INNOVATION AND DIFFUSION The capital stock changes over time due to additions from gross investment and removals due to scrapping K=N4=K1(4-S The desired rate of capacity expansion may be set initially at any level (animal spirits) but is revised over time using first-order feedback from the deviation of the rate of capacity utilisation u from its desired level ue i4=A13(u4-0) Labour is assumed to be the only current cost of production and can be decomposed into prime and overhead components. The prime unit labour coefficient is an average over the historical technological labour/ output fficients a(t) weighted by vintage (in the following the firm subscript been suppressed for simplicity) (O)K(t, e)dr/k(o It changes over time due to additions of more productive new equipment through investment and removal of marginal equipment through scrapping according to the following equation derived from(Io) by differentiation a)={K(,[a()-<a)]+S[<a)-a(T)]》/K (I1) If net investment is taking place, i.e. N>0, then all scrapping serves the of replacement investment R, so that K(t, t)=N+R, S=R and a)={M[a()-<a)]+R[a(t)-a(T)/K, which shows that replacement investment contributes more to lowering unit costs per unit of investment outlay than does expansion investment Thus unit costs are determined by the age structure of the capital stock and the history of technological change it represents. They will vary over time as a result of the scrapping and expansion strategies of the firm under the constraint of its ability to finance its investment plans, itself a function of cost and profitability proportional to prime unit labour ut at full operating capacity is assumed Overhead labour per unit out multiplied by total productive capacity K (and thus is independent of the rate of capacity utilisation, contrary to total prime labour, which is directly proportional to it The level of production is set such as to compensate for deviations of the current delivery delay(dd) from some industry-wide standard level(ddo): i=As(dd-ddo)u(r'I-u),u<I, =Ou=I and rhs above >o 8 Other current costs of production could be incorporated by making the prime unit labour coefficient and The exact functional relat reminiscent of Kaldor's technical progress function, but shows that the rate of change of average ity is a function of the marginal vintage productivities and the division of gross investment between modernisation and expansion