Exchange Depreciation, Financial Policy, and the Domestic Price Level

THE PRESENT PAPER constitutes the first part of a study designed to show the order of magnitude of the increases in domestic prices that will result, on specified assumptions regarding the relevant foreign trade elasticities and propensities, from exchange depreciation accompanied by appropriate financial policies. Exchange devaluation may be used to improve the balance of payments or to permit a relaxation of import restrictions. Only the former use is considered here, the latter being reserved for consideration in a later paper. It is assumed here that exchange depreciation is accompanied by a financial policy that leaves unchanged the level of aggregate employment. For the type of depreciation examined, such a policy is taken to be compatible with the maintenance of stability in the prices of home trade goods, although the prices of import and export goods will rise.

Abstract

THE PRESENT PAPER constitutes the first part of a study designed to show the order of magnitude of the increases in domestic prices that will result, on specified assumptions regarding the relevant foreign trade elasticities and propensities, from exchange depreciation accompanied by appropriate financial policies. Exchange devaluation may be used to improve the balance of payments or to permit a relaxation of import restrictions. Only the former use is considered here, the latter being reserved for consideration in a later paper. It is assumed here that exchange depreciation is accompanied by a financial policy that leaves unchanged the level of aggregate employment. For the type of depreciation examined, such a policy is taken to be compatible with the maintenance of stability in the prices of home trade goods, although the prices of import and export goods will rise.

THE PRESENT PAPER constitutes the first part of a study designed to show the order of magnitude of the increases in domestic prices that will result, on specified assumptions regarding the relevant foreign trade elasticities and propensities, from exchange depreciation accompanied by appropriate financial policies. Exchange devaluation may be used to improve the balance of payments or to permit a relaxation of import restrictions. Only the former use is considered here, the latter being reserved for consideration in a later paper. It is assumed here that exchange depreciation is accompanied by a financial policy that leaves unchanged the level of aggregate employment. For the type of depreciation examined, such a policy is taken to be compatible with the maintenance of stability in the prices of home trade goods, although the prices of import and export goods will rise.

Several hypothetical cases are defined by assigning sets of numerical values to the relevant coefficients (Table 1); and illustrations are given of the price effects that will result in these cases from (1) an exchange depreciation of 10 per cent and (2) a depreciation leading to an improvement in the balance of trade equivalent to 5 per cent of national output (Table 2). For some of these cases, the extent to which the price level may be expected to rise after adjustments have been made to indirect taxes for the purpose of restoring budgetary equilibrium is indicated (Table 8). Finally, the effect on the price level of a defined tendency for wage rates to rise in response to, though to lesser extent than, increases in the cost of living is illustrated (Table 9). In general, it appears that, if an appropriate financial policy is pursued, and if a wage-price spiral can be prevented, price increases are likely to be fairly moderate relative to the improvement achieved in the balance of trade, although considerable differences exist in this respect between different cases.

Table 1.

Numerical Values Assigned to Parameters in Various Cases

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Table 2.

Effects of Simple Exchange Depreciation on Prices andthe Balance of Trade ofthe Depreciating Country

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Table 3.

Appropriate Changes in Value of Output and in Domestic Expenditure Associated with Exchange Depreciation

(Expressed in percentage of the value of output)

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Table 4.

Curtailment of Domestic Expenditure (Net of Tax) to Be Brought About by Official Policy

(In per cent of value of output at factor cost; t = 1.5)

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Table 5.

Curtailment of Various Classes of Domestic Expenditure (Net of Tax) to Be Brought About by Official Policy

(In per cent of value of output at factor cost)

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Table 6.

Weighted Mean(3ΔO+ΔS)4)of the Appropriate Changes in Value of Output and in Domestic Expenditure Associated with Exchange Depreciation

(Expressed in per cent of value of output; t = 1.5)

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Table 7.

Percentage Reduction in Money Supply Required on Certain Assumptions

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Table 8.

Additional Tax Revenue Required, in Per Cent of Domestic Expenditure (∆Tr), and Percentage Rise in Cost of Absorption (∆P), Associatedwith Exchange Depreciation When Half the Additional Tax Revenue Is Raised by Taxation on Domestic Expenditure

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Table 9.

Effect of Exchange Depreciation onthe Cost of Absorption Before and After Allowance for Wage Reactions

(z = 0.5)

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Consideration is also given to the magnitude of the disinflationary effort that will be required to implement the financial policy defined as appropriate. It is shown that domestic expenditure will usually, though not always, have to be reduced below its initial level (Table 3), and that in all cases official action tending to curtail expenditure by substantial amounts will be necessary (Table 4). It is argued that only a relatively minor part of this curtailment should fall on public and private consumption (Table 5); most of it should fall on public and private investment. A broad indication—on very uncertain assumptions—of the very considerable extent to which the money supply might have to be reduced is given for certain cases (Table 7).

Nature of the Problem and Assumptions

Countries with overvalued currencies are sometimes deterred from making appropriate adjustments of their exchange rates by the fear that depreciation might necessitate a substantial increase in prices on the domestic market, and that this, in turn, through its reaction on the cost of living, might provoke an upward spiral of wages and prices. The object of this paper is to inquire how far, on various assumptions, such fears may be justified. However, in order to treat the question fruitfully, it is necessary to give it a somewhat circumscribed interpretation. Undoubtedly, if exchange depreciation is not accompanied by appropriate financial policies, or if money wages move in a rigid proportion to the cost of living, domestic prices may in some cases rise pari passu with the domestic prices of foreign currencies, thereby stultifying the depreciation as a means of improving the balance of payments. But it is as unlikely as it is undesirable that the monetary authorities of the devaluing country should remain passive in the face of the monetary and financial consequences of depreciation, and it would be tedious to examine the effects of depreciation under all the conceivable permutations and combinations of domestic policy. Moreover, the price effects arising out of the existence of a link between money wages and the cost of living are dependent on the price effects that would emerge in the absence of this link; they are more conveniently discussed at a later stage in the argument. What will be attempted here, therefore, is to indicate (1) the price effects that may be expected, in the absence of a link between wages and the cost of living, if appropriate financial policies are pursued, (2) the nature and scope of the policies that may be required, and (3) additional complications introduced by any dependence of wages on the cost of living.

The answer to (1) will be affected crucially by the degree of flexibility displayed by wages (and other factor prices) in response to changes in demand and supply. If wages were sufficiently flexible, a proper financial policy might be one that maintained the stability of the domestic price level by bringing about such adjustment in the prices of domestic factors and products as might be required to offset the price changes directly associated with the devaluation, i.e., those affecting import and export goods. In this case, of course, the effect of the devaluation on the general level of prices would, by definition, be nil, and only part (2) of our inquiry would be significant. A still higher degree of factor price flexibility would, of course, do away with the need for an exchange rate adjustment; any necessary alignment of domestic and foreign cost and income levels could then be brought about exclusively through financial policy acting on the domestic price level.

In reality, wages usually show considerable flexibility in an upward direction and some flexibility in a downward direction. Under normal circumstances, in most countries, however, they are too “sticky” to permit a reduction of any size to be brought about through demand pressure without a disproportionate sacrifice of employment and output. It is true that if, prior to an exchange depreciation, prices have been rising fairly rapidly and wages lagging behind, so that profit margins are abnormally high, it may often be possible, by curtailing monetary demand, to slow down or arrest the inflation and to prevent wages—and, even more so, domestic product prices—from rising as much as they would otherwise have done, and that this can be done without giving rise, in the process, to any excessive amount of unemployment. But it is probably illogical to assume both that a financial policy of this sort would not be applied in the absence of devaluation and that it would be applied after a devaluation. It would therefore appear prudent to assume that, while the wages of any sector of the labor force for which there is an increasing demand are likely to rise, the wages of any sector of the labor force for which there is a declining demand are for practical purposes rigid, save where a substantial increase in unemployment is allowed to emerge.

A proper financial policy is conceived, in general terms, as one that allows no substantial increase in unemployment and, subject to this, prevents any unnecessary increase in prices. That is to say, the level of domestic demand will be kept as low as is compatible with an avoidance of substantial unemployment in those sectors of industry which are disfavored by depreciation, after account is taken of the transfer of labor to sectors favored by depreciation. The wider the range of industries relatively disfavored by demand, the smaller will be the increase in aggregate money demand for the country’s products that will be necessary to prevent an increase in unemployment. Since, in this paper, the relatively disfavored sectors usually constitute a much larger proportion of total output than the relatively favored sectors, the assumption is made that a proper financial policy involves the avoidance of any increase in unemployment as a result of depreciation.

The type of exchange depreciation considered in the present paper is one that is not accompanied by any changes in the ad valorem level of import duties or in the severity1 of import restrictions. Also, only uniform exchange rates are considered.

An attempt is made to calculate the magnitude of the effects on prices that would be expected from the type of depreciation which is being examined, under various assumptions as to the magnitude of certain basic parameters, viz., (1) the proportionate importance in the economy of sectors of output and demand that are particularly involved in foreign trade, (2) the elasticities of demand and supply for foreign trade goods with respect to (a) prices and (b) aggregate domestic expenditure.

For convenience, it is assumed that in the devaluing country—which we may term Country A—three clearly demarcated types of goods exist: export goods, import goods, and home trade goods. Export goods consist of goods actually exported (in volume qx1) and of similar goods absorbed in A (qx2). Import goods consist of goods actually imported (qm1) and import-competing goods produced in A (qm2). All export goods, whether consumed abroad or at home, have the same price in A (px); so have all import goods, whether produced abroad or at home (pm); and so have all home trade goods (ph).

The volume of A’s exports is equal to A’s output, less absorption, of export goods. The former is regarded as depending on the price of export goods relative to that of home trade goods in A; the latter, as depending both on this price ratio and on the level of aggregate domestic expenditure (S) deflated by the price of home trade goods in A. (Note that domestic expenditure is defined to include expenditure on imports and to exclude export receipts.)

Thus the volume of A’s exports is taken as dependent on the price ratio and on deflated home expenditure. Similarly, the volume of A’s imports is taken as dependent on the price of imports, relative to that of home trade goods, and on home expenditure, deflated by the price of home trade goods. These relationships give rise to four of the parameters used in this study: єa, the elasticity of A’s net supply of export goods with respect to the export price ratio; λx, the elasticity of A’s demand for export goods with respect to deflated home expenditure; ηa the elasticity of A’s net demand for imports with respect to the import price ratio; and λm, the elasticity of A’s demand for import goods with respect to deflated home expenditure. It is not found necessary in this paper to split up the elasticities of A’s net demand for imports and net supply of exports into their component elasticities of demand for and supply of import goods and export goods, respectively.

The net demand in the outside world (non-A) for A’s exports is regarded as determined solely by the world market price, in non-A currency, of A’s exports: the assumption is that any responsive changes in non-A’s own prices or expenditures are proportionately so small as to be negligible. Similarly, non-A’s net supply of A’s imports is treated as a function of the world market price, in non-A currency, of A’s imports. (The world market price of A’s exports is assumed to be equivalent to the price in A; the world market price of A’s imports, however, will differ from the price in A to the extent of any import duties or any windfall profits arising from import restriction in A.) These relationships give rise to two elasticities: ηb, the price elasticity of non-A’s net demand for A’s exports, and єb, the price elasticity of non-A’s net supply of A’s imports.

In this study we have arbitrarily assumed different sets of numerical values for the parameters pxqx1, pxqx2, pmqm1, pmqm2, phqh, ηa, ηb, єa, єb, λx and λm and we have calculated the price effects of a given devaluation for each set of parameter values. Some of the numerical values have been chosen in such a way as to illustrate the influence of the different parameters, and some in such a way as to reproduce the circumstances of different sorts of countries. In reality, of course, the economic system takes time to react to disturbing factors. The values that can realistically be assigned to these parameters for any particular country will be a function of the reaction time allowed. We have, in fact, had in mind a reaction time of one to two years and have therefore been exploring the “medium-term” effects of depreciation. But the formula evolved can easily be used to calculate either short-term or long-term effects, if suitable values are assigned to the coefficients.

A more troublesome difficulty is that it cannot be assumed that any values assigned to the parameters will hold true irrespective of the nature of the disturbance. In particular, if we are starting from full employment it cannot be assumed that demand and supply elasticities with respect to price will be the same for price increases as for price declines. But since the present paper is concerned solely with price increases, the problem is not of importance here.

Price Effects of Exchange Depreciation Prior to Fiscal Adjustments

The effects on the internal price level of an exchange depreciation in Country A which is not accompanied by any change in the ad valorem level of any import restriction will now be considered.2 It is assumed that there are no export restrictions or subsidies and, for the time being, that no changes in indirect taxation accompany depreciation. Since, in the absence of unemployment, no decline will take place in domestic wage rates in any major sector of industry, depreciation is likely to be accompanied by some increase in A’s over-all cost of absorption (i.e., the price level of goods domestically consumed or invested), owing to a rise in the domestic currency price of both import and export goods. The domestic price of import goods will rise because the foreign currency price at which other countries supply them cannot be expected to fall to the full extent of the devaluation and because the home supply of import substitutes is not completely elastic; and the price of export goods will rise because the cheapening of their foreign currency price will bring about an increase in foreign demand for A’s exports impinging on a not completely elastic supply.

It is assumed that the price of home trade goods remains constant. This seems to be reasonably compatible with our assumption regarding financial policy, which is that total domestic demand will be controlled so as to prevent the emergence of any excess demand for labor in the home trade sector as labor is attracted from that sector to the foreign trade sector. Such a policy may well result in a slight net increase in wages even in the home trade sector; but since aggregate expenditure on home trade goods will have declined, there may be an associated decline in profit margins which will enable product prices to remain constant.

Although the prices of foreign trade goods will rise, they will not rise to the full extent of the devaluation. This is because (1) the decline in the demand for imports, which may be expected (in the absence of an increase in domestic expenditure) to result from their increased domestic price, will tend to bring down their supply price abroad in foreign currency, and (2) the increased supply of exports resulting from the rise in the domestic price will cause some fall in their foreign-currency demand price.

Broadly speaking, the extent to which an exchange depreciation of a given magnitude will raise the price of export goods will depend on the extent to which a decline in the foreign-currency price will evoke an additional net demand for such goods abroad, the extent to which a rise in the A-currency price will evoke an additional net supply of such goods in A, and the extent to which any change in aggregate expenditure in A will result in a change in home absorption of such goods. In other words, it will depend on the elasticity, with respect to price, of net demand abroad (ηb) and of net supply in A (єa), and on the marginal propensity to buy export goods in A (qx2 λx). Similarly, the extent to which a given depreciation will raise the price of import goods will depend on the price elasticities of net supply abroad (єb) and of net demand in A (ηa) and on the marginal propensity to buy import goods in A (qmλm).3 Since the prices of A’s import goods and export goods will increase as a result of the depreciation, while the price of home market goods will remain constant, the extent of the rise in A’s cost of absorption will be the greater, the greater the share of import goods and export goods, relative to home market goods, in A’s total absorption.

As far as price elasticities are concerned, the rise in A’s price level will be the smaller, the lower the elasticities abroad (ηb and єb) and the higher the elasticities at home (ηa and єa). High values of ηb and єb mean that a big increase in the net demand for A’s exports, and a big reduction in the net supply of A’s imports, will be generated abroad in response to any decline in their respective prices in terms of foreign currency, and this will naturally tend to raise the prices of export and import goods in A. Low elasticities abroad mean that this price-raising effect will be relatively weak. High elasticities at home mean that any increase in the price of export or import goods—consequent on a rise in the foreign net demand for them—will lead to a big increase in domestic supply and a big decline in domestic demand for these goods, which naturally tends to limit the rise in their price.

The elasticity of the net supply of exports in A will be the greater, the greater (1) the elasticities both of A’s output and of its absorption of export goods and (2) the proportion of its output of these goods that is absorbed at home. The elasticity of A’s net demand for imports will be the greater, the greater (1) the respective elasticities both of its output and of its absorption of import goods and (2) the proportion of its absorption of these goods that it produces at home. The analogous propositions hold true of the outside world in its trade with A.

Since the outside world (non-A) will normally be much larger economically than A, the ratio of absorption to output will normally be nearer to unity in non-A than in A. Mainly for this reason, the foreign trade elasticities will normally be greater in non-A than in A; and when A’s exchange rate depreciates, the average price of foreign trade goods in A will normally rise by more than half as much as the price of foreign currencies in A. Since, however, elasticities with respect to price are usually higher, save in the short run, than the corresponding demand elasticities for the product in question, and since the former tend to play a greater part, relative to the latter, in determining export than in determining import elasticities, there is a general tendency for export elasticities to be higher than import elasticities. From this it follows that export prices in A will normally rise less than import prices and may often rise less than half as much as the prices of foreign currencies in A. It would be expected that the larger the devaluing country, A, the higher would be its foreign trade elasticities, relative to those of the outside world, and the smaller the increase in prices of its foreign trade goods relative to the extent of the depreciation.

As regards the elasticities of domestic demand for, and output of, export and import goods, the elasticities of demand will vary with the extent to which individuals and firms are prepared, in their pattern of absorption, to replace these goods by home trade goods, as the prices of the former rise; such substitution will be the greater, the greater the similarity between foreign trade and home trade goods. The elasticities of home output of export and of import goods will be the greater, the greater the mobility of labor and other resources as between home trade industries, on the one hand, and those producing exportable and import-competing goods, on the other.

The influence exercised by the marginal propensities to purchase import and export goods out of home expenditure will make itself felt only to the extent that the pursuance of a proper financial policy requires some change in the aggregate level of home expenditure as exchange depreciation brings about an improvement in the balance of trade.

A distinction has to be drawn between the level of home expenditure in real and in money terms. If a country embarks on devaluation from an initial position of full employment, the observance of a proper financial policy is bound to require a significant reduction of home expenditure in real terms. Real home expenditure (absorption) is limited to that portion of real output plus real imports that is not used for export. Since, under the conditions assumed here, devaluation cannot increase the volume of output, and since, if it is not completely nullified by a rise in domestic prices, it will entail an increase in real exports and a decline in real imports, there must be a corresponding decline in real absorption or home expenditure. Failure to bring about such a decline will lead to such a rise in domestic costs and prices as to frustrate the purpose of the devaluation.

Transposed into terms of money values, however, the argument is less straightforward. True, the value of home expenditure must, by definition, be equal to the value of output plus the value of imports less the value of exports. Again, exchange depreciation will normally—though not necessarily—lead to an increase in the value of exports less the value of imports, so that, if a proper financial policy had required that the value of output should remain constant, home expenditure would have had to fall by an amount equal to the increase in the value of exports less the value of imports.

For the value of output to remain constant, however, expenditure on home trade goods would have to decline to the full extent of the rise in the value of output of export goods and import-competing goods. This is more than is called for by a proper financial policy. Since wages in all trades are assumed to be inflexible in a downward direction, and since there is something less than full mobility of labor between home trade industries, on the one hand, and export and import-substitute industries, on the other, it follows that a decline in expenditure on home trade goods, even if balanced by an equivalent increase in demand for other products, is likely to give rise to unemployment. Some rise in the value of output will therefore be appropriate, and home expenditure will not be curtailed to the full extent of the improvement in the balance of trade. Indeed, if the foreign trade elasticities in A (ηa and єa) are too low, the rise of export and import prices may not only entail a rise, rather than a fall, in the proportion of home expenditure directed to foreign trade goods; it may even divert more of A’s expenditure from home trade to foreign trade goods than it will attract resources from the home trade to the foreign trade industries. If this occurs, it will be necessary to increase rather than reduce home expenditure, thus further pushing up prices in the foreign trade sector.4

In most cases, however, it will be possible, without creating undue unemployment, to reduce home expenditure sufficiently to moderate significantly the pressure of demand and the rise in prices in the foreign trade sector. The reduction will be the greater, the higher are (1) the foreign trade elasticities in A and non-A, (2) the expenditure elasticities of demand for import and export goods in A, and (3) the proportionate importance of import and export goods in A’s domestic absorption. These are also conditions that normally tend to increase the effect of a given devaluation in improving the balance of trade.

It is not clear that a relatively large foreign trade sector in A will contribute to keeping down the rise in prices of import and export goods resulting from a given devaluation; while it will enhance the moderating effect of any decline in home expenditure, it will also tend to reduce A’s price elasticities. But whatever may be the effect on the price of foreign trade goods, the effect on A’s general price level, or cost of absorption, is unambiguous and important. Given the rise in the price of import and export goods, it is clear that the greater the share of these goods in total absorption, the greater will be the rise in the general price level.

The financial measures required to bring about an appropriate adjustment of domestic expenditure may include some adjustment in the rates of taxation on consumption or investment. A consideration of the price effects resulting from such adjustments will be postponed until financial policies have been considered.

The manner in which the various factors discussed above—other than the fiscal repercussions just mentioned—combine to determine the proportionate increase in the general price level associated with a given proportionate depreciation of the rate of exchange is described in algebraic terms in Part I and Part II(a) of the Appendix. Strictly speaking, the formula applies only to infinitesimally slight devaluations, but it gives an approximation to the correct results for moderate devaluations.

Nine cases are defined in Table 1, each characterized by a different combination of numerical values for the relevant parameters in A and non-A. For each case, the effect that an exchange depreciation of 10 per cent would have on prices of foreign trade goods, on the cost of absorption, and on the balance of trade are shown in Table 2. The meaning of the various symbols used in these tables are set forth below; the brief description given here of the elasticities is to be interpreted in the light of the fuller definitions given above.

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The first seven cases are defined so as to illustrate the direction and magnitude of the influence that the individual parameters exercise, in the event of exchange depreciation of the type under investigation, on prices, the balance of trade, etc. Case 1 is taken as the standard of comparison, and other cases differ from it only with respect to a single parameter or group of parameters. The parameter or group of parameters from which the numerical value in any particular case diverges from that of case 1 is indicated by italics.

Cases 1, 8, 9, 10, and 11 are supposed to be more or less realistic typical country cases. Case 8 is a large, and case 9 a small, industrial country; case 10 a large, and case 11 a small, primary producing country. Case 1 may be regarded as an “average” country. The choice of elasticities has been based on the following assumptions:

(1) Large countries tend to have higher foreign trade elasticities at home (ηa and єa) and tend to encounter lower foreign trade elasticities abroad (ηb and єb) than do small countries of the same type.

(2) Industrial countries tend to have a more elastic export supply than do primary producing countries of the same size; this is linked to the fact that home consumption of exportable goods tends to be more important in industrial than in primary producing countries.

(3) The demand for imports tends to be less elastic for industrial countries than for primary producing countries because of the higher proportion of necessary food and raw materials.

(4) Industrial countries tend to encounter a less elastic world demand for their exports than is encountered by primary producing countries; although the products of the industrial countries are of a less necessary type, they are more specialized and less easily substitutable for those of competing countries.

(5) Industrial countries tend to encounter a less elastic world supply of their imports than do primary producing countries, because both the supply and the demand for primary products abroad tend to be less elastic than for industrial goods.

In choosing the elasticities, some account—but not too much—has been taken of such estimates of these elasticities as have been calculated for particular countries by econometric methods. For export supply elasticities (єa and єb), such estimates are almost entirely lacking. Estimates for import demand elasticities (ηa and ηb) are available, but good reason exists for believing them to be highly uncertain and, in most cases, too low.

On the basis of the numerical values assigned to the parameters under the respective cases in Table 1, calculations have been made of the percentage changes in the prices of exports (px) and imports (pm), the general price level or cost of absorption (P), and the balance of trade (B) that will result from a 10 per cent exchange depreciation in Country A.6 The last has been calculated on the assumption of a degree of import restriction equivalent to an ad valorem import duty of 50 per cent.

Consider, first, cases 1 to 7. In consonance with the foregoing argument, the price level is seen to rise somewhat more steeply where, as in cases 3 and 4, the foreign trade elasticities in A are low, and to rise somewhat less where, as in case 2, the expenditure elasticities in A are high, or where, as in cases 5 and 6, the foreign trade elasticities in non-A are low. The fact that the price rise in case 5 is almost as great as in case 1 is because the decline in domestic expenditure (S) in case 5 is much smaller than in case 1 so that the smaller rise in px is nearly offset by the greater rise in pm. The most substantial price rise of all occurs in case 7, where it is due to the relatively large importance of foreign trade in the economy as a whole.

In regard to the special cases 8–11, the most important factor in determining the degree of price rise is clearly the size of the foreign trade sector—which varies inversely with the size of the country, but tends to be larger in industrial than in primary producing countries of a given size. This accounts for the relatively large price increases in 9 and 11 and the relatively small increases in 8 and 10. The increases in px are, as would be expected, greater for small countries 9 and 11 than for large countries 8 and 10, and greater for primary producers 10 and 11 than for industrial countries 8 and 9. More surprising are the results for import price: pm rises more in the industrial than in the primary producing countries, and more in the large than in the small countries. The reason why pm is shown as rising more in case 8 than in case 10, and in case 9 than in case 11, despite the fact that the foreign supply is assumed to be more elastic for the industrial imports of cases 10 and 11 than for the primary product imports of cases 8 and 9, is that the price elasticity of demand for imports is also assumed to be higher in the former than in the latter pair of cases. The reason why pm rises more in case 8 than in case 9, and in case 10 than in case 11, is not connected with the size of the price elasticities at all; these would tend to lead to the opposite results. The reason lies in the fact that the proportionate decline in home expenditure is very much greater, and in addition the proportion of this decline in expenditure that falls on foreign trade goods is much greater, in the small countries with a relatively large foreign trade sector (cases 9 and 11) than in cases 8 and 10.

Thus far, we have been concerned with the effect on prices of an exchange depreciation of a given magnitude. Fundamentally, however, what is important to governments in considering the advisability of an exchange rate adjustment is something else, namely, the effect on prices of whatever exchange depreciation is required to bring about a given improvement in the balance of payments in terms of foreign currency. When considered from this new angle, the relative price-raising effects of exchange depreciation in the different cases change quite appreciably.

Consider, first, the degree of improvement in A’s trade balance,7 measured relative to the value of A’s output, that results, in the different cases, from a given percentage depreciation. The balance of trade effect of depreciation depends to some extent on the intensity of import restriction applied in A (even though, by the basic hypothesis in this paper, the severity of the restriction remains unchanged as the exchange rate falls). In Table 2, the degree of restriction has been assumed to be equivalent to an ad valorem import duty of 50 per cent. As will be seen from Table 2, the balance of trade effects vary far more widely, as between the various cases, than do the price effects. Over the range of parameter values considered here, the improvement in the balance of trade tends to be the greater, the higher are A’s own foreign trade elasticities (including the expenditure elasticities of demand for foreign trade goods), and also the higher is the elasticity of net import demand in non-A. Where, as in many of the cases, A’s net import elasticity (ηa) is unity, variations in non-A’s net export elasticity have little effect on the balance of trade; but where, as in cases 3, 8, and 9, ηa is less than unity, the improvement in the balance will be the greater, the less elastic is non-A’s net export elasticity. But the main factor in determining the effect on the balance of trade, measured as a proportion of the value of output, is simply the relative importance of the foreign trade sectors. This factor operated powerfully in cases 7, 9, and 11. The particularly small improvement in the balance of trade in case 5 is due to the low elasticity of net demand for A’s exports abroad; and the particularly large improvement in case 11 is due to the combination of high foreign trade ratios and particularly high levels of ηa, ηb and εb. An improvement in the trade balance amounting to 18 per cent of the value of output seems an extraordinary effect to achieve from a 10 per cent devaluation. It has to be borne in mind, however, that if an improvement of this order were brought about it would be extremely difficult to carry out a financial policy sufficiently disinflationary to fulfill the assumptions of the model by keeping the price level of home trade goods from rising. On the other hand, it should seldom be necessary to achieve an improvement of this order, and a country of this type should be able to rectify every normal disequilibrium with a relatively slight exchange depreciation.

As will be seen from the last column of Table 2, the proportionate rise of the cost of absorption associated with a given improvement in the trade balance is much less affected by the relative importance of the foreign trade sectors than is either the balance of trade effect or the price effect of depreciation, taken separately. As can be seen by comparing case 7 with case 1, however, high foreign trade ratios, being associated with high marginal propensities to buy foreign trade goods, tend somewhat to reduce the rise in P; a similar result is seen in case 2, where the expenditure elasticities of demand for foreign trade goods are high. The greatest price rise of all occurs in case 5, because of the low value of the elasticity of net demand abroad for A’s exports. A low elasticity of net demand for imports in A (case 3) also makes for a high price rise, as does a low elasticity of net supply abroad for A’s imports (case 4). The substantial price rise in case 8 (the large industrial country) is due to the low elasticities of net demand for imports both in A and in non-A. Here, however, it should be repeated that such a country may not often require a correction of its trade balance as large as 5 per cent of the value of its output. The very small price rise in case 11 is due to its high elasticities of net demand for imports in A and in non-A and to its high foreign trade ratios. In general, save in case 5, the price increases seem quite moderate in relation to the improvements in the balance of trade.

Financial Policies Required

If the price level is to rise as little, and the balance of trade is to improve as much, with a given devaluation, as indicated above, the aggregate level of domestic absorption will have to be so adjusted as to maintain constant prices and full employment without excess demand in the home trade goods industries. By definition, domestic expenditure, or the value of domestic absorption, is necessarily equal to the value of output less the balance of trade, all the component elemerits being valued at domestic prices, either net or gross of expenditure taxes. But the balance of trade at domestic prices consists of the balance of trade at world prices less the excess of the domestic over the world market value of imports.8 It follows that the domestic expenditure (net of expenditure taxes) should decline with devaluation by the amount by which the balance of trade, at world market prices, tends to improve,9 plus the extent to which the excess of the domestic over the world market value of imports tends to decline, less the extent to which the value of output, at factor cost, tends to rise, when equilibrium as described above is maintained in the home trade goods industries.

The magnitude of the appropriate changes in A’s expenditure, the value of output, and the excess of the domestic over the world market value of imports associated with (1) a 10 per cent depreciation and (2) a depreciation resulting in a 5 per cent improvement in the trade balance, respectively, are shown for various selected cases in Table 3.10

Let ∆V stand for the percentage change in the value of output at factor cost,

S for the change in domestic expenditure (net of tax) as a percentage of the initial value of output,

R for the change in the excess of the domestic over the world market value of imports (expressed as a percentage of the value of output), and

B, as in Table 2, for the change in the balance of trade at world market prices.

It will be seen that the appropriate level of domestic expenditure declines in all cases, save case 8. The increase in expenditure in that case is associated with the comparatively low elasticities of foreign net demand for A’s exports and the resulting small influence of depreciation on the trade balance. The rise in export prices is so small in that case that not enough labor is attracted from industries producing home trade goods to compensate for the switch in demand from these industries to pay for higher priced imports. At the other extreme, the decline in domestic expenditure required for a 10 per cent depreciation in case 11 is enormous—18 per cent of the value of national output; this is associated with a very large improvement in the balance of trade and a considerable decline in the value of imports which, since the ad valorem severity of import restriction is constant, reduces the excess of the domestic over the world market value of imports. A decline in expenditure of this magnitude might well be impossible to achieve in practice. On the other hand, a 10 per cent depreciation may very well be unnecessary in such a case. As will be seen from the right hand side of the table, the decline in S required in connection with a given improvement in the balance of trade is not much greater in case 11 than in other cases.

The extent of the disinflation to be carried out by official action in the event of exchange depreciation, however, is not measured by the required decline in domestic expenditure alone; it must, in addition, suffice to counteract any increase in expenditure that may naturally tend to arise from the target improvement in the balance of trade, the increase in national income, etc., associated with the exchange depreciation.

In order to indicate the order of magnitude of the disinflationary effort that may be required in typical cases, an illustrative calculation is made below for case 1 on the assumption of a depreciation of 10 per cent and on stated assumptions regarding the magnitude of the relevant structural coefficients. These coefficients are chosen to fit the basic assumption that, initially, some 75 per cent of total absorption consists of private consumption, 15 per cent of public consumption, and 10 per cent of (net) investment. (All figures are expressed in percentages of the value of national output.)

(1) The required decline in domestic expenditure, net of consumption and investment taxes (S), is 3.66.

(2) If indirect taxes are assumed at 8 per cent on consumption and investment, the required decline in domestic expenditure at market prices is 3.95.

(3) Assume that half the margin between the domestic and the world price of imports accrues to importers as “windfall gains,” that the transfer of interest on the national debt from government to individuals amounts to 5, and that all industry is in private hands. Then private incomes initially amount to 110. Assume that the income tax takes 8 per cent of this income, leaving a post-tax income of 101.2, of which 12 per cent is saved. Private consumption at market prices is thus, initially, 89.1. The rise in the cost of absorption, owing to devaluation, is 3.42 per cent. Therefore, if private consumption were to remain unchanged in real terms, it would have to increase in money terms by 3.05.

However, we shall assume that there is a marginal propensity to consume of 0.6, so that real private consumption declines by 60 per cent of the decline in real private incomes. Now the fall in the purchasing power of private incomes is 3.46;11 but money incomes rise by 1.83,12 which, less income tax, amounts to 1.68. Therefore, real private incomes fall by 1.78. If 60 per cent of this is subtracted from real private consumption, private consumption in money terms will rise by 1.98.13

(4) There appears to be no good reason why the remaining constituents in absorption—government absorption of goods and services and private investment—should not tend, in the first instance, to remain unchanged in real terms. For government absorption it is convenient to assume this as a starting point for estimating the degree of final disinflation that may be necessary. Moreover, since it is assumed that the volume of output is not affected by the devaluation and that the average price of output rises almost as much as the cost of investment goods, it seems plausible that the tendency, at constant interest rates, would be to maintain an unchanged volume of private investment. Since aggregate domestic expenditure at market prices was initially 118.914 and private consumption was assumed above to be 89.1, the remaining categories of expenditure accounted together for 29.7. If these tend to remain constant in real terms, money expenditure on these items will tend to rise by 1.02.

(5) When the results of (3) and (4) are added together, domestic expenditure will tend to rise by some 3.00. When this is added to the required decline in expenditure given in (2) above, it appears that official action would be required to curtail domestic expenditure by some 6.95 at market prices. For the purpose of making a comparison with national output at factor cost, this should be netted of indirect taxes; when this is done, the curtailment required amounts to some 6.44 per cent of the value of national output.

It should be noted that the inflationary gap that has to be bridged by official action lies between the amount of the target improvement in the balance of trade (some 5.3 per cent of the value of output) and the amount of the required decline in real absorption (some 7.4 per cent of the value of output). This is no accident. The amount by which the required decline in real absorption exceeds the target improvement in the balance of trade corresponds to the decline in real national income.15 The amount by which the required decline in real absorption exceeds the inflationary gap corresponds to the fall in real consumption resulting from the decline in real national income; and the amount by which the inflationary gap exceeds the target improvement in the balance of trade corresponds to the decline in real national savings resulting from the decline in real national income.

Table 4 shows the extent of the curtailment of expenditure to be brought about by official action for the cases presented in Table 3, on assumptions as to tax rates, transfer incomes, and consumption ratios that are similar to those made above for case 1.

For the various cases, it is clear that the differences in the extent of the deflationary effort required on the part of the authorities in connection with a 10 per cent devaluation are largely associated with differences in the size of the improvement achieved in the balance of trade; for a given improvement in the latter, much the same effort is required (see Table 4, column 2). The slightly greater effort required to achieve a given improvement in the trade balance in case 8 is due to the big loss of real income arising out of a deterioration in the terms of trade; this is only partly offset by the relatively small loss of real income from reduced imports16 and the relatively large spontaneous reduction in real absorption. In case 11, there is very little deterioration in the terms of trade; there is, however, a substantial loss of real income from a decline in imports and, since half of this falls, in the first instance, on state rather than private income, the spontaneous decline in real consumption is relatively small.

How much of the required curtailment of expenditure should fall on consumption and how much on investment? How much of the needed disinflation should be carried out by budgetary, and how much by monetary, policy? These questions are interrelated, for the view that is taken as to the appropriate change in public saving—the excess of current account receipts over current account expenditures in the public sector—will largely determine the answer to the first question, as well as affect the answer to the second.

Prima facie, there seems no very good reason why devaluation should affect the proportion of national income devoted to public saving. Although some important qualifications to this principle will be admitted later, let us adopt it for the present, with the additional simplifying assumption that the proportion of public saving deemed appropriate in Country A is zero and that a state of zero public saving—a balanced budget on current account—prevails in the predevaluation situation. On these assumptions, most of the required curtailment of expenditure will fall on investment. The position may, once more, be illustrated from case 1.

With A’s exchange rate depreciating by 10 per cent, the budgetary implications are as follows:

(1) The decline in target domestic expenditure (prior to indirect taxation) amounts to 3.66. At a tax rate of 8 per cent, the corresponding fall in the yield of general indirect taxation will be 0.29. The yield of import taxation will decline by 0.22.17 Target private income, however, will rise by 1.83; and at an 8 per cent tax rate, the income tax yield will increase by 0.15. Altogether, the tax revenue corresponding to target levels of consumption and private income will fall by 0.36.

(2) Initially, the tax revenue was 38.0, of which 8.818 was from general indirect taxation, 8.819 from indirect taxation on expenditure, and 5 from import duties; 5 was paid out in interest transfers, leaving 17.6 available to be spent on public consumption at market prices. With the rise in the cost of absorption, public expenditure for an unchanged volume of public consumption at market prices would therefore be 0.60.20

(3) From (1) and (2), the excess of public consumption over tax revenues corresponding to target levels of national income and expenditure would appear to be 0.96.

(4) Assume that real public consumption should be reduced in the same proportion as private. Since a reduction of 1.07 in real private consumption has been assumed above (page 306), the corresponding reduction in public consumption is 0.21.

(5) In order to restore a balanced budget on current account, the remaining gap of 0.75 will have to be eliminated by additional taxes and reductions in public consumption. In order to maintain proportionality between reductions in private and public consumption—and since only 60 per cent of any fall in private incomes will result in a fall in private consumption—it will be necessary to cut public consumption by a further 0.09 and to increase taxation by some 0.66.

(6) If the budget is balanced in this way, public consumption at market prices will have been curtailed by 0.30 and private consumption by 0.40,21 making 0.70 in all. On a net-of-tax basis, this is equivalent to 0.65, against a total required curtailment of expenditure of 6.44. The remaining curtailment of expenditure, amounting to 5.79 per cent of the national output, will have to come from public or private investment.

(7) For an exchange depreciation that will lead to an improvement in the trade balance equal to 5 per cent of the value of output, the required curtailment of investment expenditure would be 5.49.

The results of similar calculations made for all the cases appearing in Table 4 are shown in Table 5.

The table shows certain variations among cases as to the extent to which mere restoration of budgetary balance will curtail consumption expenditure for a devaluation of a given balance of trade effect. In case 8 this curtailment is relatively small, because the tendency toward a budget deficit arising from the decline in import and expenditure taxes is relatively small; this again is due to the relatively low level of ηb the elasticity of foreign demand for A’s exports. On the other hand, the curtailment achieved by budgetary policy in case 11 is relatively large because of the relatively powerful tendency toward a decline in import and absorption taxes, owing to the high import demand elasticities abroad and at home and the high marginal propensity to import.

In all cases, much the largest part of the required curtailment of expenditure falls on investment. It should be remembered, however, that, from the standpoint of national wealth, the cut in home investment is largely compensated by the increased rate of accumulation—or reduced rate of loss—of net claims on the outside world and/or of metallic reserves, associated with the improvement in the balance of trade.

The proposition that much the greater part of the required curtailment of absorption should fall on investment is open to certain important qualifications, both of principle and of practice:

(1) The illustrative figures given in Table 5 are calculated on the assumption of unchanged interest rates. But for the required reduction in investment to be carried out, it will be necessary to raise interest rates, or, more precisely, to increase the scarcity of investible funds. This development may well evoke some increase in private savings and may even be held to justify an increase in the level of public savings, if any. To this extent an additional part—which is not, however, likely to be very large—of the burden of contraction will be transferred from investment to consumption.

(2) More important in practice is that, if an overrapid contraction of investment should seem likely to give rise to undue unemployment in capital goods industries—which may not be the industries particularly stimulated by the devaluation—there may be a case for temporarily raising the level of public savings by raising taxes and so spreading over a wider industrial front the deflationary pressure involved in the decline in home absorption. The importance of this point will be appreciated when it is recalled that, in the foregoing discussion, it has been assumed that the amount of investment prior to the depreciation amounted to no more than 10.5–12 per cent, according to the case in question, of the value of national output. Thus, what is called for by Table 5, in the event of a depreciation that improves the balance of trade by 5 per cent of the value of output, is approximately a cutting in half of the pre-existing volume of investment. On the other hand, the need for a decline in home absorption will manifest itself only gradually as the devaluation gradually takes effect on the balance of trade.

(3) Finally, allowance has to be made for irrationality in the savings policy of governments. Although the level of public savings or dissavings should logically be determined in relation to national income, the level of private savings, and the scarcity of capital, it may often in fact be influenced by the possibility which an external deficit provides of obtaining real resources from abroad and thus financing a budget deficit without inflationary consequences. To the extent that the improvement in the balance of trade brought about through depreciation threatens to create an inflationary situation, governments may be disposed to increase public saving more than has been assumed in the foregoing discussion. Where, however, simultaneous but mutually independent decisions are taken to reduce an external deficit by depreciation and to cut a budget deficit deemed excessive in relation to national income, it would be wrong to impute to depreciation the cut in consumption involved in the latter decision.

If, nevertheless, we continue to assume, despite the foregoing considerations, that the curtailment of home absorption is to take the form, predominantly, of a curtailment of investment, its implementation will lie primarily in the sphere of monetary and credit policy rather than of budgetary policy. In countries where a large sector of investment is under the control of the public authorities, the state should be able by direct measures to influence the level of investment. Fiscal policy may be adjusted to reduce the incentive to invest. But, in the main, the task of influencing the level of private investment, and to a lesser extent public enterprise investment, is likely to fall on monetary policy, in the broad sense that includes government policy with respect to the composition of the national debt.

The object of monetary policy should be to keep the volume of money in circulation—including checking accounts and with due allowance for the existing volume of various types of quasi-money—at a level which will so raise the price and scarcity of investible funds that the volume of investment will be curtailed to the extent required. This is likely, in most cases, to call for a considerable nonrecurrent reduction in the supply of money and a considerable permanent reduction in the rate of expansion of bank credit to domestic borrowers.

The need for money for transactions purposes may be assumed to depend primarily on the level of the value of output and, to a lesser extent, on that of domestic money expenditure. As we have already seen from Table 3, the value of output in A will usually rise somewhat because of the rise in the prices of import and export goods, although, because of weighting considerations, the proportionate increase in the value of output will not be precisely the same as the proportionate increase in the cost of absorption. On the other hand, since the improvement in the balance of trade (at domestic prices)22 is larger than the rise in the value of output, the appropriate level of domestic expenditure will usually fall. It is probable that the transactions demand for money is influenced much more by the value of output than by domestic expenditure, since the need for business balances arises mainly from the flow of current account transactions, and the need for private balances from the flow of personal incomes rather than of consumption expenditure. An average of the changes in the volume of output and in domestic expenditure, in which the weight of the former is three times that of the latter, is given in Table 6 for the cases dealt with in Tables 35.

The figures given in Table 6 give a rough impression of the changes in the money supply that would be appropriate in the event of depreciation if no changes were to occur in the velocity of circulation of money. In truth, however, the velocity of circulation is likely to increase substantially as the increased scarcity of investible funds, necessary to induce the required curtailment of investment indicated in Table 5, induces firms and individuals to make a more economical use of money balances; it follows that the supply of money should be curtailed to a corresponding extent.

Let x stand for the proportional increase in the scarcity of investible funds (as measured by some composite rate of interest) that tends to bring about a unit proportional decline in real investment (assuming the effect on consumption to be negligible) when real output remains unchanged; and let y stand for the proportional increase in the velocity of circulation that tends to result from a unit proportional increase in the rate of interest. Then a given proportional decline in investment will be associated with a proportional increase, xy times as great as itself, in velocity. But the proportional increase in velocity is, by definition, the excess of the proportional increase in the value of transactions (however defined) over the proportional increase in the money supply. It follows that the proportional decline in the money supply that is required can be measured by xy times the proportional target decline in investment less the proportional target increase in the value of transactions—as shown in Table 6.

But what is x? And what is y? Unfortunately, the available evidence as to the magnitude of these coefficients in typical cases shows a wide range of variation. Thus, an empirical study of the response of velocity to variations in interest rates in various countries over various periods shows values for y (the interest elasticity of demand for money) which vary from 0.1 for the United States in the 1930’s to 3.9 for the Netherlands in postwar years.23 Most of the more reliable results, however, show an elasticity of less than 2, especially in industrial countries. While y would be expected to rise as the rate of interest (r) itself approaches zero, there is no reason to expect any systematic relationship between y and r for normal variations of r, and none is visible in the data.

About 1x, the (negative) elasticity of investment with respect to the x rate of interest, even less is known than about y. A series of estimates for various countries relating to the interwar period and the period before World War I show that a 1 per cent variation in long-term interest rates tends to bring about a variation in gross investment (or other series related thereto), ranging from -56 per cent to zero.24 The form of the calculation implies (what is probably true) that the elasticity of investment with respect to interest will tend to increase as the interest rate rises. If interest rates are assumed to be of the order of 5 per cent, this elasticity shows a range of variation similar to that already shown for the elasticity of velocity with respect to the rate of interest. On the assumption that in the average country net investment might be about half as great as gross investment, these calculations would suggest a value of xy = ½ as a reasonable central assumption for illustrative purposes. However, there is some reason to believe that the market rate of interest constitutes a less adequate measure of the scarcity of funds from the standpoint of investors than from the standpoint of money holders and that the true value of 1x is somewhat higher than has been assumed.

However, even if a value of xy = ¼ is assumed, substantial reductions in the money supply would still have to accompany exchange depreciation, in order to hold investment and absorption down to the appropriate levels.

The proportion of investment to the value of output implicit in the calculations underlying Tables 5 and 6 is some 11 per cent in case 1, 10.5 per cent in cases 8 and 10, and 12 per cent in cases 9 and 11. From this and the data given in Table 6, the percentage decline in the money supply that is required in each case to bring about a curtailment of investment of the magnitude shown in Table 5, on the assumption that xy = ¼, can be calculated; the results are given in Table 7.

The fact that part of investment is under government control and can be curtailed directly does not necessarily imply that the contraction in the money supply should be any less severe. If the initial magnitude of public investment relative to private investment was correct, the reduction in public investment should, ideally, be no greater than would result in a rational private economy from the increased scarcity of investible funds. In order to obtain the appropriate reduction in private investment, interest rates will therefore have to be raised—and the money supply reduced—to much the same extent, whatever the relative magnitude of the private and public sectors. On the other hand if, to avoid structural unemployment or for some other reason, part of the curtailment which would otherwise fall on investment is applied to consumption, by raising taxes or reducing public expenditure, the degree of monetary contraction required will be correspondingly reduced.

The contraction in the supply of money will have to be achieved by a nonrecurrent contraction in bank credit to the domestic economy. In addition, in order to keep the amount of money at its new lower level, it will be necessary to bring about a permanent reduction in the predevaluation rate of domestic credit expansion. For the devaluation will tend to improve the balance of payments, both on current and on capital account, and hence to diminish the rate of loss of foreign assets by the banking system. If the volume of money is to remain the same, there must be a corresponding decline in the rate of accumulation of domestic assets. The improvement in the balance of payments, the effect of which on the volume of money is to be offset by domestic credit policy, will be greater, and may be much greater, than the improvement in the balance of trade, discussed above. For the flow of capital between A and the rest of the world is likely to shift in A’s favor as a result of the depreciation, both because of the rise in the price and scarcity of investible funds in A and because of the weakening or disappearance of any pessimistic anticipations that may have existed initially regarding the future movements of A’s exchange rate.

In view of the very great uncertainties regarding (1) the degree of monetary contraction necessary in order to effect a given curtailment of investment and (2) the effect of devaluation on the international flow of capital, it will usually be undesirable to fix in advance any hard and fast targets for the reduction in the money supply, or for the reduction of bank credit to domestic borrowers. Some tentative fixing of targets may well be helpful to illustrate the magnitude of the problem, but in practice it would seem best to look directly to the ultimate objective of preserving or restoring a correct level of demand pressure in the industries producing home trade goods and to turn the screw of credit contraction to whatever point is necessary to achieve this objective.

Mention was made above (see (5), page 309) of an increase in taxation, amounting to 0.66 of the value of output, that would be appropriate in case 1 as a contribution toward meeting the budgetary deficit brought about by declines in revenue and increases in expenditures arising out of a 10 per cent exchange depreciation. To some extent, the additional revenue will doubtless be raised in the form of indirect taxation on domestic absorption: indeed, since the effect of the depreciation, and the accompanying financial policy, is to increase the revenue from direct taxation, and to lower the revenue from indirect taxation, it might well be deemed appropriate to raise all the additional revenue by indirect taxes. If import duties are raised (from the 25 per cent assumed in the above calculations), the only effect will be to curtail the fortuitous incomes of the possessors of import licenses; to the extent that expenditure taxes are increased, however, price levels (cost of absorption) will be raised above those indicated in Table 2. The magnitude of the additional taxation required, expressed as a percentage of domestic expenditure, and the total amount of the price increase occasioned by an exchange depreciation, assuming that half the additional revenue is raised from expenditure taxes, are shown in Table 8, for selected cases.

Only in case 11 does the tax adjustment that is required to preserve a balanced budget significantly affect the increase in the general level of prices. Perhaps the main significance of these adjustments is slightly to mitigate the advantages enjoyed by a country with high foreign trade elasticities in being able to secure a big improvement in its balance of trade with a small rise in prices. When exchange depreciation accompanied by a relaxation of import barriers is studied in our later paper, we may find these taxation effects to be of considerably greater importance.

Linking of Wages to Cost of Living

The price increases mentioned in preceding sections of this paper have been calculated on the assumption that wage rates are unresponsive to changes in the cost of living. Virtual wage stability was assumed in the industries producing home trade goods,25 and wages in industries producing foreign trade goods were implicitly assumed to rise only to the extent required to attract labor from the home trade goods industries without causing substantial unemployment in the latter.

If, however, wages rise generally in response to the increase in the cost of living, increases additional to those discussed thus far will clearly take place in A’s product prices and cost of absorption. The latter, however, will not rise to the full extent of the rise in wages; only the prices of home trade goods will rise to this extent, the increase in the prices of foreign trade goods being damped down through the influence of demand and supply in non-A. The effect of the general rise in A’s wages on the prices of foreign trade goods relative to home trade goods will be the same as the effect of an exchange appreciation of equal magnitude.

Thus, if a depreciation of x per cent leads to an initial price rise of xy per cent, which leads to a wage rise of xyz per cent, there will be a secondary price rise of approximately xyz (1-y) per cent. This again, through its repercussion on wages, will lead to a tertiary price rise of xyz2(1-y)2, and so on indefinitely. However, if z (1-y) is positive and less than unity, the price increments will be successively smaller and the aggregate price rise will amount to xy1-z(1-y) percent. This price increase will be the higher, the nearer either y or z is to unity, but it will never be greater than the depreciation itself. To take an example: if a 10 per cent depreciation (x = 0.1) leads to an initial price rise of 4 per cent (y = 0.4), and if a 4 per cent price rise leads to a 2 per cent rise in wages (z = 0.5), the ultimate price increase will be approximately 5.7 per cent.

Since an increase in wage rates exercises an effect on the balance of trade similar to that of exchange appreciation, any repercussions of price changes on wage rates, such as those described above, will tend to reduce the improvement in the balance of trade (in terms of foreign currency) that will result from a given exchange depreciation. Therefore, in order to attain a given improvement in the balance of trade, a larger exchange depreciation will be necessary, and the enhancement which the connection between wages and the cost of living gives to the price increase resulting from exchange depreciation will be greater for a depreciation yielding a given improvement in the balance of trade than it will be for an exchange depreciation of given magnitude.

The formula for the price rise associated with a depreciation yielding a given improvement in the balance of trade is somewhat simpler than that for the price rise associated with a given depreciation, viz., xy1-z. To secure a given improvement in the balance of trade, a given decline in real wages is necessary; and if, for example, money wages are raised by four fifths of any rise in prices (z = 0.8), prices will have to rise 5 times as much as they would otherwise have done.

Table 9 illustrates the ultimate price increases to be expected for the various cases examined in Table 8, on the assumption of (1) an initial price increase (including the price increase resulting from the adjustment of indirect taxation) as shown in that table and (2) a 50 per cent response of wages to increases in the cost of absorption (z = 0.5).

It is noteworthy that, for a given exchange depreciation, the extent to which the mechanism of the wage spiral multiplies the initial price increase is the greater, the smaller is that initial increase; this mechanism therefore tends to equalize price increases in different cases. For a depreciation leading to a given improvement in the balance of trade, this multiplier is not only much larger than that for a given exchange depreciation, but it is uniform and equal to what it would be in a closed economy.

APPENDIX

Part I

Let qx1, qx2, qx1, qm1, qm2 and qh stand, respectively, for the volume of A’s exports, absorption of export goods, imports, output of import goods, and output (or absorption) of home trade goods.

Let
qmqm1+qm2qxqx1+qx2

Let px, pm and ph stand, respectively, for the home market price, in A currency, of A’s export goods, import goods, and home trade goods.

Let
Sqmpm+qx2px+qhph
stand for A’s domestic expenditure.

Let t stand for the ratio of pm to the world market price, in A currency, of A’s import goods.

Let c stand for the price of A currency in terms of non-A currency.

Let A’s export supply function be

qx1=f1(pxph,Sph)(1)

Let A’s import demand function be

qm1=f2(pmph,Sph)(2)

Let non-A’s export supply function be

qm1=f3(pmct)(3)

Let non-A’s import demand function be

qx1=f4(pxC)(4)

With reference to equation (1), let

εa[δqx1δ(pxph1).pxphqx1](5)

stand for the price elasticity of A’s net supply of export goods, and

λx[δqx1δ(Sph1)Sphqx2](6)

stand for the elasticity, with respect to domestic expenditure, of A’s demand for export goods.

With reference to equation (2), let

ηa[δqm1δ(pmph1)pmphqm1](7)

stand for the (negative) price elasticity of A’s net demand for import goods, and

λm[δqm1δ(Sph1)Sphqm](8)

stand for the elasticity, with respect to domestic expenditure, of A’s demand for import goods.

With reference to equation (3), let

εb[δqm1δ(pmCt1)pmCtqm1](9)

stand for the price elasticity of non-A’s net supply of A’s imports.

With reference to equation (4), let

ηb[δqx1δ(pxC)pxCqx1](10)

stand for the (negative) price elasticity of non-A’s net demand for A’s exports.

Now Ph is assumed to be constant, i.e.,
dphdc=0

Then, from equations (1), (5), and (6),

dqx1dc=qx1px1εadpxdcqx2S1λxdSdc(11)

From (4) and (10),

dqx1dc=qx1px1c1ηb(cdpxdc+px)(12)

From (2), (7), and (8),

dqm1dc=qm1pm1ηadpmdc+qmS1λmdSdc(13)

From (3) and (9),

dqm1dc=qm1pm1c1εb(cdpmdc+pmpmct1dtdc)(14)

From (11) and (12),

dpxdc=qx1pxc1ηbqx2pxS1λxdSdcqx1(εa+ηb)(15)

From (13) and (14),

dpmdc=qm1pmc1εb(1t1dtdc)qmpmS1λmdSdcqm1(εb+ηa)(16)

Now, by definition,

dSdc=d(pmqm)dc+d(pxqx2)dc+d(phqh)dc(17)

It is assumed that any reserves drawn from the production of home trade goods will be employed elsewhere at equally valuable work, i.e., that

phdqhdc=px(dqx1dc+dqx2dc)pmdqm2dc(18)
Then, since
dphdc=0
dSdc=pmdqm1dcpxdqx1dc+qmdpmdc+qx2dpxdc(19)

From (11), (13), and (19),

dSdc=S{dpmdc(qmqm1ηa)+dpxdc(qx2qx1εa)}Spmλmqmpxλxqx2(20)

Let units be so chosen that, in the initial position, px = pm = c = 1.

Then, from (15) and (20),

dpxdc=qx1ηb(Sqmλmqx2λx)qx2λx(qmqm1ηa)dpmdcqx1(εaηb)(Sqmλmqx2λx)qx2λx(qx2qx1εa)(21)

And from (16) and (20),

dpmdc=qm1εb(Sqmλmqx2λx)(1t1dtdc)qmλm(qx2qx1εa)dpxdcqm1(εb+ηa)(Sqmλmqx2λx)qmλm(qmqm1ηa)(22)

Let

fqx2λx(qmqm1ηa)
gqx1ηb(Sqmλmqx2λx)
hqx1(εa+ηb)(Sqmλmqx2λx)qx2λx(qx2qm1εa)
fqmλm(qx2qx1εa)
gqm1εb(Sqmλmqx2λx)
hqm1(εb+ηa)(Sqmλmqx2λx)qmλm(qmqm1ηa)

Then, from (21),

dpxdc=gfdpmdch(23)

and from (22),

dpmdc=g(1t1dtdc)fdpxdch(24)
Since t is constant, i.e.,
dtdc=0
, ∴ from (23) and (24),
dpxdc=ghfghhff(25)

and

dpmdc=gh+fghhff(26)

APPENDIX

Part II

(a) Let P stand for the cost of absorption.

Then, by definition, and since
dphdc=0
,
dPdc=qmdpmdc+qx2dpxdcqm+qx2+qh(27)
(b) Let
B[c(qx1pxt1qm1pm)]
stand for A’s balance of trade in non-A currency, and
Bh[qx1pxt1qm1Pm]
stand for A’s balance of trade in A currency.
Then, since px = pm = c = 1, and
dtdc=0
,
dBhdc=qx1dpxdc+dqxdct1qm1dpmdct1dqmdc(28)

from (12), (14), and (28),

dBhdc=qx1(1ηb)dpxdcqm1t1(1+εb)dpmdcqx1ηbt1qm1εb(29)

and

dBdc=dBhdc+Bh(30)
(c) Let
V(pxqx+pmqm2+phqh)
stand for the value of output.
Then, from (18), and since
dphdc=0
dVdc=qxdpxdc+qm2dpmdc(31)
(d) Let
R{qm1pm(1t1)}
stand for the excess of the home market value of imports.
Then, from (14), since
dtdc=0
dRdc=qm1(1t1){(εb+1)dpmdc+εb}(32)

(e) Let Sr stand for real absorption.

Then, by definition,
dSrdc=pmdqmdc+pxdqx2dc+phdqhdc

∴ from (18),

dSrdc=dqm1dcdqx1dc(33)

∴ from (29),

dSrdc=dBhdc+(qx1dpxdcqm1t1dpmdc)+(1t1)dqm1dc(34)

(f) Let Y(V+R) stand for national income and Yr(YP) for real national income.

Now,

Y=Bh+S(35)
Yr=BhP+Sr

and

dYrdc=dSrdc+dBhdcBhdPdc(36)

From (30), since c = 1,

dYrdc=dSrdc+dBdcB(1+dPdc)(37)

From (34),

dYrdc=(qx1dpxdcqm1t1dpmdc)+(1t1)dqm1dcBdPdc(38)

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*

Mr. Fleming, Chief of the Special Studies Division, is a graduate of Edinburgh University. He was formerly a member of the League of Nations Secretariat, Deputy-Director of the Economic Section of the U.K. Cabinet Offices, U.K. representative on the Economic and Employment Commission of the United Nations, and Visiting Professor of Economics at Columbia University. He is the author of numerous articles in economic journals.

1

The severity of import restrictions can be measured by the amount of the ad valorem import duty that would have an equally restrictive effect.

2

That is, the ad valorem level of import duties, if these constitute the effective limitation on imports, or the ad valorem equivalent of quantitative restrictions, if these constitute the effective limitation.

3

Since ph the price of home trade goods, is assumed to remain constant, it drops out of the definition of the various foreign trade elasticities in A. Thus ηa and єa become straightforward elasticities with respect to pm and px respectively, λx and λm likewise resolve into elasticities with respect to money expenditure in A. qm is short for qm1+qm2.

4
This will happen if
qm1ηa+dpxdpmqx1εa<qm+dpxdpmqx2.
5

Strictly speaking, the equivalent in A’s currency of the increase in the foreign currency value of A’s trade balance.

6

For details of these calculations, see Appendix, Part I, Part 11(a), and Part 1Kb).

7

Strictly speaking, the A-currency equivalent of the improvement in the foreign-currency trade balance.

8

Here the domestic value of imports is based on the domestic price before payment of any expenditure taxes but after payment of any import taxes.

9

Strictly speaking, the improvement in the trade balance referred to here is the improvement in the domestic-currency trade balance, but since, with a degree of import restriction equivalent to 50 per cent ad valorem, we are in effect assuming that the balance of trade is initially in equilibrium, it can be interpreted also as the domestic-currency equivalent of the improvement in the foreign-currency balance; see Appendix, Part II(b), equation (30).

10

The basic formulas underlying this calculation are found in Appendix, Part 11(a), (b), (c), and (d).

11

3.42 per cent of 101.2.

12

V-∆R/2= 2.05–0.22.

13

3.05–1.07.

14

108 per cent of 110.

15

See Appendix, Part 11(f). The statement is strictly true only when the trade balance is initially equal to zero.

16

The adverse effects exercised by exchange depreciation on real national income arise, as can be seen from the Appendix, Part 11(f), equation (38), from two factors: (1) a deterioration in the terms of trade, and (2) a decline in the volume of imports, the adverse influence of the latter being weighted by the margin between the domestic and the world market price of imports.

17

0.5 times ∆R.

18

0.8 times 110.

19

0.8 times 110.

20

3.42 per cent of 17.6.

21

0.6 times 0.66.

22

That is, the improvement, in A currency, in the balance of trade less the excess of the home market over the world market value of imports.

23

From an unpublished study by William H. White.

24

See J. Tinbergen, Statistical Testing of Business Cycle Theories: A Method and Its Application to Investment Activity (League of Nations, Geneva, 1939).

25

Strictly speaking, a slight rise in wages even in these industries may have been implicitly assumed—large enough to keep prices of home trade goods from falling as the scale of operation in these industries is reduced.