As a point of departure for rigorous, if simplistic, mathematical analysis of various subsidiary topics, the neoclassical theory of growth sketched -much too briefly - above has undoubted virtues. However, the underlying assumption of optimal growth in equilibrium is very troubling. In this context, it is important to note a number of difficulties, as follows: (1) the real multi-sector, multi-product economy is never actually in equilibrium and (2) if it were, there would be no opportunity or incentives for entrepreneurs to innovate. In an equilibrium world, technology would stagnate. The traditional solution to this problem, since von Neumann (1945 ), has been to regard technological progress as exogenous, like the biblical 'manna from heaven'. As it happens, we adopt a modified version of this view, for reasons discussed in Chapters 2 and 3.
Furthermore, the notion of growth and development along an optimum path is problematic. For instance, (3) the real economy is a complex nonlinear system, and non-linear systems do not exhibit equilibrium states. Moreover (4) while entrepreneurs at the micro-scale undoubtedly try to optimize their own activities at least within the limits of bounded rationality (for example, Conlisk 1996), the aggregate results of many micro-optimizations virtually guarantee a non-optimal result at the macro-scale.8 Moreover, (5) even if the complex non-linear economic system could be optimized by a hypothetical social planner, a dynamic optimum is not the same as a static optimum. (In other simpler words, notwithstanding Koopmans' ingenious effort (Koopmans 1960; Koopmans et al. 1964) one cannot simultaneously optimize for the present, and for a later time.)
Figure 1.1 Simple Salter cycle scale of production
Finally, and most important, (6) notwithstanding Georgescu-Roegen's contributions (1966, 1984) - especially with regard to insisting on the fundamental distinction between 'funds' (which are unchanged) and 'flows' (which are consumed) - the lack of any general theory to explain physical production in physical terms (that is, in terms of energy and materials) is extremely troubling. It is the latter problem, more than any other, that has motivated this book.
While technical progress is normally treated as an exogenous driving force, there is an endogenous mechanism that can explain some aggregate economic growth in equilibrium - beyond that which is accounted for by labor and capital accumulation - without radical (structure-changing) technological innovations. The mechanism in question is a simple positive feedback between increasing consumption, investment, increasing scale and 'learning-by-doing'. These result in declining costs and declining prices, stimulating further increases in demand and investment to increase supply (Figure 1.1). The phenomenon of feedback is addressed later (Chapter 5) in greater detail.
However, if learning and economies of scale are the only types of technological change allowed by the model, there must be declining returns and an eventual limit to growth as the potential for incremental improvements in existing products and production technologies are exhausted. However, neoclassical economic theory cannot explain radical (Schumpeterian) innovations, insofar as many, if not most, radical innovations are not the outcome of rational investment projects. For every big winner there may be many losers, and the eventual big winners are often just lucky beneficiaries of the work of others. In fact, the early risk-takers rarely see a positive return. To put it another way, the expectation value of most risky investments in radical innovation is negative, and to that extent inconsistent with the rationality and 'greed' (profit maximization) axioms. Hence, though radical innovation is essential for long-term economic growth, and the social rate of return is clearly positive, the closed neoclassical economic model does not explain the radical innovations that change the structure of the economy.
Finally, there is no essential role in the Solow model for energy or materials, except as a consequence (not a cause) of economic growth. This is significant, because if resource consumption is not needed to explain growth, then 'decoupling' growth from resource consumption - a popular notion in some current discussions of sustainability9 - is conceptually easy: From the theoretical perspective, it seems, they were never coupled in the first place. There is also no role for wastes and pollutants in the closed Walrasian equilibrium system, where all products are abstractions. The neoclassical conceptualization implies that wastes and emissions - if they exist at all - do no economic harm and can be disposed of at no cost. It is unclear how much of the neoclassical apparatus can survive when this simplification is abandoned.
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