Abstract
Harrod not only introduced seminal concepts in the theory of imperfect competition, the trade cycle and dynamics, but also made key conceptual contributions to the development of international trade and finance. These are included in his book International Trade first published in 1933 and include the foreign trade multiplier, the Balassa–Samuelson effect, the crawling peg, the transfer problem and the combination of an adjustment mechanism combining both the elasticities and multiplier as adjustment mechanisms. He also introduced the asymmetry of adjustment between creditor and debtor which was pivotal to Keynes’s Clearing Union proposal. Furthermore, Harrod provided a plan for world monetary stability without a world money. Finally, he also addressed the problem of the world trade cycle using a central concept of his dynamics, a steady advance.
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Notes
- 1.
Keynes was the editor of the series from 1922 to 1936.
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- 4.
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See Endres (2005).
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The first edition of International Economics comprised nine chapters (I. Introduction; II. The gain from Foreign Trade; III. Potential and Actual Gain; IV. Comparative Price Levels; V. Foreign Exchange; VI. The Balance of Trade; VII. When the Gold Standard is Abandoned; VIII. World Monetary Reform: IX. Tariffs). In the second edition, Harrod rewrote Chapter VI. The Balance of Trade and replaced Chapters VII and VIII (When the Gold Standard is Abandoned; VIII World Monetary Reform) with The Trade Cycle and A Reformed World. The third edition did not include changes. The fourth edition replaced Chapter VII (The Trade Cycle) with Correcting an Imbalance, and Chapter VIII (A Reformed World was rewritten) and Chapter IX (Tariffs) were suppressed. In the fifth edition, Harrod added two chapters (After 1958 and Renewed Crisis) and the chapter on Foreign Exchange and international reform were substantially revised.
- 7.
According to mainstream economic theory, free trade creates welfare gains by allowing consumers and firms to purchase from the cheapest source of supply. This ensures that production is located according to comparative advantage. In other words, free trade allows the principle of comparative advantage to operate by suppressing discrimination between such sources of supply as may exist. The properties of the standard mainstream free trade model based on comparative advantage, the Heckscher–Ohlin or Heckscher–Ohlin–Samuelson model (the Heckscher–Ohlin [H–O] model was renamed Heckscher–Ohlin–Samuelson [H–O–S] after Samuelson formalized the basic properties of the H–O model) are to be found in four well-known theorems: (i) the Heckscher–Ohlin theorem, (ii) the Stolper–Samuelson theorem, (iii) the Rybczynski theorem, and (iv) the factor-price equalization theorem. The Heckscher–Ohlin theorem establishes a relationship between factor scarcity and factor embodiment in a commodity such that countries export the commodity which intensively uses the abundant factor. It provides the basis for the gains from trade argument, such gains consisting of the increase in output and real income for a given set of inputs or domestic resources resulting from trade. The Stolper–Samuelson theorem complements the above theorem by stating that the intensive use of a factor of production for export (i.e., the abundant factor) raises its rate of return above that of all other factors. In turn, the consequent increase in the supply of that factor of production will lead to an increase in the output of the commodity that is intensive in that factor of production (the Rybczynski theorem). Lastly, the factor-price equalization theorem, stating that trade equalizes factor returns across countries, wraps up the case for free trade. Under conditions of perfect competition, trade in goods acts as a substitute for factor mobility. Under conditions of imperfect competition, free trade does not result in the full equalization of commodity prices and factor returns across countries. However, free trade does reduce differentials and thus acts as a force for convergence. The introduction of dynamic factors such as spill-over effects does not alter the validity of the basic analysis. Indeed, it can be shown that if knowledge is freely mobile and equally accessible among countries, patterns of specialization are determined by comparative advantage. See Helpman (2004) and Grossman and Helpman (1994). The existence of economies of scale can lead to trade creation through production, consumption, and cost reduction effects. The production effect allows the transfer of production to the lower-cost trading partner. The consumption effect refers to the gain in the consumer surplus due to lower prices. The cost reduction effect denotes a switch to cheaper sources of supply. Dunn and Muti (2000) identify three effects that can increase the efficiency of free trade: (i) a shift in output that increases its price by more than its average cost; (ii) a scale effect that reduces firms’ average costs of production when output expands; (iii) an increase in trade permitting greater diversification of the final goods and intermediate inputs being traded. That is, by construction in mainstream theory, static and dynamic trade theories are one and the same thing when free trade (implying laissez-faire and laissez-passer) prevails. There is absolutely no fundamental distinction between the two.
- 8.
See also, Harrod (1947, p. 313): “It is important that persons of intellectuality should seek to revive Free Trade doctrines. Not only are they good economics, but also they tend to that interchange of product, of idea, and of travel, which is so important to civilization.”
- 9.
The Balassa–Samuelson effect explains the stylized fact that countries with a higher income per capita will have higher prices for their non-traded goods (for example services). Harrod noted this fact in Chapter IV (Comparative Price Levels): “Consumable C goods…are likely to be more expensive in more efficient countries” (1933, p. 80). The explanation is provided by Kravis–Heston–Summers (1982, p. 21): “As a first approximation it may be assumed for purposes of explaining the model that the prices of traded goods, mainly commodities, are the same in different countries. With similar prices for traded goods in all countries, wages in the industries producing traded goods will differ from country to country according to differences in productivity- a standard conclusion of Ricardian trade theory. In each country the wage level established in the traded goods industries will determine wages in the industries producing nontraded goods, mainly services. Because international productivity differences are smaller for such industries, the low wages established in poor countries in the low-productivity traded goods industries will apply also to the not-so-low productivity service and other nontraded goods industries. The consequences will be low prices in low-income countries for services and other nontraded goods.” In its most general form, it states that a rising productivity of traded goods relative to non-traded goods leads to real exchange rate appreciation. Hence countries with a higher GDP per capita tend to experience greater real exchange rate appreciation. See also Kravis and Lipsey (1983) and Bhagwati (1984). Samuelson (1994, pp. 207–208) exemplifies Harrod’s prescience through several quotes. He uses the 1957 edition, but the same text is found in the 1933 edition of International Economics .
- 10.
Harrod (1936), p. 146 makes a clear analogy between the foreign trade multiplier whose value is determined by the propensity of people to spend on foreign goods and the closed economy multiplier whose value is determined by the propensity of people to save.
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Goods of type C do not enter in the equation since what is spent by one individual is transferred to another individual so that income gains and losses offset each other.
- 13.
This example assumes that the proportion of income spent on tradable goods A and B (that is the propensity to import) does not change. However, if the situation involves a decline in the price of a commodity, the mechanism at work is more complex since the intensity of the adjustment depends on the price elasticity of demand. If the price elasticity of demand is less (greater) than one, the fall in total income will exceed (be below) that of the A and B industries (ibid., p. 113). Kahn discussed Harrod’s presentation of his geometric progression (Letter of Kahn to Harrod, 18 April 1932, CIPC, edited by Besomi D. (2003), Vol. I, p. 153).
- 14.
A fall in world prices requires a fall in nominal wages to avoid a decline in the majority output of tradable goods industries and hence a rise in unemployment in the non-tradable industries. Nonetheless, the fall in wages implies a decrease in expenditure. Harrod postulates that most necessities and foodstuff belong to the tradable goods industries implying that the demand for these goods is price inelastic relative to non-tradable goods. As a result, a fall in domestic income derived from a decline in world prices is likely to be perceived with greater intensity in the non-tradable industries relative to the tradable industries.
- 15.
The transfer problem dealt with the consequences placed on the German economy after WWI by the Peace Treaty (the Treaty of Versailles) obliging Germany to pay reparations payments. Keynes argued that in order to comply with reparation payments Germany had to generate an export surplus which meant a substantial reduction in labor production costs (i.e., efficiency earnings). Even so, a reduction in export prices would not do the trick due to low prices elasticities which could actually reduce the value of German exports. Keynes defined the transfer problem as follows: “The transfer problem consists in reducing the gold rate of efficiency earnings of the German factors of production sufficiently to enable them to increase their exports to an adequate aggregate total” (Keynes 1983 [1939], CW, XI, p. 455). He estimated that Germany would have to increase the value of its exports by 40% (“a formidable task,” ibid., p. 456). He did not venture to guess the percentage by which money wages would have to fall to bring about a reduction in efficiency earnings. Moreover he indicated that a reduction in efficiency earnings would actually hurt Germany’s export performance: “…a reduction in efficiency earnings does not help her, and may injure her…Where the world’s demand for Germany’s goods has an elasticity of less than unity, i.e. where a reduction in price stimulates demand less than in proportion, so that the greater quantity sells for a less aggregate sum” (ibid., p. 456). Ohlin argued that in addressing the transfer problem, Keynes had focused on the supply side (relative price effect) while forgetting the demand (income effect) side of the issue. Ohlin framed his argument in terms of the concept of “buying power.” An indemnity paying country transfers buying power to the receiving country which increases its demand for foreign and domestic goods. This increases imports while at the same time leads to a fall in exports as a direct result of the substitution of domestic for export goods. Since Ohlin assumes that increased demand is directed mostly at home produced goods (the marginal propensity to consume is higher than the marginal propensity to imports), their price increases above that of exports and imports. The exact opposite chain of events occurs in the indemnity paying country. Thus, Ohlin concluded that the adjustment need not require any significant change in export prices and hence an “organized shifting in demand” could bring about the export surplus required by the payment of reparations. See Ohlin (1929a, b, 1933). Underlying Keynes’s and Ohlin’s argument on the transfer problem was a different view of the causality between international financial flows and the trade balance. For Keynes, the historical experience showed that international flows adapted to the changes in the trade balance. For Ohlin, the trade balance adjusted to the change in international financial flows. The German case exemplifies the analysis and debates surrounding the transfer problem. However, its importance also responded, in part, to the fact that in the 1920s inter-allied war debts, which also implied cross-country financial flows, were an important source of fragility and obstacle to economic recovery. Also, according to Harrod (1951, p. 397), Keynes was interested in the German transfer problem because he thought that the arguments were relevant to understanding the impact of foreign investment in a country’s standard of living. Harrod treated the transfer problem (the payment of an indemnity) as one that pertains to the current account under the assumption of no capital movements. However, he then proceeded to relax the assumption of no capital mobility and analyzes a second case, namely that of outward foreign direct investment.
- 16.
Harrod also mentioned changes in the size of the home population but this fell outside the scope of the book.
- 17.
As he argued: “Deflationists sometimes argue that the only way to avoid a slump is to prevent the preceding boom. It is better to say that the only way to avoid a slump is to engineer a boom. If a slump has occurred and no boom is allowed to occur prosperity can never return. Stabilization should be introduced after and not before the boom…To propose stabilization after a severe slump is merely lunatic” (Harrod 1933, p. 151). In the 1930s, the effects of the bust (contraction) were considered by some prominent economists (Hayek and later Schumpeter) as natural and healthy, and as a cleansing of the bad elements. “Liquidation” was one of the phases of the cycle identified by Juglar (1889) and became associated with the Austrian Theory of the business cycle (see, for example, Schumpeter 1969 [1939]; Hayek 1933) and with passive policies adopted by the Federal Reserve and the Edgar Hoover administration that deepened the Great Depression (see White 2010 for a contrary opinion). Eichengreen (1999, pp. 8, 12) defines it as: “… liquidationism, according to which business cycle downturns served the Darwinian function of weeding out the weak enterprises least well adapted to a dynamic economy.”
- 18.
With all its limitations, exchange rate interventions were thought more efficient than the imposition of tariffs.
- 19.
As Harrod explains (ibid., p. 173): “If the changes are to be as small as this why should they not be dispensed with altogether…Corrective changes in the foreign exchange rates of 2 per cent per annum amount to 22 percent in ten years…a maladjustment of 22 percent between home rewards and world prices…is a major disaster.”
- 20.
- 21.
Harrod was of the opinion that the GT did not make much progress on the balance of trade beyond the exposition of the Treatise on Money (TM) that was in his opinion “make shift” (Harrod 1948, 102). In an open economy under a fixed exchange rate regime such as the gold standard, the analysis of the TM required an extension of the fundamental equations to incorporate balance of payments consideration. Within this framework, the price level of output as a whole depends on per unit cost and on the difference between national investment and savings. National investment equals to the sum of domestic investment \(I_{1}\) and the current account balance (B). National savings equals the sum of domestic savings \(\left( {S_{1} } \right)\) and foreign lending (L) minus gold outflows (G). Thus, Eq. (…) of Chapter 2 becomes (1) \(\pi = \frac{W}{E} + \frac{{\left[ {\left( {I_{1} + B} \right) - \left( {S_{1} + L - G} \right)} \right]}}{O}.\) For a given per unit labor cost, the equilibrium condition becomes (2) \(I_{1} + B = S_{1} + L - G \Leftrightarrow I_{1} = S_{1} \,{\text{and}}\,G = 0.\) Under an open economy with a fixed exchange rate regime, variations in the interest rate could not fulfill simultaneously both internal \((I_{1} = S_{1} )\) and external equilibrium \((G = 0)\) conditions. Starting from a position of full equilibrium an increase in thrift will result in an excess of internal savings over investment \((I_{1} > S_{1} )\) and the market rate of interest will exceed the natural rate of interest. A decrease in the market rate of interest to overcome the resulting deflation and slump would result in gold outflows \((G > 0)\) and foreign exchange reserve losses. If the authorities wanted to abate gold outflows, they could increase the market rate of interest. Whatever the policy options, the results would be similar: price and profit deflation would ensue resulting in decreases in output and employment. Under these circumstances, Keynes thought of two possible remedies: a decrease in the per unit cost of production \(\left( {\frac{W}{e}} \right)\) or an increase in home investment which would restore the natural rate of interest to its previous level. The reduction in unit labor costs would decrease further the price level of output as a whole but would restore the balance between profits and costs. However, Keynes not only explicitly reiterated his earlier posture regarding downward wage rigidity (“money costs of production show but little resistance to an upward movement,” TM, p. 165) due to trade union power (p. 347) but also argued that it was a dangerous remedy in a capitalistic and democratic society (p. 346) (see also CW, Vol. XIII, p. 360). Hence his preference to increase investment via loan financed public works, calling it “my favorite remedy.” In 1931, in his Harris Lectures, Keynes proposed that the United States decrease their rate of interest to remedy unemployment rather than carry out a public works program arguing that the country could be considered a closed economy. In the TM, Keynes neglected the fact that the resulting increase in income by increasing imports could affect in a negative way external equilibrium. Harrod noted this flaw in Keynes’s reasoning. See Young (1989).
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- 24.
Harrod mentions J. Meade’s (Balance of Payments) as a further elaboration and formal refinement of his multiplier and also the work of Fritz Machlup (ibid.).
- 25.
Profits is also a determinant of exports but Harrod decides to exclude it from the analysis (ibid., p. 121).
- 26.
Harrod also thought that the Keynesian multiplier is instantaneous. In fact, in the GT, Keynes clearly distinguished between the instantaneous (logical) and dynamic versions of the multiplier. As Keynes explained (Keynes, GT, pp. 122–123): “It is obvious that an initiative of this description (increase in aggregate investment) only produces its full effect on employment over a period of time. I have found, however, in discussion that this obvious fact often gives rise to some confusion between the logical theory of the multiplier which holds good continuously, without time-lag, at all moments in time, and the consequences of an expansion in the capital-goods industries which take gradual effect, subject to time-lag and only after an interval.”
- 27.
In his writings, Harrod made several remarks reinforcing this point. In line with his free trade beliefs, Harrod made important qualifications to use of tariffs as a resource allocation mechanism and, as a way, to increase employment (Chapter 9 [Tariffs] included in the first three editions of International Economics ). In the latter case, Harrod argued that using tariffs involved a decrease in wages but that a better solution consisted in increasing productivity at the level of existing factor incomes. He also thought that a reduction in wages raised equity issues (1933, p. 200; 1947, pp. 196–197). In the fourth edition of International Economics, he defended a wage reduction but only under a situation of a fundamental disequilibrium (1957 [1933], p. 156). Later on he noted: “While the wages problem has presented greater difficulties in recent years, it would be wrong to suppose that in the nineteenth century there was normally a downward movement of wages whenever unemployment occurred or increased” (Harrod 1969, p. 208).
- 28.
Harrod understood that according to Keynes, a policy of flexible wages would not ensure full employment (Harrod 1969, p. 208). For Keynes, within the logic of classical theory, wage flexibility was a necessary but insufficient condition to achieve full employment positions. Full employment required, in addition to wage flexibility, interest rate flexibility (Pigou 1944, p. 16). Hence Keynes argued (GT, p. 266): “It is, therefore, on the effect of a falling-wage and price-level on the demand for money that those who believe in the self-adjusting quality of the economic system must rest the weight of their argument: though I am not aware that they have done so.” Keynes also argued that due to other motives (i.e., expectations) the effects of falling wages on the levels of output and employment could very well be opposite to those postulated by the Classics. The purely monetary nature of the rate of interest prevented its adjustment toward a position of full employment equilibrium. This sets a limit to the decline in the marginal efficiencies of capital and thus to the rate of growth of real capital.
- 29.
When discussing the classical theory, Harrod refers to Ricardo and to J. S. Mill whose “views have…been regarded as constituting the classical theory par excellence” (Harrod 1957 [1933], p. 111). In his Principles of Political Economy (1904, 1865), Mill illustrated the classical price–specie flow adjustment mechanism by comparing a barter with a money economy and concluding that the same results are achieved in both cases. As he explained (Vol. II, pp. 131–133): “Under (barter)… a country which wants more import than its exports will pay with for, must offer its exports at a cheaper rate, as the sole means of creating a demand for them sufficient to re-establish the equilibrium. When money is used the country seems to do a thing totally different…let us see if it differs in its essence or only in its mechanism…we are now supposing that there is an excess of imports over exports…The imports require to be permanently diminished, or the exports to be increased; which can only be accomplished by prices…the country requiring more imports than can be paid for by exports…has more of the precious metals…in circulation, than can permanently circulate, and must necessarily part with some of them before the balance can be restored. The currency is accordingly contracted; price fall, and among the rest, the prices of exportable articles; for which…there arises, in foreign countries, a greater demand: while imported commodities have possibly risen in prices, from the influx of money into foreign countries…This is the very process which took place on our original supposition of barter…In a barter system, the trade gravitates to the point at which the sum of the imports exactly exchanges for the sum of the exports: in a money system, it gravitates to the point at which the sum of the imports and sum of the exports exchange for the same quantity of money…money is to commerce only what oil is to the machinery…a contrivance to diminish friction.” The impact of capital movements on the balance of payments was introduced later on by F. W. Taussig (1859–1940). See Taussig (1927, 1917). Harrod pointed to the following limitations of price–specie flow doctrine: the active intervention of central banks to neutralize movements of gold since WWI, the existence of price stickiness, the flow of investment was no independent of the balance of trade; the flow of gold cannot “secure at the same time a balance of trade and a position of full employment” (supply and demand balance at the current level of employment and this need not be full employment; variations of in the level of employment may be due to expectations and optimism and pessimism).
- 30.
Note that in both cases, the transmission mechanisms involve changes in the interest rate. This was precisely the argument made by Keynes in his evidence to the McMillan Committee (1930) which bore the influence of the TM. As Keynes explained, the balance of trade fluctuates under the influence of prices whereas the balance on capital transactions fluctuates under the influence of variation in relative interest rates. Bank rate policy has the virtue that it works on both the trade and financial account of the balance of payments. The effect on prices is much slower than that on financial flows. See Keynes, CW, Vol. XX, pp. 39–42.
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- 32.
See Keynes’ How to Pay for the War (1972 [1940], CW, Vol. IX, pp. 367–439). In How to Pay for the War, Keynes produced for the first-time national income statistics on the basis of estimates published previously by Colin Clarke (see Moggridge 1992, p. 631; Skidelsky 2000, p. 70). The estimates were provided for the fiscal year running from the 1 April 1938 to the 31 March 1939 (see Keynes 1978 [1939], CW, Vol. XXII, pp. 52–74). These were followed by budge estimates (Keynes, ibid., pp. 124–132). How to Pay for the War provided estimates of the output gap to maintain internal balance. In The Theory of International Economic Policy, Meade complemented this analysis and combined income effects (including with the use of the foreign trade multiplier) with price effects and Marshall–Lerner stability conditions. His focus was on external and internal balance using exchange rate and financial policy (Meade 1951, Chapters X–XIII). As he recognized, his analysis was that of comparative statics (ibid., p. viii) and not dynamics. Meade recognized Harrod’s International Economics as one of the sources of his analysis. Harrod (1957, p. 291) praised Meade’s taxonomic analysis.
- 33.
See also Harrod (1963, p. 210). Investment is ex post.
- 34.
Modern texts express the multiplier for an open economy as \(\frac{1}{s + m}\). This formulation is exactly similar than that of Harrod above. However, since they postulate that s = 1–c, the multiplier becomes \(\left( {\frac{1}{{\left( {1 - c} \right) + m}}} \right)\). Instead for Harrod, the expressions \(\frac{1}{s + m}\) and \(\frac{1}{1 - c}\) are equivalent. See footnote 13 above for a more detailed explanation. Clark (1938) has a similar approach as Harrod: “The basic concept of the theory of the multiplier of course is that any increment of money national income…may be spent on home-produced consumption goods or services, may be saved, or may be spent on imported goods. For an increment of national income of one unit, we may denote these three elements as c, s and m, so that c + s + m = 1. If these three components of marginal income remain constant for a moderate time, we can determine a multiplier” (Clark 1938, p. 439). Some of the debates of early Keynesian models focused on whether or not autonomous imports should be part of the analysis the multiplier. Clark (1938) was of the opinion that autonomous imports matter, and for example, an increase in autonomous imports has the same impact as a decline in exports (p. 438).
- 35.
Note that the equality between savings and investment does not imply internal equilibrium. Moreover, there is no causal relation between the savings and investment equality and the external balance. As he puts it: “We should not call the imbalance of external payments and the imbalance between savings and investment two kinds of disequilibrium, for they are indissolubly linked together and are the mirror image of each other” (Harrod 1957 [1933], p. 143). As a result, as put by Harrod (1969, p. 210): “The state of the external balance cannot be used to indicate that domestic investment is excessive or the reverse.” This is a very important point for it questions the basis of the causality between internal and external balances upheld by mainstream economics that views the latter simply as a result of the former (an excess of investment over savings) requiring thus a contraction in domestic spending.
- 36.
Meade’s analysis is illustrated in Chapters V and VI of his book, and the theoretical discussion on the conflicts between external and internal balance are found in Chapter X (pp. 114–124). Meade’s four-fold classification was made popular by Swan’s diagram (1963 [1955], p. 457). Swan’s diagram shows how “employment and the balance of payments both depend on the level of spending and on relative costs.” The diagram shows real expenditure on the X-axis and the cost ratio (index measuring the competitive position of an economy) on the Y-axis. Swan’s analysis referred to the specific case of the Australian economy (see also Swan 1960).
- 37.
The exact example provided by Harrod (1957 [1933], pp. 154–155) is as follows. Let x be the price level of country’s i exports and let x also be the volume of exports, so that \(x * x\) equals the value of exports. Assume a fall in the factor prices such that the price of exports falls by one point. The increase in exports is equal to \(\varepsilon_{\text{fd}}\) “where this term stands for the elasticity of foreign demand for exports” (the amount by which export supply increases as a result in the decline in the price of exports by one unit). The loss of income as a result of the fall in the price of exports is equal to \(x(1 * x)\). The gain in income as a result of the fall in the price of exports is \(\varepsilon_{\text{fd}} \left( {x - 1} \right).\) And the net gain is \(\varepsilon_{\text{fd}} \left( {x - 1} \right) - x.\) The fall in the price of exports also dampens the domestic demand for imports. Harrod assumes that a decline in export prices by one point maintaining world prices constant has the same effect of on the domestic for foreign goods as an increase in foreign prices by one point maintaining domestic prices constant. The consequent decline in the value of imports is equal to \(\varepsilon_{\text{hd}} * x\). The total effect is equal to \(\varepsilon_{\text{fd}} \left( {x - 1} \right) - x + \varepsilon_{\text{hd}} x\). If this effect is positive, the total gain resulting from a reduction of in export prices by one point is equal to:
$$\begin{aligned} \varepsilon_{\text{fd}} \left( {x - 1} \right) - x + \varepsilon_{\text{hd}} x > 1 &\Leftrightarrow \varepsilon_{\text{fd}} \left( {x - 1} \right) - x + \varepsilon_{\text{hd}} x > 0 \\ \Leftrightarrow \varepsilon_{\text{fd}} \left( {x - 1} \right) + \varepsilon_{\text{hd}} x > x \end{aligned}$$(6.18)Dividing Eq. (6.18) by \(x\),
$$\varepsilon_{\text{fd}} \frac{{\left( {x - 1} \right)}}{x} + \varepsilon_{\text{hd}} > 1,$$(6.19)where \(\frac{{\left( {x - 1} \right)}}{x}\) is the change in the price of exports expressed in proportional terms. Thus, Eq. (6.20) can be written as Eq. (6.9) above in the text \(\varepsilon_{\text{fd}} \dot{p}_{x} + \varepsilon_{\text{hd}} > 1\).
- 38.
See Harrod (1963, p. 26): “the curative effect of a realignment of costs and prices was subject to a condition. That is that the elasticity of the foreign demand for a country’s exports and the elasticity of her demand for imports should be sufficiently great. The formula is that the sum of those two elasticities must be greater than one.” See also Harrod (1952, p. 105) for a similar statement. The Marshall–Lerner conditions can be derived as follows. Start with a balanced trade situation and infinite supply elasticities. Let BT = balance of trade and equal to
$$x - m * {\text{RPIE}},$$(6.20)where x, m and RPIE are equal to exports, imports, and the relative price of imports in terms of exports. The impact of a devaluation on the trade balance can be ascertained by expressing Eq. (6.20) in terms of changes,
$$\Delta {\text{BT}} = \Delta x - {\text{RPIE}} * m - m * \Delta {\text{RPIE}}$$(6.21)Dividing both sides of \(\Delta {\text{BT}}\) by \(\Delta {\text{RPIE}},\)
$$\frac{{\Delta {\text{BT}}}}{{\Delta {\text{RPIE}}}} = \frac{\Delta x}{{\Delta {\text{RPIE}}}} - \frac{{{\text{RPIE}} * m}}{{\Delta {\text{RPIE}}}} - \frac{{m * \Delta {\text{RPIE}}}}{{\Delta {\text{RPIE}}}}$$(6.22)And factoring by \(\frac{x}{\text{RPIE}}\) Eq. (6.22) can be expressed as,
$$\frac{{\Delta {\text{BT}}}}{{\Delta {\text{RPIE}}}} = \frac{x}{\text{RPIE}}\left( {\frac{\Delta x}{{\Delta {\text{RPIE}}}} * \frac{\text{RPIE}}{x} - \frac{\Delta m}{{\Delta {\text{RPIE}}}} * \frac{\text{RPIE}}{M} - 1} \right)$$(6.23)where \(\frac{\Delta x}{{\Delta {\text{RPIE}}}} * \frac{\text{RPIE}}{x} = \frac{{\frac{\Delta x}{{\Delta {\text{RPIE}}}}}}{{\frac{\text{RPIE}}{x}}} = {\text{price}}\,{\text{elasticity}}\,{\text{of}}\,{\text{country's}}\,i\,{\text{exports}} = \varepsilon_{\text{fd}}\)
$$\frac{\Delta m}{{\Delta {\text{RPIE}}}} * \frac{\text{RPIE}}{M} = \frac{{\frac{\Delta m}{{\Delta {\text{RPIE}}}}}}{{\frac{\text{RPIE}}{m}}} = {\text{price}}\,{\text{elasticity}}\,{\text{of}}\,{\text{country's}}\,i\,{\text{imports}} = \varepsilon_{\text{hd}}$$Replacing \(\varepsilon_{\text{fd}} \,{\text{and}}\,\varepsilon_{\text{hd}}\) in Eq. (6.23),
$$\frac{{\Delta {\text{BT}}}}{{\Delta {\text{RPIE}}}} = \frac{x}{\text{RPIE}}\left( {\varepsilon_{\text{fd}} - \varepsilon_{\text{hd}} - 1} \right)$$(6.24)According to Eq. (6.24) a devaluation has a positive effect on the balance of trade if \(\varepsilon_{\text{fd}} - \varepsilon_{\text{hd}} - 1 > 0\) or \(\varepsilon_{\text{fd}} - \varepsilon_{\text{hd}} > 1,\) which is Eq. (6.12).
The Marshall–Lerner conditions are traced to Marshall (1923), Lerner (1944), and Robinson (1937) although none of these authors provided a formal treatment of these conditions. Vanek (1962) provides the mathematical derivation under the case where the elasticities of supply are not infinite.
- 39.
Production takes time and involves entering into a series of contracts over time so that a change in relative prices a say a time t may not affect the final output.
- 40.
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Pérez Caldentey, E. (2019). International Economics. In: Roy Harrod. Great Thinkers in Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-74085-7_6
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