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International Economics, Robert A. Mundell, New York: Macmillan, 1968, pp. 17 - 42.
Transfers, Productivity, and Taxes
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 ma 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 cb 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, -dDa = dDb = 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 cb + mb = 1 = ca + ma.3 We could make use of this result to translate the above expression into a number of equivalent forms. the most convenient for our purposes is the familiar one,
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 - ma - mb = 0) will no change in the terms of trade be required. If ma + mb > 1, the receiving country experiences a deficit; if ma + mb < 1 the paying country suffers a deficit.
To correct the disequilibrium, equal to (1- ma - mb) dT, a change in the terms of trade is required. But we already know from the stability condition that a change in the terms of trade causes an excess supply of B's good (or an excess demand for A's good, or improves A's balance, or worsens B's balance) by an amount equal to
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 Ua and Ub are, respectively, the real incomes of A and B. Substituting for dP/dT from (3) we obtain an approximate quantitative measure of the change in the real income evaluated at pretransfer prices
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 ma and mb (the marginal propensities to import) are, the smaller is the increase in real income of the receiving country, since income effects enter only in the denominator of (6).6
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 dXa*, then the change in demand for imports in country A is
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 (ma = I - ca = 0).7
Equation (7) can be translated into proportional changes by multiplying both sides by X (output) and dividing by P, with the following result:
where sigmaa 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 Pa is the rate of growth of domestic product in A.
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 sigmab and rhob are, respectively, the income elasticity of demand for imports in B and the rate of growth of output in 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 dXa* and applying equation (7) we obtain the following criterion:
Real income will be increased by growth provided etaa + etab > 0 + ma, 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, etaa = eta'a + ma Manipulating (11) we get
Thus real income will increase in the growing country if , eta'a > 1 - etab that is, if the compensated elasticity of demand for imports in the growing country is
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 ma = RW/VS. Now the deficit in A's balance of payments at constant terms of trade is:
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): etab - 1 = epsilonb. 8 The criterion can thus be expressed as . .
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, - etaa'IdP, which measures the increase in demand for imports in A. On the other hand, the increase in supply of imports forthcoming from B due to the change in the terms of trade is epsilonbIdP. The excess demand at constant real income in A is thus -(eta'a + epsilonb)IdP. The deterioration in A's terms of trade that leaves A's real income unchanged is therefore too great or too little to relieve the excess demand due to the productivity change depending on whether eta'a + epsilonb>< 0. The criterion for the change in real income is thus established, since, depending on whether the terms-of-trade change has been too great or too little, real income increases or decreases.
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 pushes 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 ta 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 (ta = 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, maIa dta. Adding the terms we get the excess demand for imports due to the tariff at constant terms of trade, that is, (-etaa + ma)Idta = -eta'aI dta. This excess demand must be eliminated, at the new equilibrium, by a change in the terms of trade. We then have the following criterion:
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 Pta (where ta is 1 plus the ad valorem rate of tariff). We are interested in how Pta will change as a result of an increase in tn. that is, in the sign of
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 etaa refers to the elasticity of the revenue-redistributed offer curve in A.
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 etab ma 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 ma >< etab 1.
where P and ta are initially equal to 1. Substituting for dP/dta, from equation (13), we obtain
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 - epsilonbIdta = (1- etab)Idta. On the other hand, the redistribution of the tariff proceeds and the resulting increase in domestic expenditure in A increases the demand for imports by maIdta. Subtracting the change in supply of imports from B from the increase in demand for imports in A we get the excess demand for imports at constant domestic prices, that is, (etab + ma1)Idta. If the foreign demand is less than unit elastic (foreign supply elasticity is negative), an improvement in A's terms of trade results in an increase in supply of imports from B; but against this must be set the increased demand for imports in A resulting from the spending of the tariff proceeds. If the former effect is greater than the latter, the relative price of imports must fall. If, for example, the foreign elasticity of supply were - 0.6 (implying an elasticity of demand equal to 0.4) while the domestic marginal propensity to import were 0.5, the tariff would cause, at constant domestic prices, an excess supply of B's good equal to 0.1Idta; to eliminate this excess supply of B's good, the relative (tariff-inclusive) price of imports must fall, and the terms of trade must improve by more than the tariff.
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, taua as the annual change in A's tariff, and taub as the annual change in B's tariff, we can obtain the following criterion:
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
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 goodhence 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
etaya is the elasticity of demand for Y in A.14 (P and tcya are both initially taken to be 1.)
Now the tax proceeds amount to ya dtcya, so that the increase in demand for y due to their disposition is maya dtcya. Adding the two effects we get the excess demand at constant terms of trade,
where eta'ya is the compensated elasticity of demand for y in A, that is, the elasticity of demand for Y after consumers have been compensated for the change in real income implicit within the price change. This gives us the following criterion:
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 zeroimplying 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 (etaa 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 (ya = 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 is the compensated elasticity of supply of Y in A, and represents the elasticity of the production transformation curves.15 Only by this term does the last criterion in (18) differ from the criterion for a change in the domestic price ratio after the imposition of a tariff [see equation (14)]. If a tariff will raise the domestic relative price of imports, so will a consumption tax on the import good. The converse is not true. Even if the foreign offer curve is inelastic and the domestic marginal propensity to import is low, high substitution effects in production will be sufficient to ensure a rise in the tax-inclusive price of importables.
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 tpya 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 A's terms of trade. The criterion is, therefore,
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/tpya,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 agencysay, 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 - ma - mb also gives the denominator of the criterion, showing the direction and amount of lending required to eliminate a given excess demand.
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'aIdta . The change in the trade balance and lending of country A is, therefore,
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 inducesbecause of the "rules of the gold standard (or flexible-exchange-rate) game"a change in the terms of trade; in (23) devaluation inducesbecause 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 dta and dtb refer to the effective rate at which trade taxes are changed in A and B; changes in trade subsidies are subtracted from changes in trade taxes. Similarly, dtca and dtcb represent the effective rate at which consumption taxes or subsidies are changed in A and B; a tax on the consumption of import goods combined with an equal tax on the consumption of home goods would leave the effective rate unchanged. Similarly, for production taxes dtpa and dtpb.)
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 dtca and dXb* equal to zero. This leaves the equation
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 ( Chap. 4), Meade,  Samuelson , and Johnson ; and for a survey of earlier literature see Viner (, pp. 290-377).
5 Leontief  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 (, 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 dDb / dXa* = 0; but expenditure in A increases pari passu with output, that is, dDa / dXa* = 1. Then, forming elasticities from the terms of the left, we get equation (7).
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 (, pp. 337-338).
9 Mill was aware (, 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 (, 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 (, e.g., p. 153). Their importance has been brought out by Bhagwati , who used the term " immiserizing growth," by Corden , and by Johnson  .
10 Marshall writes (, 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 .
11 To derive (13) directly differentiate
since dDa / dta = I; that is, expenditure in A rises by the value of the tariff proceeds.
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 .
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  and to Metzler .
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 Ia = ya -Ya we get, by differentiation,
where epsilonya is the elasticity of supply of Y in A. (A similar result holds for country B.) The elasticities etaya and etaa coincide only when there is no home production of the imported good .
15 The compensated elasticity of supply deserves some explanation. From the two relations:
It can now be shown that etaya - ma = eta'ya, the compensated elasticity of demand for Y in A; and that epsilonya + ma = epsilon'ya the compensated elasticity of supply of Y in A. We have dIa = dyadYa,from the definition of the demand for imports. Now dIa contains an income effect equal to - maIa dP, where - Ia dP measures the change in real income of country A looked at as a whole. The term dya contains an income effect equal to - maya dp where -ya dP measures the change in real income of people of country A looked at in their role as consumers alone. Finally, the term d Ya contains an income effect equal to ma Ya dP, where Ya dP measures the change in real income of producers of Y in country A. We now have the following relations:
dIa = (dIa)' - maIa dP; dya = (dya)' - maya dP; d Ya = (d Ya)' + ma Ya dP where the primes denote pure substitution effects. Substituting in dIa = dyad Ya we
(dIa)' - maIa dP = (dya)'- maYa dP - [(d Ya) + ma Ya dP].
The income effects on the two sides cancel and the proof of the relation between compensated elasticities follows readily. Dividing by Ia dP, multiplying by P, and changing signs we obtain
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 epsilon'ya is the elasticity of a production-indifference (production-possibility) curve. The identification is formally valid for small changes only.
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 (, p. 363).
17 This criterion has been used by Meade (, p. 155) and derived geometrically by Ozga , although in neither case is a distinction made between stable and unstable situations.
 J. BHAGWATI, "Immiserizing Growth: a Geometrical Note," Review of Economic Studies, 25 (June 1958).
 M. CORDEN, "Economic Expansion and International Trade: A Geometric Approach," Oxford Economic Papers, N.S. 8 (June 1956).
 F. Y. EDGEWORTH, Papers Relating to Political Economy, Vol. 2. London: Macmillan, 1925.
 W. J. FELLNER et al., Maintaining and Restoring Balance in International Payments. Princeton, N.J.: Princeton University Press, 1966.
 S. E. HARRIS, Interregional and International Economics. New York: McGraw-Hill, 1957.
 H. G. JOHNSON, "Increasing Productivity, Income-Price Trends and the Trade Balance," Econ. Jour., 64, 462-485 (Sept. 1954).
 H . G . JOHNSON, " Economic Expansion and International Trade," Manchester School Econ. Soc. Stud., 23, 95-112 (May 1955).
 H. G. JOHNSON, "The Transfer Problem and Exchange Stability," Jour. Pol. Econ., 64, 212-225 (June 1956).
 C. P. KINDLEBERGER, International Economics. Homewood, III.: Irwin, 1958.
 A. P. LERNER, "The Symmetry between Import and Export Taxes," Economica, 3, 308-313 (Aug. 1936).
 A. MARSHALL, Money Credit and Commerce. London: Macmillan, 1923.
 A. MARSHALL, The Pure Theory of Foreign Trade. London: 1879; reprinted 1930.
 J. E. MEADE, "A Geometrical Representation of Balance-of-Payments Policy," Economica, 16, 305-320 (Nov. 1949).
 J. E. MEADE, The Balance of Payments Mathematical Supplement. Lon don: Oxford University Press, 1951.
 L. A. METZLER, "Tariffs, the Terms of Trade, and the Distribution of National Income," Jour. Pol. Econ., 57, 1-29 (Feb. 1949).
 J. S. MILL, Principles of Political Economy, Vol. 2. New York: 1894.
 J. L. MOSAK, General Equilibrium Theory in International Trade. Bloomington: Indiana University Press, 1944.
 P. A. SAMUELSON, "The Stability of Equilibrium: Comparative Statics and Dynamics," Econometrica, 9, 97-120 (April 1941).
 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).
 J. VINER, Studies in the Theory of International Trade. New York: Harper & Row, 1937.