Article

Effect of Exchange Depreciation on a Country’s Export Price Level

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1950
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ONE OF THE main purposes of exchange depreciation in industrial countries is to lower export prices in order to increase the volume of exports. The question is to what extent and under what conditions exchange depreciation will achieve this objective.

When a country depreciates its currency, the gold or foreign currency equivalent of all its prices is reduced in proportion to the reduction in the value of the currency. However, various processes which tend to increase prices in the depreciating country begin to operate immediately after depreciation. These processes will offset partially, or in the limit totally, the effect of the depreciation. The purposes of this paper are to describe these processes of price increases and the factors which determine them, and to find statistical measurements for the extent of the increases and the residual net price fall in terms of gold.

The extent of the original depreciation is used as a yardstick against which to measure the price changes. Accordingly, the effectiveness1 of depreciation is defined as the ratio between the percentage net fall in price (in terms of gold) and the percentage depreciation. If, after depreciation, there is no adjustment whatever of domestic prices in national currency, the effectiveness is equal to unity, or 100 per cent; prices in terms of gold fall by the full amount of depreciation. If, after depreciation, prices in national currency rise by, for instance, 60 per cent of the amount of depreciation, the effectiveness of that depreciation would be measured as approximately2 0.4, or 40 per cent. If prices in national currency increase by the full amount of depreciation, the effectiveness would be zero.

The effectiveness of depreciation may be studied in relation to various sets of prices. In general it will be found to be smaller for wholesale prices, particularly if they include many prices of imported commodities, than for retail prices or the cost of living. In this paper, the effectiveness of depreciation is considered with particular reference to the question of possible improvement of the balance of payments of the depreciating country. On that account it is measured here in terms of movements in the export price index.3

Description of Adjustment Process

The process of price adjustment after exchange depreciation may be conveniently described by reference to Chart 1. Here the curves DD′ and S1S1′ describe respectively the demand for and the supply of a country’s exports prior to depreciation. The export price at the intersection of these two curves equals the distance AB. By depreciation the country is then assumed to lower the value of its currency in terms of foreign currencies as indicated on the left side of the chart. The percentage depreciation is equal to BCBA×100. The most immediate effect on export prices is a reduction in the same proportion: as a result of depreciation the export prices in national currency quoted on the day before will, to foreign buyers, appear to have been lowered in proportion to the depreciation. Prices in terms of gold fall to AC. The supply curve which in the very short run remains unchanged in terms of national currency moves downward to the position S2S2′ in terms of gold.

Chart 1.Determination of Export Price

But at point C there is no equilibrium between demand and supply. A new equilibrium is reached at point F where DD′ intersects S2S2′ and at a price level in terms of gold, FE, which is higher than CA, but lower than BA. This equilibrium position is temporary, however. The supply curve itself will move upward, for two reasons:

(a) There will be an automatic and prompt increase in the cost in national currency of imported raw materials entering into exports. It may be expected that the domestic price of these imported raw materials will adjust itself almost immediately and fully in proportion to the depreciation. The rise on this account of the supply curve in terms of gold above the level S2S2′ is likely to represent only a small fraction of its initial fall, depending on the percentage which the value of imported raw materials represents in the value of commodities ex-ported. For countries with very “open” economies, like those of Western Europe, this percentage may perhaps run as high as 20 per cent; for other countries, it will be much less; and for a country like the United States, it should be almost negligible.

This automatic increase in costs will occur in fully controlled economies, where both the volume and the price of imports are controlled, and in free economies, where both the volume of imports and their price are adjusted to domestic demand conditions. But in an economy where the volume of imports is controlled by a license system, etc., but prices of imported commodities are left free to reflect their scarcity, a rise of the landed cost of imported commodities up to the level of prevailing internal prices will generally tend to reduce the abnormal profits of importers rather than to increase the prices they charge. This situation probably prevails in many Latin American countries which apply import restrictions but no price controls.

(b) The rise in import prices through the effect on the cost of living on the one hand, and improved employment conditions as a result of depreciation on the other hand, will tend to raise wage rates. This factor may lead to a very considerable rise of the supply curve if the depreciating country is at or near full employment, and in particular if the population is strongly inflation-conscious. In the ultimate stage of hyperinflation, wages may actually be fixed day by day by reference to the rate of exchange; the effect will be practically the same if wages are fixed on the basis of a cost of living index and if merchants adjust their price quotations to fluctuations in the foreign exchange market. In such a situation, the cost curve will be raised quite rapidly by wage and other cost increases to the same extent that it had been lowered by depreciation, and depreciation becomes completely ineffective as a measure to lower prices.

Even without hyperinflation the supply curve will rise considerably if wage rates are fully adjusted for any increase in the cost of living. Any depreciation will then set in motion a chain of adjustments (import prices, cost of living, etc.). Since other incomes, in particular those of rentiers, are not adjusted to price increases, the process of reciprocal adjustment between the cost of living and wage rates will stop short of fully offsetting the effects of depreciation. Nevertheless, the rise of the supply curve in these circumstances will be considerably in excess of what might be expected on the basis of the ratio of imports to national income; and the effectiveness of depreciation in reducing prices will be reduced accordingly.4

In the chart a new supply curve S3S3′ has been drawn to indicate the increase from the S2S2′ level on account of the two causes mentioned. The upward movement can be measured by the distance CK. A new equilibrium will then establish itself at point H and the equilibrium price will be AL. The effectiveness of depreciation may then be indicated as LBBC.

Two further observations must be made with respect to the process of adjustment. First, if the depreciating country reduces its imports of raw materials, the world price of these materials in terms of gold may fall somewhat. Local currency prices will then not rise fully in proportion to the extent of the depreciation; but compared to prices paid by other countries, prices in local currency in the depreciating country will, after depreciation, be higher exactly in proportion to the extent of the depreciation.

Secondly, depreciation, if effective in improving a country’s balance of payments, will exercise a certain deflationary effect abroad, which is the counterpart of its inflationary effect in the depreciating country. The foreign demand curve for the country’s exports (DD′) may then be expected to move somewhat to the left. Since the deflationary influence is likely to be spread all over the world, this shift would generally not be so large and is disregarded in what follows.

Elasticities of Foreign Demand and Domestic Supply

It follows from the preceding that the price rise subsequent to depreciation may be considered as due to (a) factors determining the upward movement of the supply curve (the distance KC in Chart 1), and (b) the slopes of the supply and demand curves. The conditions affecting (a) have already been discussed. Those affecting (b) will now be considered.

Depreciation will be the more effective in lowering export prices, the greater the elasticity of supply of the depreciating country and the smaller the elasticity of foreign demand. The effectiveness will be equal to unity if either the domestic supply for exports is fully elastic or the foreign demand for the country’s exports is fully inelastic. Conversely, it will be equal to zero if either the country’s supply is wholly inelastic or the foreign demand for the country’s products is completely elastic. This will be readily verified by imagining different slopes of the supply and demand curves in Chart 1.5

The predominant factors which determine the magnitude of the elasticity of foreign demand are the following:

(a) The composition of exports. The more specialized a country’s exports, the less elastic will be the foreign demand since price substitution between its exports and the exports from other countries will tend to be limited.

(b) The share of the country’s exports in total world trade of similar commodities. The elasticity of demand for the commodities sold by an individual supplier in a given market tends to vary inversely with the relative size of that supplier.

(c) The number of competing countries depreciating at the same time. This is a special case of (b). If a number of countries depreciate at the same time, the elasticity of demand for the exports of each separately is reduced.

It would follow from the preceding that an industrial country, bulking relatively large in world trade and exporting specialized industrial articles, would experience a relatively large fall in its export prices as a result of depreciation. On the other hand, the smaller and less specialized industrial exporter would tend to meet with a smaller decline. Agricultural countries exporting standardized staples would also tend to experience only a small fall in their export prices as a result of depreciation.

Three factors may also be listed which determine the elasticity of supply:

(a) The nature of the commodities exported. Generally, the elasticity of supply of industrial products, the output of which can be adjusted in the short run, is greater than the elasticity of supply of agricultural products, except when large stocks of the latter are available.

(b) The proportion of exports to total national output of the commodities exported. Where a small proportion of the total production of a commodity is exported, a relatively small rise in price in terms of national currency may free from domestic consumption a quantity which would be large compared with the previous volume of exports of that commodity.

(c) The state of business conditions. Generally speaking in conditions of depression, when there are large stocks and ample unused capacity, the elasticity of supply would be great. In conditions of full employment, on the other hand, the supply curve will be steep and, in the limit, where all commodities that could possibly be exported are in fact exported, the elasticity of supply for export will be zero, and the effectiveness of depreciation accordingly also zero.

In conditions of full employment, which will often be accompanied by a tendency toward inflation, there are thus two factors tending to minimize the effectiveness of depreciation: the tendency of the supply curve to rise by a large proportion of the initial fall caused by depreciation, and the steepness of the supply curve. These two factors work in the same direction, but their effects are not cumulative. The more the supply curve rises, the less increase there is in the quantity exported (compared with the position before depreciation) and there-fore the smaller is the movement along the supply curve. If, in the limiting case, the supply curve in terms of gold after depreciation moves up all the way to the position S1S1′, there will be no increase in the quantity exported and therefore no influence at all of the slope of the supply curve on the export price.

Statistical Findings

So far the effect of exchange depreciation has been discussed with reference to the absolute price level of one country. Before statistical measurement can be considered, it is necessary to pass to relative prices, viz., the export price level of the country under consideration compared with the export price levels of countries exporting similar commodities. The shift from absolute to relative prices is necessary for (a) logical and (b) statistical reasons.

(a) Exchange depreciation, in order to improve the competitive position of a country, must lower the price level of the country itself not only in absolute terms but also in comparison with the price levels of competing countries. The price fall in the depreciating country may entail a fall in prices in competing countries, so that the relative price fall will be smaller than the absolute price fall of the first country.

(b) Statistically it appears necessary to measure the effectiveness of depreciation by reference to relative rather than absolute prices, because many factors in addition to fluctuations in the exchange rate influence absolute prices and thus obstruct observation of the effects of changes in rates. Since, however, these other factors may be assumed to affect competing countries roughly in the same way, the price ratio between the two countries may be assumed to reflect mainly fluctuations in the relative rate of exchange between them. Among the other factors, mention should be made in particular of fluctuations in world market prices of raw materials and fluctuations in world demand. Both have an influence on the absolute level of export prices of any one country, which often overshadows the influence of moderate fluctuations in the rate of exchange. By calculating the ratio of the export prices of one country to those of another, however, the effect of these general factors is largely eliminated.

Therefore, an endeavor will be made here to measure the effectiveness of depreciation by reference to relative export prices. The effectiveness is defined as the percentage change in the ratio of the export prices of two countries (prices in both being expressed in the same currency) which is associated with a 1 per cent change in their exchange rate.6

The effectiveness, so defined, could be estimated for any pair of countries or for every individual country compared with some weighted average of all its competitors, with weights based on the extent to which its products were in competition with those of other countries. In the examples which follow, one country of comparison, rather than a weighted average of many countries, has been taken merely for convenience; and in all the examples the one country is the United States.

A comparison between two countries yields results which may reflect the reactions of either or possibly of both. This point is analyzed in the Appendix. The conclusions of this analysis are that the comparisons of the United Kingdom with the United States and of Sweden with the United States measure primarily the effectiveness of depreciation as far as the United States is concerned; in the other cases considered, the effectiveness measured is that of the country which is being compared with the United States (i.e., France and Poland).

It was found in the preceding section that the slope and the “mobility” of the supply curve are greatly affected by the level of activity in the depreciating country; the slope of the foreign demand curve may, on the other hand, be assumed to be relatively constant under varying conditions. Accordingly, it would be expected that conditions of slump, boom, inflation, and hyperinflation would, in the order listed, show decreasing coefficients of effectiveness of depreciation. These expectations are confirmed by the examples described below and summarized in Table 1.

Table 1.Effectiveness of Depreciation under Various Supply Conditions
Supply ConditionsCountries ComparedPeriodCoefficient of Effectiveness of DepreciationChart Reference
I.SlumpU. K. —U. S.1931-330.042
Sweden—U. S.1931-330.993
France—U. S.A.IQ—I V Q 19330.955
II.BoomFrance—U. S.B.IIIQ 1936—II Q19370.355
France—U. S.C.IIIQ 1937—IV Q19380.705
III.InflationFrance—U. S.A.IQ—I V Q 19190.956
B.IQ 1920—IV Q19220.776
C.IQ 1923—III Q19240.446
D.IVQ 1924—III Q19260.336
Poland—U. S.IIIQ 1921—II Q19220.407
IV.HyperinflationPoland—U. S.IIIQ 1922—III Q192307
Poland—U. S.IIIQ—IV Q 1923Negative7

The coefficients indicate only the general order of magnitude of the effectiveness of exchange depreciation and should by no means be considered as precise measurements because, among other reasons, the number of observations on which they are based is quite small. In particular, the coefficients of effectiveness found for depreciation in slump conditions would appear to be the maximum that might be expected on theoretical grounds.7 In general, however, the effects shown are in such satisfactory accord with the expectations derived from the theoretical model developed above that we may be reasonably confident of their approximate accuracy.

Depreciation in slump conditions

Chart 2 compares quarterly figures of the ratio of British to American export price indices for manufactured products (both in terms of the same currency) and the sterling-dollar exchange rate (both ratios given as index numbers, 1930 = 100). The slope of the regression lines fitted to the points in the chart is 0.94. This would indicate that during the period considered a one per cent depreciation of the dollar vis-à-vis sterling would have lowered American prices by 0.94 per cent compared with British export prices, and it might be assumed that the effectiveness as far as a depreciation by the United Kingdom is concerned would have been of the same order of magnitude. In that period, ex-change depreciation by either the United Kingdom or the United States would probably have been almost completely effective, because of an inelastic foreign demand combined with a very elastic home supply.

Chart 2.Ratio of British to U. S. Export Price Indices, Compared with Sterling-Dollar Exchange Rate, Second Quarter, 1931—Fourth Quarter, 1933

(Index numbers, 1930 = 100; double logarithmic scale)

Such statistical estimates as are available on the price elasticity of foreign demand for the exports of both the United States and the United Kingdom in the interwar period give very low figures: for both countries, approximately — 0.4.8 While these estimates cannot be taken as having a high degree of precision it would seem plausible that the elasticities would be low. Thus, as far as the United Kingdom is concerned:

(a) British exports consist to a large extent of specialized industrial products and the possibilities of substitution for such products are usually limited.

(b) The United Kingdom bulks large in world trade in industrial products and her share in individual markets is particularly high. This “monopolistic” position also tends to make the elasticities of foreign demand for her exports low.

On the supply side in the early thirties there was large-scale un-employment, ample unused capacity, and large stocks of commodities in both the United States and the United Kingdom. In these conditions the supply of commodities for export must have been almost completely elastic.

In these same conditions there was also extremely little tendency for the supply curve of the depreciating country to move upward, either absolutely or in relation to that of the country of comparison. When Britain depreciated in 1931, the cost of many of her raw materials did not increase, since the countries from which they were imported, such as the Dominions and the Scandinavian countries, depreciated their currencies at about the same time and sometimes even to a greater extent. British wage rates continued to fall during the period 1931-33. Generally speaking, the money wage rate in the United Kingdom was closely connected with fluctuations in the cost of living and in the level of employment. The cost of living index continued to decline during this period because of the fall in import prices in terms of sterling. Although the index of employment showed some increase after the depreciation, the actual amount of unemployment remained very large and recovery did not get well under way until the building boom started in 1934. Thus all factors worked in the direction of making the depreciation almost completely effective.

The data on Sweden compared with the United States9 show a very similar picture, the relationship between percentage changes in relative prices and in the exchange rate appearing as high as 0.99 (Chart 3).

Chart 3.Ratio of Swedish to U. S. Export Price Indices, Compared with Krona-Dollar Exchange Rate, Second Quarter, 1931—Fourth Quarter, 1933

(Index numbers, 1930 = 100; double logarithmic scale)

The elasticity of foreign demand for Swedish exports with respect to price was probably small; it has been estimated as —0.37 for the interwar period.10 This low elasticity occurs in spite of the fact that Sweden’s share in world markets of manufactured products is small; it probably reflects the facts that Swedish exports consist partly of very specialized industrial products such as telephone apparatus, ball bearings and roller bearings, etc., for which substitution of competing exports is very limited, and that Sweden’s share in certain categories of goods, such as iron ore, pig iron, and iron castings, is quite large.

In Sweden, as in the United Kingdom, depression conditions prevailed in the early thirties, with unemployment and falling wages, which would make any upward shift of the supply curve improbable and tend to make for a very elastic supply curve.

Depreciation in boom conditions

The period 1933-38 for which the French experience has been analyzed may be divided into four segments, reflecting different cyclical positions in France: (a) first quarter 1933—fourth quarter 1933, (b) first quarter 1934—first quarter 1936, (c) second quarter 1936—second quarter 1937, (d) third quarter 1937—fourth quarter 1938. The effectiveness of changes in the French exchange rate in these four periods was quite different. A statistical estimate of the elasticity of foreign demand for French exports for the interwar period sets this elasticity at — 0.77;11 no statistical evidence was found to indicate that this elasticity differed in different phases of the trade cycle.

In the absence of quarterly figures for French export prices, quarterly figures of the French wholesale price index have been used. As shown in Chart 4, the changes in the annual figures of the wholesale price index and those of the export price index agree very closely.

Chart 4.Annual Averages of Wholesale and Export Price Indices in France, 1923-38

(1929 = 100)

First quarter 1933fourth quarter 1933: Slump in France. During this period the United States depreciated while France remained on gold. This case may be treated as one of exchange appreciation by France. As shown in Chart 5, the four quarters of 1933 lie very closely along a straight line on a logarithmic scale (line A) with a slope of about 0.95. This means that the French appreciation raised the relative price level of France by 95 per cent of the extent of the appreciation. The high value for the coefficient is accounted for, as in earlier cases, by the inelastic foreign demand and the elastic supply, both in France and in the United States.

Chart 5.Ratio of French to U. S. Wholesale Price Indices, Compared with Franc-Dollar Exchange Rate, First Quarter, 1933—Fourth Quarter, 1938

(Index numbers, 1930 = 100; double logarithmic scale)

First quarter 1934first quarter 1936. The relative parities remained unchanged during this period but prices in France, compared with prices in the United States, fell steadily until the fourth quarter of 1935. At the beginning of 1934, the dollar was stabilized and from then on United States export prices remained practically unchanged. The changes in relative prices were due to the fall of French export prices and were not directly connected with the exchange rates. The rapid fall of French prices was the result of a most drastic deflation policy in France, caused mainly by the deterioration of the French balance of payments and by the unwillingness to go off gold. The deflation policy took the form of a sharp reduction in government expenditures and of direct cuts of salaries, wages, retail prices, interest rates, etc.

By the fourth quarter of 1935, the French farmer became unwilling to stand further deflation and the Government took various steps to raise farm prices by increasing agricultural subsidies, etc. The net result was a progressive rise in the cost of living and in the prices of agricultural raw materials. Wage rates also showed some tendency to rise. Thus from the fourth quarter of 1935 to the establishment of the Popular Front in June 1936, French prices recovered somewhat.

Third quarter 1936fourth quarter 1937: Boom conditions in France. This was the period of the so-called “Blum experiment.” In order to promote rapid recovery of the national economy, four main policies were adopted: (a) devaluation of the franc, (b) raising wage earnings by increasing wage rates and adopting holidays with pay, (c) “reflation,” mainly by means of public works, and (d) the forty-hour week.

During this period boom conditions prevailed in France. In the first quarter of 1937, the volume of production was not much above the lowest level of the slump; France was, nevertheless, rapidly approaching a state of “full employment,” as the forty-hour week law eliminated at one stroke partial unemployment, and the supply of skilled labor suddenly became scarce. But whether full employment was genuine or artificial, its effect upon the French economy was the same. No further expansion of production was possible. The elasticity of supply of French exports was very low; hence depreciation became relatively ineffective. The upward shift of the supply curve further tended to reduce the effectiveness of depreciation. It has been estimated by Kalecki that labor costs in French industry rose by 58 per cent during the Blum experiment,12 as a result of increases of the money wage rate and the adoption of holidays with pay. Moreover, depreciation led to an increase of the cost of imported raw materials, estimated by Kalecki to have been 63 per cent.13

The slope of line B in Chart 5, which is only 0.35, reflects the supply conditions, mentioned in the preceding paragraph. Owing to these conditions, depreciation in this period led to a reduction of French prices in terms of gold compared with foreign prices by only about one third of the degree of depreciation.

Third quarter 1937fourth quarter 1938: Recession in France. The Blum Government went out of office in June 1937. Its successor, after a renewed depreciation of the franc, reversed the internal economic policy by adopting a policy of budgetary retrenchment. In the autumn of 1937, there was a recession in France. Industrial production declined continuously from November 1937 to August 1938. Wage rates and general price levels showed only very small increases. Broadly speaking, the French economy during this period was in a stage of mild recession, though not in a slump.

These conditions affected the coefficient of the effectiveness of exchange depreciation. As shown by line C in Chart 5, the coefficient for this period was 0.70.

Depreciation during inflation

In Chart 6 quarterly changes in the ratio of French to United States prices are shown in comparison with the dollar rate of exchange for the French franc from the first quarter of 1919 through the fourth quarter of 1926. Three interesting features may be observed.

Chart 6.Ratio of French to U. S. Export Price Indices, Compared with Franc-Dollar Exchange Rate, First Quarter, 1919—Fourth Quarter, 1926

(Index numbers, 1919 = 100; double logarithmic scale)

First, the points lie closely along four lines. In two cases the shift from one line to the other reflects a sharp fall of the exchange rate (A to B, and B to C), due to a very sudden and substantial fall of the exchange rate caused probably by speculative factors. In the last case (C to D) the shift represents a violent rise of relative prices, which may be interpreted as a rise of internal prices due to domestic inflationary factors to which there was no immediate adjustment of the rate of exchange.

Secondly, as the lines shift to the left their slopes gradually decrease. The slopes of the lines A, B, C, and D are, respectively, 0.95, 0.77, 0.44, and 0.33. This fall is due to the fact that, as inflation in France proceeded, the economy came nearer full employment and, in particular, all members of the economy became more inflation-conscious.14 Hence the elasticity of supply declined, and the supply curve adjusted itself more rapidly and more fully to increased import prices in terms of francs. Thus successive rounds of depreciation became less effective in lowering relative prices.

Thirdly, except for the shifts between the various lines, to which we have referred, there is no clear or consistent lag or lead between the changes in relative prices (expressed in dollars) and changes in the exchange rate. This is probably due to a combination of factors. In the earlier period, when the effectiveness of depreciation was still very large, the fall of French prices in terms of dollars was instantaneous and the subsequent upward adjustment of the supply curve was minor. In the later stages, on the other hand, when the significance of these upward adjustments became successively greater, the corrections themselves occurred quite quickly after the initial depreciation, as the population became increasingly inflation-conscious.

Depreciation during hyperinflation

The best known case of hyperinflation is that of Germany in 1922-23. During the later stages of the German inflation, the precipitous fall of the mark was accompanied by a gradual increase in the German price level in terms of gold.15 The movements of prices in Germany in 1922-23 were so rapid, however, that statistical observation became particularly difficult. Consequently, various price indices for Germany for that period show quite considerable differences, and quantitative conclusions based on such indices would be particularly liable to error. We prefer, therefore, to use Poland as an example; that country, though affected by hyperinflation, did not experience quite the dizzy speed of Germany.

Chart 716 shows a coefficient of 0.40 for the relation between a fall in the exchange rate and the decline in relative prices from the third quarter of 1921 to the period early in 1922. Such a coefficient is in accordance with that found for the later stages of the French inflation in 1923-26. Afterwards, however, from the middle of 1922 until the third quarter of 1923, while the exchange rate fell from 36 per cent to 1 per cent of its par established in 1921, relative prices did not decline further. At the end of 1923 and shortly before the stabilization, which occurred in April 1924, the phenomenon typical of hyper-inflation itself was shown. The exchange rate fell in one quarter by about nine tenths. At the same time, relative prices actually increased considerably with the result that in the fourth quarter of 1923 the zloty, according to the statistics used, was overvalued by about 40 per cent.

Chart 7.Ratio of Polish to U. S. Wholesale Price Indices, Compared with Zloty-Dollar Exchange Rate, Third Quarter, 1921—First Quarter, 1924

(Double logarithmic scale)

Thus, during the period from 1921 to the end of 1923 Poland went through three stages of effectiveness of exchange depreciation: a stage of small but positive effectiveness at first; then a stage, which lasted almost two years, of approximately zero effectiveness; and finally a stage of negative effectiveness, coinciding with the presence of hyper-inflation.

APPENDIX

The purpose of this Appendix is to show more precisely the nature of the relationship investigated in the text. For this purpose it is convenient to present in algebraic form the various relations that have been assumed to exist. Exponential equations have been selected as the type probably most suitable to reflect these relations, in particular when large price changes occur.

A number of variables and coefficients are introduced; those with subscript “w” reflect world conditions, those without subscript or accent pertain to country 1, and those without subscript, but with an accent, to country 2:

pwworld price level in terms of gold (of commodities imported by countries 1 and 2)
ywworld demand factor (affecting exports of countries 1 and 2)
p, pnational price levels of export products in countries 1 and 2, respectively
x, xexport volumes of countries 1 and 2
r, rrates of exchange of countries 1 and 2 in units of national currency per unit of gold
β, β′total1 proportional increase of supply curve in response to rise in import prices expressed in national currency
γ, γ′income elasticity of demand for exports of the two countries
η, η′elasticity of substitution of demand for exports of the two countries (negative magnitudes)
ε, ε′elasticity of supply of exports in the two countries

The following relations are assumed to hold. Constant terms are omitted.

I. Price formation (supply equations)

II. Determination of volume of exports (demand equations)

Combination of (1) and (3), and (2) and (4) yields

Hence for prices expressed in comparable units, the following are obtained:

Division of (5′) by (6′) gives

Writing ζ (a positive magnitude) for -[η+η] yields

This form is not yet satisfactory for our purposes since it defines the price ratio pp·rr as a function of four variables: pw, r, r′, and yw. Certain simplifying assumptions will be necessary to express the price ratio as a function of rr, i. e., the rate of exchange between the two countries. Various simplifications, depending on the nature of the case analyzed, may be legitimate.

(a) The two countries may be such that it is reasonable to assume that γ is approximately equal to γ′ and ∈ to ∈′. This would reduce the influence of yw, if it itself does not fluctuate too strongly, to an element of minor importance.

(b) It may further be permissible to assume that β is very near to β′. In this case the term with pw becomes insignificant. Assuming both (a) and (b), equation (8) reduces to

where 1-β1+ζ or 1-β1+ζ would represent the effectiveness of depreciation for either country.2

If, for example,

then the figure found for the effectiveness would be

A table of the values for the effectiveness for various values of β, η, and ∈ is given below. The values for the three coefficients are all assumed equal for the two countries.

Values for1-β1+ζand1-β1+ζ
β, β′
0.050.10

(1–β),
0.15

(1–β′),
0.20
∈, ∈′η, η′ζ1 + ζ0.950.900.850.80
1— 0.10.21.20.790.750.720.67
20.11.10.860.820.770.73
50.041.040.910.860.820.77
100.021.020.930.880.830.78
1— 0.5120.480.450.420.40
20.51.50.630.600.570.53
50.21.20.790.750.720.67
100.11.10.860.820.770.73
1— 1230.320.300.220.27
2120.480.450.420.40
50.41.40.710.640.610.57
100.21.20.790.750.710.67
1— 2450.190.180.170.16
2230.320.300.280.27
50.81.80.560.500.470.44
100.41.40.680.640.610.57

The assumption is now made that condition (a) is rigorously fulfilled, but condition (b) is not. Then (8) may be written as follows:

This may be arranged in two ways:

The term (pw · r) stands, it will be recalled, for the price of imported materials expressed in local currency in country 1. Hence, if this price level is constant, correlation of the price ratio (pp·rr) with rr will yield an estimate of the effectiveness for country 2 (equation 10a); and if pw · r′ is constant, correlation will yield an estimate of the effectiveness for country 1 (equation 10b).

More generally, pw · r may be assumed to fluctuate to some extent with rr. Let

Then it will readily be seen that the exponent found by correlating (pp·rr) with rr will equal β-11+ζ+ρβ-β1+ζ. For ρ = 0 and ρ = 1 this yields the answers indicated in the preceding paragraph. In general, the exponent found will be between the values for the effectiveness of the two countries provided 0<ρ<1, i.e., that absolute import prices in the depreciating country increase, but by less than the extent of depreciation.

In the statistical observations bearing on depreciation in the slump, conditions (a) and (b) would seem to be approximately satisfied. Since import prices remained more nearly constant in the countries which depreciated in 1931-32 than in the United States, the measured effectiveness of depreciation for those years probably refers more nearly to that of the United States than to that of the countries compared with the United States. But in 1933, French import prices, relative to those for the United States, declined, while the number of francs per dollar also declined; the coefficient of effectiveness, therefore, should be read primarily as applying to France.

(c) In other situations, where r and p fluctuate sharply over a short period of time, the fluctuations in pw, yw, and r′ during the same period may be comparatively negligible. The terms with pw and yw may then be left out of account even though their coefficients are not assumed to be negligible. In that case, (9) would also hold; but the coefficient found should be interpreted either as a measurement of β-11+ζ, if p and r fluctuate during the period of observation, or of β-11+ζ, if p′ and r′ fluctuate.

In the observations on depreciation or boom and inflation, conditions (a) and (b) are probably not applicable, but (c) is; in these circumstances it is the effectiveness of depreciation for the depreciating country which is measured.

Reflecting not only the direct, but also the indirect, effect via wages, i. e., corresponding to the ratio α11-α2 in footnote 4, p. 52.

The sign is reversed, compared with the exponent in (9), because r is expressed in units of national currency per unit of gold, whereas in the text depreciation is expressed as a lowering of the value of the national currency in terms of gold.

The term “effectiveness” is unambiguous if supply in the depreciating country is fully elastic. If supply is not fully elastic, the term becomes slightly awkward, since the degree of “effectiveness” depends on the elasticity of foreign demand, and a high “effectiveness” may simply indicate a low elasticity of foreign demand.

The term “approximately” is necessary since the effectiveness can strictly be defined as the percentage increase in the price of foreign exchange minus the percentage increase in prices only for an infinitely small degree of depreciation.

Generally, at present, improvements in the balance of payments on the import side are more likely to be sought through import controls than by relying on the effects of relative prices.

If the price level in the country (represented by the cost of living) is indicated by p, the wage level by I, and import prices by pm—all as index numbers with their base at the moment of depreciation—and the ratio of imports to national income by ai and of wages to national income by α2, the following equations show the changes that will take place as a result of an increase in import prices when wage rates are tied to the cost of living:

Hence:

Since α2 would in most countries be of the order of 50 per cent, the wage adjustment would double the original impact of the rise of import prices. If incomes of other classes, eg., of entrepreneurs, were also adjusted on the basis of the increase in prices, the domestic price level would tend to increase more. To represent the limiting case, where all domestic incomes would be so adjusted, we can write α2 = 1 — α1, in (1); this would transform (3) into Δp = Δpm. (Cf. J. J. Polak, “On the Theory of Price Control,” Review of Economic Statistics, Vol. xxvii, 1945, pp. 10-16.)

The point may also be shown algebraically. Apart from any upward movement of the supply curve, the effectiveness of depreciation would be represented by the fraction:

This fraction will be between zero and one and will reach these two limits in the four cases indicated in the text.

Prof. Harris has developed a concept of “price adjustment” to exchange depreciation which he defines in a manner very similar to our definition of the effectiveness of depreciation, viz., Adjustment = 1—Effectiveness (Seymour E. Harris, Exchange Depreciation, Cambridge, 1936, p. 69).

The theoretical maximum would be 1 minus the import component of exported commodities. For the United Kingdom this would be about 80; for the United States, very nearly 1. Alternative values for various assumed values of the coefficients are shown in a table in the Appendix. But the calculations obviously do not have the degree of precision necessary to make anything out of small differences.

See T. C. Chang, “Statistical Note on the World Demand for Exports,” Review of Economics and Statistics, Vol. xxx (1948), p. 107.

The slight fluctuations of the value of the krona to that of sterling, which did not exceed a few per cent during this period while both currencies fell sharply, preclude a significant comparison between Sweden and the United Kingdom.

T. C. Chang, op. cit.

T. C. Chang, op. cit.

M. Kalecki, “The Lesson of the Blum Experiment,” Economic Journal, Vol. 48, p. 26.

Ibid.

The first line should be interpreted mainly as an adjustment of the sale of exchange to the postwar price level after the end of “pegging” of the franc.

See C. Bresciani-Turroni, The Economics of Inflation (London, 1936), pp. 136-45.

The prices compared are the Polish wholesale price index and the U. S. wholesale price index. In view of the extremely wide movement of Polish prices, it is of relatively minor importance which country is chosen for comparison or what series is selected for the country of comparison.

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