International Economics, Robert A. Mundell, New York: Macmillan, 1968, pp. 65 - 84.

# A Geometry of Transport Costs in International Trade Theory 1,2

### Robert A. Mundell

Transport costs have been neglected in the pure theory of international trade, most of which is expounded on the assumption that transport costs are absent. The purpose of this paper is to present a simple geometric method for depicting transport costs in offer-curve diagrams, and to apply the method to analyze transport costs in the context of the terms of trade, the transfer problem, the optimum tariff, and real factor returns.

To avoid introducing a third industry -the transport industry- I shall employ a drastic, but very useful, assumption regarding the nature of transport costs: Transport costs are met by the wastage of a proportion of the goods traded.3 This assumption will mean that only a proportion of the goods exported will be received as imports by the other country (the remainder being "used up" as costs of transport) in the case where each country provides the resources for transporting its own exports; that a proportion of its exports will be used up for every unit of the good imported in the case where each country provides the resources for transporting its imports; and that some of each country's resources will be used up in transporting each good in the case where each country shares in the transport of each good. The meaning of the assumption will become clearer later in the paper.

#### The Geometry

First we shall show how offer curves must be modified to take account of transport costs. Assume two countries, A and B, exporting commodities X and Y, respectively. For the moment, neglect the costs of transporting Y.

Assume first that the cost of transporting X is incurred in X itself, so that only a proportion of A's exports are received as imports by B. Call this proportion Kx. There are two ways in which the offer curves can be modified to determine the new equilibrium, the choice depending on whether it is more convenient to work with c.i.f. (cost, insurance and freight) or f.o.b. (free on board) offer curves. Thus, we can modify A's offer curve to show that she offers less X per unit of Y, landed in B, because part of her exports are used up as costs of transport; or we can modify B's offer curve to show that B demands more X per unit of Y, f.o.b., since she must use up some of A's #### Figure 5-1.

exports to land X in B. In Figure 5-1, Oa and Ob are the offer curves of A and B before transport costs have been considered, and Oa is the schedule of A's offers of X landed in B, that is, Oa is A's c.i.f. offer curve. This curve is determined by subtracting from the X value of Oa the amounts of X that would be required to transport that X, so that for any given value of Y, the X value of O'a is a proportion, Kx, of the X value of Oa. Equilibrium is determined by the intersection of A's c.i.f. offer curve, O'a, with B's offer curve, Ob, at the point Qb . At this equilibrium, country A exports LQa of X and imports OL of Y, and country B exports OL of Y and imports LQb of X. Country A receives as imports the same amount of Y as country B exports, because no Y is used up as transport cost; but country B receives as imports only the proportion Kx of A's exports, the difference being used up as transport cost. Thus QaQb is the cost of landing LBb of X in B.

Equilibrium can be determined by the intersection of the c.i.f. offer curves or by the intersection of the f.o.b. offer curves. In Figure 5-1, Ob is B's c.i.f. offer curve, the amounts of Y that B offers to land in A for quantities of X landed in B; and O'a is A's c.i.f. offer curve. Alternatively, country B's f.o.b. offer curve (not drawn) would show the quantities of Y offered by B in return for quantities of X, f.o.b. in A; and A's f.o.b. offer curve is Oa, since there are no costs of transporting Y. The f.o.b. offer curves would intersect at Qa.

The price of OH of X in B is HQb of Y, and in A it is HJ of Y. This is equivalent to saying that the price of OH of X is HQb, c.i.f., or HJ, f.o.b., where the amount of JQb of Y is the price, in terms of Y, paid for transport costs. Thus the domestic price ratio in A is alpha and in B is beta. The terms of trade, when both export and import prices are calculated c.i.f., are determined by the intersection of the c.i.f. offer curves; and when prices are calculated f.o.b., the terms of trade are determined by the intersection of the f.o.b. offer curves. Thus the c.i.f. terms of trade are the same as B's domestic price ratio, and the f.o.b. terms of trade are the same as A's domestic price ratio. This conclusion is obvious, since there are no costs of transporting Y.

Price ratios are related by the proportion Kx. Let the P's denote prices, the subscripts, commodities, and the superscripts, countries. Then Let us now assume that both countries share in the transport of X, and retain the assumption that Y is transport-free. Transport costs incurred in Y mean that some Y is used up in transporting a unit of X; call this fraction ax. In Figure 5-2, ax is represented by the slope of the line OK. Now to find the c.i.f. offer curve of A, first deduct from Oa the costs of transport incurred in X (as in Figure 5-1), to get O'a and then add the line OK vertically to O'a to get øa- The c.i.f. offer curve, O'a shows the schedule of amounts of X landed in B that A is willing to offer B at different price ratios. Country A is willing to offer LQa of X, f.o.b., in return for OL of Y, but deducts from this PQa #### Figure 5-2.

of X, and demands PQb more of Y, to pay the costs of transport.4 The price of OH of X to B is thus HQb of Y, c.i.f., or HJ of Y, f.o.b. The terms of trade calculated at c.i.f. prices are beta and, calculated at f.o.b. prices, alpha. The price ratios are related in the following way: Until now we have considered only the cost of transporting X. If there are costs of transporting Y as well, both offer curves must be modified. To keep the geometry simple, I have assumed in Figure 5-3 that transport costs are

` Figure 5-3.

incurred only in the good of the exporting country, which means that some X is used up in shipping X and some Y is used up in shipping Y. The curves O'a and O'b are the c.i.f. offer curves of A and B, respectively; these curves intersect at P. The trading equilibrium of A is at Qa, where she exports LQa of X in return for HP of Y, so her domestic price ratio is given by the line alpha. The trading equilibrium of B is at Qb, where she exports HQb of Y in return for OH of X, so her domestic price ratio is beta.

Country A exports LQa of X but B receives only LP, since PQa is used up as the cost of transporting X. Country B exports HQb but only HP reaches A, since PQb of Y is used up as transport cost. The points Qa and Qb must be points of equilibrium, as they lie on the offer curves of A and B, respectively, and the difference between the exports of one country and the imports of the other country is wasted as transport costs.

The terms of trade with prices calculated c.i.f. are given by a line from the origin to the point of intersection of the c.i.f. offer curves, that is, OP. The f.o.b. terms of trade are given by a line from the origin to the intersection of the f.o.b. offer curves (not drawn), and can easily be shown to be OP'. The price ratios are related in the following way: Since the c.i.f. and f.o.b. terms of trade are the slopes of the lines OP and OP' respectively, the following relation holds: from which it can be seen that the f.o.b. terms of trade and the c.i.f. terms of trade will be equal when Kx = Ky.

A final case will be considered, the case where one country provides all the transport services. In Figure 5-4 the proportion Kx is the fraction of A's #### Figure 5-4.

exports of X that are received as imports by B after deducting the costs of transporting X, but before deducting the costs of transporting Y incurred in X. The cost incurred in X of transporting a unit of Y is given by the slope of the line OJ. The c.i.f. offer curve of A is O'a, which is always a proportion, Kx, of the X value of Oa; and the c.i.f. offer curve of B is O' b, which is formed by adding horizontally to øb the line of OJ. The c.i.f. offer curves intersect at P, giving the c.i.f. terms of trade, OP. (The price of OH of Y in B is HQb of X, and PQb of X is required to transport OH of Y to A, and so on.) The f.o.b. terms of trade must be calculated by reversing the position of O'a and O' b: instead of subtracting the cost of transporting X from A's offer curve, add it to B's offer curve (horizontally), and, similarly, subtract the cost of transporting Y from A's offer curve. The f.o.b. terms of trade are then a line from the origin to the point of intersection of these f.o.b. offer curves and will be larger or smaller than the c.i.f. terms of trade depending on whether ax is greater or less than 1- Kx.

The relation between the price ratios is The above analysis suggests an alternative way of finding an equilibrium, a method analogous to that which Lerner made famous in his analysis of tariff equilibrium . Given the offer curves Oa and Ob in any of the above four diagrams, a pencil, alpha O beta, can be rotated around O until two points are found on Oa and Ob between which transport costs will just consume the difference between the exports of one country and the imports of the other country. The equilibrium in Figure 5-1 is then the same as for a tariff imposed by A where A's government spends all the proceeds of the tariff on the home good; Figure 5-2 shows the equilibrium where A's government divides its expenditure of the tariff proceeds between PQa of its own good and PQb of imports; Figure 5-3 shows the equilibrium where each country imposes tariffs and spends the proceeds on its home good; and Figure 5-4 represents the case where each country imposes tariffs, and A's government spends the proceeds on its own good whereas B's government spends the proceeds on imports.

#### The F.O.B. and C.I.F. Terms of Trade

There are four measures of the terms of trade. These are: (1) country A's domestic price ratio, the ratio of the f.o.b. price of X and the c.i.f. price of Y; (2) country B's domestic price ratio, the ratio of the f.o.b. price of Y and the c.i.f. price of X; (3) the f.o.b. terms of trade, the ratio of the f.o.b. prices; and (4) the c.i.f. terms of trade, the ratio of c.i.f. prices. In empirical studies it is important that these measures of the terms of trade be distinguished.

If domestic price ratios are used in calculating the terms of trade, a reduction in transport costs incurred in either good (because of, say, an innovation) will improve the terms of trade of both countries simultaneously, provided both offer curves are elastic. This is clear from an inspection of any of the above four diagrams, because a reduction in transport costs squeezes the price ratios together, and both countries offer more exports in return for more imports as a consequence of the reduced price of imports.

A reduction in transport costs incurred in, say, Y, must improve country A's terms of trade irrespective of the elasticities; but it will improve or worsen country B's terms of trade depending on whether country A's offer curve is elastic or inelastic (regardless of the elasticity of B's offer curve). This is demonstrated in Figure 5-5, where it is assumed that there are no costs of transporting X. Equilibrium is determined by the intersection of country B's c.i.f. offer curve, Ob, with Oa; the amount PaPb of Y s used up as transport cost. Country A's terms of trade are given by a line from the origin #### Figure 5-5.

to Pa,and country B's by a line to Pb. Now suppose the reduction in transport costs alters B's c.i.f. offer curve to O"b The new points of equilibrium are P'a and P'b; country A's terms of trade have improved to OP'a and country B's have worsened to OP'b . This result depends on the inelasticity of Oa but not on the elasticity of Ob.

If one country provides all the transport services, then a reduction in the cost of transporting one good will have the same effect on the domestic price ratio in each country as an equivalent reduction in the cost of transporting the other good. This follows from the assumption that a reduction in demand for a country's resources used for transport has the same effect on the returns to those resources as a reduction in demand for that country's exports.

But which measure of the terms of trade should be used? For a country that does not provide any transport services, the appropriate measure of the terms of trade is her domestic price ratio, that is, the ratio of f.o.b. export prices to c.i.f. import prices. An alternative procedure would be to calculate both import and export prices f.o.b., and to include in the import index the price of the transport services imported (to carry imports). For a country that provides all the transport services the answer is less clear. If all prices are calculated f.o.b., the inclusion of transport services in the export price index only would fail to reflect the cost of transporting imports. For welfare purposes, the best measure is to use import prices c.i.f., and export prices f.o.b., including in the export price index the price of the transport services exported (to carry exports); or, alternatively, calculating both import prices and export prices, c.i.f., and neglecting exports of transport services. In general, however, the appropriate measure depends on the use to which the index is to be put.5

#### The Transfer Problem

In the classical model considered here, the balance of trade must change by an amount equal to the transfer, and expenditure in A and B must change by an amount equal to the change in the balance of trade. The simplest way to develop a criterion for changes in the terms of trade after transfer is to consider the effect on demand of these changes in expenditure, at constant prices. With no impediments to trade, and assuming that B is the transferring country, then B's terms of trade will improve or worsen, depending on whether there is an increase or a decrease in the demand for B's export good. There will be an increase or decrease in the demand for B's export good after transfer, depending on whether A's marginal propensity to import is greater or less than B's marginal propensity to consume her own good, because A's expenditure increases, and B's expenditure decreases, by an amount equal to the transfer itself. This is equivalent to saying that B's terms of trade will improve or worsen depending on whether the sum of the marginal propensities to import is greater or less than unity. This criterion can then be translated into a number of other criteria, the most convenient for our purposes being that used by Samuelson: The terms of trade of the transferring country will improve, remain the same, or worsen as Ma / Ca >< Cb / Mb, where Ma , Ca , Mb , and Cb are the marginal propensities to import and consume goods in A and B, respectively.6

In the absence of trade impediments, nothing can be said a priori about the direction of change in the terms of trade. With transport costs, two effects must be considered: First, transport costs raise the c.i.f. price of imports and thus change the demand for the good of the country whose resources are used up as transport services. With reference to the first factor, it is theoretically possible that the higher relative price of imports in each country increases the marginal physical propensity to import, although this is an unlikely result, since it implies a marginal propensity to import appreciably greater than the average propensity to import.7 The most that can be said about the first factor, in the absence of additional knowledge of demand conditions, is that if the marginal propensity to import is equal to the average propensity (that is, if the indifference map is " homothetic"), then the marginal propensity to import will be smaller with, than without, transport costs.

The direction of bias given to the criterion by the second factor depends on which good is used as the transport good. If the good of the exporting country is used, then A's (the receiving country's) increase in demand for B's good, because of the transfer, will cause an additional increase in demand for B's good to carry it; and B's decrease in demand for A's good will involve an additional decrease in demand for A's good used as transport costs. Thus the assumption that each country provides the transport services for its own exports creates a presumption that the transfer will improve the terms of trade of the transferring country, contrary to the orthodox direction. On the other hand, if each country provides the transport services for its own imports, there is a presumption that the terms of trade will change in the orthodox direction. The increase in demand in A for B's good involves an increase in demand for A's good used as transport costs, and the decrease in demand in B for A's good involves a decrease in demand for B's good used to carry A's good: this tends to worsen the terms of trade of the transferring country. But when some of both goods are used as transport costs, nothing can be said as to any presumption unless further empirical information is available regarding the proportions in which the transport requirements are combined.

Figure 5-6 illustrates the transfer problem when transport costs are incurred in the good of the exporting country.8 The points Qa and Qb are the initial trading positions of A and B on their respective offer curves.The lines alpha and beta are the pretransfer price ratios in A and B, and epsilon represents the f.o.b. terms of trade. Now suppose that country B makes a transfer to country A equal in value to ON of B's good, c.i.f. The costs of delivering ON of Y to A are NM, so B must transfer OM. After the transfer is made, the new offer #### Figure 5-6.

curves of A and B begin at their new endowment positions, N and M, respectively.

As in the no-impediment case, we consider the changes in demand at constant prices. Draw a' from A's new endowment position N, parallel to a. Consumers in A, at constant prices after transfer, would move up a' to the point where the latter is tangent to an A indifference curve, that is, to Q'a. Consumers in B at constant prices would move up beta' to the point where beta' is tangent to a B indifference curve, that is, to Q'b Now draw QaQ'a and extend it to the X axis at Ea, and draw QaQb, and extend it to the Y axis at Eb; the slopes of the lines QaQ'a and QbQ'b are the ratios of the marginal physical propensities in each country.9 But these slopes do not take into account the changes in the quantities of X and Y required for transport costs. What is relevant for the criterion with real impediments are the marginal propensities to spend on imports, which include the amount spent on transport costs. Now at Ea, where no Y is imported, the transport costs of Y imports are of course zero; at Qa, transport costs are PQa; and at Q'a transport costs are equal to Q'aP'a. The new line traced out by these points, PP'a, is the transport-modified expenditure line and its slope is the ratio of A's marginal propensity to spend on imports and her marginal propensity to spend on domestic goods. Similarly, PP'b is B's transport-modified expenditure line and its slope is the ratio of B's marginal propensity to spend on domestic goods and her marginal propensity to spend on imports.

Now draw epsilon' parallel to epsilon from M; clearly, the points P'b and P'a must lie along this line, since the horizontal distance between beta' and epsilon' measures the cost of transporting X, and the vertical distance between alpha' and epsilon' measures the costs of transporting Y. Then, if the pretransfer price ratios are to remain unchanged, the horizontal distance between Q'a and Q'b must be exactly equal to the amount of X used up as transport cost, and the vertical distance must exactly equal the amount of Y used up as transport cost; otherwise, Q'a and Q'b are not equilibrium positions and the terms of trade would have to change. For the terms of trade to remain unchanged, then P'a must coincide with P'b, and the lines PP'a and PP'b must be the same.

The geometric criterion is thus established. The terms of trade of B, the transferring country, will improve, stay the same, or worsen depending on whether the slope of PP'a >< the slope of PP'b . That this is the geometric form of Samuelson's criterion can be shown as follows: The slope of but GQa / GEa is the slope of Q'aQ'a, that is, the ratio of A's marginal physical propensity to import and her marginal physical propensity to consume, so the slope Similarly, the slope of so the criterion becomes whether which is Samuelson's criterion Now so the criterion is equivalent to whether or in terms of the marginal propensities to spend.

In Figure 5-6 the terms of trade of the transferring country improve, because the slope of PP'a (Ma / Ca) is greater than the slope of PP'b (Cb / Mb), causing an excess demand for B's good. It is easily seen from the diagram (or from the above formulas) that transport costs incurred in the export good increase the likelihood that the transferring country's terms of trade improve, since PP'a is steeper than QaQa and PP'b is flatter than QbQb. Against this must be set the effect of the higher price of imports in changing the marginal propensities to import.

Transport costs incurred in the good of the importing country result in an increased demand for the receiving country's good used as transport costs due to her increased imports, and a decreased demand for the transferring country's good used as transport costs because of her reduced imports, in this case the terms of trade will be more likely to turn in the orthodox direction. When transport costs are incurred in both goods, the presumption as to the direction of change in the terms of trade depends on the proportions in which these are combined. This case is represented in Figure 5-7, but for simplicity we have assumed that there are no costs of transporting Y. The initial equilibrium is the same as in Figure 5-3, with A and B initially in equilibrium at Qa and Qb; in the initial equilibrium, RQa of X and RQb of Y are used up in landing FQb of X in B. Country A's domestic price ratio, alpha, is also the f.o.b. terms of trade, and country B's domestic price ratio, beta, is also the c.i.f. terms of trade, since there are no costs of transporting Y.

Country B makes a transfer of OM of Y, all of which reaches A, as there are no costs of transporting Y. At unchanged prices, A moves up its price line alpha' to Q'a and B moves up its price line beta' to Q'b, the points where the price lines are tangent to indifference curves. Draw QaQa and extend it to Ea on the X axis; this line is the ratio of the marginal physical propensities to import and consume, and since there are no transport costs to be paid on A's imports, it is also the ratio of the marginal propensities to spend on imports and consumption.

Draw QbQ'b and extend it to the Y axis at Eb; this is the ratio of the marginal physical propensities to consume and to import in B. Because transport #### Figure 5-7.

costs must be paid on B's imports, this line is not the same as the ratio of the marginal propensities to spend; to find the latter, connect QaP'b with Eb.

The geometric criterion for changes in the terms of trade is whether the slope of QaQ'a is greater or less than the slope of QaP'b. The slope of QaQ'a is Ma / Ca, because there are no costs of transporting Y, and the slope of OaP'b is But is the amount of Y required to transport a unit of X, that is, ax; so the slope of QaP'b is equal to Our criterion then becomes whether Kx reduces, and ax raises, the right-hand argument, so with transport costs incurred in both goods it is impossible to determine a priori the bias given to the criterion. In Figure 5-7, since QaBb is steeper than QbQ'b the effect is to decrease the likelihood that the terms of trade will turn in favor of the transferring country.

When there are costs of transporting both X and Y, the terms of trade of the paying country, B, will improve, stay the same, or deteriorate. as which includes Samuelson's criterion as a special case when ax and ay are zero. In practical terms the criterion implies that the greater the share the transferring country has in providing transport services for its own exports, and the smaller the share it has in transporting its own imports, the more likely it is that the terms of trade will move in favor of the transferring country. If its own ships carry a large proportion of its exports, but only a small proportion of its imports, then, since the transfer is effected by an increase in its exports and a decrease in its imports, demand for the factors of production in the transferring country will increase, and their prices will rise, unless this effect is offset by an income consumption bias in each country for domestic goods. It should be noted that a monopoly of transport services by either of the countries does not in itself provide any presumption as to the direction of the change in the terms of trade, but if it were known that transport costs represented a higher proportion of the value of one good than the other, then such a presumption could be said to exist. For example, if Britain's merchant fleet carried most of her exports and imports, and Britain made a transfer to the United States (the end of Marshall Plan aid), then the British terms of trade would be more, or less, likely to turn in her favor, depending on whether her exports were "heavy" or "light" relative to her imports. Or, if Canada's exports were "heavier" than her imports, a capital movement from the United States to Canada would be more likely to cause an improvement in Canada's terms of trade the smaller the share of Canada and the larger the share of the United States in providing transport services.

In summary, transport costs result in higher import prices and thus affect the marginal physical propensities to import, but unless one accepts the "symmetrical ignorance" argument, it cannot be demonstrated a priori that they will be lower. Even if this argument is accepted, whether or not a "presumption" exists depends on which country provides the transport services, and on how important transport costs are in one good relative to their importance in the other.

#### The Optimum Tariff

If a country is following an optimum tariff policy, then a reduction in costs of transport is likely to necessitate a change in the optimum tariff rate. To examine the implications of a change in transport costs, we shall compare the optimum tariff without transport costs with the optimum tariff with transport costs. To keep the analysis simple we shall assume that transport costs are incurred in the good of the exporting country only, and that there are no costs of transporting X. We also assume that there is no retaliation, and that tariff proceeds are redistributed to consumers.

The optimum tariff is the tariff that will make the domestic marginal rate of substitution of X for Y equal to the marginal rate of transformation of X into Y through foreign trade. Geometrically, this means that country A's optimum tariff is that which will force country B to trade at the point where an A-indifference curve is tangent to B's offer curve. In Figure 5-8 this point is P, where Ia, an A-indifference curve, is tangent to Ob, country B's offer curve. #### Figure 5-8.

The tariff that will make P a trading equilibrium is determined by extending the tangent at P to L on the X axis. The optimum tariff, then, is the elasticity of B's offer curve, so the optimum tariff formula10 is The price ratio in B (also the terms of trade) is beta, and the price ratio in A is alpha. Before tariff proceeds have been redistributed, A-consumers consume at Q, on Oa; and after tariff proceeds (OL in terms of X) have been redistributed, they consume at P. The curve O'a is A's tariff-modified offer curve, which will pass through P when the tariff is optimal.

To find the optimum tariff when there are costs of transporting Y, we first draw country B'sc.i.f. offer curve, O'b, in Figure 5-8. This is now country A's marginal rate of transformation of X into Y through foreign trade, so the optimum tariff with costs of transporting Y is determined at the point where an A-difference curve is tangent to O'b; in the optimum tariff formula we substitute the elasticity of O'b, which we shall designate as epsilon'b. Whether the optimum tariff without transport costs is larger or smaller than the optimum tariff with transport costs depends on whether the elasticity of Ob is smaller or larger than the elasticity of O'b, at the points where each curve is tangent to an A-indifference curve.

To determine how epsilonb and epsilon'b are related, consider the point R on O'b directly below P on Ob Since the Y-value of Ob, that is, RM, is always a constant proportion (Kx) of the Y value of Ob, that is, PM, then a proportional movement along O'b must equal the same proportional movement along Ob  O'b. Therefore, the tangent at R, when extended, must meet the tangent at P, when extended, on the X axis at L; then, since LM/LO measures the elasticity of Ob at P, it must also measure the elasticity of O'b at R. The two elasticities at P and R are equal, and this holds for similar points along Oband O'b .

If an A-indifference curve is tangent to O'b at R, the optimum tariff with and without transport costs is the same, and a reduction m the costs of transporting Y does not change the optimum tariff. In this case, country A's tariff-modified offer curve, O'a, passes through both P and R, and its elasticity between these points is unity. Thus the optimum tariff will be the same with and without transport costs if the elasticity of A's tariff-modified offer curve is unity. But when O'a is not unit elastic, an A-indifference curve is tangent to O' to the right or to the left of the point R, and to compare the level of optimum tariffs in the two cases we must know something about the direction in which the elasticity of O'b (or Ob) is changing as the point of equilibrium moves farther from the origin. If Obwere an offer curve of constant elasticity over the relevant range, then the level of optimum tariff would be the same in the two cases regardless of the elasticity of O'a.

In Figure 5-8, O'a is inelastic, so A's optimum tariff will be higher or lower with, than without, transport costs depending on whether the elasticity of Ob or O'b decreases or increases as the volume of trade increases. On the other hand, if  I'a were elastic, the converse would be true. Thus, to compare the two cases it is necessary to know the elasticity of the tariff-modified offer curve, and the direction in which the elasticity of the other country's offer curve iS changing as the volume of trade increases. Under the assumption that tariff proceeds are redistributed, it is impossible to determine, a priori, the relation between A's tariff-modified offer curve and her free-trade offer curve; it iS perfectly consistent with convex indifference curves and the absence of inferior goods for one curve to be elastic while the other is inelastic. It iS also impossible to determine, in the absence of further knowledge of tastes, in which direction elasticities change as the volume of trade increases. Perhaps a "presumption" could be established (but it is a very weak presumption) in the following way. The elasticities of the offer curves at the origin are infinite but become less elastic as the volume of trade increases; thus it is likely that demand for imports becomes less responsive to price changes as the quantity of goods imported increases. If this presumption were valid, then a reduction in transport costs would suggest that a downward or an upward adjustment in tariffs is required, depending on whether A's tariff-modified offer curve is inelastic or elastic.

No general conclusion is possible even in  this simple case, without empirical knowledge of the elasticities, so we shall not pursue the matter further.

#### Real Factor Returns

Under the Heckscher-Ohlin assumptions, where each country exports its abundant-factor-intensive commodity, a reduction in transport costs will affect the functional distribution of the national income. The direction in which factor returns change depends on the direction in which the domestic price ratio changes; the absolute return of the abundant factor will rise or fall, and the absolute return of the scarce factor will fall or rise, depending on whether the domestic price of exportables relative to the domestic price of importables rises or falls. This follows directly from the analogy to tariff theory.ll

If both offer curves are elastic, a reduction in transport costs incurred in either good will improve the terms of trade (calculated with f.o.b. export prices and c.i.f. import prices) of both countries and thus increase the absolute return of the abundant factor and decrease the absolute return of the scarce factor. If country B's offer curve is inelastic, while country A's is elastic, then a reduction in transport costs incurred in B's good will improve the terms of trade and thus the real income of the abundant factor in both countries; but a reduction in transport costs incurred in A's good will improve B's and worsen A's terms of trade, thus raising the real income of B's and lowering that of A's abundant factor. The converse is true if A's offer curve is inelastic while B's is elastic. If both offer curves are inelastic, a reduction in transport costs incurred in one good will worsen the terms of trade of that country and improve the terms of trade of the other country, and thus change absolute factor returns.

#### Concluding Remarks

It remains to consider briefly our assumptions regarding the nature of transport costs. The transport industry is an intermediate-goods industry, and when trade takes place, and transport costs are involved, resources have to be released from the final-goods industries to produce an intermediate good-transport costs. Our assumption that some final goods must be used up in transport is a means of avoiding a three-dimensional diagram in which the production possibilities of a country are depicted by a three-good transformation locus. The assumption that Kx and ax are constant implies that final goods can be converted into the transport good at constant opportunity costs, but this assumption is easily modified by making Kx and ax depend on the volume of trade. For example, if Kx decreases as the volume of X exported increases, and axincreases as the volume of Y imported increases, increasing opportunity costs are implied. With increasing opportunity costs, however, the relative share of each country in providing transport services will depend on the terms of trade, and different points of equilibrium on the offer curves will imply different values of Kx, Ky, ax, and ay, as the terms of trade change.

Transport costs depend on the distance between countries. The greater the distance, the smaller are Kx and Ky, the larger are ax and ay, and the more closely are the c.i.f. offer curves squeezed together; if the distance is sufficiently large, opportunities for gains from trade are eliminated, and trade ends.

#### Notes

1 Adapted from: Can. Jour. Econ. Pol. Sci., 23, 331-348 (Aug. 1957).

2 I am grateful to H. G. Johnson, J. E. Meade, and S. A. Ozga for helpful comment on and criticism of an earlier draft of this article. I am especially indebted to Professor Johnson for his method of representing the transfer problem with transport costs.

3 This assumption was first used by Samuelson in his analysis of the transfer problem .

4 I have assumed throughout that transport costs are not required to "ship transport costs." Thus, in Figure 5-2, the proportion ax measures the amount of Y used up in transporting X after transport costs incurred in X have been deducted. To make the alternative assumption it is necessary only to change the proportions Kx and ax.

5 Haberler (, pp. 28-29) discusses this problem but says that the correct procedure in empirical studies is to include the price of transport services in the computation of the terms of trade. It is not clear whether he means that export and import prices should be calculated c.i.f., or whether transport costs should be counted as an export or import. If the latter, should the indexes be calculated with reference to c.i.f. or to f.o.b. prices ?

6 For recent discussions of the transfer problem, see Meade (, chap. 7), Samuelson , and Johnson .

7 For a discussion of this problem, see Samuelson (, part I, pp. 295-299).

8 Professor Samuelson writes (, part II, p. 282): " Our graphical analysis . . . fails to handle the real transport case, because then the final consumption points for the two countries do not coincide, instead differing by a vector representing the amount of goods actually used up in transport." This section shows that the problem is nevertheless amenable to purely graphical analysis; the methods employed here were suggested by Professor Johnson.

9 These lines relate to behavior between points; the "Engel's curves" are not necessarily straight lines.

10 See, for example, Meade (, p. 76).

11 Stolper and Samuelson  showed that, under the Heckscher-Ohlin assumptions, with constant terms of trade, tariffs increase the scarcity, and thus the real income, of the scarce factor. Metzler  qualified the argument taking into account changes in the terms of trade, making use of a criterion derived by Lerner . Lerner's criterion showed that a tariff would increase the price of importables relative to exportables in the tariff imposing country if the foreign elasticity of demand plus the domestic marginal propensity to import were greater than unity. In the case of transport costs, the criterion does not involve the marginal propensity to import, as the transport costs are used up rather than (as in the case of tariff proceeds) redistributed to consumers.

#### Literature Cited

 M. FRIEDMAN, "The Case for Flexible Exchange Rates," Essays in Positive Economics. Chicago: University of Chicago Press, 1953.

 H. G . JOHNSON, " The Transfer Problem: A Note on Criteria for Changes in the Terms of Trade," Economica, XXII-XXIII, 113-121 (May 1955).

 A. P. LERNER, "The Symmetry between Import and Export Taxes," Economica, 3, 308-313 (Aug. 1936).

 J. E. MEADE, Trade and Welfare. Fair Lawn, N.J.: Oxford University Press, 1955.

 J. E. MEADE, A Geometry of International Trade. London: Oxford University Press, 1952.

 L. A. METZLER, "Tariffs, the Terms of Trade, and the Distribution of National Income," Jour. Pol. Econ., 57, 1-29 (Feb. 1949).

 P. A. SAMUELSON, " The Transfer Problem and Transport Costs: I, The Terms of Trade When Impediments Are Absent, II, Analysis of Effects of Trade Impediments," Econ. Jour., 57, 278-304 (June 1952); 59, 264 290 (June 1954).

 P. A. SAMUELSON, Foundations of Economic Analysis. Cambridge: Harvard University Press, 1953.

 W. F. STOLPER and P. A. SAMUELSON, "Protection and Real Wages," Rev. Econ. Stud., 9, 58-73 (Nov. 1941).