It reflects a modern concern to establish a more systematic understanding of the process of creative destruction

Figure 3

Is there still retardation of output growth? In one particular sense, the answer is yes. Since we have established that, the ratio Y(t)/K?(t) is described by a Gompertz curve it follows automatically that the rate of increase in this ratio is subject to retardation, whatever the rate of technical progress and whatever the growth rate of the market. In this relative sense, output retardation is confirmed even though the niche is growing over time. However, this is not the meaning of retardation used by Kuznets and Burns, who focused their empirical and theoretical explanation on the absolute levels of output. To unravel the effect on the growth rate of the level of output we proceed in several steps.
From (8) we find the output growth rate to be equal to

from which it follows that

As in the case of the stationary environment, the trajectory of the growth rate remains monotonic with time but now there are three possible outcomes, shown in figure 4, depending on the initial value of g(0) relative to the growth rate of the niche, G. If g(0) = G then the normal expansion path is one of constant exponential output growth at this rate. If g(0) < G then the output growth rate accelerates over time to approach G asymptotically from below. Only if g(0) > G will the industry experience retardation in the Kuznets/Burns sense, and this in turn requires that the initial scale of the industry, Y₀, is sufficiently small relative to the initial niche, K?. It follows from (11) that we can write the precise condition for output retardation as

Figure 4

24We can summarise this argument as follows. The condition Y₀ < K? sufficient to ensure that the initial growth rate of the industry is positive and remains positive. For output retardation, it is also necessary that, Y₀/K? < e ^{? A}, which is more likely to be satisfied the smaller is the niche growth rate relative to the intrinsic growth rate of the industry. Expressing it differently, retardation occurs whenever the initial level of output Y₀ is less than the value given by K?e ^{? A}. In sum, relative retardation is assured although absolute retardation is not. Whatever the outcome, output growth at a constant rate would only apply by fluke.