1 – Introduction
1Harrod’s reflections on imperfect competition are at the heart of his inquiry into the theory of business fluctuations [Besomi, 1998; Aspremont, Dos Santos Ferreira and Gérard-Varet, 2011; Assous, 2015]. Harrod formulated his view of cycle theory within a two-step process constituted by his 1934 paper on “Doctrines of imperfect competition” and his 1936 book, The Trade Cycle.
2First, Harrod emphasized the importance for trade cycle theory of imperfect competition because of its compatibility with decreasing cost. “The key which the doctrines of imperfect competition provide for solving the mystery [concerning movements away from the general equilibrium of output] is that […] industries may be subject to the law of decreasing costs (in the long and short periods)” [Harrod, 1934: 465]. His exploration of the implications of decreasing cost led him to conclude that imperfect competition provides an equilibrium approach to business cycles relying upon the existence of multiple long period equilibria. Instability then may result from alternative producers’ (correct) expectations leading the economy to experience successive periods of high and low equilibria.
3Second, during 1935, Harrod was gathering the analytical components – the accelerator and the multiplier – of The Trade Cycle, and devising a new mechanism to generate an equilibrium model of advance, which was at the same time sufficiently unstable as to promote cyclical growth (cf. Bruno and Del Pont Legrand ). In resorting to imperfect competition, Harrod then explained that turning points could result from changes to the values of the coefficients of the multiplier and the accelerator. This provides the context for the Law of Diminishing Elasticity of Demand, which states that when people become more affluent, they pay less attention to price changes. By showing that changes in demand elasticity likely change income distribution shares, Harrod defines an explicit mechanism that describes how the economy adjusts during different phases of the economic cycle and its eventual stabilization. He killed two birds with one stone. In addition to the stability issue, without resorting to the Law of Diminishing Returns, he managed to explain the stylized fact that “the commodity price fluctuation has greater amplitude than that of (money) rewards to prime factors.” [Harrod, 1936a: 84]
4The first readers of The Trade Cycle were generally aware that the relevant coefficients determining the “line of steady-advance” were assumed not to be constant, and that their variation was central to Harrod’s growth cycle analysis. Somewhat strangely, most mentioned only in passing, the importance of Harrod’s Law of Diminishing Elasticity of Demand and its implication on the dynamics. Most comments were limited to the relevance of Harrod’s law for explaining the behaviour of price along the business cycle.
5We examine this episode in the history of macroeconomics in four steps. In Sections 2 and 3, we restate Harrod’s 1936 basic model of imperfect competition and clarify the role of the Law of Diminishing Elasticity of Demand in Harrod’s analysis of income distributive shares. Section 4 considers the possible different ways in which changes to demand elasticity are likely to stabilize the economy over the cycle. We argue that a reconsideration of this law has strong implications for Harrod’s explanation of business cycle turning points. Section 5 provides a brief survey of the reviews of Harrod’s trade cycle model published in the 1930s.
2 – In quest of a new “stabilizer”
6Harrod addressed the problem of instability at the micro and macro levels. At the micro level, three determinants of the capitalist producer’s level of output are identified: (i) the rate at which factors are hired; (ii) the power of those factors to produce; and (iii) the rate at which producers can exchange their products. The “stabilizing forces” associated with each of these determinants are supposed to depend on “(i) Plasticity of Prime costs, (ii) the Law of Diminishing Return and (iii) – under imperfect competition only – the Law of demand” [Harrod, 1936b: 30]. Points (i) and (ii) determine how much the marginal product of each factor varies if an individual producer expands output, while (iii) states that marginal revenue is negatively related to output, with demand elasticity determining the slope of the marginal revenue curve. As long as the marginal cost curve is increasing and the marginal revenue curve is decreasing, Harrod concludes that there will be a stable equilibrium.
7At the macro level, these three determinants are reconsidered. First, because of growing population, Plasticity of Prime cost is no longer a great stabilizing force: in a “modern world”, total output may increase over a period of time without any pressure for a rise in the rate of pay for prime factors. Second, because of growing capital stock, the Law of Diminishing Returns has a slight effect, particularly when output is low.  Harrod conceded that the only tendency towards diminishing returns, accounting for some part of the changes in prices, might result from the employment of progressively inferior quality labour, and growing carelessness on the part of management: “in the normal cycle the human factor is much more important. As output increases duds may be taken on…” [Harrod, 1936b: 53] However, this factor may not be so important. After a first weeding out of inefficient plants, Harrod seriously doubted there would be a marked increase in marginal returns. Thus, at the macro level, a large part of the stability process remains to be accounted for.
8This was the point when Harrod introduced the Law of Diminishing Elasticity of Demand whose stabilizing force was considered critical: “This is a stabilizer and, in the writer’s judgement, of greater importance than the other two” [Harrod, 1936b: 30], although Harrod admitted that its “very existence” was not “certainly established”. Nonetheless, he “ventured to believe that it is the most important of the three” forces [Harrod, 1936b: 30]
9To see the problem, consider the depiction in Figure 1, which shows a decreasing marginal revenue curve and an increasing marginal cost under monopolistic competition: the price on the vertical axis is a relative price (relative to the general price level). The horizontal axis shows the quantity of goods. As long as equilibrium is studied at the micro level, the marginal cost and marginal revenue curves are drawn on the assumption that all other prices and income (as well as everything else) remain constant. For example, let us say that at a given price, an excess supply of goods appears. The standard adjustment mechanism is as follows: because marginal revenue is greater than marginal cost, entrepreneurs sustain losses and the quantity produced decreases. The process continues until the equilibrium price p* and quantity q*, are reached.
10What would happen at the macro level if, for some reason, an excess supply of goods were to appear? Now, what might bring about an equilibrium between aggregate supply and aggregate demand if the three determinants exert no stabilizing or de-stabilizing influence over output?
… as output falls there will be no change in rates of pay to prime factors, no change in their marginal productivity as output recedes, and no increasing elasticity of demand. Then, if a fall in prices occurs, the system will move irretrievably to the position of zero outputs. If it stops short of that it must be because some stabilizing forces have come into being – wages rates have fallen, or marginal productivity has increased as output receded, or demand has become more elastic and sufficiently so to offset the drop in prices. In absence of the first two stabilizers, this law established that as long as any excess supply of goods will appear, prices will drop output will fall and this will make individual demand curve more elastic.
12Let us say that firms have produced huge excess. Now, let us say that a decrease in the quantity supplied lowers income. Then, because demand depends upon income as well as prices, as the quantity supplied falls, the marginal revenue curve shifts back to, say, MR1. Then the income adjustment force comes into play alongside the price adjustment force. It can be seen that these forces push in opposite directions. The relative price effect (movement down along the marginal revenue curve) brings us closer to equilibrium, while the income effect shifts the marginal revenue curveto the left, moving us further from equilibrium. Without knowing the relative magnitudes of the shifts, we cannot say whether equilibrium will be achieved. It is for precisely this reason that Harrod concludes that the Law of Demand “does not apply to the community as whole” and highlighted the importance of the Law of Diminishing Demand Elasticity.
13The Law of Diminishing Demand Elasticity is important because it determines precisely how much the marginal revenue curves will shift as quantity (global income) varies. By postulating this Law, Harrod was hence able to clarify the relationship between aggregate demand and aggregate supply. In the presence of an excess supply of goods, as income falls, demand elasticity increases, and a negative shift to profit occurs, followed by a decrease in the saving rate, which eventually comes with a rise in aggregate demand. Thus, as long as income keeps falling, the gap between aggregate supply and aggregate demand eventually vanishes.
14In a nutshell, when money wages are fixed (no plasticity of primary factors) and the marginal product of labour remains unchanged (no decreasing returns), changes in income provide all the adjustment. The assumption that income distribution changes due to the change in demand elasticity allows to explain why income ceases to fall in the case that an excess supply of goods appears. As soon as the profit margin falls and a shift to profit takes place, aggregate demand increases and the excess supply of goods vanishes. We now need to look at how Harrod justified his law.
3 – The law of decreasing demand elasticity and the shift to profit
15In his 1936 trade cycle book, Harrod assumes that entrepreneurs can make marginal revenue equal to marginal cost. This is the condition for the maximization of profit in any given set of circumstances. In his view, this assumption was critical for an investigation of the economy’s dynamics:
The leading principle of the theory of imperfect competition is that entrepreneurs tend to equate marginal cost to marginal revenue. This is a tendency which should operate in the short period. Insufficient attention appears to have been paid to this in trade-cycle studies. The following considerations are based on the supposition that it is realized.
17Harrod was well aware that systematic mistakes were at the heart of the turning point in his business cycle analysis:
for instance, it will be shown later why orders given for capital goods in the very last phase of the boom must inevitably prove unprofitable. But to suppose that in the short-period decisions how much current to produce there is systematic error in one direction enduring throughout the whole phase of the boom or the whole phase of the slump by all or most entrepreneurs seems to me altogether far-fetched.
19As soon as entrepreneurs are assumed to equate marginal revenue to marginal cost, two important conclusions can be drawn with regard to the observed movements in profits and prices. Maximum available profit per unit can only change if one or both of two things occur: (i) a change in the relation between the marginal and the average prime cost of production; (ii) a change in the relation between marginal revenue and price. Abstracting from fixed costs, we have:
21where APC is the variable average cost and? is the gross profit (i.e. inclusive of depreciation and interest). This equation expresses the profit margin for the individual firm. For the whole economic system, where ? is the elasticity of demand, we have:
23which allows us to conclude that the profit margin (i) increases with output, since with normal U cost curves the ratio APC/MC decreases along the relevant extent of marginal cost, (ii) decreases with elasticity of demand. Harrod’s proposal of the Law of Diminishing Demand Elasticity emphasizes point (ii).
24The Law of Diminishing Demand Elasticity results mainly from the psychological principle underlying consumers’ and business establishments’ habits. On the one hand, Harrod thought the expected value from searching for better opportunities among close substitutes was a decreasing function of their income. Rich people, unlike poor people, want to avoid the discommodity of searching for the cheapest market, and tend to “slip by imperceptible stages into careless habits” as their income expands.  On the other hand, for enterprises, in good times, “imaginative planning is … more remunerative than attention to rigid economy.” 
25The view that the shape of the marginal revenue curve may be an important factor in determining the income distributive share is easily illustrated. If the counter-cyclicality of demand elasticity is taken for granted, for a given marginal cost, the profit share will decrease/increase once the slump/recovery has set in.
The greater the shift to profit, the smaller the increase of consumption entailed, in accordance with the multiplier, by the given increase of net investment, and the more likely is the existing rate of increase of capital goods to be found to be excessive. This is certainly a striking paradox, since high profit is usually supposed to be the signal for headlong advance. But the reasoning on which it is based seems to be irrefutable. It could only be disputed by a denial of the view that a larger proportion of high profit than of general income tends to be saved. Moreover, it accords with the observed fact that a spectacular accumulation of profit occurs only in the later phase of the boom, that is, shortly precedes a break in that boom.
27The importance of Harrod’s cost analysis and Law of Diminishing Demand Elasticity for the dynamics of saving lies in the fact that it enhances the tendency of profits to rise relative to wages, as activity increases. A change in distribution favourable to profits, increases the propensity of the community to save. Thus, the Law of Diminishing Elasticity of Demand has a crucial influence in causing the value of the multiplier to fall as activity increases. It is worth considering in detail the implication of these variations on the dynamics of the economy.
4 – Instability, the cycle and the law of diminishing elasticity of demand
28The main idea proposed by Harrod is that “by a study of the interconnections between the multiplier and the Relation (the Acceleration Principle) the secret of the trade cycle may be revealed.” [Harrod, 1936b: 70] More specifically, Harrod believed that changes in investment are transformed into changes in output as a result of the multiplier and, in turn, these changes in output, through the operation of the acceleration principle, induce further changes in investment, which then feed into further changes in output, and so on. According to Harrod, this cumulative mechanism is in line with Keynes’s proposition in his Treatise on Money, that if investment exceeds saving, the system will be stimulated to expand, and vice versa. However, Keynes’s argument relies on static equilibrium while Harrod assumes dynamic equilibrium. On the one hand, expansion in a static economy means a new level of income higher than the previous level. On the other hand, in a dynamic economy, expansion occurs as soon as there is a divergence between the “line of steady-advance” of the economy and the current rate of growth. Harrod defines the line of steady advance as:
… one in which the ratio of the increment of output to the previous level is constant… the proportionate increase of net investment on the given day over net investment on the day preceding is equal to the proportionate addition to the stock of capital goods available for the use on a given day. The experience of the given day will be the primary test as to whether the advance is likely to remain steady.
30Harrod defined three variables that would appear to be the main determinants of the equilibrium dynamics since they govern the value of the line of steady-advance of the economy: (i) the propensity to save among agents that receive an income; (ii) the change in profit share resulting from a change in output (shift to profit); and (iii) the desired capital-output ratio for new capital goods. According to Harrod, these determinants are dynamic because “they determine the rate of growth of output, whereas the static determinants relate to the level of output at a particular point of time.” [Harrod, 1936b: 89–90]
31These three variables comprise all the elements determining whether the existing rate of advance is to be increased, maintained or diminished. Note that, in this view, the definition of the line of steady-advance in The Trade Cycle differs from Harrod’s 1939 definition of the “warranted growth rate”. In his 1939 contribution, the “warranted growth rate” of the economy appears as an “equilibrium state of the economy” since it determines: “The level of output at which producers will feel in the upshot that they have done the right thing, and which will induce them to continue in the same line of advance. Stock in hand and equipment available will be exactly at the level they would wish to have them.” [Harrod, 1939: 22]
32In The Trade Cycle, the “line of steady-advance” of the economy is only a “state of the economy” that will be preserved if and only if the three dynamic factors remain constant over time. Also according to Harrod, along the line of steady-advance, there is no chance for variations in these three determinants to be offset, and the cycle is inevitable. However, Harrod immediately underlines that there are some stabilizing mechanisms that prevent the connection between the relation and the multiplier to be destabilizing for the whole economy. The first mechanism relies on interest rate changes during the cycle that may offset the cumulative effect of the accelerator (the relation):
Drawing again from the field of observation, we find interest rates tending to be high in the boom and low in the slump. Thus, so far as the rate of interest is concerned, net investment is discouraged in the boom. And this is right and proper. The stimulus to net investment afforded by the Relation being so great, it is fortunate that we have the rate of interest to provide some counterweight.
34Consequently, these changes in the interest rate may reduce the desired level of investment by entrepreneurs during the different phases of the cycle.
35The second—and more interesting—mechanism proposed by Harrod, relies on a change in the share of profits during the cycle: “We may suppose that what actually happens when investment increases is… a redistribution of income favourable to profit-earners.” [Harrod, 1936b: 71]
36This change in the share of profit (also called the ‘shift to profit’) appears as a crucial stabilizing mechanism during the various phases of the cycle since it has a direct impact on one of the three determinants of the dynamic equilibrium and reduces the potential destabilizing impact of the multiplier effect. In fact, the saving ratio that defines the value of the multiplier would be constant over time if attitudes to saving and the distribution of income between profits and wages remained unchanged. However:
A shift to profit occurs in the boom and a shift away from it in the slump, and profit-earners save a larger proportion of income. Since a larger proportion of income is saved for both these reasons, when income is higher, the proportionate rise in income and output required to elicit a given proportionate increase of savings need not to be as great as the proportionate increase of savings.
38As a consequence, the shift to profit that occurs during the boom leads to a higher level of the saving ratio for the whole economy, whereas during a slump, a reverse mechanism appears. According to Harrod, this means that the value of the multiplier is “endogenous” since it decreases during a boom and increases during a slump, preventing the economy from a pernicious cumulative process. According to Harrod, this stabilizing change in profit is possible only if one assumes imperfect competition since: “the shift to profit is represented as due mainly (i) to the operation of the law of diminishing returns, and (ii) to the diminishing elasticity of demand, as output increases.” [Harrod, 1936: 75]
39As already underlined, Harrod was not convinced that the Law of Diminishing Returns was able to explain the shift to profits, and he proposed the Law of Diminishing Elasticity of Demand as the main explanation. Thus, it would seem that Harrod was well aware that the saving function in relation with demand elasticity cannot be assumed to be constant, and that its variation was at the heart of explanations of the turning points in the cycle. Hence, if the Law of Diminishing Elasticity of Demand does not apply, when the marginal cost becomes constant, there is no shift in profits to explain the changes in the propensity to save in periods of boom or slump. The turning point could be explained only as a consequence of changes in the capital–output ratio, which would discount part of Harrod’s explanation of the turning points.
40In modern terms, we could describe Harrod’s explanation of the trade cycle as intrinsically non-linear. By relating income distribution to market structure, Harrod managed to establish the micro foundations of non-linear saving rate dynamics without resorting to the Law of Diminishing Return. This then led him to devise a mechanism that allowed simultaneous handling of cycles and growth. Harrod also was able to explain the stylized fact related to price and prime factors. Although central to Harrod’s dynamics, the effects of changes to income distribution resulting from variations in the elasticity of demand were not discussed by his contemporaries.
5 – Concluding remarks
41For the majority of Harrod’s contemporaries, explaining why rising income makes demand less elastic, causing the value of marginal revenue associated with a given price to fall, does not seem to have been a primary preoccupation. Robinson , in her review of Harrod’s essay on the trade cycle, and later Kalecki , were the first to point that two crucial countervailing factors, namely the variability along the cycle of both the number of active firms (hence of the degree of concentration) and of their aptitude to collude might affect the degree of monopoly in the opposite direction:
The degree of monopoly does not depend only on the imperfection of the market for a commodity, but also on the number of separate units of control engaged in selling it, and, since the fear of loss is more powerful than the hope of gain, the tendency towards restrictive combinations is stronger in a slump than in a boom.
43In addition, several commentators criticized Harrod for neglecting factors that in their view were more important [Stafford, 1937; Hansen, 1937]. In particular, many reviewers argued that higher incomes would allow a wider range of substitutes. With regard to producers’ demand for factors and instrumental goods, they suggested that rising prices might encourage continued vigilance when placing contracts, because of the many disadvantages of passing on higher costs to the consumer. They argued that conditions of obviously imperfect competition did not appear to encourage the raising of prices. Producers do not care about the risk to trade connections, upsetting advertising campaigns, losing good will and imperilling real business equity for transient advantages. The more imperfect the competition, the more these considerations appear to prevail. However, if demand tends to become less elastic in good times, and traders do not take advantage of this situation, then Harrod’s law fails as an explanation for rising prices and profits.
44It is interesting to note that, by resorting to monopolistic competition, Micha? Kalecki  comes very close to Harrod’s theory of income distribution. However, his analysis, unlike Harrod’s, was based on the determinants of the profit margin in both Robinson’s argument related to changes in the degree of collusion, and the law of diminishing returns. First, Kalecki admits that more spectacular rises in profit margins are likely to occur in those industries where output fluctuates considerably, and where average (prime) costs are heavily influenced by output, for example, the mining, iron, steel and raw materials sectors. Second, (and this works in the opposite direction to profit margin), the threat of entry of new competitors is likely to be low when economic activity is low, and be less encouragement to reduce prices. In other words, firms already in the market may feel less worried about higher mark-ups on cost in periods of low activity, but periods of high economic activity are a good time to enter the market since customers may be finding it difficult to find suppliers. These two effects work in opposite directions and may perfectly cancel out each other. If they do so, the assumption that the profit margin is constant during the business cycle is sensitive. If businesses are highly sensitive to the threat of entry, and the law of diminishing returns operate slightly, then the profit margin may be countercyclical: the profit margin will be higher when activity is low than when activity is high. If businesses are only weakly sensitive to the threat of entry and the Law of Diminishing Returns operates slightly, then the profit margin will be procyclical.
45According to Kalecki, the considerable stability of the profit share over the longer term is the result of simultaneous changes in the degree of imperfection of the market and of increasing real costs in raw materials sectors. In contrast to Harrod, Kalecki concludes that the propensity to save remains constant during all the business cycle. Kalecki implicitly dismisses Harrod’s argument of business cycle turning points based on changes in the propensity to save. In other words, because distribution effects are assumed to be negligible, the only stabilizing effects must necessarily arise from changes in the acceleration coefficient.
46Finally, several authors have questioned the practical importance of Harrod’s Law of Diminishing Elasticity of Demand for the study of the economic cycle, on the grounds that it is irrelevant to assume that elasticity is perfectly known by entrepreneurs. Stafford [1937: 73] points out that:
In reality new elements enter into the problem – of uncertainty, concerning demand and rivals policies, of cost, of the nature of producers’ interest in their businesses, and finally, of the meaning of marginal revenue. M. Harrod places too great a stain upon the useful preparatory results obtained in the field of imperfect competition, without gaining anything substantial from it.
48However, most authors are reluctant to admit that while Harrod assumes that investors might make systematic mistakes in certain phases of the cycle, producers can be assumed to have perfect expectations when deciding how much current output to produce.
Department of Economics, University of Paris I, Pantheon-Sorbonne, PHARE. E-mail: Michael.Assous@univ-paris1.fr
Université de Nice Sophia-Antipolis, GREDEG-CNRS, SKEMA Business School, OFCE DRIC. E-mail: Olivier.Bruno@gredeg.cnrs.fr
University of Lille 1 and Clersé CNRS. E-mail: email@example.com
“Prime work costs are said to rise in the short period on the principle that increasing quantities of prime factors applied to a given quantity of fixed equipment must yield diminishing returns. But the period to which that dictum relates is too short for trade cycle analysis. It is well known that within the course of the boom, plant is rapidly extended, sometimes even beyond the limit of requirements at the peak.” [Harrod, 1936a: 86] His approach conflicts with Keynes who, assuming that the quality of capital as well its stock can be considered given in the short-run, admitted that the Law of Diminishing Return is likely to operate in the short-run.
“With an expanding income, a man may slip by imperceptible stages into careless habits. A contraction recalls him to his senses. He is loath to relinquish enjoyments to which he has become accustomed and immediately begins to cast about for means of meeting adversity with the least inconvenience to himself. That same force of habit, which in times of improvement tends to make him an imperfect buyer reinforces his activity when it is a question of economizing. He seeks to economise with the smallest possible loss of substantial utility.” [Harrod, 1936a: 87]
“The same force acts upon business establishments. The management will take greater pains to avoid a given reduction of dividends than to secure an increase of like amount when dividends are rising in any case. The prospect of bankruptcy may be still more stimulating. There is no reason to suppose that the professions, so often made by the management in the depression, that they are exerting special efforts to secure economy, are mere eye-wash. Economy is always profitable. But there are good psychological reasons why its benefits should be more vividly appreciated when depression sets in.” [Harrod, 1936a: 87]
“Economists are too apt to think of the search for the cheapest market as a continuous and all-pervasive process. That is, in fact, only true of dealers in an organized market, of Ricardo in the money market. For others, whether consumers or producing firms, the search for cheapness entails special efforts made on special occasions. During te growing affluence of the boom habits become hardened, part of the extra means are taken out in the wastage due to not bothering too much. When incomes begin to fall people are forced to economize; cherished habits have to be abandoned willy-nilly. At this point they are shaken out of their lethargy; they begin to sit up and take notice. They resent and resist the curtailment of their wonted pleasures and become willing to take great pains to seek ways and means for mitigating their hardships. Their efforts to find cheapness become strenuous and eager. Nor are commercial firms exempt from this influence upon their purchase policy; they, too, have received a nasty jolt and must strain every nerve to reduce costs; there is no reason to suppose that these are empty. It is not unreasonable to suppose that entrepreneurs, faced with bankruptcy as they often are, devote quite unusual attention to this subject.” [Harrod, 1936b: 86–7]