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

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-