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

Secular Expansion and the Gompertz Process
16In economic ecology, the analogue to speciation or mutation is innovation, rather more precisely a radical innovation that creates a new line of productive activity. Therefore, we begin with a radical innovation, the type that leads to a new industry built around a new product with its own process of production and introduced into the prevailing market environment. This product has certain fixed performance characteristics relative to the other products with which it is in competition, and at a price p(t), all other prices being given, the long-run level of demand is given by
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?, being the elasticity of long-run demand. This long run notion of demand describes the situation that would prevail when the evolutionary process has run its course, when consumer learning and the further formation of preferences has ceased. Notice carefully that actual demand is always less than this long-run level. The Gompertz process postulates that this learning process can be summarized by the following differential equation

Hence, the actual demand level Y(t)_D approaches n(t) asymptotically over time. Here, the constant ? dictates the rate of demand-side learning. At a given price, a given niche is filled at a rate determined by this learning process. Now, if, as is highly likely, p(t) is also changing over time, it is apparent that the actual path of demand growth need not follow a Gompertz curve, although a Gompertz process generates it. A theory of industrial growth in which the product price is arbitrarily determined is obviously unsatisfactory; we need a theory of how the price of the new commodity is determined and how it changes over time. To internalise price formation within the growth process requires a statement of the supply side, in particular, of the growth of capacity to supply the expanding market. The view we take here is that firms set the price relative to unit costs in order to finance growth at a particular rate, so that capacity growth is proportional to current profitability. As long as profitability is above the cost of capital, the industry invests to expand capacity. What this price is will depend on investment requirements per unit of capacity expansion and the capital market condition that impinge on the flow of funds into the new industry. Firms have to learn the appropriate level of capacity and the investment analogue to the demand side learning process is

Where d/dt log Y(t)s is the growth rate of capacity. The coefficient ? captures, in a rough and ready way, rules about the funding of investment, the capital requirements per unit of output and the conventions determining the rate of depreciation. To begin with, we abstract from further technical progress and any elements of non-constant returns to scale and let the industry have a fixed level of unit cost, defined to include the normal return on investment,

Holding p(t) constant, (3) integrates to give an exponential growth curve for the secular growth of productive capacity, a process in which profit drives finance and investment without limit. It follows that for any arbitrary p(t) we have two growth curves giving radically different paths for demand and capacity. Naturally, such unbalanced market situations are not likely to characterise the secular trend of the industry. [15][15]The industry is closed to foreign trade. Hence, the obvious step is to require capacity (output) and demand to grow together with the price adjusting along this secular path to bring about the required co-ordination of the new market. We call such a secular path a “normally co-ordinated path”, a “normal path” for short, and it provides a benchmark case against which to judge other possibilities. Combining (2) and (3) by setting Y(t)_D = Y(t) _s = Y(t) and taking account of (1) and (4), we find that this normal, balanced process of expansion satisfies the equation

Where, the coefficients B and K are given by

Each of the parameters B and K combines together the economic influences on the growth process, in terms of learning and long run demand, investment and long run costs of production, in a clearly identifiable way. These coefficients are not arbitrary but reflect in a precise way the underpinning market process by which a new activity grows into its niche. Now the surprising feature of this normal path is that it also describes a Gompertz process even though the price of the product, profit margins and the scale of long run demand are varying endogenously during the process of secular expansion. It is useful now to define log Y(t) = x(t) so (5) can be written as

which, integrates to give

Whence we have the equation for the Gompertz curve

with Y(?) = K and Y(0) = Y₀. Output increases along the balanced secular path, to fill the niche completely, tracing a sigmoid curve with the inflexion point where Y(t) = K/e. As far as the balanced growth rate is concerned, we have

since Y₀ < K,
While, the rate of retardation is given by

Now the interesting aspect of this account is that we have isolated the retardation phenomena without having to introduce technical change, other than that implied by the foundation of the industry, pace Burns and Kuznets. The retardation dynamics are driven by the interaction between learning and capacity expansion and there is no technical progress subsequent to the initial innovation. Retardation is a consequence of creating and filling the niche according to the rules of learning and capacity accumulation, and it is clear that the rate of retardation declines at an exponential rate towards zero. Slackening of the rate of technical progress is not necessary to experience retardation of output. Solving for the path of normal price as a function of current output we find

Clearly, p(t), decline over time, and always declines relative to the given unit cost level h ₀, so that total revenues decline relative to total costs. Since profits and growth are so closely linked, it follows automatically that retardation and a squeeze on profit margins are two sides of the same coin. This, of course, mirrors Schumpeter’s famous depiction of profits as “at the same time the child and victim of development” or, as he put it, profit is “related to the creation of new things, to the realisation of the future value system” (1934, p. 154).
We have referred already to the ecological parallels to our secular growth process, and here it is appropriate to interpret K as the carrying capacity of the industry and B as its intrinsic rate of increase. Notice that K is not dependent upon the two primitive rates of learning, ? and ?, while B is dependent on the long-run demand elasticity, ?. Figure 1a should help in the interpretation of these remarks.