Homepage International Economics

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

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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.

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
*K*_{x}. 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

exports to land *X* in *B*. In Figure 5-1,
*O*_{a} and
*O*_{b} are the offer curves of *A* and
*B* before transport costs have been considered, and
*O*_{a} is the schedule of *A*'s offers
of *X* landed in *B*, that is,
*O*_{a} is *A*'s c.i.f. offer curve. This
curve is determined by subtracting from the *X* value of
*O*_{a} 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,
*K*_{x}, of the *X* value of
*O*_{a}. Equilibrium is determined by the
intersection of *A*'s c.i.f. offer curve,
*O'*_{a}, with *B*'s offer curve,
*O*_{b}, at the point
*Q*_{b} . At this equilibrium, country *A*
exports *LQ*_{a} of *X* and imports
*OL* of *Y*, and country *B* exports *OL *of *Y*
and imports *LQ*_{b} 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
*K*_{x} of *A*'s exports, the difference
being used up as transport cost. Thus
*Q*_{a}*Q*_{b} is
the cost of landing *LB*_{b }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,
*O*_{b} 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
*O*_{a}, since there are no costs of transporting
*Y*. The f.o.b. offer curves would intersect at
*Q*_{a}.

The price of *OH* of *X* in *B* is *HQ*_{b} of
*Y*, and in *A* it is *HJ* of *Y*. This is equivalent
to saying that the price of *OH* of *X* is
*HQ*_{b}, c.i.f., or *HJ*, f.o.b., where
the amount of *JQ*_{b} 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 *K*_{x}. 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
*a*_{x}. In Figure 5-2,
*a*_{x} is represented by the slope of the line
*OK. *Now to find the c.i.f. offer curve of *A*, first deduct from
*O*_{a} 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
*LQ*_{a} of *X*, f.o.b., in return for
*OL* of *Y*, but deducts from this
*PQ*_{a}

of *X*, and demands *PQ*_{b} more of *Y*, to pay the
costs of
transport.^{4}
The price of *OH* of *X* to *B* is thus
*HQ*_{b }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 *Q*_{a}, where
she exports *LQ*_{a }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
*Q*_{b}, where she exports
*HQ*_{b} of *Y* in return for *OH*
of *X*, so her domestic price ratio is *beta*.

Country *A* exports *LQ*_{a} of *X* but *B* receives
only *LP*, since *PQ*_{a} is used up as
the cost of transporting *X*. Country *B* exports
*HQ*_{b} but only *HP* reaches *A*,
since *PQ*_{b} of *Y* is used up as transport cost. The
points *Q*_{a} and
*Q*_{b} 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 *K*_{x} =
*K*_{y}.

A final case will be considered, the case where one country provides all
the transport services. In Figure 5-4 the proportion
*K*_{x} 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,
*K*_{x}, of the *X* value of
*O*_{a}; 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 *HQ*_{b} of
*X*, and *PQ*_{b} 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
*a*_{x} is greater or less than 1-
*K*_{x}.

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 [44]. Given the offer curves
*O*_{a} and
*O*_{b} in any of the above four diagrams, a
pencil, *alpha O beta*, can be rotated around *O* until two points
are found on *O*_{a} and
*O*_{b} 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
*PQ*_{a} of its own good and
*PQ*_{b} 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.

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,
*O*_{b}, with
*O*_{a}; the amount
*P*a*P*_{b} of *Y* s
used up as transport cost. Country *A*'s terms of trade are given by
a line from the origin

to *P*_{a},and country *B*'s by a line to
*P*_{b}. 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 *O*_{a }but not on the
elasticity of *O*_{b}.

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}

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 *M*_{a }/
*C*_{a} ^{>}_{<
}*C*_{b }/
*M*_{b}, where *M*_{a
}, *C*_{a} ,
*M*_{b} , and *C*_{b
}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 *Q*_{a} and
*Q*_{b} 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

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

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

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 *GQ*_{a }/ *GE*_{a
}is the slope of
*Q'*_{a}*Q'*_{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} (*M*_{a}
/ *C*_{a}) is greater than the slope of
*PP'*_{b} (*C*_{b} /
*M*_{b}), 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
*Q*_{a}*Q*_{a} and
*PP'*_{b} is flatter than
*Q*_{b}*Q*_{b}. 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
*Q*_{a} and
*Q*_{b}; in the initial equilibrium,
*RQ*_{a }of *X* and
*RQ*_{b} of *Y* are used up in landing
*FQ*_{b} 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
*Q*_{a}*Q*_{a} and
extend it to *E*_{a }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 *Q*_{b}*Q'*_{b} and extend
it to the *Y* axis at *E*_{b}; this is the
ratio of the marginal physical propensities to consume and to import in
*B*. Because transport

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
*Q*_{a}*P'*_{b} with
*E*_{b}.

The geometric criterion for changes in the terms of trade is whether the
slope of
*Q*_{a}*Q'*_{a} is
greater or less than the slope of
*Q*_{a}*P'*_{b}. The slope of
*Q*_{a}*Q'*_{a} is
*M*_{a} /
*C*_{a}, because there are no costs of transporting
*Y*, and the slope of
*O*_{a}*P'*_{b} is

But

is the amount of *Y* required to transport a unit of *X*, that
is, *a*_{x}; so the slope of
*Q*_{a}*P'*_{b} is
equal to

Our criterion then becomes whether

*K*_{x} reduces, and
*a*_{x} 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
*Q*_{a}*B*_{b} is
steeper than
*Q*_{b}*Q'*_{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
*a*_{x} and
*a*_{y} 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.

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 *I*_{a}, an *A*-indifference curve,
is tangent to *O*_{b}, country *B*'s offer
curve.

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
formula^{10
}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
*O*_{a}; 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
*O*_{b} 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 *epsilon*_{b} and
*epsilon'*_{b} are related, consider the point
*R* on *O'*_{b} directly below *P*
on *O*_{b} Since the *Y*-value of
*O*_{b}, that is, *RM*, is always a constant
proportion (*K*_{x}) of the *Y *value of
*O*_{b}, that is, *PM*, then a proportional
movement along *O'*_{b} must equal the same
proportional movement along *O*_{b}
*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 *O*_{b} 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 *O*_{b}and
*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
*O*_{b}) is changing as the point of equilibrium
moves farther from the origin. If
*O*_{b}were 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
*O*_{b} 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.

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.

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 *K*_{x }and
*a*_{x} 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 *K*_{x }and
*a*_{x} depend on the volume of trade. For example,
if *K*_{x }decreases as the volume of *X *exported increases,
and *a*_{x}increases 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
*K*_{x},
*K*_{y},
*a*_{x}, and
*a*_{y}, as the terms of trade change.

Transport costs depend on the distance between countries. The greater the
distance, the smaller are *K*_{x} and
*K*_{y}, the larger are
*a*_{x} and
*a*_{y}, 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 [91].

4 I have assumed throughout that transport costs are not
required to "ship transport costs." Thus, in Figure 5-2, the proportion
*a*_{x }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 *K*_{x} and
*a*_{x}.

5 Haberler ([16], 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 ([58], chap. 7), Samuelson [90], and Johnson [31].

7 For a discussion of this problem, see Samuelson ([90], part I, pp. 295-299).

8 Professor Samuelson writes ([90], 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 ([55], p. 76).

11 Stolper and Samuelson [99] 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 [63] qualified the argument taking into account changes in the terms of trade, making use of a criterion derived by Lerner [44]. 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.

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

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

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

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

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

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

[90] 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).

[91] P. A. SAMUELSON, *Foundations of Economic Analysis. *Cambridge:
Harvard University Press, 1953.

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

© Copyright Robert A. Mundell, 1968