: uniform increase in tariffs raises the relative wage of the country whose commodities (23) = A-1 command the larger share in world spending. This result occurs for two reasons. and - A'(w(1 + t*)) First, at the initial relative wage a larger share of spending out of tariff rebates falls From (23) it is apparent that on the goodsthe of presence the country commanding of a tariffs in either or both countries must give larger share in world demand. Second, the rise to nontraded goods because- in this case tariff induces new nontraded goods and therefore increases net demand for the The trade balance equilibrium condition borderline commodity of the country whose at international prices becomes, in place of residents have the larger income, or equiv- (19), alently, the larger share in world income. If countries are of equal size as measured (24) (1 - X)Y/(1 + t) = by the share in world income, such a uni- (1 - X*)Y*/(1 + t*) form tariff increase has zero effect on rela- where Y and Y* denote incomes inclusive tive wages, but of course reduces well-being of lump sum tariff rebates. Using the fact in both places. Multilateral tariff increases, that rebates are equal to the tariff rate times in this case, unnecessarily create some non- the fraction of income spent on imports, we traded goods, and artificially raise the rela- arrive at the trade balance equilibrium con- tive price of importables in terms of do- dition in the form:'0 mestically produced commodities in each country exactly in proportion to the tariff. (25) X(1 -*) 1 + t*x* (L*/L) IV. Money, Wages, and Exchange Rates where X and X* are functions of (w,t,t*). In this section we extend the discussion of I0Tariff rebates in the home country are equal to the Ricardian model to deal with monetary R = (I - A) Yt/(l + t). With Y = WL + R we there- aspects of trade. Specifically we shall be in- fore have Y = WL(l + t)/(l + At) as.an -expression terested in the determination of exchange for income inclusive of transfers. From equations (20) rates in a flexible rate system, in the process and (23) we have X = A[w/(1 + t)] and A* = A*[w(1 + t*)], having substituted the tariff instead of adjustment of to trade imbalance under transport costs as the obstacle to trade. fixed rates, and in the role of wage sticki-

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms 832 THE AMERICAN ECONOMIC REVIEW DECEMBER 1977 ness. The purpose of the extension is to in- tary changes or velocity changes in one tegrate real and monetary aspects of trade. country will be reflected in equiproportion- ate changes in prices in that country and, in A. Flexible Exchange Rates the exchange rate in the fashion of the neutral-money Quantity Theory. However, The barter analysis of the preceding sec- a real disturbance, as (28) shows, definitely tions is readily extended to a world of does have repercussions on the nominal ex- flexible exchange rates and flexible money change rate as well as on the real equilib- wages. Assume a given nominal quantity of rium. money in each country, M and M*, re- Using the results of Section II, we see spectively. Further, in accordance with the that an increase in the foreign relative labor classical Quantity Theory, assume constant force causes, under flexible exchange rates expenditure velocities V and V*.ll A flexible and given M and M*, a depreciation in the exchange rate, and our stipulating the ab- home country's exchange rate as does uni- sence of nonmonetary international asset form technical progress abroad. A shift in flows, will assure trade balance equilibrium real demand toward foreign goods likewise and therefore the equality of income and leads to a depreciation of the exchange rate spending in each country. The nominal as well as to a reduction in real Z. A rise in money supplies and velocities determine foreign tariffs will also cause our currency nominal income in each country: to depreciate. Each of these real shifts is assumed to take place while (M, M*) are (27) WL = MV and W*L* = M* V* unchanged and on the simplifying proviso where W and W* (now in capital letters) that real income changes leave V and V* denote domestic and foreign money wages unchanged. in terms of the respective currencies. Fur- ther, defining the exchange rate e as the B. Fixed Exchange Rates domestic currency price of foreign exchange, the foreign wage measured in terms In the fixed exchange rates case we as- of domestic currency is e W*, and the rela- sume currencies are fully convertible at a tive wage therefore is w W/e W*. parity pegged by the monetary authorities. From the determination of the equilib- In the absence of capital flows and steriliza- rium real wage ratio co by our earlier "real" tion policy, a trade imbalance is reflected in relations, we can now find an expression for monetary flows. In the simplest metal the equilibrium exchange rates: money model, the world money supply is redistributed toward the surplus country at (28) e = (1/&I)(W/W*) = precisely the rate of the trade surplus. We assume that the world money supply is (11F.) (MV/M* V*) (L*/L) given and equal to G, measured in terms of where (27') defines equilibrium money domestic currency. The rate of increase of wages: the domestic quantity of money is therefore (27') W = MV/L equal to the reduction in foreign money, valued at the fixed exchange rate e: and (29) M= W* = M* V*/L* where Al dM/dt. In this simple structure and with wage For a fixed rate world we have to de- flexibility, we can keep separate the determine in addition to the real variables Co terminants of all equilibrium real variables and z, the levels of money wages W and W* from all monetary considerations. Mone- as well as the equilibrium balance of pay- IIThis is a strong assumption since it makes mentsspend- associated with each short-run equi- ing independent of income and nonliquid assets evenlibrium. in In the long run the balance of pay- the short run. ments will be zero as money ends up

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redistributed internationally to the point W R' where income equals spending in each country. In the short run an initial misallo- G / cation of money balances implies a discrepancy between income and spending and an associated trade imbalance. To char- acterize the preferred rate of adjustment of cash balances in the simplest and most man- ageable way, we assume that spending by // each country is proportional to money holdings.'2 On the further simplifying assumption that velocities are equal in each country, V = V*,13 world spending is equal to 0 - (30) VM + eV*M* - VG FIGURE 4 For the tastes and technology specified in Section I, world spending on domestically produced goods is given by ing from (11) for the equilibrium relative wage Zi, we can employ equations (32) and (31) VG f b(z)dz t- (w)VG (33) to determine money wage levels. The equilibrium determined by equations z= A-'(w) (32) and (33) can be analyzed in terms of Figure 4. The figure emphasizes the separa- In equilibrium, world spending on our tion of real and monetary aspects of the goods must equal the value of our full-em- equilibrium under our assumptions of ployment income WL: traded goods only, and no distribution effects. From the ratio of (32) and (33) we ob- (32) WL = t(w) VG tain the equilibrium relative wage C as a Equilibrium requires, too, that world spend- function of tastes and technology solely ing on foreign goods equals the value of from the barter model. This equilibrium re- foreign full-employment income: lative wage is plotted as the ray OR in Fig- ure 4. (33) eW*L* = [1 - (w)]V6 The equality of world income and spend- Equations (32) and (33) express what ing would seem to be the joint determination of real and monetary variables. But, in fact, (30') WL + eW*L* = VG we could have taken the shortcut of recog- nizing that the real equilibrium is precisely is shown as the downward sloping straight that of the barter analysis developed in Sec- line GG, which is drawn for given velocity, tion I. Dividing (32) by (33) and substitut- world quantity of money, and labor forces. Point E is the equilibrium where relative prices and the level of wages and prices are 12The assumption that spending is proportional to such that all markets clear. At a level of cash balances is only one of a number of possible wages and prices higher than point E, there specifications. Conditions for this expenditure function to be optimal are derived in Dornbusch and Michael would be a world excess supply of goods, Mussa. In general, expenditure will depend on both and conversely at points below E. income and cash balances. Figure 4 immediately shows some com- 131n the long-run equilibrium, higher V than V* parative static results. Thus a doubling of leaves us with a smaller share of the world money both countries' labor forces, from the stock than foreigners, but with nominal and real income shares in the two countries the same as when analysis of the barter model, will leave the V= V*. relative wage unaffected but will double

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms 834 THE AMERICAN ECONOMIC REVIEW DECEMBER 1977 world output. Given unchanged nominal the adjustment process: changes in the spending VG, wages and prices will have to terms of trade, in home and/or foreign halve. This would be shown by a parallel price levels, in relative prices of traded and shift of the GG schedule halfway toward the nontraded goods (there being none of the origin. A shift in demand toward the home latter), in double factoral terms of trade; country's output by contrast would rotate and any discrepancies in the price of the the OR ray to a position like OR' since it same commodity between countries. The raises our relative wage. The ensuing mone- features of the adjustment process of this tary adjustment is then an increase in our section rely on 1) identical, constant expen- money wage and money income and a de- diture velocities, 2) uniform-homothetic decline in foreign wages, prices, and incomes mand, and 3) the absence of trade impedi- (point E'). ments. If velocities were constant but The real and nominal equilibrium at differed between countries, the absolute point E in Figure 4 is independent of the levels of money wages and prices, though short- and long-run distribution of the not relative wages or prices, would depend world quantity of money. The independence on the world distribution of money. Relaxa- of the real equilibrium derives from the uni- tion of the uniform-homothetic taste as- form homothetic tastes. The independence sumption would make equilibrium relative of the nominal equilibrium is implied by prices a function of the distributions of identical velocities. What does, however, spending. Finally, the presence of non- depend on the short-run distribution of traded goods would, together with Ricardo's world money is the transition periods' bal- technology, provide valid justification for ance of payments. As in the absorption ap- some of the behavior of relative prices and proach of Sidney Alexander (1952), we price levels frequently asserted in the litera- know this: when goods markets clear, the ture; this behavior is studied in more detail trade surplus or balance of payments M of in the next section. the home country is equal to the excess of income over spending, or: C. The Price-Specie Flow Mechanism under More General Conditions (34) M= WL- VM

With the nominal wage independent of the We now discuss the adjustment process distribution of world money, equation (34) to monetary disequilibrium and enquire therefore implies that the trade balance into the price effects associated with a redis- monotonically converges to equilibrium at tribution of the world money supply when a rate proportional to the discrepancy from there are nontraded goods. Common ver- long-run equilibrium:"4 sions of the Hume price-specie flow mechanism usually involve the argument that in (34') M = V(M - M); M = 0 ()G the adjustment process, prices decline along The assumptions of this section were de- - with the money stock in the deficit country, signed to render inoperative most of the tra- while both rise in the surplus country. There ditional mechanisms discussed as part of is usually, too, an implication that the deficit country's terms of trade will necessarily 14Suppose V> V* and our share of the world worsen in the adjustment process and in- money supply is initially larger than our equilibrium deed have to do so if the adjustment is to be share. Then, as we lose M, total world nominal income and nominal GNP falls. Always our share of nominal successful. world GNP stays the same under the strong demand Section IVB demonstrated that the redis- assumptions. Total world real output never changes tribution of money associated with mone- during the transition; only regional consumption tary imbalance need have no effects on real shares change. Therefore, both countries' nominal variables (production, terms of trade, etc.) price and wage levels fall in the transition, but such balanced changes have no real effects on either the and on nominal variables other than the transient or the final real equilibrium. money stock and spending. While this is

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms VOL. 67 NO. 5 DORNBUSCH ET AL.: RICARDIAN MODEL 835 clearly a very special case, it does serve as a ing to nontraded goods, shifting some of benchmark since it establishes that the our resources to their production at the ex- monetary adjustment process would be ef- pense of our previous exports. We not only fective even in a one-commodity world. export fewer types of goods, but also import To approach the traditional view of the more types, and import more of each adjustment process more clearly and pro- (& rises and z falls). vide formal support for that view, we con- During the transition, while the real sider an extension to the monetary realm of transfer corresponding to our deficit is tak- our previous model involving nontraded ing place, our terms of trade are more goods. We return to the assumption that a favorable than in the long-run state. The fraction (1 - k) of spending in each coun- new gold raises both their W* and our W, try falls on nontraded goods, and accord- but in addition, our W is up relative to their ingly equations (32)- and (33) become: W*. Therefore the price level of goods we continue to produce is up relative to the (32') WL = 0 (w) VG + (1 - k)yVG; price level of goods they continue to pro- yMI G duce. This is true both for our nontraded (33') eW*L* = [k - O(w)]VG goods and for our exportables. The prices of goods we produce rise relative to the + (1 - y)(1 - k)VG prices of goods they produce in proportion These hold both in final equilibrium, and in to the change in relative wages. transient equilibrium where specie is flow- Thus the price levels in the two countries ing. Equations (32') and (33') imply that have been changed differentially by the the equilibrium relative wage does depend specie flow and implied real transfer. But on the distribution of the world money sup- that does not mean that any traded good ply. Solving these equations for the equilib- ever sells for different prices in two places. rium relative wage we have: In fact the divergence in weighted average (consumer) price levels is due to nontraded (35) z = zi5 d > goods. The price level will rise in the gold- discovering country relative to the other An increase in the home country's initial country the greater is the share of non- share in the world money supply y raises traded goods in expenditure, 1 - k. It is a our relative wage. bit meaningless to say, "What accom- Using this extended framework, we can plished the adjustment is the relative move- draw on the analysis of the transfer problem ments of price levels for nontraded goods in in Section II to examine the adjustment that the two countries," since we have seen that follows an initial distribution of world the adjustment can and will be made even money between the two countries that dif- when there are no such nontraded goods. fers from the long-run equilibrium distribu- It is meaningful to say, "The fact that peo- tion. ple want to direct some of their expenditure Suppose our M is initially excessive, say to nontraded goods makes it necessary for from a gold discovery here. Assume also resources to shift in and out of them as a re- that the gold discovery occurred when the sult of a real transfer, and such resource world was in long-run equilibrium with the shifts take place only because the terms of previous world money stock. As a result of trade (double-factoral and for traded goods) our excess M, we spend more than our do shift in the indicated way." earnings, incurring a balance-of-payments The adjustment process to a monetary deficit equal to the rate at which our M is disturbance is stable in the sense that the flowing out. In effect, the foreign economy system converges to a long-run equilibrium is making us a real transfer to offset our distribution of money with balanced trade. deficit. As seen earlier, we, the deficit coun- To appreciate that point, we supplement try, are devoting some of our excess spend- equations (32') and (33') with (34) that con-

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms 836 THE AMERICAN ECONOMIC REVIEW DECEMBER 1977 tinues to describe the monetary adjustment lative price, wage, and income movements. process. We note, however, that now W and They are, of course, in no way essential to W* are endogenous variables whose levels the existence of a stable adjustment process, in the short run do depend on the distribu- nor is there at any time a need for a dis- tion of the world money supply. A redistri- crepancy of prices of the same commodity bution of money toward the home country across countries in either case. 16 would raise our spending and demand for A final remark concerns the adjustment goods, and reduce foreign spending and de- to real disturbances such as demand shifts mand. As before, spending changes for or technical progress. It is certainly true traded goods offset each other precisely so that whether the exchange rate is fixed or that the net effect is an increase in demand flexible, real adjustment will have to take for nontraded goods at home and a decline place and cannot be avoided by choice of an abroad. As a consequence our wages will exchange rate regime. So long as wages and rise and foreign wages decline. Therefore, prices are flexible, it is quite false to think starting from full equilibrium, a redistribu- that fixed parities "put the whole economy tion of money toward the home country will through the wringer of adjustment" while create a deficit equal to in floating rate regimes "only the export and import industries have to make the real (36) dM/dM= -V(1 6) 0 < 1 < I adjustment." It is true, however, that once where 6 is the elasticity of our nominal we depart from flexible wages and prices wages with respect to the quantity of money there may well be a preference for one ex- and is less than unity.'5 Equation (36) im- change rate regime over another. The next plies that the price-specie flow mechanism section is devoted to that question. is stable. It is interesting to observe in this context D. Sticky Money Wages that the presence of nontraded goods in fact slows down the adjustment process by com- The last question we address in this sec- parison with a world of only traded goods tion concerns the implications of sticky (contrary to J. Laurence Laughlin's turn. of money wages. For a given world money the century worries). As we saw before, with supply, downward stickiness of money all goods freely tradeable, wages are inde- wages implies the possibility of unemploy- pendent of the distribution of money, and ment. We assume upward flexibility in accordingly 6 = 0. Further we observe that wages, once full employment is attained. the speed of adjustment depends on the re- We start with a fixed exchange rate e. lative size of countries. Thus the more equal The relation between wages and the world countries are in terms of size, the slower quantity of money is brought out in Figure tends to be the adjustment process. 5. Denote employment levels in each coun- In concluding this section we note that try, as opposed to the labor force, by the nontraded goods (and/or localized de- new symbols L and L*, respectively; denote mand) are essential to the correctness of nominal incomes by Y and Y*. The equality traditional insistence that the adjustment of world income and spending is again process necessarily entails absolute and re- shown by the GG schedule, the equation of which now is

I5The value of 6 can be calculated from equations (37) VG = Y + eY* - WL + W*L* (32') and (33') to be 16The continuum Ricardian technology is special in that there can be no range of goods both imported and 6 (1 - k)y(l Y(- k- kY)) + E produced at home. Therefore, the cross elasticity of supply between nontraded goods and exports must be where e is the elasticity of the share of our traded greater than the zero cross elasticity between non- goods in world spending, e -tYw/lt > 0. The elas- traded goods and imports. Consequently, a transfer ticity 6 is evaluated at the long-run equilibrium where must shift the terms of trade (for goods and factors) in y t-/k. If A '(z) falls slowly, e will be large. the stated orthodox way, favorably for the receiver.

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Y R' plied reduction in our relative wages and G / the resulting increase in our relative income are shown in Figure 5 by the rotation from \/t OR to OR'. E ~~~R The new equilibrium is at E' where our money income and employment have risen y~~ while income and employment decline abroad. Thus an increase in the foreign wage rate, by moving the terms of trade against us, shifts comparative advantage and employment toward the home country. The extent to which the home country bene- Y eY* fits from the adverse terms of trade shift in 0 ET* terms of employment will depend on both

FIGURE 5 the substitutability in demand and the elasticity of the A (z) schedule in Figure 1. We observe, too, that the move from E to E' where W and W* are the fixed money will bring about a transitory balance-of- wages set at too high sticky levels. The payments surplus. Given the initial distribu- schedule is drawn for given money wages, a tion of money and hence of -spending, the given world quantity of money, and a foreign decline in income and the increase pegged parity for e. The ray OR now is pre- at home implies that we will spend less than determined by the given sticky relative wage our income and therefore have a trade sur- i = W/eW*. From equations (32) and (33) plus. This surplus persists until money is re- the ratio of money incomes Y/eY* is just a distributed to match the new levels of in- function of the relative wage now given ex- come at '. ogenously by rigid money wages and the ex- Next we move to flexible exchange rates. change rate: Under flexible rates an increase in the foreign money wage W*, given money supplies (38) Y/eY* - (WeW*) in each country, will similarly have real re- percussion effects on relative prices and em- '(W) < 0 ployment at home. Now employment in each country is determined by money sup- Point E is the nominal equilibrium where plies and prevailing wages: by assumption the world quantity of money is insufficient relative to wage rates to en- (39') L = VM/ W; L* - VM*/ W* sure full employment. Although that equilibrium is one with unemployed labor, it is Given the employment levels thus deter- efficient in other respects. Specifically, geo- mined, we know from the analysis of the graphic specialization follows comparative earlier barter model that there is a unique advantage as laid out above, but now labor relative wage at which the trade balance employed adjusts to sticky wage patterns of achievesequilibrium. The higher is M*/ W*, specialization. the higher will be employment abroad- Employment levels Land L* now are de- and, therefore, the higher will be our rela- termined by (39) tive wage a. It is thus apparent that an increase in the foreign money wage, W*, will (39) L-= Y/W, L* - reduce employment abroad. Employment where Y and Y* are the equilibrium levels declines only in proportion to the increase of nominal income determined by equations in wages and thus declines by less than it (37) and (38) or by point E in Figure 5. would under fixed exchange rates when Consider now the impact of a foreign in- specie is lost abroad. crease in money wages. The effect of the im- We saw in the barter model that a reduc-

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms 838 THE AMERICAN ECONOMIC REVIEW DECEMBER 1977 tion in effective foreign labor causes a de- surplus causes our exchange rate to appre- cline in our relative wage, but that the ciate until the initial employment levels and decline in our relative wage falls propor- therefore trade balance equilibrium are re- tionately short of the foreign reduction in stored. The demand shift is fully absorbed labor. Now, at the initial exchange rate, the by a change in the terms of trade and a shift increase in foreign wages reduces our rela- in competitive advantage that restores de- tive wage and their employment in the same mand for foreign goods and labor. proportion. The decline in our relative wage Real and nominal equilibria are thus seen is therefore excessive. Domestic goods are to be uniquely definable in our continuum underpriced and the exchange rate appre- model with constant-velocity spending de- ciates to partly offset the gain in cost com- terminants. The difference between sticky petitiveness. The net effect is therefore a and flexible wage rates under fixed exchange decline in our relative wage and an appre- rates is understandable as the difference be- ciation of our exchange rate (a decline in e) tween (a) having the crucial relative wage zi that falls short of the foreign increase in be imposed in the sticky wage case with em- wages. Since our terms of trade unambig- ployments having then to adjust; or (b) hav- uously deteriorate without any compensat- ing the full employments be imposed and C ing gain in employment, it must be true that having to adjust. Under floating exchange welfare declines at home. Abroad, the loss rates, sticky nominal wages impose employ- in employment is offset by a gain in the ment levels in each country and the crucial terms of trade, but there too the net effect is relative wage Z then adjusts to those em- a loss in welfare under our strong Mill- ployment levels. Ricardo assumption. APPENDIX The adjustment to money wage disturbances under fixed and flexible rates differs Historical Remark in several respects. Under fixed rates employment effects are transmitted, while Figure 1 seems to be new. G. A. Elliot under flexible rates they are bottled up in (1950) gives a somewhat different diagram, the country initiating the disturbance. one that makes explicit the meaning of Under fixed rates the terms of trade move Marshall's 1879 "bales" (which, by the way, one for one with money wage, while under happen to work only in the two-country flexible rates exchange rate movements constant labor costs case). In terms of the partly offset increases in the foreign money present notations, Elliott plots for the U.S. wage rate. offer curve the following successive points The difference between fixed and flexible traced out for all w on the range [0, oo ]: on rates in relation to the adjustment process is the vertical axis is plotted our total real im- further brought out by an example of a real ports valued in foreign labor units ("our disturbance. Consider a shift in world de- demand for bales of their labor," so to mand toward our goods. Under fixed rates speak), namely, the resulting increase in our relative income will, from (38), move us in Figure 5 from f [P*(z)/w*]C(z)dz = j a*(z)C(z)dz E to E'. Employment rises at home and falls abroad. Demand shifts are fully reflected in employment changes. Under flexible rates, and on the horizontal axis, our total real by contrast, with given wages and money, a exports valued in home labor units ("our demand shift has no impact on employ- supply of bales of labor to them"), namely, ment-as we observe from (39). At the initial exchange rate the demand shift would rz give rise to an excess demand for our goods J[P(z)/w][Q(z) - C(z)]dz= and to an excess supply abroad. Domestic income and employment would tend to rise L - a(z) C(z)dz while falling abroad. The resulting trade

This content downloaded from 134.84.192.102 on Tue, 18 Aug 2020 22:59:10 UTC All use subject to https://about.jstor.org/terms VOL. 67 NO. 5 DORNBUSCH ET AL.: RICARDIAN MODEL 839

It is to be understood that 2 is a function of G. A. Elliott, "The Theory of International w, namely the inverse function A '(w); also Values," J. Polit. Econ., Feb. 1950, 58, that C(z) are the amounts demanded as a 16-29. function of our real income L and of the F. Graham, "The Theory of International P(z)/ W function defined for each, namely Balances Re-Examined," Quart. J. Econ., min [wa(z), a*(z)]. Because we have a con- Nov. 1923, 38, 54-86. tinuum of goods, we avoid Elliott's Gottfried Haberler, The Theory of Inter- branches of the offer curve that are seg- national Trade, London 1937. ments of various rays through the origin. R. W. Jones, "Presumption and the Transfer The reader will discern by symmetry con- Problem," J. Int. Econ., Aug. 1975, 5, siderations how the' foreign offer curve is 263-74. plotted in the same (L, L*) quadrant, by James Laurence Laughlin, Principles of Money, varying w to generate the respective coor- New York 1903. dinates John S. Mill, Principles of Political Economy, London 1848. rz David Ricardo, On the Principles of Political a(z)C*(z)dz, Economy and Taxation, 1817; edited by P. Sraffa, London 1951. L* a*(z)C*(z)dz P. A. Samuelson, "The Transfer Problem and Transport Costs: The Terms of Trade When Impediments are Absent," Econ. Our model forces the Elliott-Marshall J., June 1952, 62, 278-304; reprinted in diagram to generate a unique solution under Joseph Stiglitz, ed., Collected Scientific uniform-homothetic demand. Unlike our Papers of Paul A. Samuelson, Vol. 2, Figure 1, the Elliott diagram can handle Cambridge, Mass., ch. 74. the general case of nonhomothetic demands , "The Transfer Problem and the in the two countries; but then, as is well Transport Costs, II: Analysis of Effects known, multiple solutions are possible, of Trade Impediments," Econ. J., June some locally stable and some unstable. The 1954, 64, 264-89; reprinted in Joseph price one pays for this generality is that, as Stiglitz, ed., Collected Scientific Papers Edgeworth observed, the Marshallian of Paul A. Samuelson, Vol. 2, Cambridge, curves are the end products of much im- Mass., ch. 75. plicit theorizing, with much that is inter- , "Theoretical Notes on Trade Prob- esting having taken place offstage. lems," Rev. Econ. Statist., May 1964, 46, 145-54; reprinted in Joseph Stiglitz, ed., Collected Scientific Papers of Paul A. REFERENCES Samuelson, Vol. 2, Cambridge, Mass., ch. 65. S. Alexander, "The Effects of a Devaluation S. Smale, "Structurally Stable Systems Are on the Trade Balance," Int. Monet. Fund Not Dense," Amer. J. Math., 1966, 88, Staff Pap., Apr. 1952, 2, 263-78. 491-96. J. S. Chipman, "A Survey of International Frank W. Taussig, International Trade, New Trade: Part I: The Classical Theory," York 1927. Econometrica, July 1965, 33, 477-519. Jacob Viner, Studies in the Theory of Inter- G. Debreu, "Economies with a Finite Set of national Trade, New York 1937. Equilibria," Econometrica, May 1970, 38, C. Wilson, "On the General Structure of 387-92. Ricardian Models with a Continuum of R. Dornbusch and M. Mussa, "Consumption, Goods: Applications to Growth, Tariff Real Balances and the Hoarding Func- Theory and Technical Change," unpub- tion," Int. Econ. Rev., June 1975, 16, lished paper, Univ. Wisconsin-Madison, 415-21. 1977.

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