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