A Model of the Trade Cycle Author(s): Nicholas Kaldor Source: The ...

A Model of the Trade CycleAuthor(s): Nicholas KaldorSource: The Economic Journal, Vol. 50, No. 197, (Mar., 1940), pp. 78-92Published by: Blackwell Publishing for the Royal Economic SocietyStable URL: http://www.jstor.org/stable/2225740Accessed: 21/04/2008 15:44Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=black.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We enable thescholarly community to preserve their work and the materials they rely upon, and to build a common research platform thatpromotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.http://www.jstor.org

A MODEL OF TRE TRADE CYCLEl. TRE following pages do not attempt to put forward any" new " theory of the Trade Cycle. The theory here presentedis essentially similar to alI those theories which explain the TradeCycle as a result of the combined operation of the so-called" multiplier " and the investment demand function as, e.g., thetheories put forward in recent years by Mr. Harrod and Mr.Kalecki. 1 The purpose of the present paper is to show, bymeans of a simple diagrammatic,apparatus, what are the necessaryand sufficient assumptions under which the combined operationof these two forces inevitably gives rise to a cycle.2. The baslc principle underlying alI these theories may besought in the proposition-a proposition that is really derivedfrom Mr. Keynes' General Theory, although not stated there inthis form-that economic activity always tends towards a levelwhere Savings and Investment are equa!. Here the termsSavings and Investment are used, of course, in a sense differentfrom the one according to which they are always and necessarilyequal-in the ex-ante, and not the ex-post sense. Investmentex-ante is the value of the designed increments of stocks of alIkinds (i.e., the value of the net addition to stocks plus the valueof the aggregate output of fixed equipment), which differs fromInvestment ex-post by the value of the undesigned accretion (ordecumulation) of stocks. Savings ex-ante is the amount peopleintend to save-i.e., the amount they actually would save if theycorrectly forecast their incomes. Hence ex-ante and ex-postSaving can differ only in so far as there is an unexpected changein the amount of incorne earned.If ex-ante Investment exceeds ex-ante Saving, either ex-postInvestment will fall short of ex-ante Investment, or ex-post Savingwill exceed ex-ante Saving; and both these discrepancies willinduce an expansion in the level of activity. If ex-ante Investmentfalls short of ex-ante Saving either ex-post Investment willexceed ex-ante Investment, or ex-post Saving will fall short ofex-ante Saving, and both these discrepancies will induce a contraction.This must be so, because a reduction in ex-post Savingas compared with ex-ante Saving will make consumers spend lesson consumers' goods, an excess of ex-post Investment over ex-ante~1 Harrod, The Trade Oycle,. Kalecki, "A Theory of the Business Cycle,"Review oJ Economie Studies, February 1937, reprinted in Essays in Theory oJEconomic Fluctuations.

MAROH 1940] A MODEL OF TRE TRADE OYOLE 79Investment (implying as it does the accretion of unwanted stocks)will cause entrepreneurs to spend less on entrepreneurial goods;while the total of activity is always determined by the sum ofconsumers' expenditures and entrepreneurs' expenditures. Thusa discrepancy between ex-ante Saving and ex-ante Investmentmust induce a change in the level of activity which proceeds untilthe discrepancy is removed.3. The magnitudes df both ex-ante Saving and ex-ante Investmentare themselves functions of the level of activity, and bothvary positively with the level of activity. Thus if we denote thelevel of activity (measured in terms of employment) by x, bothSand I (ex-ante Savings and Investment) will be single-valuedfunctions of x 1 and both ~~ and ~~ will be positive.The firstof these expresses the basic principle of the "multiplier" (thatthe marginal/propensity to consume is less than unity),2 and thesecond denotes the assumption that the demand for capitaI goodswill be greater the greater the level of production. 3If we regard the S(x) and I(x) functions as linear, as in theabsence of further information one is inclined to do, we have twopossibilities :-(i) ~~ exceeds ~~, in which case, as shown by Fig. 1,4 therecan be only a single position of unstable equilibrium, since above1 Sand I are, of course, both functions of the rate of interest in addition tothe level of activity. But the rate of interest, at any rate in the first approximation,could itself be regarded as a single valued function of the level of activity,and thus its infiuence incorporated in the S(x) and I(x) functions. (It is notnecessary to assume, in order that:; should be positive, that the rates of interest-short and long term-are constant. We can aHow for some variation as theratés' of interest, to be associated with a change in investment and incomes, providedthis variation is not large enough to prevent the change in incomes altogether.AH that we are excluding here is a banking policy which so regulatesinterest rates as to keep the level of incomes constant.)2 :~ is, of course, the reciprocal of Mr. Keynes' investment multiplier, which. l dO dS18 defined as l _ dC' where dX = l - dX'dx3 This assumption should not be confused with the " acceleration principle "(of Prof. J. M. Clark and others), which asserts that the demand for capitaI goodsis a function of the rate oj change of the level of activity, and not of the level ofactivity itself. The theory put forward below is thus not based on this " accelera·tion principle" (the generaI validity of which is questionable), but on a muchsirnpler assumption-i.e., that an increase in the current level of profits increasesinvestment demando4 In Fig. l, as in aH subsequent diagrams, the level of activity is measuredalong Ox and the corresponding value of ex-ante Investment and Saving along Oy.

80 TRE ECONOMIC JOURNAL [MARCHthe equilibrium point 1>8, and thus activity tends to expand,below it S >1, and hence it tends to contract. If the Sand 1functions were of this character, the economic system wouldalways be rushing either towards a state of hyper-inflation withfull employment, or towards a state of complete collapse withzero employment, with no resting-place in between. Sincerecorded experience does not bear out such dangerous instabilities,this possibility can be dismissed.yoFIG. l.x(ii) ~~ exceeds ~~, in which case, as shown in Fig. 2, therewill be a single position of stable equilibrium. (This, I believe,is the assumption implied in Mr. Keynes' theory of employment.)If the economic system were of this nature, ,any disturbance,originating either on the investment side or on the savings side,yso s FIG. 2.xwould be followed by the re-establishment of a new equilibrium,with a stable level of activity.l Hence this assumption fails in theopposite direction: it assumes more stability than the real worldappears, in fact, to ,possesso AIso, if there is any justification inthe contention of the "accelerationists," the possibility of ~~1 Except in so far as the existence of time.lags of adjustment might prevent,on certain assumptions, the new equilibrium from being reached. Cf. Appendixbelow.

1940] A MODEL OF THE TRADE OYOLE 81being greater than ~~' at any rate for certain values of x, cannotbe excluded.For ~~ could be many times greater than dx, while~~ can never be more than a fraction of dx.4. Since thus neither ofthese two assumptions can be justified,we are left with the conclusion that the I(x) and S(x) functionscannot both be linear, at any rate over the entire·range. And, infact, on closer examination, there are good reasons for supposingthat neither of them is lineare(a) In the case of the investment function it is probable that~~ will be 81'IUJ,ll, both for low and for high levels of x, relativelyto its " normal "level.yIt will be small for low levels of activityoFIG. 3.·xbecause when there is a great deal of surplus capacity, an increasein activity will not induce entrepreneurs to undertake additional-construction: the rise in profits will not stimulate investment.(At the same time, the level of investment will not be zero, forthere is always some investment undertaken for long-perioddevelopment purposes which is independent of current activity.)But it wili also be small for unusllally high levels of activity,because rising costs ofconstruction, increasing costs and increasingdifficulty of borrowing will dissuade entrepreneurs from expandingstili faster-at a time when they aIready have large commitments.Hence, given some "normal " value of ~~' appropriatefor "normal " levels of activity, the I(x) function will deviatefrom linearity in the manner suggested in Fig. 3.(b) In the case of the savings function, the situation appearsto be exactly the other way round: ~~ is likely to be relativelylarge, both for low and high levels of activity, as compared withits normallevel. When incomes are unusually low, savings are cutNo. 197.-VOL. L.G

82 TRE ECONOMIC JOURNAL [MARCHdrastically, and below a certain level of incorne they will benegative. When incornes are unusually high, people are likely tosave not only a higher amount, but also a larger proportion oftheir income.! These tendencies, for society as a whole, arelikely to be reinforced by the fact that when activity is at a lowlevel, an increasing proportion of workers' earnings are paid outof capitaI funds (in the form of unemployment benefits); whilewhen activity is at a high level, prices will tend to rise relativelyto wages, there will be a shift in the distribution of incomes infavour of profits, and thus an increase in the aggregate propensityto save.Rence ~~ will deviate from its normal level in themanner suggested in Fig. 4.yoFIG. 4.In what follows it· will be assumed that the two functionsconform to these criteria. But, as the reader will note, ouranalysis would remain valid even if on:ly one oj the two functionsbehaved in the manner suggested, while the other was lineare5. Given these assumptio11S about the behaviour ofthe savingsand investment functions, and assuming further that the normalvalue of ~~ is greater than the normal value of ~~, the situationwill be one of multiple equilibria, as shown in Fig. 5. A and B(in the diagram) are both stable positions, for at points belowA or B, 1>8, hence activity tends to expand; above it 8 >1, hellceactivity tends to contract. ° is an unstable position in bothdirections, and hence not a possible position of equilibrium. Thesignificance of point °is simply that if activity happens to beabove 0, there will be a process of expansion which will come to ahalt at B; if it happens to be below 0, there will be a process ofcontraction until equilibrium is reached at A. .1 Thus there is something like a " customary standard of Iiving" based onthe " normallevel " of incomes, and, corresponding to it, there is a certain normalrate of savings. If incomes are much beIow it, individuais will attempt to maintaintheir standard of living by consuming capitaI; if incomes are much above it,they will tend to save a disproportionate amount.x

1940] A MODEL OF TRE TRADE CYCLE 83Hence the economic system can reach stability either at acertain high rate of activity or at a certain low rate of activity.There will be a certain depression level and a certain prosperitylevel at which it offers resistance to further changes in eitherdirection. The key to the explanation of the Trade Cycle is tobe found in the fact that each of these two positions is stable onlyin the short period: that as activity continues at either one ofthese Ievels, forces gradually accumulate which sooner or Iaterwill render that particular position unstable. It is to an explanationof the nature of these forces that we must now turno6. Both S(x) and I(x) are "short-period" functions-i.e.,they assume the total amount of fixed equipment in existence,and hence the amount of real income at an~ particular Ievel ofySBFIG. 5.xactivity, a~ given. As these factors change in time, the Sand Icurves wiII shift their position; but according as activity is highor low (equilibrium is at B or at A) they will shift in differentways.(i) When activity is high (equilibrium at B), the Ievel ofinvestment is high, the total amount of equipment gradualIyincreases, and so, in consequence, the amount of consumers' goodsproduced at a given level of activity. As a result the S Cllrvegradually shifts upwards (for there will be more consumption,and hence more saving, for any given activity); for the samereason the I curve gradually falls. (The accumulation of capitaI,by restrictin.g the range of available investment opportunities,will tend to make it. fall, while new inventions tend, on the whole,to make it rise. But the first of these factors is bound to be morepowerful after a time.) As a result, the position of B is graduallyshifted to the left and that of O to the right, thus reducing thelevel of activity somewhat and bringing Band O nearer to eachother (see Fig. 6, " Stage II ").

84 TRE ECONOMIC JOURNAL [MARCHThe criticaI point is reached when, on account of these movements,the I and S curves become tangential and the pointsBand O faII together (" Stage III "). At that point equilibriumbecomes unstable in a downward direction, since in the neighbourhoodof the point S >1 in both directions. The Ievel of activitywill now faII rapidly, on account of the excess of ex-ante Savingsover ex-ante Investment, until a new equilibrium is reached at Awhere the positioIi is again stable. 1 , 2(ii) _When activity is Iow, the movement of the 1 and S curveswill tend to be in the opposite direction. For if at the Ievel ofinvestment corresponding to A investment is not sufficient tocover replacement, so that net investment in industriaI pIant andequipment is negative,3 investment opportunities gradually1 The route followed in the transition from B to A might be either along theI curve or the S curve, according to whether ex-post Saving is adjusted to ex-anteInvestment, or ex-post Investment to ex-ante Saving-i.e., according as thedisappointment of expectations occurs on the side of incomes, or in the level ofentrepreneurial stocks.2 The fall in the rate of activity during the transition need not be very rapid,and may even take some years. This is because both entrepreneurs and con·sumers take some time to adjust their scale of purchases to their changed rate ofearnings. If the process is at all prolonged, the two curves will be back at their"normal" position (as shown in Fig. 5 or " Stage IV " in Fig. 6) by the timepoint A is reached.3 It is not necessary, of course, that total net investment should be negative,since investment can take forms (such as armaments, etc.) whose constructiondoes not reduce the available opportunities for the future.

1940] A MODEL OF THE TRADE CYCLE 85accumulate and the I curve will shift upwards; and this tendencyis likely to be reinforced by new inventions. For the same reason,the graduaI decumulation of capitaI, in so far as it causes realincome per unit of activity to fall, willlower the S curve.! Thesemovements cause the position of A to shift to the right and thatof. G to shift to the left (thus separating Band C ànd bringingA and C nearer to each other), involving a graduaI improvementin the level of activity (Stages IV and V). This will proceeduntil A and G fall together (the two curves again become tangential),when a new criticaI situation is reached; the positionbecomes unstable in an upward direction, since I >S on eitherside of the equilibrium point; an upward cumulative movementwill follow which can only come to rest when position B is reached(Stage VI). Thereafter the curves gradually return to theposition shown in Stage I, and the cyclical movement isrepeated.7. The necessary and sufficient assumptions under which thecombined operation of the saving and investment functions inevitablygenerate a èyclical movement which nowhere tends tocome to rest, can therefore be set out as follows :-(l) The "normal value" of ~;, valid for normal levels ofactivity, must'be greater than the corresponding value of~~.(2) The "extreme values" of ~~, valid for abnormally highor abnormally low levels of activity, must be smaller than thecorresponding values of ~~.(3) The level of investment at the upper equilibrium paintmust be sufficiently large for the I(x) function to JaZZ (in time)relatively to the S(x) function; and at the lower equilibrium pointit must be sufficiently small for the I(x) function to rise (in time)relatively to the S(x) function.In other words, the position ofzero' net investment must fall within the limits set by the levelsof investment ruling at B + C and A +. C, in Stage III andStage VI, respectively.If condition (1) did not obtain, equilibrium at C (which is infact the " normal " equilibrium position) would be stable, instead1 It is possible that even if net investment is negative, real output per headshould gradually rise in time (on account of the introduction of superior or more" capitalistic " processes of production during the depression), as a result of whichS would tend to rise rather than falle But this makes no difference so long as theI curve rises faster than the S curve.

86 THE ECONOMIC JOURNAL [MARCHof unstable; equilibrium would tend to get established there, and,once established, the shifts in the I and S curves, due to capitaIaccumulation or decumulation, would merely lead to graduaIchanges in the level of activity unti! a position of stationarinessis reached; they would not generate cyclical movements. Ifcondition (2) was not satisfied (at any rate as regards low levels ofactivity) 1 the system, as we have seen, would be so unstable thatcapitalism could not function at alI. Finally, if condition (3) didnot obtain, the cyclical movements would come to a halt at somestage, owing to a cessation of the movements of the S(x) andI(x) functions.This is not to suggest that in the absence of these three conditionscyclical phenomena would be aItogether impossibIe.Only they would have to be explained with the aid of differentprinciples; they could not be accounted for by the savings andinvestment functions alone.8. In fact, conditions (1) and (2) are almost certain to besatisfied in the real world; doubt could only arise in connectionwith condition (3). It can be taken for granted, of course, thatnet investment will be positive while equilibrium is at position B;but it is by no means so certain that net investment will benegative while equilibr:ium is at position A.2 It is quite possible,for example, that savings should fall rapidly at a relatively earlystage of the downward movement, so that position A is reachedwhile net investment is stilI positive. In that case the Sand Icurves will stilI move in the same direction as at B, with the resultthat the position A is gradually shifted to the left, until netinvestment becomes zero. At that point the moven'lents of theI and S curves will cease; the forces making for expansion orcontractiQn come to a standstill. Alternatively, we might assumethat net investment at A is initially negative, but in the course ofthe graduaI improvement, the position of zero net investment isreached before the forces of cumulative expansion couId come intooperation-i.e., somewhere during Stages IV and V, and beforethe cycle r:eaches Stage VI. In this case, too, the cyclical movementwill get into a deadlock.1 It is possible that the point B should be situated beyond the position of fullemployment-i.e., that in the course of the upward movement the state of fullemployment should be reached befolfe ex-ante Savings and Investment reachequality. In that case the upward movement would end in a state of cumulativeinflation, which in turn would, sooner or later, be brought to a halt by a rise ininterest rates sufficient to push the point B inside the full-employment barrier.From then onwards the cyclical movement would proceed in exactly the samemanner as described.2 The term " net investment " here is used in the sense defined in § 6 (ii).

1940] A MODEL OF THE TRADE CYCLE 87Hence the forces making for expansion when we start from astate of depression are not so certam in their operation as theforces making for a down-turn when we start from prosperity;the danger of chronic stagnation is greater than the danger of achronic boom. A boom, if left to itself, is certain to come to anend; but the depression might get into a position of stationariness,and remain there until external changes (the discovery of newinventions or the opening up of new markets) come to the rescue.9. The preceding analysis offers also certain indicationsregarding the determination of t~e period and the amplitude ofthe Cycle. The period of the Oycle seems to depend on two timelags,or rather time-rates of movement: (i) on the rate at whichthe Sand Icurves shift at any particular level of investment(this, of course, will vary with the level of investment, and willbe faster when investment is high or low, than in the middle);(ii) on the time taken to complete a ,t' cumulative movement "­i.e., the time required for the system to travel from B + O to Aor from A + O to B (Stages III and VI).The second of these factors obviously depends on the velocitywith which entrepreneurs and consumers adjust their expectationsand thus their buying-plans to unexpected changes in the situation.The first factor, on the other hand, seems to depend on technicaldata, on the construction period and durability of capitaI goods.The shorter the construction period, the greater will be the outputof capitaI goods, per unit' period, at a given rat~ of investment;the shorter the life-tjme of capitaI goods, the larger willbe the percentage addition to total equipment represented by agiven output of capitaI goods. Hence the shorter the construction-period,and the lower the durability, the faster will be therate of Sllift of the Sand I curves at any given rate of investment;the shorter the length of the Trade Cycle. 1As regards the amplitude, this depends on the shapes of theI and S curves, which determine the distance between A and B,at their "normal" position (i.e., at Stages I and IV). Theamplitude will be alI the smaller the shorter the range of activityover which the "normal values" of ~~ and ~~ are operative.1 If the " capitaI intensity " of investments varies in the different phases ofthe CycIe in an inverse relation to the rate of investment (i.e., is less in boomperiods than in depression periods), this will tend to reduce the period of theCycIe, as compared with a situation where the capitaI intensity is constant, sinceit will increase the rate of shift of the Sand I curves. ConverseIy, if capitaIintensity varied in direct relation with the rate of investment, this wouId Iengthenthe periodo Finally, if capitaI intensity showed a steady increase throughout theCycIe, this wouId Iengthen the boom periods and shorten the depression periods.

88 TRE ECONOMIC JOURNAL [MAROHVariations in the amplitude of successive cycles, 011 the otherhand, seem to depend entirely on extraneous factors, such as newillventions or secular changes ·in habits of saving. There appearsto be no necessary reason why, in the absen.ce of such factors, tlleamplitude should be gradually decreasing or vice-versa.!lO. Our model should also enable us to throw some light onproblems of economic policy. Rere I confine myself to twopoints. (i) It appears that measures taken to combat thedepression (through public investment) have much more chanceof success if taken at a relatively early stage, or at a relatively latestage, than at the bottom of the depressione If taken early, theproblem is merely to prevent that graduaI fall in the investmentfunction relatively to the saving function which carries the cyclefrom Stage II to Stage III. But, once Stage III is passed, nothingcan prevent the switch-over from the B-equilibrium to the A­equilibrium, and then the problenl becomes one of raising theinvestment demand schedule sufficiently to lift the position toStage VI (at which the forces of expansion come into operation).The amount of public investment required to achieve this isobviously much greater in the early phase of the depression (atStage IV) than in the later phase (at Stage V). Thus just whenthe depression is at its worst the difficulty of overcoming it is thegreatest. (ii) The chances of "evening out" fiuctuations by" anti-cyclical " public investment appear to be remote. For ifthe policy is successful in preventing the downward cumulativemovement, it will also succeed in keeping the level of privateinvestment high; and for this very reason the forces making fora down-turn will continue to accumulate, thu;s making the needfor continued public investment greater. Thus, if, on the basisof past experience, the Government Authority contemplates afour years public investment pIan, in the beliefthat thereby it canbridge the gap between one prosperity-period and the ne~t, it ismore likely that it might succeed in postponing the onset of the1 At first sight one might think that this question aiso depends on endogenousfactors: that the cycle will be "damped" (amplitude of successive cyclesdecreasing) if the point of zero net investment is so situated that there will be netcapitaI accumulation over the cycle as a whole, and vice versa. But this is notso. If there is net accumulation over the cycle as a whole (i.e., the accumulationover the boom period exceeds the decumulation during the depression), then, inthe absence of extraneous changes, the position B at the corresponding stages ofsuccessive cycles will be situated more and more to the Ieft; but the position Awill aiso be situated more to the Ieft, with the result that, though there will be agraduaI fall in the average Ievei of activity, there need be no decrease in thedeviations around the average. The same holds, mutatis mutandis, if there isnet decumulation over the cycle as a whole.

1940] A MODEL OF THE TRADE CYCLE 89depression for four years than that it will prevent its occurrencealtogether. 1 If the Trade Cycle is really governed by the forcesanalysed in this paper, the policy of internaI stabilisation must beconceived along different lines.NICHOLAS KALDORL,ondon School oj Econon~ic8.APPENDIXIt may be interesting to examine the relations of the modelhere presented to other models ofthe Trade Cycle based on sirnilarprinciples. The one nearest to it, I think, is Mr. Kalecki's theory,givenin Chap. 6 ofhis Essays in the Theory ojEconomie Fluctuations.The differences can best be shown by employing the same typeof diagram and the same denotation as used by Mr. Kalecki. Letincorne be measured along OY, and the rate of investrnent decisionsalong OD. Let D t == ([Je(Y t ) represent the rate of investoofment decisions at time t, given the quantity ofequipment available.Let the family of curves ([Je 1... etc., represent this function fordifferent qu~ntities of available equipment, where e 1 represents asmaller quantity of equipment than e 2 , and so ono Let Y t + T ==1 This argument is strictly valid only for a closed system; it is not valid inthe case of a country which receives its cyclical impulses from abroad. For in thatcase the cyclical variations in the demand for exports can be taken as givenirrespective of what the Govemment is doing; the chronological order of the" lean years " will not be altered by the attempt at suppressing them. Thus apolicy of this type is much more likely to be successful in a small country, likeSweden, than in large countries, such as Britain or the United States, whichthemselves generate the cyclical forces and transmit them to others.y

90 TRE EcONOMIe JOURNAL [MARCRf(D t ) be the level of income at time t + 7 as a function of investmentdecisions at the time t. This is the same as our savingsfunction,which, for simplicity, and following Mr. Kalecki, weregard here as a straight line, independent of the amount ofequipment. (7 represents the time lag between investmentdecisions and the corresponding income, which, as Mr. Kaleckihas shown, depends partly on the construction-period of capitaIgoods, and partly on the lag between income and consumption.)The meeting-points of @e curves and the f curve are positions ofshort-period equilibrium, where Savings==lnvestment; the equilibriumis stable when the @e curve cuts thef function from above,it is unstable when it cuts it fro~ ,below. Let RR represent thelocus of points on the @e cu:r;yes where the level of investmentdecisions corresponds to replacement so that net investment iszero. This curve is slightly rising, from left to right, since thehigher the amount of equipment in existence, the greater theamount of investment needed for replacement. The point ,Orepresents the position of long period or stationary equilibrium,where Savings==lnvestment and net investment is zero.Under our assumptions, where ~~ exceeds d~ for certaindDvalues of Y, there must be certain levels of equipment at whichthe @ curves cut thef function not once, but three times. In ourdiagram this will be the case if equipment is greater than e 2andless than e 4 • Given this assumption, and assuming further .thatthe replacement level, for the critical amounts of equipment, fallsbetween the limits of stability-i.e., between points F and G inthe diagram-the system can never settle down to a stationaryequilibrium, but moves around it in a cycle. If we assume thatthe time-Iag 7 is small relatively to the time needed to reachsuccessive @ curves (i.e., relatively to the rate at which the totalquantity of equipment is increasing), so that a position of shortperiodequilibrium can be reached before significant changes occurin the amount of equipment in existence, the cyclical movementof the system will be indicated by the trajectory AGBF. For ifwe start from any arbitrary point, such as k, the cumulative forceswill increase income and investment decisions until the systemreaches l, and thereafter activity will move downwards (owing tothe graduaI accumulation of equipment) along the f line until itreaches F. At that point equilibrium becomes unstable, and adownward moving cumulative process is set up whièh lands thesystem at A. Here investment is less than replacement, and thegraduaI reduction iI1- available equipment will increase activityuntil the system reaches G, at which the situation again becomesunstable, a,n upward cumulative movement follows which landsthe system at B. Thus if we start from any point outside thetrajectory, the system will move on to it, and the same followsif we start from any point inside. Hence, even if we started fromthe position of stationary long-period equilibrium (O), the un-

1940] A MODEL OF TRE TRADE CYCLE 91stability of the situation there must generate forces which set upa cycle.It follows, further, that if alI the fundamental data whichdetermina the functions should be small-i.e.,that ~f should but slightly exceed

92 TRE ECONOMIC JOURNAL (MARCH 1940be shown only as a result of a happy coincidence, of a particularconstellation of the various time-lags and parameters assumed.The introduction of the assumption of unstable positions ofequilibrium at and around the replacement level provides, however,as we have seen, an explanation for a cycle of constantamplitude irrespective of the particular values of the time-lagsand parameters involved. The time-lags are only importanthere in determining the period of the cycle, they have no significancein explaining its existence.Moreover, with the theories of the Tinbergen-Kalecki type,the amplitude of the cycle depends on the size of the initial shock.Here the amplitude is determ~ed by endogeneous factors and theassumption of " initial shocks " is itself unnecessary.