An Essay in Dynamic Theory ⑧ R.F. Harrod The Economic Journal, Vol. 49, No. 193. (Mar., 1939), pp. 14-33. Stable URL: http: //links.jstor.org/sici?sici=0013-0133%28193903%2949%3A193%3C14%3AAEIDT%3E2.0.CO%3B2-7 The Economic Journal is currently published by Royal Economic Society. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. jstor's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. P Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http: //www.jstor. org/journals/res.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is an independent not-for-profit organization dedicated to creating and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support @jstor.org. http: //www.jstor.org/ Mon Sep1800:2112006
AN ESSAY IN DYNAMIC THEORY 1. THE following pages constitute a tentative and preliminary attempt to give the outline of a "dynamic"theory. Static theory consists of a classification of terms with a view to systematic hinking, together with the extraction of such knowledge about the adjustments due to a change of circumstances as is yielded by the " laws of supply and demand. It has for some time appeared to me that it ought to be possible to develop a similar classification and system of axioms to meet the situation in which certain forces are operating steadily to increase or decrease certain magnitudes in the system. The consequent "theory"would not profess to determine the course of events in detail, but should provide a framework of concepts relevant to the study of change analogous to that provided by static theory for the study of rest The axiomatic basis of the theory which I propose to develop onsists of three propositions--namely, (1)that the level of a community's income is the most important determinant of its supply of saving;(2)that the rate of increase of its income is an important determinant of its demand for saving, and (3)that demand is equal to supply. It thus consists in a marriage of the acceleration principle” and the“ multiplier” theory, and is a development and extension of certain arguments advanced in my Essay on the Trade Cycle 2. Attempts to construct a dynamic theory have recently been proceeding upon another line--namely, by the study of time lags between certain adjustments. By the introduction of an appropriate lag the tendency of a system to oscillate can be established. In these studies there is some doubt as to the nature of the trend on which the oscillation is superimposed apposing 1 Especially in Ch. 2, secs, 4-5. The"Acceleration Principle "was. there in this connection. The study of the condition in which demand and supply are flowing at an unaltered rate has long been known as Static Theor implies that the equilibrium of prices and quantities resulting therefrom is analogou state of rest. By analogy, therefore, a steady rate of ease of demand, which is our first matter for consideration in dynamic the d a major effect of which ig e by th However, the use of the expression Acceleration Principle in the sense of my relation is rapidly accelerating in current literature, and I reluctantly bow t the force majeure of usage
MARCH 1939 AN ESSAY IN DYNAMIC THEORY damping measures could be introduced, to counteract the oscilla tion caused by the lag, would the system be stationary or advanc ng? And at what rate Dynami hrow some light upon this Moreover it is possible, and this the following argument seeks establish, that the trend of growth may itself generate forces making for oscillation. This, if so, would not impair the im portance of the study of the effect of lags. But it may be that the attempt to explain the trade cycle by exclusive reference to them is an unnecessary tour de force. The study of the operation of the forces maintaining a trend of increase and the study of lags should go toge 3. The significance of what follows should not be judged solely by reference to the validity or convenience of the particular equations set forth. It involves something wider: a method of thinking, a way of approach to certain problems. It is necessary to"think dynamically. The static system of equations is set forth not only for its own beauty, but also to enable the economist to train his mind upon special problems when they arise. Fe instance, an economist may pose to himself the question, What would be the effect on the system an increase of e xports or of labour-saving invention By reference to the static equations, he then proceeds to work out the new equilibrium position sup- posing the new higher level of exports to be maintained in perpetuity or the labour-saving invention to be incorporated in the productive technique once for all But let the question be: Suppose the level of exports begins and continues to increase steadily, or suppose its rate of increase to increase, or suppose labour-saving inventions begin to be made suffice.The static theorist may hope to reduce this suppos oe in a steady or growing stream; then the static method will steady increase th a succession of steps up, each having the same effect. But if the following argument is correct, the effect on the moving equilibrium of advance may often be in the opposite direction to the effect on the static equilibrium produced by each of the steps considered singly. A new method of approach- indeed, a mental revolution--is needed Once the mind is accustomed to thinking in terms of trends of increase, the old static formulation of problems seems stale, flat and unprofitable. This is not to deny to static theory its own appropriate sphere. It will become apparent which kind of prob- lem belongs to each branch of study. 4. I now propose to proceed directly to the Fundamental
THE ECONOMIC JOURNAL [MARCH Equation, constituting the marriage of the acceleration principle and the multiplier theory. This probably gives too much importance to the acceleration principle, and the necessary modi fication is introduced subsequently. Let G stand for the geometric rate of growth of income or output in the system, the increment being expressed as a fraction of its existing level. G will vary directly with the time interval chosen per mo stand for the warranted rate of growth. The warranted rate of growth is taken to be that rate of growth which, if it occurs, will leave all parties satisfied that they have produced neither more nor less than the right amount. Or, to state the matter otherwise it will put them into a frame of mind which will cause them to give such orders as will maintain the same rate of growth. I use the unprofessional term warranted instead of equilibrium, or moving equilibrium, because, although every point on the path of output described by Go is an equilibrium point in the sense that producers if they remain on it, will be satisfied, and be induced to keep the same rate of growth in being, the equilibrium is, for reasons to be explained, a highly unstable one If ao is output in period 0 and a, output in period 1, G Ro. Since we suppose the period to be short, to or al may alternatively stand in the denominator wo and an are compounded of all individual outputs. I neglect questions of weighting. Even in a condition of growth which generally speaking is steady, it is not to be supposed that all the component individuals are expanding at the same rate Thus even in the most ideal circumstances conceivable. G. the actual rate of growth, would diverge from time to time from gao, the warranted rate of growth, for random or seasonal causes. et 8 stand for the fraction of income which individuals and corporate bodies choose to save, is total saving divided by o or ar. This may be expected to vary, with the size of income, the phase of the trade cycle, institutional changes, etc. Let C stand for the value of the capital goods required for production of a unit increment of output. The un value used to measure this magnitude is the value of the unit increment of output. Thus, if it is proposed in month 1 to raise the output of shoes, so that in month l and all subsequent months output is one pair higher than in month 0, and the machine required to do this-neglecting all other capital that may be required--has a value 48 times the value of a pair of shoes, C per month=48
1939] N ESSAY IN DYNAMIC THEORY 17 The value of C is inversely proportional to the period chosen C per annum =4 in this case. 1 The value of C depends on the state of technology and the nature of the goods constituting the increment of output. It may be expected to vary as income grows and in different phases of the trade cycle; it may be some- what dependent on the rate of interest Now, it is probably the case that in any period not the whole of the new capital is destined to look after the increment of output of consumergoods. There may be long-range plans of capital development or a transformation of the method of producing the pre-existent level of output. These facts will be allowed for in due course. For the moment let it be assumed that all new capital goods are required for the sake of the increment of output of consumers' goods accruing Hin. serving proof for the next paragraph, we may now write the undamental Equation in its simplest form 2 It should be noticed that the warranted rate of growth of the system appears here as an unknown term, the value of which is determined by certain " fundamental conditions"-namely, the propensity to save and the state of technology, ete. Those who define dynamic as having a cross-reference to two points of time may not regard this equation as dynamic; that particular defini tion of dynamic has its own interest and field of reference I prefer to define dynamic as referring to propositions in which rate of growth appears as an unknown variable. This equation is clearly more fundamental than those expressing lags of 5. The proof is as follows. Let Cp stand for the value of the increment of capital stock in the period divided by the increment of total output. Cp is the value of the increment of capital per a month is the unit, the number of shoes added per period is 1, if a year 144. The value of G per annum is 12 times as great as that of G per month, since the numerator of G per annum is 144 times as great and the denominator 12 times as great as the numerator and denominator respectively of G per month The number of machines added per month is l E 48 shoes E 48 units ofineremen of output. C per month 48. The number of machines added per year is 12 =48x 12 shoes. Thug the value in shoes of the annual increment of eapital required to produce an annual increment of 144 shoes is 48 x 12 units. There fore C per annum =144 of C per month. a Since the value of G varies directly and that of C inversely with the unit period chosen, and the value of a is independent of the unit, the validity of the equation is independent of the unit period chosen. No. 193.-VOL. XLIX
NHE卫 CONOMIC JOURNAL MARCH unit increment of output actually produced. Circulating and fixed capital are lumped together 1(a) is a truism, depending on the proposition that actual saving in a period(excess of the income in that period over consumption)is equal to the addition to the capital stock. Total saving is equal to ro. The addition to the capital stock is equal to Cp(i-wo This follows from the definition of C. And 发b Cp(a G is the rate of increase in total output which actually occurs; Cp is the increment in the stock of capital divided by the increment in total output which actually occurs, If the value of the incre- ment of stock of capital per unit increment of output which actually occurs, Cp, is equal to C, the amount of capital per unit increment of output required by technological and other conditions(including the state of confidence, the rate of interest, ete. )then clearly the increase which actually occurs is equal to the increase which is justified by the circumstances. This means that, since Cp includes ll goods(circulating and fixed capital), and is in fact production minus consumption per unit increment of output during the period, the sum of decisions to produce, to which g gives expression, are on balance justified-i.e, if C=Cp, then G= Ge, and(from 1(a) above) This is the fundamental equation, stated in paragraph 4, which determines the warranted rate of growth. To give numerical alues to these symbols, which may be fairly representative of odern conditions: if 10 per cent. of income were saved and the capital coefficient per annum(C) were equal to 4, the warranted rate of growth would be 2 per cent per annum It may be well to emphasise at this point that no distinction is drawn in this theory between capital goods and consumption good In measuring the increment of capital, the two are taken together the increment consists of total production less total consumption Some trade-cycle theorists concern themselves with a possible lack of balance between these two categories no doubt that has its importance. The theory here considered is more fundamental or simple; it is logically prior to the considerations regarding lack
AN ESSAY IN DYNAMIC THEORY of balance, and grasp of it is required as a preliminary to the study of them erminology recently employed by distinguishe authorities, C, is an ex post quantity. I am not clear if C should be regarded as its corresponding ex ante. C is rather that addition to capital goods in any period, which producers regard as ideally suited to the output which they are undertaking in that period For convenience the term ea ante when employed in this article ill be used in this sense The truism stated above, 1(a), gives expression to Mr. Keynes proposition that saving is necessarily equal to investment--that is to ex post investment. Saving is not necessarily equal to ea ante investment in this sense, since unwanted accretions or depletions of stocks may occur, or equipment may be found to have been produced in excess of, or short of, requirements If ec post investment is less than ea ante investment, this means that there has been an undesired reduction of stocks or insufficient provision of productive equipment, and there will be a stimulus to further expansion of output; conversely if eac post investment exceeds ex ante investment. If ea post investment is less than ea ante investment, saving is less than ex ante investment In his Treatise on Money Mr. Keynes formulated a proposition, which has been widely felt to be enlightening, though experience has led him subsequently to condemn the definitions employed as more likely to be misconstrued than helpful. He said that if investment exceeded saving, the system would be stimulated to expand, and conversely. If for the definitions on which that proposition was based, we ubstitute the definition of e ante invest ment given above, it is true that if ec ante investment exceeds saving, the system will be stimulated, and conversely. This truth may nt for the feeling of satisfaction which Mr Keynes'proposition originally evoked and the reluctance to abandon it at his behest. In many connections we are more interested in ea ante than in ex post investment, the latterincluding as it does unwanted accretions of stocks. Mr. Keynes'propos tion of the Treatise may still be a useful aid to thinking, if we substitute for Investment ' in it ex ante investment as defined above 7. Two minor points may be considered before we proceed with the main argument (i)It may be felt that there is something unreal in t analysis, since the increase in capital which producers will regard as right in period 1 is in the real world related not to the increase
THE ECONOMIC JOURNAL [MARCH of total output in period 1, but to prospective increases in subse quent periods. This objection may be divided into two parts (a)In view of the fact that much of the outlay of capital is con nected with long-range planning, it may be held that the funda mental equation gives too much weight to the short-period effect of the acceleration principle. This objection is freely admitted nd allowed for in the subsequent modification of the equation (b)It may further be objected that even in the sphere in which the acceleration principle holds there must be some lag between the increased provision of equipment(and stocks )and the increased flow of output which they are designed to support There may be some force in this. But the point is deliberately neglected in this part of the argument, along with all questions of lags. The study of these lags is of undoubted importance, but a division of labour in analysis is indispensable, and in this case the neglect is necessary in order to get the clearest possible view of the forces determining the trend and its infuence as such. More over, the lag referred to in this sub-heading(b)may properly be regarded as unimportant, since, in the event of a steady advance (G) being maintained, the difference between M -o and a2-a1 ill be of the second order of small quantities. In other words it matters not whether we regard the increment of capital as required to support the increment of total output in the same period or in the one immediately succeeding it 8. (ii)In the demonstration given above (paras. 6 and 7) reference was made to the distinction between the ex post and the ea ante increase of capital goods. No reference was made to the distinction between ex post and eac ante saving. Suppose that G is not equal to G, might not the discrepancy show itself on the other side of the equation, not in any divergence of Cp from C, but in ea post saving not being equal to ea ante saving I have no very clear view as to possible causes likely to operate in a systematic way to distort ex post from ea ante saving, or of the probable importance of such distortions. It is said, for instance that in a time of rising prices, fixed-income classes will not adapt cheir modes of life simultaneously, and so may save less than they would be disposed to do had they clearly foreseen the impending own rise of income, and so spend less than they would have been 1 Be it noted that ex ante is here used of defined in the expression ex ante investment it is the saving whi choose to make in any period, were they able to adapt expenditure simultaneously with the changing circumstances of the period
1939] AN ESSAY IN DYNAMIC THEORY This question of the possible divergence of ea post inte saving must be kept entirely distinct from that of the varia tions in s in the different phases of the trade cycle, which not only are admitted, but also play a part in the argument. &may vary because the level of income or of profit is abnormally swollen or The neglect of these possible divergences has no importance for the argument, since they will have the same effect on growth as the divergences of Cp from C for which they may serve as substitute. Thus if G exceeds G o, the right-hand side of the equation must exceed &/C. If the whole of this effect is found in C, it will be less than C, and this is a stimulus to expansion. 1 Firms finding themselves short of stock or equipment will increase their orders. If. on the other hand, the whole of this effect found in a divergence of ex post 8 from ex ante 8, ea post s will be greater than ea ante 8. Savers will find that they have saved more than they would have done had they foreseen their level of income or the level of prices correctly. Consequently they will be simulated to expand purchases, and orders for goods will conse- quently be increased. Throughout the following pages the reader, whenever he finds a reference to the excess or deficiency of Cp compared with C, may substitute, if he prefers it, a su deficiency or excess of ex post saving compared with ex ante saving without affecting the course of the argument 9. We now come to a point of major importance, constituting he difference between the dynamic equilibrium(warranted rate of growth)and the static equilibrium. Normally the latter is stable and the former unstable. This gives a prima facie reason alys Some recent writers have been disposed to urge that the static quilibrium is not so stable as is sometimes claimed. Suppose hat an increased output of a commodity, constituting a departure from equilibrium, is tried, so that its supply stands at a point at which the supply curve is above the demand curve. It is argued that, instead of a relapse at once occurring, reducing supply to the point of intersection of the supply and demand curves this showing the stability of the old equilibrium-the upshot depends on how all parties now proceed. It is suggested that there may be a tendency to waltz round the point of intersection or, more broadly, that in the backward adjustment there may be 1 The reader who is surprised that an excess of G over Gw is stimulating will find the explanation in the next paragraph
THE卫 CONOMIC JOURNAT MARCE wide repercussions disturbing the whole system. It is even held that the whole question of the stability of the static equilibrium, in the sense of the tendency of a relapse to it when a random departure occurs, is itself a dynamic problem, which cannot be looked after by the system of static equations. I have the impression that this type of criticism exaggerates the importance of this problem, and constitutes to some extent a failure to see the wood for the trees, and that on its own ground the theory of static equlibrium is well able to hold its own But when we look at the dynamic equilibrium, new vistas are pened. The line of output traced by the warranted rate of growth is a moving equilibrium, in the sense that it represents the one 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. tock in hand and equip ent available will be exactly at the level which they would wish to have them. Of course what applies to the system in general may not apply to each individual separately. But if one feels he has over-produced or over-ordered, this will be counterbalanced by an opposite experience of an equal importance in some other rt of the field But now suppose that there is a departure from the warranted rate of growth. Suppose an excessive output, so that G exceeds Go. The consequence will be that Cp, the actual increase of capital goods per unit increment of output, falls below C, that du stock or shortage of equipment, and the system will be stimulated o further expansion. G, instead of returning to Go, will move farther from it in an upward direction, and the farther it diverges the greater the stimulus to expansion will be. Similarly, if G falls below Ga, there will be a redundance of capital goods, and e exerted this will cause a further vergence and a still stronger depressing influence; and so on Thus in the dynamic field we have a condition opposite to that which holds in the static field. A departure from equilibrium nstead of being self-righting, will be self-aggravating. Go repre- sents a moving equilibrium, but a highly unstable one. Ofinterest this for trade-cycle analysis Suppose an increase in the propensity to save, which means that the values of 8 are increased for all levels of income. This necessarily involves, ceteris paribus, a higher rate of warranted growth. But if the actual growth was previously equal to the warranted growth, the immediate effect is to raise the warranted
