THE ECONOMIC IOURNAI DECEMBER is embodied in vintages, and the resulting capital stocks are not assumed to start in, and in general need not converge to steady-state distributions The capital stock(measured in units of productive capacity) of each firm is represented as an aggregation over nondecaying vintages between the current period t and the scrapping date T(t) K()=K(4,)dr where k,(t, t)is gross investment at time t(in capacity units) K(4,t)=k(,n)if T(o)<t<t and o otherwise This aggregate capital stock may be a composite of different technologies as well as different vintages of a single technological trajectory. A payback calculation is performed by each firm with its desired payback period(which may differ between firms) to determine a desired scrapping date for its capital stock Tar(t) by solving P(D)/(c(a)-c(0)]=b, here P(t)is the price of new capital equipment per unit capacity, c(... )is the unit operating cost at time t of the vintage in question, and b, is the target payback period of the ith firm The actual scrapping date adjusts to this desired date via a first-order catch p procedur T=z max [Au(la-1),o where zu is a rationing parameter between o and I(the ratio of current cash How to desired gross investment) which may arise if the ith firm, due to financial constraints, is not able to finance its desired investment programme fully (otherwise it is I). The amount of capacity scrapped as a result of this decision(as well as a possible desire to reduce overall capacity)is S=kt, T)T Net expansion (or contraction) of capacity is governed by a desired rate r for each fir technologically obsolete equipment should beemingly'self-evident' rules have been applied to decide when 7 In the economics literatu ced by new cquipment, One calls for an old vintage to replacement when unit variable costs exceed the price attained per unit of output. A substantial specialised literature exists, however, dealing with optimal replacement beginning with Terborgh(Terborgh, 1949;see also Smith, 1961). Under suitable assumptions about the rate of future technical progress this leads to the so-called square root rule. k criterion is a reasonable approximation to in this ru calculations to be widely For a discussion of optimal replacement in the evolutionary framework emp ere see Silverberg (987)