Homepage International Economcs

* International Economics*, Robert A. Mundell, New York: Macmillan,
1968, pp. 17 - 42.

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The first policy change we shall consider is a unilateral payment from one
country to the other. This involves two parts: a *financial *transfer
and a *real* transfer. The financial transfer refers to the accumulation
and liquidation of debt on the part of individuals or governments in each
country, while the real transfer refers to the induced movement of goods.
Assume that *A* is the transferring country.

In the case of a private flow of capital lenders in *A* buy the debt
of borrowers in *B*, the former financing the purchase out of an excess
of saving over investment, the latter disposing of the proceeds by an excess
of investment over
saving.^{2}
Because of the identity of income-less-lending and expenditure [equations
(9) and (10) of Chapter 1], the excess of investment over saving in *B*
and saving over investment in *A* must each equal the transfer.

In the case of intergovernmental transfers such as reparations payments or
foreign aid, the government in *A* (the paying country) grants credits
to *B*, the former financing the credits by means of, say, an income
tax, the latter disposing of the proceeds by means of, say, an income subsidy.
Again, because of the identity of income-less-lending and expenditure, the
budget surplus in *A* and the budget deficit in *B* are each equal
to the transfer.

Whatever the type of transfer and however it is financed and disposed of,
domestic expenditure in *A* is reduced, and in *B* is increased,
by the amount of the transfer. These changes in expenditure induce changes
in demand that, at constant terms of trade, create disequilibrium in the
balance of payments. The transfer problem may then be posed as the problem
of determining the direction and extent of the change in the terms of trade
required to eliminate

*The Terms of Trade.* To find the effects of a transfer on the terms
of trade we first determine the excess demand created by the expenditure
changes at constant terms of trade. This can be done in terms of either good,
as an excess demand for one good implies an excess supply of the other good.

The reduction in domestic expenditure in *A* decreases the demand for
*Y* in *A* at constant terms of trade by

where *m*_{a} is the marginal propensity to spend
on imports in *A*. The increase in domestic expenditure in B increases
the demand for *Y* in *B* by

where *c*_{b} is the marginal propensity to spend
on home goods in *B*. The excess demand at constant terms of trade is
therefore the sum of these changes, or

noting that the changes in expenditure in each country are equal to the change
in lending, that is, *-dD _{a} =
dD_{b} = dT* . Now expenditure in each country
is divided between home goods and imports, so that the sum of the marginal
propensities to spend on home goods and imports is unity; thus

which states that transfer creates an excess demand for, or excess supply
of, the good of the transferring country depending on whether the sum o t
e marginal propensities to spend on imports is greater or less than 1. Only
if the special case where the receiving country increases its consumption
of the two goods in the same proportion that the paying country does without
them (1* - m _{a} -
m_{b} = 0*) will no change in the terms of trade
be required. If

To correct the disequilibrium, equal to (1-
*m _{a}* -

The excess demand for *B*'s good at constant terms of trade must, at
the new equilibrium, be equal to the excess supply of *B*'s good caused
by the actual change in the terms of trade. Equating of (1) and (2) therefore
provides the general criterion for the change in the terms of trade:

It may be seen that the higher the price elasticities of demand for imports
are, the smaller will be the change in the terms of trade (a small price
change relieves a large excess demand). In the limiting case where one of
the elasticities is infinite, no change in the terms of trade is required.
Similarly, the closer to 1 is the sum of the marginal propensities to import,
the smaller is the excess demand to be eliminated by a change in the terms
of trade, and so the smaller is the actual change in the terms of
trade.^{4}

*Real Income.* How is real income affected by a grant or gift from one
country to the other? In the reparations discussions of the interwar period
the view was widely held that the terms of trade of the paying country must

The pretransfer offer curves (not drawn) are assumed to intersect
initially at *Q'*. Assume that country *A* makes a payment equal
to *OH* of *X *to country *B*. Then at constant terms of trade
expenditure in *A* is reduced and in *B* is increased by *OH*
of *X* or *ST* of *Y*. These changes in expenditure induce
*A* to buy *UR* less of *Y* and *B* to buy *UW *more
of *Y*, creating an excess demand for *Y* and a deficit in
*A*'s balance of payments equal to *RW*. To eliminate this excess
demand a deterioration in *A*'s terms of trade is required until a new
equilibrium such as *Q* is achieved. The new equilibrium *Q* is
determined by the intersection of the new offer curves *HA* and
*HB* which originate from the new endowment-position *H*.

The criterion for the change in the terms of trade following transfer may be derived as follows: Define the marginal propensities to import in each country,

Then the deficit in the balance of payments of country *A*
due to the transfer at constant prices (in terms of *Y*) is:

fall, thus imposing an additional burden. The change in real income implicit
within the change in the terms of trade was called the *transfer burden*.

The change in real income due to transfer is composed of two effects-the
direct effect of the change in expenditure, and the income effect implicit
within the change in the terms of trade. Thus the real income of the receiving
country improves by more or less than the transfer itself, depending on whether
the terms of trade improve or worsen. For small changes we can approximate
the income effect of a change in the terms of trade by the change in cost
of the initial volume of imports, that is, by *I dP*. The change in
real income as a result of the transfer is therefore approximately

where *U _{a}* and

Using the relationship between income elasticities and marginal propensities developed in Chapter 1, we can manipulate (5) to get

From this criterion it can be seen that the real income of the receiving
country will be lower following a transfer, only if the system is
unstable.^{5}
Assuming stability, the higher *m _{a}* and

Assume that the country experiencing the productivity increase is completely specialized and that expenditure increases by the full amount of the increase in output. We shall first determine the effects of a change in productivity on the terms of trade, and then its influence on real income.

*The Terms of Trade*. To determine the effect of a change in productivity
on the terms of trade we first determine the excess demand created for one
of the goods on the assumption that the terms of trade are constant. If output
and expenditure in country *A* increases by
*dX _{a}**, then the change in demand for imports
in country

since expenditure (equals money income) increases by the full amount of the increase in output. At constant terms of trade no change occurs in country B, so this is also equal to the excess demand for imports in A. This excess demand must be eliminated by a change in the terms of trade. The criterion is therefore

This result is obvious: An increase in the world output of *X* must
lower the relative world price of *X*. The only exception (apart from
constant costs and incomplete specialization, or perfect substitution in
consumption) is the case where the country that has grown spends all its
increased income on its own good (*m _{a} = I -
c_{a} =
0*).

Equation (7) can be translated into proportional changes by multiplying both
sides by *X* (output) and dividing by *P*, with the following result:

where *sigma*_{a} is the marginal propensity
to spend on imports divided by the average propensity to spend on imports
-- that is, the income elasticity of demand for imports. In terms of growth
rates the criterion is

where *pi* is the percentage deterioration of *A*'s terms of trade
per unit of time and *P _{a}* is the rate of growth
of domestic product in

By following a similar procedure for country *B* we can find the annual
percentage change in the terms of trade when both countries are growing:

where *sigma _{b}*

*Real Income*. A more interesting question is whether or not real income
will increase or decrease as a result of a change in productivity. An increase
in productivity affects real income in two ways that work in opposite directions.
At constant terms of trade, real income would increase by the full amount
of the change in output. Against this must be set the negative income effect
of the actual deterioration in the terms of trade. We can therefore measure
the change in real income by adding th~- effects of the change in real income
at constant terms of trade to the reduction in income due to the change in
the terms of trade. The change in real income is
Dividing by
*dX _{a}** and applying equation (7) we obtain
the following criterion:

Real income will be increased by growth provided
*eta _{a} + etab > 0 +
m_{a}*, that is, if the sum of the elasticities
of demand for imports is greater than 1 plus the marginal propensity to import.
Note that violation of this condition is consistent with stability.

To clarify the meaning of (11) we can make use of the relationship used in
the previous section between "ordinary" and "compensated" elasticities of
demand for imports-in particular, *eta _{a} = eta'_{a} +
m_{a} *Manipulating (11) we get

Thus real income will increase in the growing country if ,
*eta' _{a}* > 1 -

Figure 2-2.

Quadrant I illustrates trade equilibrium with the initial offer
curves, *OA* and *OB*, intersecting at *Q'*. Quadrant II
illustrates production and consumption equilibrium in country *A*: Output
in *A* is initially *OZ* of *X*; consumption equilibrium is
at *C* (the length and slope of *ZC* is equal to the length and
slope of *OQ'* ).

Suppose that output and expenditure in *A* increase to
*OZ* in terms of *X*. Then at constant terms of trade inhabitants
of *A* demand more of both goods (in the absence of inferior goods),
wishing to consume at point like *D*. This means that, at any given
terms of trade, *A* demands more imports than before the productivity
change so that *A*'s offer curve unambiguously shifts to the right (quadrant
I). At the original terms of trade there is an excess demand for *Y*
and a deficit in *A*'s balance of payments equal to *RW*. The
disequilibrium induces deflation in *A* and inflation in *B* and
a deterioration in *A*'s terms of trade.

To connect the ratio of the change in the terms of trade
*TQ/QM* to the increase in output *ZZ'*, i.e., to derive a criterion
for the change in the terms of trade, first define the marginal propensity
to import in *A*. Since expenditure increases by *VS* at constant
terms of trade and the demand for imports increases by the vertical distance
between *C* and *D*, i.e., by *RW*, we have
*m _{a} = RW/VS*. Now the deficit in

where *dX* = ZZ'*. On the other hand we know from the
analysis of Figure 1-2 that

It is easily seen that the shift in *A*'s offer curve
is greater the higher is the marginal propensity to import in *A*, and
that if the latter is zero no shift occurs (all the extra expenditure in
*A* is spent on home goods). The change in real income in *A*,
as a result of the productivity increase, is *HG*, measured at pretransfer
prices. The criterion.

is zero for small changes in output when *Z'G*-extended
passes through *C*. The numerator of this criterion can be derived directly
by examining the conditions under which a change in the terms of trade to
*Z'C *can be an equilibrium. Note that this result is not possible if
*OB* is elastic.

greater than 1 minus the ordinary elasticity of demand for imports in the
other country. This criterion can be further simplified by substituting in
it the well-known relation between the elasticity of demand for imports and
the elasticity of supply of exports (*epsilon*):
*eta _{b}* - 1 =

An alternative, direct method of getting this criterion is to apply the
*method of comparative statics*. To find whether real income in the
growing country increases or decreases, first determine the excess demand
for imports on the tentative supposition that real income in *A *is
constant. If real income is constant, the terms of trade move against
*A* so there is a pure substitution effect, *-
eta _{a}'IdP*, which measures the increase in demand
for imports in

The result shows that a country may be worse off with, than without, the
improvement in productivity. Growth may be
"damnifying,"^{9}
Too rapid growth of the export industries of one country, and the resultant
attempt to push exports onto world markets, results in such a large decline
in the terms of trade that the negative income effect of the change in relative
prices is greater than the positive income effect of the increase in domestic
output at constant prices. The case of the group of primary-producing countries
readily presents itself. Within a single multi-regional economy it might
be found that U.S. agriculture is another example.

The possibility does not of course provide a valid argument against growth. In the first place, the conditions under which increasing productivity can affect real income perversely are quite strict: The foreign elasticity of demand must be less than 1 and perhaps appreciably so if home substitution effects are high. Second (and more important), since world income as a whole increases, by compensation both countries (or sectors) in the world economy could be made better off than before. Finally, the damnified country can always impose taxes on trade sufficient to reap at least some of the benefits of the productivity increase. Obviously the perverse effect is not possible if the growing country is following an optimum tariff policy, since that implies an elasticity of demand in the foreign country greater than unity.

A tax or subsidy on trade introduces a divergence between foreign and domestic
price ratios. Equal taxes on exports or imports create the same divergence
between foreign and domestic prices ratios (if trade is balance), so that
the *real *effects of import and export taxes are symmetrical. A tax
on imports at constant terms of trade raises the relative price of imports
in the taxing country and therefore *draws *resources away from export
industries into import-competing industries. A tax on exports at constant
terms of trade lowers the relative price of exports in the taxing country
and thus *pushe*s resources into import-competing industries. With balanced
trade the revenues collected by the two taxes are the same. We may therefore
speak of trade restriction or trade promotion without specifying whether
the tax or subsidy is on exports or
imports.^{10}

There are two analytic methods of treating the disposition of the tariff proceeds. We may assume that the government spends the tariff proceeds on the two goods in a given proportion, or we may suppose that tax proceeds are redistributed as income subsidies to consumers. The latter method, which is used here, is simpler because it avoids the necessity of introducing a government demand equation, and does not give rise to asymmetries when dealing with trade subsidies. In the following analysis it should be remembered that we are in fact examining the effects of tariffs combined with this method of disposing of the proceeds.

*The Terms of Trade.* To determine the effect of a tariff on the terms
of trade first compute the excess demand for imports at constant terms of
trade. At constant terms of trade the relative price of imports in the
tariff-imposing country (*A*) rises by the full amount of the tariff.
Then, with *t _{a}* representing 1 plus the ad
valorem rate of tariff, the change in demand for imports before redistribution
of the proceeds is

assuming initial free trade (*t _{a}* = 1). To
this change in demand must be added the increase in demand for imports occasioned
by the redistribution of the tariff proceeds, that is,

Tariffs normally improve the terms of
trade.^{11}

The degree to which a tariff will improve the terms of trade depends on the
elasticities. The more elastic the foreign offer curve is, the smaller will
be the improvement in the terms of trade due to a tariff, and, in the limiting
case where the foreign offer curve is perfectly elastic, the terms of trade
remain unchanged (the only exception). On the other hand, if the foreign
offer curve is
elastic,^{l2}
the greater is the compensated elasticity of demand for imports at home,
the more effective will a given tariff be in improving the terms of trade;
in the limiting case where *eta' _{a}* is infinite,
the terms of trade will improve in the same proportion as the (ad valorem)
tariff.

The above propositions are related to the classical notion about the division of the gains from trade between large and small.countries. Because small countries tend to be more completely specialized than large countries, it was generally believed that the offer curve of a small country was less elastic than that of a large country. This means that the gain per unit of trade going to a small country was likely to be larger than that going to a large country. The corollary of the proposition is that since the small country already reaped a large proportion of the gain from trade, opportunities for increasing that gain further through tariff restriction were correspondingly small. On the other hand, large countries, gaining little from trade, could exact a larger gain by imposing tariffs and forcing small countries to trade at a less favorable price ratio.

*The Domestic Price Ratio.* A common motive for trade restriction is
the protection of import-competing industries. In order that these industries
be protected, the domestic relative price of imports (inclusive of the tariff)
must rise. We shall therefore derive the criterion for the change in the
domestic price ratio following a tariff.

The domestic price ratio in country *A* is
*Pt _{a}* (where ta is 1 plus the ad valorem rate
of tariff). We are interested in how

The offer curves of *A* (not drawn) and *B*
(*OB*) intersect at the free-trade equilibrium *Q*. Suppose that
this equilibrium is disturbed by the imposition of a tariff by *A*'s
government. At constant terms of trade the price of *Y* in *A*
rises by the full amount of the tariff *LO/OM* and trade equilibrium
in *A* moves to a point on *A*'s original offer curve, such as
*H*. But when tariff revenues equal (approximately) to *OL* in
terms of *X* are redistributed to consumers the demand for both goods
increases. The equilibrium point for *A* at constant terms of trade
therefore moves to a point such as *J* on *A*'s revenue-redistributed
offer curve. At constant terms of trade the tariff-cum-income subsidy results
in an excess supply of *Y* and a surplus in *A*'s balance of payments
equal to *QW* since the new equilibrium at *J* must be below
*Q* if substitution effects are positive. *A*'s terms of trade
improve until the excess supply *WQ* is relieved. Assume that the new
equilibrium is at *Q'*.

The excess demand for imports in *A* at constant terms
of trade is:

Note that *eta _{a}* refers to the
elasticity of the revenue-redistributed offer curve in

For the domestic price ratio in *A* to be unchanged at
the new equilibrium, as a result of the tariff, the slope of the
*A*-indifference curve at *Q*' must be the same as the slope of
the indifference curves of *A* and *B* at *Q*. But in that
case the marginal propensity to import in *A* is equal to *RQ/TQ*
(for small tariffs): and since

it follows that eta_{b} — m_{a} —
1 = 0. This is the borderline case. It is easily seen that the slope of
*A*'s indifference curve at *Q'* is flatter or steeper than that
at *Q* as m_{a} ^{>}_{<}
eta_{b}— 1.

where *P* and *t _{a}* are initially equal
to 1. Substituting for

A tariff raises the domestic price of imports if the sum of the foreign
elasticity of demand for imports and the domestic marginal propensity to
import is greater than
1.^{13} The
only exception is the case previously mentioned in which the home offer curve
is infinitely elastic, in which case the domestic price ratio remains unchanged.

The criterion can be derived also by following the method of comparative
statics. We consider the excess demand for imports on the assumption that
the domestic price ratio remains unchanged. In that event the terms of trade
improve by the full amount of the tariff, so that the change in supply of
imports from *B* is -
*epsilon _{b}Idt_{a}* =
(1-

The possibility that a tariff may lower the domestic market price of the import good is consistent with the assumption of stability. It means that a tariff may have an adverse protective effect. To protect the domestic industry imports must be subsidized instead of taxed. Under no circumstances, however, would a country ever find it beneficial in fact to subsidize imports to protect the domestic industry. For the adverse protective effect to occur the foreign demand must be inelastic, and in that case a tariff must always result in an improvement in national welfare (more imports are obtained for fewer exports). If an optimum tariff policy is being followed, an additional increase in the tariff always raises the relative price of imports in the tariff-imposing country and thus has a normal protective effect.

*Tariff Changes in Both Countries. *If both countries adjust their tariff
rates simultaneously, the extent and direction of the disequilibrium depend
on the size of the tariff changes and the elasticities of demand. In bilateral
tariff negotiations it may be useful to know what adjustment in the tariffs
of both countries will leave the balance of payments or the terms of trade
unaltered. The answer to this question can readily be obtained from equation
(13), making appropriate adjustments for country *B*. If we write
*pi* as the annual rate of improvement of country *A*'s terms of
trade, *tau _{a}* as the annual change in

To prevent any change in the terms of trade, the numerator must be zero; tariffs must then be changed at a rate inversely proportional to the compensated elasticities of demand for imports. [Note that equation (13) applies with a changed sign to subsidies, as subsidies are simply negative tariffs.]

Suppose the authorities in one country wish to make a grant to another country but, for political or other reasons, want to present the gift in the form of alterations in tariffs. Alternatively, suppose that one country wishes to exact a transfer of real income from another country without imposing a formal tribute. Can this be accomplished efficiently by changes in trade taxes ?

To show that it can, consider first the relation between trade taxes and
subsidies. Suppose that country *A* subsidizes exports (or imports)
while country *B* taxes imports (or exports). In that case the same
goods are being taxed, the only difference being that the customs duties
are collected by officials of different nationality. Trade is subsidized
in *A* and taxed in *B*. If the increase in trade subsidies in
*A* is equal to the increase in trade taxes in *B* this combined
policy is equal to a transfer of income from *A* to *B* equal to
the value of the tax-subsidy payments. Because the tax in *B* cancels
the subsidy in *A*, price ratios in the two countries must be the same.
The change in real income, evaluated at the original price ratio, in each
country is given by

Figure 2-4.

Initial equilibrium is at *Q* on the contract curve
*KK.* Suppose that *A* subsidizes, and *B* taxes, trade at
the same rate *OT/TM*. Then *A*'s and *B*'s offer curves bend
down to *OA' *and *OB'*, respectively, intersecting at *Q'*
(they still originate from *O*). Since the price ratio in *A *remains
equal to the price ratio in *B*, *Q'* must be on the contract curve.
The slope of the indifference curves at *Q' *are, from the transfer
analysis, greater or less than the slope at *Q* depending on whether
the sum of the marginal propensities to import is greater or less than unity.
The terms of trade are now *OQ'*, necessarily worse for *A* if
the system is stable. Real income in *A* falls to the same extent as
if *A* had made a gift of *OT* of *X* to
*B*.

Suppose now that only *B* has a tax (equal to
*OT/TM*) so that trade equilibrium is at *S*. To restore efficiency
(Pareto optimum), *A* can impose a subsidy equal to *B*'s tariff,
attaining the equilibrium (worse for *A*, better for *B*)
*Q'*. A more interesting possibility is for *A* to bribe *B*
to remove the tariff, the value of the bribe being the transfer necessary
to effect an equilibrium between *W* and *L* (better for both than
5). Or if *A* is already receiving gifts from *B* then tariff reduction
in *B* and the elimination of gifts to *A* (i.e., " Trade, not
Aid ") can make both *A* and *B* better off.

But (16) is the same as the criterion for the change in real income after
transfer [equation (6)] if *I dt*, the value of the tax-subsidy receipts,
is substituted for the transfer.

Taxes on commodities, as distinct from taxes on trade, make it necessary to distinguish between consumers' and producers' price ratios. A consumption tax or subsidy creates a divergence between the price ratio facing consumers in the taxing country and all other price ratios, whereas a production tax causes a discrepancy between the price ratio facing producers and all other price ratios.

Eight taxes and subsidies in each country are possible, but of these it will not be necessary to consider more than two. A subsidy is a negative tax, so that we need consider only taxes. And a tax on one good is equivalent to a subsidy on the other good because of our assumptions about the disposal of tax proceeds and the financing of subsidy payments. Because of these assumptions an equal tax on the two goods has no effect on equilibrium; this follows because each tax is combined with an income subsidy, and an income subsidy has the same effect as an equal subsidy (or an equal reduction in taxes) on the two goods. But if an equal tax on the two goods does not affect equilibrium, then neither does a tax on one of the goods combined with the elimination of a subsidy of equal amount on the other good—hence it follows that a tax on one of the goods is equivalent to a subsidy on the other. Thus we need only consider one consumption tax and one production tax.

To find the effects of a consumption tax on the terms of trade first determine
the excess demand caused by the tax at constant terms of trade. Let us suppose
that a tax is imposed by country *A* on the consumption of imported
good *Y*. Then at constant terms of trade the price of *Y* to consumers
in *A* rises by the amount of the tax. Before the redistribution of
the tax proceeds, the change in demand for *Y* in *A*, at constant
terms of trade, is

*eta _{ya}* is the elasticity of demand for

Now the tax proceeds amount to *y _{a}
dt_{cya}*, so that the increase in demand for

where *eta' _{ya}* is the compensated elasticity
of demand for

The compensated elasticity term is positive (it represents the elasticity of a consumption indifference curve), so that a consumption tax on the imported good generally improves the terms of trade of the taxing country. This conclusion is to be expected, because a tax on the imported good diverts demand away from that good, thereby causing an excess world supply of it.

There are some special cases we may consider:

**1.** In the unusual case where *eta' _{ya}* is
zero—implying no substitution in consumption (a kinked consumption
indifference curve at that point)—the terms of trade do not change.

**2.** If the foreign offer curve is perfectly elastic, any excess demand
can be eliminated by shifts in production or consumption at constant cost
in the foreign country so there results no change in the terms of trade.

**3.** If the domestic offer curve is perfectly elastic
(*eta _{a}* is infinite), it is now necessary to know whether
this is due to perfect substitution in production (incomplete specialization
at constant cost) or perfect substitution in consumption; if the former is
the case the denominator of (17) is infinite, so the terms of trade do not
change, but if the goods are perfect substitutes in consumption both the
denominator and the numerator are infinite so that the terms of trade change
by the full amount of the tax.

**4.** If there is no domestic production of the imported good the tax
has the same effect as a tariff (*y _{a} =
Ia and eta'_{ya} =
eta'_{a})*.

This analysis applies also to a subsidy on the consumption of the good that is exported and, with a change of sign, to a subsidy on the imported good or a tax on the exported good.

Does a consumption tax necessarily raise the market price of the taxed good relative to that of the untaxed good ? By analogy to the effect of a tariff on the domestic price ratio we should not expect this to be so. The market (relative) price of importables is PtCyaS which we assume to be initially unity. The change in this price ratio due to the consumption tax is

where *epsilon' _{ya}*

To find the effects of a production tax on the terms of trade, first consider the excess demand caused by the production tax at constant terms of trade. If a tax on the production of the import good is imposed and the proceeds of the tax are redistributed to producers, there remains only a pure substitution effect, a movement along the production-possibility curve. At constant terms of trade (which is also the price ratio facing domestic consumers) the excess demand for imPorts. after the redistribution of the proceeds, is equal to

where *t _{pya}* is equal to unity plus the tax
and eya is the elasticity of the transformation curve. This excess demand
must be eliminated by a worsening of

With increasing opportunity costs eya is always positive, so the terms of trade of the taxing country fall. Again this applies to a production subsidy on the exported good and, with a change of sign, to a production subsidy on the imported good and a production tax on exported goods. This conforms to common sense. A tax on the production of any good decreases the production of that good and increases the production of the other good, causing a rise in the relative world price of the taxed good.

The price ratio facing producers is
*P/t _{pya}*,which is initially taken to be 1.
This will change as a result of a tax depending on the sign of

The analogy to equations (14) and (18) readily presents
itself.^{l6}

A tariff, at constant terms of trade, raises the price of imports to both
consumers and producers in the taxing country by the full amount of the tariff.
Any other system of taxes which does the same thing will have the same effect
on the terms of trade as a tariff. Thus taxes on trade can be duplicated
by taxes on commodities. We can establish these relations either by showing
that the tax combination affects the price ratios facing consumers and producers
in the same way as a trade tax, or by adding the effects of the criteria
obtained above in each case. By either method it is readily shown that a
tariff (on *Y*) or an export tax (on *X*) is equivalent in real
terms to:

**(a) **A consumption tax on *Y* plus a production subsidy on
*Y*,

**(b) **A consumption tax on *Y* plus a production tax on *X*,

**(c) **A consumption subsidy on *X* plus a production subsidy on
*Y*, and

**(d)** A consumption subsidy on *X* plus a production tax on
*X*.

And because trade subsidies are negative trade taxes, an export subsidy (on
*X*) or an import subsidy (on *Y*) can be duplicated by:

**(e)** A consumption subsidy on *Y* plus a production tax on
*Y*,

**(f)** A consumption subsidy on *Y* plus a production subsidy on
*X*,

**(g)** A consumption tax on *X* plus a production tax on *Y*,
and

**(h) **A consumption tax on *X* plus a production subsidy on
*X*.

From these relations it follows that (1) the effects of devaluation can be duplicated or frustrated by changes in commodity taxes and subsidies (since devaluation is equivalent to an import tariff plus an export subsidy), (2) the optimum tariff can be duplicated by commodity taxes, and (3) income transfers can be duplicated by changes in commodity taxes in both countries. An additional application is to customs unions; an agreement over tariff reduction has little force if it is not combined with agreement over the domestic tax structures.

Consideration of the commodity-tax structure is necessary before evaluating
the desirability of tariff reductions. If there are commodity taxes and subsidies
in each country none of the well-known welfare propositions of international
trade theory holds. In particular, from a free-trade (that is, no
*trade* taxes) position, it can be shown that, if there are commodity
taxes and subsidies: (1) both countries simultaneously may be better off
without, than with, trade; (2) a country may gain by a deterioration in its
terms of trade even if the initiating cause occurs in the foreign country;
(3) a small tariff may worsen the welfare of the tariff-imposing country
even if the foreign offer curve is not infinitely elastic; and (4) the imposition
of a tariff may simultaneously improve the welfare of both countries. These
propositions follow because commodity taxes overextend or underextend trade.

Thus far we have dealt with the effect of policy changes on the terms of trade, the latter adjusting through price-level or exchange-rate variations. It was argued earlier that authorities may adopt other policies that prevent, or render unnecessary, changes in the terms of trade. This would be the case if authorities pegged the exchange rate and stabilized domestic price levels, relying on, say, trade controls to correct disequilibria. The purpose of this section, then, is to show how the results already obtained can be applied to other mechanisms of adjustment. The procedure to be followed is the same as before: First, state the postulate on which dynamic behavior is based, then deduce the condition of dynamic stability, and then examine the excess demands caused by the policy changes.

Suppose that authorities peg the exchange rate and stabilize the domestic price level in each country. The price level may be stabilized in a variety of ways but the simplest for our purpose is to suppose that authorities inflate domestic expenditure by means of a budget deficit when there is deflationary pressure (excess supply of its export good) and deflate domestic expenditure by means of a budget surplus when there is inflationary pressure (excess demand for its export good). We may assume that the deficits and surpluses are financed and disposed of by drawing on or accumulating credits with an international agency—say, the International Monetary Fund (IMF). Since

Let equilibrium be initially at *Q* with the government
of *A* making the annual payment *OH* to the government of
*B*. It is assumed that exchange rates are fixed and that each government,
by means of fiscal policy, stabilizes export price levels.

Suppose that the equilibrium is disturbed by, say, a private
flow of capital of *HL* from *B* to *A*, and that this induces
an excess of saving over investment in *B*, and an excess of investment
over saving in *A*, equal to the transfer. If the sum of the marginal
propensities to import is less than unity, as in the diagram, the Engel curve
of *A* (*AA*) must be flatter than the Engel curve of *B*
(*BB*); the capital flow therefore induces an excess demand for
*A*'s good and an excess supply of *B*'s good, and a surplus in
*A*'s and a deficit in *B*'s balance of payments.

To correct the disequilibrium, *A*'s government deflates
expenditure by means of a budget surplus and turns the proceeds over to the
IMF; and *B*'s government inflates expenditure by means of a budget
deficit borrowing from the IMF. This process continues until the inflationary
pressure in *A* and the deflationary pressure in *B *are eliminated,
i.e until the equilibrium *Q* and the net lending position *OH*
are restored. By similar analysis st can be shown that a movement of capital
from *A* to *B* in excess of *OH* (say to *OK*) will
cause deflationary pressure in *A* and inflationary pressure in
*B*, necessitating government action in each country to eliminate the
disequilibrium. In either case the equilibrium *Q* is stable.

If, on the other hand, the sum of the marginal propensities
to import exceeds unity the dynamic system just described would be unstable.
This may be seen by considering again a movement of capital from *B*
to *A* of *HL*. This time the capital movement causes an excess
supply of *A*'s good and an excess demand for *B*'s good. A's
government therefore inflates expenditure and *B*'s government deflates
expenditure, moving the system ever further from equilibrium.

an excess supply of one country's good implies an excess demand for the other country's good, it follows that one country will be borrowing at the time another country is lending; and because of the identity of income (including loans) and expenditure, the rate of lending by one country is equal to the rate of borrowing in the other country, and both are equal (with appropriate signs) to the rate at which the budgets are out of balance.

Whether or not a system based on these rules is stable depends on the
effectiveness of the deflation-inflation policy in relieving excess demand
for the deflating country's good and excess supply of the inflating country's
good. But it is easily seen that this is equivalent to whether a transfer
from one country to another will cause an excess supply of the transferring
country's good. The system is therefore stable or unstable depending on whether
the sum of the marginal propensities to import is less than or greater than
1. The term 1 - *m _{a}* -

To determine the effects of policy changes on lending in a system obeying
the above rules, we (as before) find the excess demand due to the policy
change with no lending. For example, the excess demand for imports due to
a tariff in country *A* is -
*eta' _{a}Idt_{a}* . The
change in the trade balance and lending of country

If the system is stable the tariff improves the trade
balance.^{l7}
Or we may consider the change in lending and the trade balance due
to an increase in productivity in, say, country B:

Assuming stability, country A must lend to country *B* to maintain
equilibrium in the balance of payments.

In a similar fashion we can find the effects on lending of all the policies discussed in previous sections. It may be helpful to consider two cases. Suppose that country A devalues its currency. Applying the same method we find that the criterion for the change in the balance of trade and lending is

It should be noticed that (23) is the reciprocal of (3), the criterion for
the change in the terms of trade after transfer. The interpretation is different.
In (3) the stability condition is that the sum of the elasticities is greater
than 1, whereas in (23) the stability condition is that the sum of the marginal
propensities to import is less than 1. In (3) lending induces—because
of the "rules of the gold standard (or flexible-exchange-rate) game"—a
change in the terms of trade; in (23) devaluation induces—because of
the "rules of the IMF game"—a change in the balance of trade and lending.
An interesting result is the following: If the "IMF system" is unstable,
the gold standard (or flexible exchange) system is stable; and if the gold
standard (or flexible exchange) system is unstable, the IMF system is stable.
*Instability* of one system therefore implies *stability* of the
other system, although not vice versa. This relation holds because the sum
of the marginal propensities to import is less than the sum of the elasticities
of demand for imports.

Finally, consider a trivial case. A change in capital exports has no ultimate effect on net lending! In the IMF system there is only one equilibrium rate of lending (in the absence of other trade policy changes), just as, in the classical system, there is only one equilibrium value of the terms of trade (assuming that the equilibrium is unique). This trivial case is cited for purposes of comparison with the classical contention that devaluation, from a position of equilibrium, does not change the terms of trade or the balance of trade; instead, it initiates price level changes which restore the equilibrium terms of trade. A displacement of the variable of adjustment from equilibrium initiates dynamic forces which induce a return to equilibrium.

Similar analysis can be applied to systems of adjustment based on tariff tax, or productivity changes.

The results of the preceding analysis may all be summarized by introducing all policy parameters into the balance-of-payments equation and differentiating. We obtain

where the same terminology is used as before except that effective tax rates
are used. (Thus *dt _{a}*

The policy equation (24) shows the relation between policy changes that are
necessary to maintain equilibrium in the system; it can be used to show the
policy changes that are necessary to offset the disequilibrium caused by
other policies. Suppose, for example, country *A* wishes to know the
rate at which it must tax import goods to relieve a disequilibrium caused
by an increase in productivity in the foreign country. To find the answer,
set all policy changes except *dt _{ca }*and

The productivity change in *B* causes a surplus in *A*'s balance
that can be relieved by a reduction in the rate at which consumption of import
goods (export goods) are taxed (subsidized) in *A*. Any other relation
between two or more policy changes can in this way be determined.

l Adapted from: *Amer. Econ. Rev.*, 50, 68-110 (March
1960).

2 The conventions in the literature usually ignore the problems associated with interest payments, despite the fact that, from a conceptual standpoint, they involve wealth effects that cannot be legitimately ignored. For this reason it is perhaps preferable to restrict the applicability of the model to remittances of interest or gifts.

4 To obtain the criterion directly, differentiate the balance-of-payments equation:

Then by forming elasticities and taking *P* initially
equal to unity, we get (3)

For a sample of recent literature on the transfer problem see Mosak ([68] Chap. 4), Meade[54], [57] Samuelson [90], and Johnson [32]; and for a survey of earlier literature see Viner ([103], pp. 290-377).

5 Leontief [40] discovered an example consistent with convex
indifference curves, where the change in the terms of trade in favor of the
paying country is so great that its real income improves as a result of the
transfer. Equation (6) proves that this cannot happen unless the system is
unstable. The identification of this *Leontief effect *with instability
was first made by Samuelson ([88], p. 29).

6 Transfer analysis has many applications in economic theory. It applies to any redistribution of income between sectors, individuals, or groups within a country. In the Keynesian problem of income redistribution a gift of tax-cum-subsidy from the rich to the poor increases or decreases effective demand depending on whether the marginal propensity to spend (MPS) of the rich is less or greater than that of the poor. In public finance theory an increase in government spending financed by new taxes stimulates effective demand if the MPS of the government is greater than that of the public. And in monetary theory a fall in the price level stimulates effective demand if the MPS of creditors is greater than that of debtors (including governments and central banks)

Expenditure in *B* is constant (in terms of *B*'s good), so
*dD _{b }/ dX_{a}* = 0*;
but expenditure in

8 This relationship can be derived from the income=expenditure
conditions discussed in Chapter 1. With no international lending, we have,
for country *B*,

Note that when the elasticity of demand is 1, the elasticity of supply of exports is zero; this means that the same amount of exports is spent on imports regardless of the terms of trade.

A geometric proof of this relation can easily be got from Marshall's analysis ([52], pp. 337-338).

9 Mill was aware ([66], pp. 150 -53) that an increase in productivity would lower the commodity terms of trade and even the factoral terms of trade if foreign demand, in the latter case, were inelastic. Edgeworth interpreted ([12], p. 10) Mill's passage as indicating that a country could be "damnified" by growth, supplying the necessary assumption to make Mill's analysis correct. The first derivations of the criteria (8) and (12) were achieved by Meade ([57], e.g., p. 153). Their importance has been brought out by Bhagwati [5], who used the term " immiserizing growth," by Corden [8], and by Johnson [29] [30].

10 Marshall writes ([51], pp. 180 -81): "The considerations which can be urged for and against the levying of an import tax on a particular commodity differ widely from those appropriate to a particular export tax: and this is perhaps the origin of an opinion, which seems to pervade a good deal of economic discussion, that a general tax on all imports would have widely different effects from a general tax on all exports. In fact the two taxes would have the same effect: provided they were evenly distributed, equal in aggregate amount, and their proceeds were expended in the same way." He then shows how this can be proved. Bastable, Edgeworth, and others were also aware of the symmetry. For a modern treatment see Lerner [44].

11 To derive (13) directly differentiate

since *dD _{a} / dt_{a} =
I*; that is, expenditure in

The qualitative direction of change in the terms of trade following the imposition of a tariff was admitted by Ricardo and known to most of the later classical economists. The algebraic criterion can be got from Meade's analysis [57].

12 Note that if the foreign offer curve is inelastic, the terms of trade may improve by more than the tariff, provided the home offer curve is not perfectly elastic; if the latter is perfectly elastic the maximum change in the terms of trade is equal to the rate of the tariff.

13 The classical economists, many of whom tried to determine whether a country gained more or less than the amount of the tax, generally employed the criterion 719 S I, assuming, implicitly or explicitly, that the tax proceeds were spent on domestic goods, or that the tax was on the transit of goods that would be reexported. Modern discussions of this point owe much to Lerner [44] and to Metzler [63].

14 The elasticity of demand for an imported good is never
larger than the elasticity of demand for imports of that good. The exact
relation can be derived from the definition of the demand for imports. From
*I _{a} = y_{a}
-Y_{a}* we get, by differentiation,

whence

where *epsilon _{ya}* is the elasticity of supply
of

15 The compensated elasticity of supply deserves some explanation. From the two relations:

It can now be shown that *eta _{ya} -
m_{a} = eta'_{ya}*, the
compensated elasticity of demand for

*dI _{a} = (dI_{a})' -
m_{a}I_{a} dP;
dy_{a} = (dy_{a})' -
m_{a}y_{a} dP*;

(*dI _{a})' -
m_{a}I_{a} dP =
(dy_{a})'-
m_{a}Y_{a} dP - [(d
Y_{a}) + m_{a}
Y_{a} dP]*.

The income effects on the two sides cancel and the proof of the relation
between compensated elasticities follows readily. Dividing by
*I _{a} dP*, multiplying by

where the primes denote that the elasticities contain no income effects. (For the interpretation given in this paragraph I am indebted to A. Harberger, a referee of my original AER article, unknown to me at the time.

These elasticities have a simple interpretation: *eta' _{a
}*iS the elasticity of a trade-indifference curve,

*eta' _{ya }*is the elasticity of a
consumption-indifference curve; and

Criterion (17) can be derived directly by differentiating:

l6 Criterion (19) can be derived directly by differentiating:

The effects of consumption and production taxes on the terms of trade had not been formally analyzed in the literature before the article from which this paper is adapted appeared, although the general direction of their influence was known to many classical writers. See, for example, Viner ([103], p. 363).

17 This criterion has been used by Meade ([14], p. 155) and derived geometrically by Ozga [22], although in neither case is a distinction made between stable and unstable situations.

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Economic Studies, *25 (June 1958).

[8]* *M. CORDEN, "Economic Expansion and International Trade: A Geometric
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[12] F. Y. EDGEWORTH, *Papers Relating to Political Economy, Vol. *2.
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[29] H. G. JOHNSON, "Increasing Productivity, Income-Price Trends and the
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[32] H. G. JOHNSON, "The Transfer Problem and Exchange Stability," *Jour.
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[40] C. P. KINDLEBERGER, *International Economics. *Homewood, III.:
Irwin, 1958.

[44] A. P. LERNER, "The Symmetry between Import and Export Taxes,"
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[51] A. MARSHALL, *Money Credit and Commerce. *London: Macmillan,
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[52] A. MARSHALL, *The Pure Theory of Foreign Trade. *London: 1879;
reprinted 1930.

[54] J. E. MEADE, "A Geometrical Representation of Balance-of-Payments Policy,"
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[63] L. A. METZLER, "Tariffs, the Terms of Trade, and the Distribution of
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[66] J. S. MILL, *Principles of Political Economy, Vol. *2. New York:
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[68] J. L. MOSAK, *General Equilibrium Theory in International Trade.
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[88] P. A. SAMUELSON, "The Stability of Equilibrium: Comparative Statics
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© Copyright Robert A. Mundell, 1968