Substitutability and sustainable economic growth

Endogenous growth theory has enjoyed a surge of research activity since the seminal papers of Romer (1986, 1990) and Lucas (1988); both built on a rich literature going back to Adam Smith (1776). The application of endogenous growth theory to ecological issues has been more recent, but no less fertile than its application elsewhere. Researchers have applied endogenous growth theory to sustainability subject to pollution and resource use. These applications have the desirable properties of satisfying biophysical constraints and the laws of thermodynamics as well as deriving conditions for growth to continue indefinitely. Endogenous growth models in particular focus on endogenous technological progress as the means to overcome diminishing marginal returns to physical capital (and, in the case of ecological models, soiling the environment) and thus sustain growth indefinitely. Such models focus on balanced growth in which growth rates are constant designed to mimic Kaldor\u27s (1958) stylized facts. These are razor edge constraints that simplify solutions and ignore the rich dynamics of possibly reaching sustainable paths. In addition, the assumption of zero or an exogenous rate of population growth are additional razor edge conditions. Christiaans (2004) has shown the feasibility conditions for balanced growth involving output elasticities are razor edge conditions. ^ These facts and the general observation that balanced growth paths obtain instantaneously lead us to relax growth rate constraints and examine the underlying dynamics through simulation. In so doing, we re-introduce a flexible production technology, GCES (Mukerjee, 1963), that permits exploration of the relation between factor substitution and sustainability. Further, we introduce minimum resource constraint production technology in both the Cobb-Douglas and GCES regimes, and, we introduce a policy function that attenuates apparent excess saving. ^ None of the models analyzed exhibits sustained growth. Typically physical capital accumulation overwhelms output driving the marginal product of physical capital (and the level of consumption) to zero in a few hundred years. We observe three idiosyncracies of balanced growth models and suggest ways to address the shortcomings of the dynamic models derived from the underlying dynamic optimization problems. ^ One of these approaches is to perturb the utility maximizing agent\u27s decision calculus in the problems addressed herein with a fuzzy logic decision calculus. That is, such decisions do not satisfy the axioms of expected utility theory, rather they fit with non-conventional, non-expected utility theory (Starmer, 2002). This approach is outlined in Chapter 4 but the solution is not carried out; that is a future research program.