Devaluation and the Terms of Trade

The Review of Economic Studies, Ltd.

Devaluation and the Terms of TradeAuthor(s): Charles KennedySource: The Review of Economic Studies, Vol. 18, No. 1 (1950 - 1951), pp. 28-41Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2296104 .

Accessed: 25/06/2014 02:24

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Oxford University Press and The Review of Economic Studies, Ltd. are collaborating with JSTOR to digitize,preserve and extend access to The Review of Economic Studies.

http://www.jstor.org

This content downloaded from 91.229.229.205 on Wed, 25 Jun 2014 02:24:44 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=oup

http://www.jstor.org/stable/2296104?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Devaluation and the Terms of Trade

1.

Whatever his field of study, the economic theorist is always faced with the same methodological problem. Is he to choose the method of partial equilibrium analysis and achieve simplicity while neglecting repercussions in the rest of the economic system which may have an important bearing on his problem ? Or, alternatively, is he to take into account such repercussions, thus seriously complicating his analysis and diminishing his chance of obtaining intelligible results ? There is only one legitimate way out of this dilemma. It may be possible to make assumptions wvhich enable one to achieve the necessary simplification of the actual complex economic system, without unduly distorting the picture. The Keynesian system is no doubt the most impressive example of the use of this technique. With the help of a number of sweeping though not unreasonable assumptions, the closed economic system has been reduced to an easily manageable set of relationships.

Because of the greater complexity of international trade, it has always been extremely difficult, if not impossible, to make similarly effective assumptions in that field. Traditionally, a less respectable means of escape from the methodological dilemma has been sought. Repercussions have simply been taken for granted. A good example of this approach is to be found in the passage from Edgeworth, which is quoted in the opening paragraph of Dr. Mosak's General-Equilibrium Theory in International Trade.'

a movement along a supply-and-demand curve of international trade should be considered as attended with rearrangements of internal trade; as the movement of the hand of a clock corresponds to considerable unseen movements of the machinery.2

By this device, one obtains the simplicity of partial equilibrium analysis and at the same time one has the comfortable feeling that one has taken everything into account. But the simplicity is, of course, of a spurious kind, and the method can hardly be regarded as satisfactory. The economist may occasionally be asked to tell the time, but his main task is to discover how the clock works.

Later writers in the field of international trade have often retained the traditional outlook. Mrs. Robinson's work on the four elasticities of foreign trade in her two pioneer essays on the foreign exchanges3 suffers very largely from this defect. It is my intention in this article to treat of one, and only one, of the problems which Mrs. Robinson tackles; but, in doing so, we shall venture a little further below the surface. In Beggar-my-Neighbour Remedies for Unemployment Mrs. Robinson has found an expression in terms of the four elasticities of demand and supply for the condition that the devaluation of a country's currency should have an adverse effect on its terms of trade.4 We shall find that, unless we are to regard the elasticities concerned as being used in a special and not very helpful sense, her result is only valid subject to an important simplifying assumption, which is not made explicit in the text and which has only been hinted at in more recent discussion. The implicit use of this assumption means that some of the practical conclusions she reaches in her essay must remain open to question. We shall find also, however, that when we begin to

28



DEVALUATION AND THE TERMS OF TRADE 29

take account of some of the internal repercussions of a fall in the rate of exchange, the problem rapidly becomes too complicated to permit of any simple solution. Never- theless some points of interest will emerge.

II.

Mrs. Robinson's method is to assume a small fall in the exchange value of the home country's currency and then to suppose that equilibrium is again reached in the markets for its exports and imports. The change in the home price of exports can then be expressed in terms of the relationships between the change in the supply of exports and the change in the home price and between the change in the demand for exports and the change in the foreign price. Similarly, the change in the home price of imports can be expressed in terms of the relationships between the change in the demand for imports and the change in the home price and between the change in the supply of imports and the change in the foreign price. Mrs. Robinson writes these four relationships in elasticity form, and is able to show with little difficulty that the change in the

terms of trade will be adverse or favourable according as '" is greater or less than Eh

where ek and ef are respectively the elasticities of home demand for imports and

foreign demand for exports, and -qh, and qf are the elasticities of home supply of exports and foreign supply of imports.5

Whether one can accept this simple result depends on whether the above four relationships expressed in elasticity form can properly be regarded as elasticities of demand and supply. Mr. Kahn has given the game away on this score in a recent article.6 He is there concerned with two of these relationships in a somewhat different context; but in designating them as elasticities he is careful to use the convenient shelter of inverted commas. It is, I think, worth while quoting his explanation:

Before we proceed to attribute imaginary magnitudes to the two elasticities, we must explain why, in defining them above, we made use of inverted commas. The point is one which Professor Pigou has recently brought to light. As ordinarily understood, the elasticity of foreign supply of imports would show the relationship between an increase in the volume of production by foreigners of the commodities in question and the rise in prices (measured in terms of overseas wage units) required to elicit such an increase in productionl. But the responsiveness of foreigners' production to a rise in prices will be increased if it is accompanied by an increase in the supply to foreigners of the goods exported by the country under review: an increase in England's exports of cotton-goods will assist the process of diverting foreign labour from foreign cotton-mills to foreign wheat-fields, with the result that the relevant elasticity of foreign supply of wheat will be greater than it would be if measured in the ordinary way.

For a similar reason, the relevant elasticity of foreign demand for exports is greater than the same elasticity measured in the ordinary way: a given rise in the price of cotton-goods will be more effective in choking off demand if it is accompanied by an influx of labour from foreign wheat-fields into foreign cottoti- inllS 7



30 THE REVIEW OF ECONOMIC STUDIES

Now what Mr. Kahn is in effect saying is thait the demand of any country for imports will depend not only on the price of imports, but also on the price of substitutes for imports; and that its supply of exports will depend not only on the price of exports, but also on the price of the other commodities in the production of which the factors could be employed.8 Thus the relationships between the actual change in a country's demand for imports and the actual change in their price and between the actual change in its supply of exports and the actual change in their price cannot properly be regarded as elasticities of demand and supply, for it is likely that there will also be some change in the price of home goods for the domestic market, wvhich are a substitute for imports and in the production of which factors are employed which might be used in the production of exports.

I am unable to make out whether Mrs. Robinson has simply overlooked the internal repercussions of a fall in the exchange rate or whether she has taken them for granted. It is difficult to believe the former in view of her remarks when she first makes mention of the four elasticities in her earlier essay. There she is ready to recognise that the home elasticity of supply of exports is influenced by the home elasticity of demand for exportable goods; and that the home elasticity of demand for imports is influenced by the home elasticity of supply of rival commodities.9 On the other hand she seems reluctant to go the one step further and admit, for example, that the home elasticity of supply of commodities rival to imports may be influenced by the foreign elasticity of demand for exports; wvhich must be the case if similar factors of production are employed in the production of both types of commodity.

I am inclined to think that there may be an altogether different explanation for her neglect of internal repercussions. When, later in her second essay, she briefly considers the effects of changes in incomes and activity on the terms of trade, she is quite aware of the possibility of shifts in the demand curve for imports and in the supply curve for exports.'0 My suspicion is that Mrs. Robinson has banished any consideration of repercussions on the price of home goods from her mathematical treatment of the problem in terms of the four elasticities and is including such repercussions as among the effects of changes in incomes and activity. Thus, if the price of imports rises, the change in the demand for imports is considered in the light of the elasticity of demand for imports, but anly change in the amount spent on imports and consequently in the amount spent on home goods involves a change in incomes and activity, and is considered qualitatively later. Similarly, if the price of exports rises, the effect on the supply of exports is considered in the light of the elasticity of supply of exports; but the consequences of any change in the amount of factors employed in the production of exports are considered among the effects of an increase in activity.

As an analytical procedure this is clearly quite unsatisfactory. That Mrs. Robinson should feel justified in using it is to be explained, I think, by a mistaken belief on her part that the effects of changes in incomries and activity on the Position of the demand and supply curves come somehow later in time than the movements along the demand and supply curves. Two quotations will serve as illustration:

The fall in the world price of export goods in the first instance will be greater the less elastic is the foreign demanid for them, and the more elastic is the home supply."




Any increase in the balance of trade . .. will lead to an increase in home incomes and activity.12

Now opinions may differ as to whether the multiplier effects of a change in the balance of trade take place after a time-lag or not. Mrs. Robinson appears not to have realised, however, that a change in the balance of trade itself represents a change in incomes-certainly in money incomes, and, except under extremely rigid conditions of supply, in real incomes and activity as well. Thus, when Mrs. Robinson treats of the problem " in the light of " the four elasticities, she overlooks the fact that the elasticities cast a shadow as well; that, for example, any change in the amount spent on imports means in general that there will be a change in the demand for home goods. The latter effect is simultaneous with and inseparable from the former; and to attempt, as Mrs. Robinson seems to do, to take account of the latter only later when she is discussing the consequences of a change in incomes and activity is to make nonsense of her earlier analysis in terms of the four elasticities.

The last few paragraphs have inevitably been somewhat conjectural. Mrs. Robinson, concerned as she is with a wider problem, is unable to give very much space to a discussion of her assumptions and method. And it is very likely that, in attempting to find an explanation for the omission of the repercussions on home prices from her analysis, I have done less than justice to her thinking. Be that as it may, it will be agreed that, as it stands, her treatment of the problem in terms of the four elasticities is incomplete and therefore unsatisfactory. If we are to accept her result, inverted commas must be given to all four elasticities. The simplicity of her result is therefore illusory. Our task in the remainder of this article will be to attempt to make good this shortcoming.

III.

I find it hard to believe that an elasticity in inverted commas will prove a useful tool of economic analysis. The better procedure would seem to be to take any change in the price of home goods into account. This is the technique that we shall adopt in the present section. It has the added advantage that it enables us also to take account of the effect of changes in income on the demand for imports, although in this connection we shall have to assume that the demand for imports is independent of changes in the distribution of income.

Let us imagine that there are four different kinds of goods: exports (E), imports (I), home goods (H), and foreign goods (F). Units for the four kinds of goods are so chosen that their respective prices (e, i, h and f) measured in terms of home currency are all equal to unity in the initial position. The foreign exchange value of the home currency is also taken to be unity in the first instance, so that the foreign prices of exports, imports, home goods and foreign goods (e', i', h' and f' respectively) are also initially equal to unity. In order to confine our attention to the direct effects of the change in the rate of exchange, we shall assume that the demand for goods for investment purposes, both at home and abroad, remains constant throughout. For purposes of simplification, we shall also make the not very plausible assumption that exports and imports are required for consumption purposes only, so that, for example, the supply of exports will not be directly influenced by the price of imports.'3

One more digression must be made before we continue. We must explain why we are measuring prices in units of home currency and not, as Mrs. Robinson does, in




home wage-units. The device of measuring prices in home wage-units has one advantage but also one serious disadvantage. On the one hand it makes the analysis of the effects of devaluation on the terms of trade immediately applicable to the case of a fall in money wages. On the other hand it depends for its efficacy on the constancy of money wages while the new equilibrium is being reached. Mrs. Robinson is quite ready to make this last assumption, since for her it serves another purpose as well. For when discussing the effects of the different " beggar-my-neighbour" expedients she wishes to ensure that each expedient is allowed to produce its own full effect. Thus, she writes, for instance:

. . . it must not be supposed that the influence of a fall in the exchange rate on the balance of trade is counteracted by a rise in money wages.'4

I believe that in this particular case MIrs. Robinson is chasing a will-o'-the-visp. A fall in money wages is equivalent to a fall in the exchange rate only in so far as it implies a proportional fall in all prices and incomes. It is not enough, therefore, to assume constancy of money wages alone, if we are to allow devaluation to produce its " full" effect. We must also assume constant rewards to other factors. There seems to me no difference in principle between an increase in prices which arises when an increase in demand is confronted by a scarcity of labour and one which arises when an increase in demand is confronted by a scarcity of capital or entrepreneurship. If we are to allow the fall in the exchange rate to produce its own " full " effect, we must surely suppose that there is no scarcity of any factor and consequently no change in internal prices at all. But to assume this is to assume away our problem; for the adverse change in the terms of trade would simply be proportional to the fall in the exchange rate.

I am concerned in this article only with a discussion of the effects of devaluation on the terms of trade. It seems unnecessary, therefore, to impose the restrictions on the conditions of supply which are implied by the assumption of constant money wages. For our purpose, all that is required is that we should be able to assume some definite and continuous functional relationship between the supply of exports (and the supply of home goods) and the money prices of exports and home goods.'5 Once such an assumption is made, the changes in money wages as prices change are imma- terial. For they can influence the final equilibrium prices only through their effect on the distribution of income; and we have assumed that the demand for imports (and, we should add, the demand for home goods) depends on total money income and is independent of its distribution.

Having at last cleared the ground sufficiently, we can proceed to build our structure. Let us take the supply side first. We have assumed that the supply of exports depends on the price of exports and the price of home goods. It remains to decide on the form this functional relationship should take. It seems reasonable to suppose that the supply of exports depends partly on the ratio of the price of exports to the price of home goods and partly on the absolute price of exports. We shall give the relationship this form. In passing we may notice that such an approach is perfectly consistent with conditions of supply such that some of the factors are specific to the production of exports and some non-specific; and that it is also consistent with incomplete utilisation of factors. We may therefore express our relationship in the form

E- e,h




Similar considerations apply to the supply of home goods, and we may write:

H = (h, )

On the demand side, the demand for imports (and the demand for home goods) will depend on the price of imports, the price of home goods, and on total money income. Here, also, we have to choose a suitable form for this relationship to take. For our purposes, it will be helpful to look upon the demand for imports (and the demand for home goods) as depending partly on the home-goods-value of total income and partly on the ratio of the price of imports to the price of home goods. We may then write:

I =I(h ' ) where Y = eE + hH and stands for total money income in the home country. Like- wise, in the case of the demand for home goods, we may write:

H=H(y )i,) H Hh i h)

Similar relationships apply abroad, which may be written:

I (i'); F-F(f' f);

E=E(-E , fe); F F ( if4');

where Y' i'I + f'F and stands for total money income abroad measured in foreign currency.16

Consider now a small fall in the exchange value of the home currency in the proportion k. This will result in small changes in the home price of the four kinds of goods of 8e, 8i, 8h and 8f. Corresponding changes in the foreign price of exports, imports and foreign goods will be 8e - k, 8i - k, and 5f - k respectively. We must next consider the effect on the demand and supply of each kind of good of small changes in the four home prices. Differentiating the above relationships we obtain as approxima- tions:

aE = be (Ee + E h h Eh

3E = (3e-k) E, + (8i-k) Ef-(Ji'+If +F-, +I)+(f-k)

[E Ff'I F 1 I )-Ee]

e ee AH=8e.Hh+ 8hKHh-Hh);

H=e. H h(Ee+Eh +H + E)+ 8i. H1k + 8h[H h((Hh-E -H -E)-H-hJ.

SI= (8i-k)SIi'+I (8f-k) If




1-Se .1 I h Ee+Ee+He E) +Si. .Ih+ Ah [I h (Hh-Eh-_Hh- E)-I h]

SF = (3i-k) Fj, +(f -k)(Ff' F

8F= (ae-k) F - + (8i-k) F f (Ii'+I - +F , +I) +(3f-k)

[F Yf, Ff- I w F ft -I --I-F e

where Ee, for example, stands for the partial derivative of E with respect to e, e

remaining constant. On the supposition that equilibrium is reached in all four markets, so that 8E -= E, etc., we have four equations from which the four unknowns Se, 8i, 8h and 8f may be obtained. The change in the terms of trade will be adverse or favourable according as (8i - 8e) is positive or negative. Solving for 8i and Se in the four equations and simplifying, we obtain an expression for (8i - 8e), namely:



DEVALUATION AND THE TERMS OF TRADE

H

-4

+

+

-4

0

a) j-.4

4-4

0

a)

+ ,£.

-4

+

a) 14

I o. I,.=

a)

a) 1t

*'* 1 ) !3.)1 <"

0

0

/0-1*,

I

% I

4.4

i

m

% 1-

I m-, +-1

(L 14-

>.

i--4

+

+

I I,

. 1-

I

+ a)

-1 Z

I1 a)1

*^ j-

C.)

<"lC

-4 '4-4

a) I"

-4

± -4

± a)

± a) y

± a)

i-4

I % I

I

11

+ U 1^; ^S

I i

>4 14

,H1

+

aP I 4:

a) 1

a) I,-

I

Q 1,< aCl

0

q-

+ I-

-1

I ! 1

<D l'^ .#

te<

-4 +

% I^

+

-4

I

I

-4

1

i-4

. -4

l-4

a)

+ a) IC

a) Il

C)

+ a) 11

a3)

Ip

35

/*

(

<



THE REVIEW OF ECONOMIC STUDIES

The condition, then, that the change in the terms of trade should be adverse is that the above expression (I) should be positive. It will be seen that for the home country alone eight different relationships are involved in the expression: four price-

e e i supply relationships, E , Ee, Hh and Hh; two price-demand relationships, Ih and

i Y Y H ; and two income-demand relationships, I Y and H h .Thus in all sixteen relation-

ships and two constants (the initial quantities of exports and imports, E and I respectively) are involved. The complexity of the result should not, therefore, surprise us; and our earlier assertion that the simplicity of Mrs. Robinson's result was illusory appears justified.

Nevertheless this complexity is unfortunate, since it means that the economic significance of the expression is extremely hard to discover. Further insight into the problem can be obtained only by examining a number of special cases. In the sections which follow, we shall restrict ourselves to three such exercises:

I. We shall seek to discover what further assumptions are necessary for Mrs. Robinson's result to hold good.

2. We shall examine the special case in which the factors of production are fully employed either at home or abroad; also the case in which factors are fully employed both at home and abroad.

3. We shall examine the special case of the home country trading with a foreign country identical with the home country as far as the relevant relationships are concerned.

IV.

Our condition can be reduced to Mrs. Robinson's condition if two assumptions are made. The first of these is explicit in her text but not the second. We must assume

Y Y Y' y, firstly that all of the income-demand relationships, I , H- E, -,and F -~, are zero.

In other words, a change in the home-goods-value of income at home gives rise only to a change in saving and not to a change in demand for imports or home goods. If, then,

e i we make the further assumption that Hh is very large compared with H and H ,

it e' and that Ff' is very large compared with F ,and F ,X our condition reduces to that of

Mrs. Robinson. Dividing numerator and denominator of the expression (i) by Hh and Ff', and neglecting small terms, we obtain as our condition that the change in the terms of trade should be adverse:

k. e e )(Ii '

+ i) > o. sinc e + hav e taken initial p rices to be unity, (Ee )/E is equivalent to the

NQW since we have taken initial prices to be unity, (Ee+Eij/Eis equivalent to tle

36




elasticity (in the strict sense) of home supply of exports, and I / to minus the elas-

ticity of home demand for imports. Also (Ii' + I ,)I is equal to the elasticity of

foreign supply of imports and E / E to minus the elasticity of foreign demand for

exports. Thus if we divide numerator and denominator by E.I and substitute Mrs. Robinson's notation, the inequality becomes:

'qhqf-Ef E h>0f

( h + Ef ) (Nf + E h) So long as none of the elasticities is negative, the denominator in the above expression will always be positive. The inequality, therefore, reduces to:

7ihs f- h Ef > 0, which is Mrs. Robinson's result.

This means, in other words, that Mrs. Robinson's result is only valid subject to the assumption that the production of home goods can be easily expanded without prejudice to the production of exports, and that the production of foreign goods can be easily expanded without prejudice to the production of imports.17 We may conclude, therefore, that Mrs. Robinson is not justified in applying her result to the case of an agricultural community whose elasticity of supply of exports is very low.18 In this case it is very likely that its elasticity of supply of home goods will be low also; so that the conditions under which her result is valid do not obtain.

V.

Our next task is to examine the special case of full employment of factors of production in one country, say the home country. By " full employment of factors" I mean that the production of home goods can be expanded only at the expense of the production of exports, and vice versa; and that therefore the supply of exports and the supply of home goods depend only on the ratio of the price of exports to the price of home goods, and not on the absolute prices. Both Ee and Hh then become zero. Returning to our original expression (i), we see that all the elements of the second column of the determinant in the numerator become zero, so that the whole expression reduces to zero. Consequently (8i - 8e) is equal to zero and there can be no change in the terms of trade.

The case of full employment of factors of production, both at home and abroad, is also of considerable interest. In this case Ff' and Ii become zero, as well as Ee and Hh. If we now look at the determinant which is the denominator of our expression (i), we see that in these conditions the sum of each row is equal to zero. The determinant, tlherefore, reduces to zero. Thus both numerator and denominator reduce to zero, so that no solution is possible in this special case.

These last two results are at first sight puzzling. However, the reasons for them are not hard to discover if we use another approach to the problem, that of counting equations and unknowns. Let us take the latter case first. If there is full employment of factors both at home and abroad, then the demand and supply of each kind of good are influenced only by price-ratios, and not by absolute prices. This entitles us to treat one kind of good, say home goods, as numeraire and express the prices of the




three other kinds of good as relatives of the price of home goods. In this way we reduce the number of unknowns to three-namely, the three price-ratios-but we still have four equations-the demand-supply equations in the four different markets -with which to determine them. Here the fourth equation does not follow from the other three, for the reason that we have not assumed that the whole of income either at home or abroad is spent on goods. We have had to make provision for saving also, in order to make changes in the balance of trade possible. Our system is therefore over-determined.

That this should be so need not surprise us. For to expect a determinate solution with our present assumptions would be like asking a closed economic system to reach equilibrium without allowing either the level of income or the rate of interest to vary. If we wished to make anything of this special case, we should have to introduce into the system another variable, for example, the rate of interest. (Perhaps this is the right place to emphasise that we have hitherto been assuming implicitly either that the banks keep rates of interest constant or that the rates do not influence the demand for goods whether for consumption or investment purposes.)

If there is full employment of factors in the home country only, the situation is altered. Only price-ratios need be considered as far as the home country is concerned, but absolute prices are important abroad. We have, therefore, as three unknowns, the foreign price of foreign goods, the foreign price of exports and the foreign price of imports. We have only to add a fourth unknown, the foreign price of home goods, since the price-ratios at home can be expressed in terms of the foreign prices. Thus we have four unknowns-the four foreign prices-and four equations. The four foreign prices are therefore uniquely determined. This means that a fall in the exchange value will always be exactly compensated by rises in the home prices, and it confirms our result that there will be no change in the terms of trade in these conditions.

VI.

Lastly, we must examine the special case of two countries with identical supply and demand relationships. This means that Ee = Ii', etc. We shall also assume for purposes of simplication that all the income-demand relationships are zero. In these circumstances our expression (I) simplifies to:

i i ~ ~ ~~~~~~~e e H . Ee + Ih. Hh + Ee. Hh + Hh. E-Ee. H-

_ _ _ _ _ _ _ __h_ _ _ _ h ~ h e k. ' i~ ~ e fe e e() H-l Ee+ 2Ee)-IfjHh-2H )+Ee.Hh+ Hh.Eh-Ee H-

If we make the further assumption that trade was balanced in the initial position, so that E = I, and that the quantity of home goods was initially equal to the quantity of foreign goods, we can divide numerator and denominator by E.H, so converting all the relationships in the expression into elasticities. In the remainder of this section, we shall regard all the relationships in (2) as elasticities.

Something should be said first about the signs of these elasticities. In normal e

circumstances, i.e. with normal-sloping supply and demand curves, Ee, Hh and E -

ie will all be positive, while I and H -will be negative. The only elasticity to give us any

i difficulty in this respect is H j, the elastici'ty of demand for home goods (also the elas-




i ticity of demand for foreign goods). This is, of course, related to Ih ,the elasticity of

demand for imports (also the elasticity of demand for exports). Roughly speaking,

H- will be in the neighbourhood of E/H, when Ih = o and will increase as I-increases h h' ~~~~~~~~~~~~~h

numerically, being about zero when Ih= I.

Let us look first of all at the denominator. The denominator is positive except

for the first term H (Ee + 2Ee), which will be negative for low numerical values

of I - There is thus a likelihood that the denominator will be positive, but it will be

negative if all the supply elasticities and I h the elasticity of demand for imports (also exports), are sufficiently low numerically. When the denominator is negative, it is likely that the numerator will be negative also, although it is possible for it to be

positive, a necessary condition being that Hh. Eh-should be greater numerically than

I h Hh - Heh. The above condition follows from the fact that the denominator

minus the numerator is equal to: i e i e\

2H E- 2 I (Hh - H h). *.................... (3) hK h h hj Let us now turn to the more usual case where the denominator is positive. Before

we confine our attention to the numerator, there is another interesting result to be

drawn from (3) above. If H h > o (I h <-I approximately) the denominator of (2) must

not only be positive, but also numerically greater than the numerator. This follows from the fact that the denominator must always be greater algebraically than the numerator, the difference never exceeding twice the denominator. In other words, so long as the elasticity of demand for imports (also exports) is large, the proportional change in the terms of trade, whether it be adverse or favourable, can never be greater than the proportional fall in the exchange rate.

The numerator of (2) may be positive or negative; but it will be positive if the supply elasticities are sufficiently large compared with the demand elasticities. It is instructive, I think, to compare the numerator of (2) with what Mrs. Robinson's result would be in similar conditions. With identical elasticities at home and abroad, Mrs. Robinson's condition that the change in the terms of trade should be adverse becomes:

q)h> Ek. It will be remembered that rph corresponds to (Ee + Eh ) in our notation,

i anld Eh to - I f.It is clear, therefore, that her condition leaves out of account the first

and last terms of the numerator of (2). Of these two terms, the last will always add a positive amount to the numerator, while the first will be positive for high numerical

i values of I X the elasticity of demand for imports (also exports), and negative for low

values of I hThus, as a result of our taking into account repercussions on the prices of




home and foreign goods, a favourable change in the terms of trade appears on the whole less likely in this particular case. This is certainly so when the elasticities of demand for imports and exports are high; owing, however, to the influence of the first term of the numerator of (2), a favourable change in the terms of trade may be more likely than Mrs. Robinson's result would suggest, when the elasticities of demand for imports and exports are low.

Let us collect our results in this section. We have seen that if the supply elasticities and the elasticities of demand for imports and exports are all low, the change in the terms of trade is very uncertain. It may be adverse or favourable, large or small. We have seen that, if the supply elasticities are sufficiently large compared with the demand elasticities, then the change in the terms of trade will be adverse; but that in this connection Mrs. Robinson's formula underestimates the likelihood of an adverse change for high values of the elasticities of demand for imports and exports, and may overestimate it for low values of these elasticities. Lastly, we have seen that for high values of these elasticities of demand the change in the terms of trade will always be smaller than the fall in the exchange rate.

VII.

One can but conclude this article on a negative note. In the foregoing paragraphs we have taken only the first and perhaps most essential step towards a comprehensive treatment of the problem. We would be wise to remind ourselves of the many simpli- fications we have made. We have reduced the very large number of types of commodity in the real world to four only. We have taken no account of the import content of exports. We have assumed that changes in the distribution of income have no effect on the demand for commodities. We have left unconsidered all reactions on rates of interest and on opportunities to invest. And we have made further special assumptions as we went along. Yet with the help of all this simplification and of a great deal of tedious, if pedestrian, mathematics, we have achieved regrettably little in the way of positive result.

This I believe to be in the nature of the problem. It turns out indeed to be a far more complex problem than the simplicity of Mrs. Robinson's treatment would suggest. Nevertheless, so long as factors of production are not fully employed, it is a real problem, and one which may have considerable practical importance. The Keynesian nature of the problem should, I think, be emphasised. We saw in section V that any classical approach was entirely inapplicable. However, the unfortunate truth remains that as soon as we dispense with the classical assumption of full employment in the field of international trade we find ourselves in very difficult waters. Possibly, in the end, inverted commas may prove to be our only practicable means of support.

Oxford. CHARLES KENNEDY.

NOTES.

ICowles Commission: The Principia Press, Inc., 1944.

2 F. Y. Edgeworth: Papers Relating to Political Economy, London, 1925, Vol. II, p. 32. 3 Joan Robinson: Essays in the Theory of Employment, 2nd Ed., Blackwell, p. 134 et seq. 4 Op. cit., p. i63n. 6 To my reckoning, Mrs. Robinson's footnote (p. I63) is not quite accurate. With her notation, the

adverse change in the terms of trade is p- , if by " change " we mean proportional change. But this




expression is not equal to K (f- f, but rather to K (h ^+ f) h fff - I . The condition that ch 7h

btah t KL(Eh ± f) ( -F f)J

this last expression is greater than unity reduces to the condition that h7 is greater than -f , provided that

the slopes of the supply and demand curves have the usual signs. Since Mrs. Robinson makes this assumption earlier (p. I39n), the correctness of her final result is not in question.

6 R. F. Kahn: " Tariffs and the Terms of Trade," REVIEW OF ECONOMIC STUDIES, Vol. XV (I). 7 Ibid., p. 17. 8 For a further discussion of this point, the reader should refer to Section III of Mr. Graaff's very

interesting recent article: " On Optimum Tariff Structures," REVIEW OF ECONOMIC STUDIES, Vol. XVII (I). Mr. Graaff's article appeared when the present article was already in preparation.

9 Op. cit., p. 138. 10 Ibid., p. i66. 11 Ibid., p. I62. My italics. 12 Ibid., p. i66. My italics. 13 In practice, the price of imports is likely to influence the supply of exports and of home goods through

its effect on the cost of living and thus on wage demands. We must assume that any such influence is absent from our model.

14 Op. cit., p. I6o. 15 That there should be a definite relationship between supply and money prices is not, I think, an

unreasonable assumption, particularly when only small changes in money prices are envisaged, But that the functional relationship should be continuous is admittedly not very plausible: in practice, the responsiveness of supply to a rise in price may very well be different from the responsiveness to a fall in price.

16 A word on notation here may assist the reader. Demand relationships are distinguished from supply relationships by being italicised. Foreign prices and income are distinguished from home prices and income by primes.

17 This may be the right place to refer to Professor Brown's work on the foreign exchanges: A. J. Brown, " Trade Balances and Exchange Stability," Oxford Economic Papers, No. 6. Professor Brown is concerned with the effect of devaluation on the trade balance, but many of the difficulties we have encountered in our analysis of the effect on the terms of trade are common to both problems. Professor Brown is not unaware of these difficulties. Thus, for example, on p. 64, he recognises the desirability of making allowance for some change in the general price-level in each country, but he feels bound for the sake of simplicity to restrict himself at this point to the case where all elasticities of supply are infinite. Like Mrs. Robinson, however, he seems too ready to assume that these difficulties arise only as a result of the action of the multiplier, and he is content in the first instance to carry out an analysis in terms of elasticities on the assumption of a constant level of activity (p. 58), although it should in fairness be mentioned that a signi- ficant parenthesis at the foot of p. 58 indicates that he is not altogether happy about this. Now we have argued above that it is impossible to keep separate the working of the elasticities from changes in the level of activity. This conclusion will emerge strikingly from the analysis of our next section, where we discuss the case of full employment. We shall discover in effect that to assume constant levels of activity is to assume away the whole basis of the problem.

18 Op. cit., p. I64. Cf. also A. J. Brown, op. cit., p. 73.



Date post:	31-Jan-2017
Category:	Documents
Upload:	charles-kennedy
View:	212 times
Download:	0 times

Devaluation and the Terms of Trade

Documents