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

Figure 2

21It is one thing to consider the empirical effects of exogenous shocks, which fracture the growth process and may be identifiable with the aid of econometric techniques that isolate breaks in trend. It is quite another matter to work through the effects of changes in the determinants of the growth process for each change of the parameters defines new values for the niche and/or the intrinsic rate of expansion. In this regard, there are an immense number of possibilities. We could, for example, let various “shocks” be generated stochastically but here it is perhaps more important to clarify the impact of “smooth” changes in the environment. Thus, in the following section we turn our attention on the case of an exponentially growing environment, for which the Gompertz framework has a number of distinct advantages. In so doing we can focus on the question raised by Burns and Kuznets as to the link between retardation of output and retardation of technical progress. The strong focus of the Kuznets/Burns hypothesis is that the cause of output retardation is retardation in an exogenously give rate of technical progress.
Retardation, Technical Progress and Long-Run Demand Growth
22The conclusion reached in the previous section is that retardation of output growth is related to technical progress in a very specific and so far limited sense. It follows because the act of creation of the new activity opens up a new economic niche and the filling of that niche through consumer learning and capacity expansion produces the phenomena called retardation. No other notion of technical progress is required to produce this outcome. Yet this is only a partial statement of the Kuznets/Burns argument. Neither assumed that growth took place within a stationary environment, changes in the competitive relations between commodities, population growth and reductions in production costs were central to their vision. How might these additional elements be incorporated in our depiction of a normal process and what implications would this have for the idea of retardation? To proceed, we introduce two classes of “smooth” development of the industry environment. In relation to demand, we might expect that the long-run curve shifts over time at a rate which reflects the growth of population, the growth of total income and the income elasticity of demand for the new commodity as modified by the influence of competitive and complementary relations with other commodities. To establish the basic issues we first replace (1) by (I)
23

Where n ₁ is the exponential rate of growth of the long run demand curve, its value reflecting the impact of changes in population growth and growth in per capita income on the demand for the new commodity. Take its value as a given, positive parameter. Consider next the impact of ongoing technical progress throughout the growth process; progress that explores the potential implicit in the radical innovation, reduces unit costs and thus expands the long run niche for the industry.
As we have already explained, Kuznets and Burns put great emphasis in the exhaustion of technical possibilities in the industry to explain why the rate of reduction in unit costs could only be expected at a declining rate and thus induce retardation. Similarly, we have seen that Schmookler, in his critique of this supply side logic, argued that retardation in technical progress reflected limiting forces on the demand side of the industry as expressed through a declining elasticity of demand over time. Both positions have merits but what is needed is a form of explanation that makes the rate of technical progress an endogenous feature of the industry. Unfortunately, there is no immediately plausible and convincing way to invoke the idea of an endogenous technical progress function. However, the line of enquiry opened up by Allyn Young is one clear way forward. To do this we distinguish two elements in the industry rate of cost reduction at a point in time: a given rate of disembodied exogenous progress and an endogenous embodied component to progress that depends on the rate of investment and, given the capital output ratio, the extension of the market and thus output growth (Eltis, 1973; Scott, 1989). We treat these elements as independent and additive and note that such a formulation is not unconnected to the Kaldor/ Verdoorn representation of technical progress, linking this latter to investment in capacity and thus to the growth rate of output. No one should pretend that this is entirely satisfactory but neither is it an entirely misleading place to start the discussion of technical progress. Hence, we write the following expression for the technical progress function rate of technical progress T.

where h ₁ is the exogenous rate of cost reduction and ? is the progress elasticity that chains together cost reduction to investment and investment to the growth of capacity. If we take this as a starting point then we can integrate the technical progress function to give (IV) instead of (4) above

Unit costs are no longer constant and they are partly determined in the process of filling the niche. Notice that in making the rate of cost reduction increase with the rate of growth of the market we make the expansion of the market expand the market yet further. As Knight once expressed the matter, growth in capitalism is a “self exciting process” (Knight, 1935, p. 170). Others, Young and Kaldor included, would concur and see the interaction between market and technology as a cumulative process. It is a process of proper endogenous growth.
If we now incorporate (I) and (IV) in our process of normal expansion we can write this as

or as

Where, the new coefficients are defined as

If a normal process is to exist it is clear that we must impose the condition ?? < 1, otherwise the long run niche can no longer be defined and the dynamics of normal expansion break down. Subject to this requirement, B? is the new intrinsic rate of expansion of the industry, K? is proportional to the initial value of the niche K, and G is the long run rate of growth of the niche.
Integrating this non-autonomous relation, by parts as necessary, we have a new equation for the normal expansion process

where A = G/B? is the long run rate of growth of the niche divided by the intrinsic rate of expansion of the industry.
For large t, it is clear that log Y(t) tends toward log K?(t) which is growing exponentially at the rate, G. This niche growth rate is higher the higher is the growth rate of demand (n ₁) and the faster is the rate of cost reduction as expressed by larger values of (h ₁) and (?) in the technical progress function. It is also larger, the larger is the elasticity of demand (?). However, it is also clear that Y(t) no longer follows a Gompertz curve, in fact, the path of Y(t) is now given by

where  is a modifying function, which for large t grows exponentially at rate G.
Since the market niche is growing at an exponential rate, it is no longer obvious that there can be retardation of output growth at each point on the normal trajectory. To proceed, it makes sense to enquire how Y(t) is growing relatively to the ever-increasing scale of this niche. Is there a sense in which output catches up, relatively speaking, that it comes to fill the niche? Since log K?(t) = log K? + Gt it follows that, on subtracting this from (8) we find that

and this leads to a clear and perhaps surprising result. It tells us that it is the ratio of output to its niche value, K?(t), which follows a Gompertz curve (10) towards an upper asymptote, and that the value of this long run asymptotic ratio is e ^{? A}. That is, log [Y(t)/K?(t)] tends towards the ratio, G/B?, the natural growth rate of the niche divided by the intrinsic growth rate of the industry (Figure 3). It follows that the niche is progressively but not completely filled, Y(t) never catches up with K?(t), and remains relatively further away the greater is G, relative to B. The reason for this is not difficult to fathom. Since the industry tends towards a constant, positive growth rate, that of the niche, the price can never fall into equality with unit costs as it did in the case of a stationary environment. A positive profit margin is always needed to finance growth at the long-run rate, and this excess of the normal price over the changing level of unit cost exactly prevents output fully filling the expanding niche. In this regard, the process of industrial growth reflects an argument familiar in ecology. In a changing environment, the long-term population values of a species are not determined by carrying capacity alone but by this in relation to the intrinsic rate of increase of that population.