Neoclassical Growth Models with Resources and Technical Change

Another installment. I'm more uncertain about whether I'm getting the story right here. So comments are even more welcome. I've had none so far :(


Growth Models with Resources and Technical Change

In addition to substitution of capital for resources, technological change might permit growth or at least constant consumption in the face of a finite resource base. Stiglitz (1974a) showed that in a Cobb Douglas framework with exogenous technical progress that consumption will grow over time if the rate of technological change divided by the discount rate is greater than the output elasticity of resources.

Growing total factor productivity obviously makes sustainability technically easier to achieve and sustainability may be possible even with an elasticity of substitution of less than one. Once again, technical feasibility does not guarantee sustainability. Depending on preferences for current versus future consumption, current depletion may as a result be faster (Smulders, 2005). This result is related to the Khazzoom-Brookes postulate or rebound effect discussed below. As noted above, due to externalities in knowledge production there may be too little innovation in an endogenous growth world. As a result, depletion of a non-renewable resource is nonoptimal, but this rate could be either too fast or too slow.

Recent work (e.g. Aghion and Howitt, 1998; Barbier, 1999; Scholz and Ziemes, 1999; Groth and Schou, 2002; Grimaud and Roug, 2003; Di Maria and Valente, 2008) exploits endogenous growth theories to analyze capital–non-renewable resource economies. Initial work by Aghion and Howitt (1998) finds that an AK type model with essential nonrenewable resources cannot allow for unbounded growth in consumption while a Schumpetarian type model can. A Schumpetarian model with a renewable resource that affects utility directly can allow unlimited growth, but only under unlikely assumptions. But if the renewable resources do not affect utility, continued growth would be easier than in the non-renewable case. Smulders (1999) provides a survey of earlier endogenous growth work and Smulders and de Nooij (2003) and Di Maria and Valente (2008) provide references to the more recent literature. An aim of much of this literature is to determine whether, and under what circumstances, technical progress is effective in ensuring sustained consumption (Bretschger, 2005). A general finding is that the rate of resource augmenting progress must be strictly positive and at least equal to the discount rate to obtain non-declining consumption in the long run (Di Maria and Valente, 2008).

Tahvonen and Salo (2001) develop a model economy with both renewable and non-renewable energy resources that is both very general and more realistic than the earlier neoclassical literature (e.g. Solow, 1974). The models have extraction costs for fossil fuels and production costs for renewable energy resources, which also rise as cheaper sources are exploited first. The model can incorporate no technological change, exogenous technical change, and learning by doing, a form of endogenous technical change. They assume that technical knowledge in extraction increases proportionally to extraction and that technical knowledge in final production is proportional to the capital stock. The optimal development of such an economy appears to mimic history much more effectively than other neoclassical models based on the Solow-Stiglitz capital-non-renewable resource model. The economy passes through pre-industrial, industrial, and post-industrial eras as the use of fossil fuels first rises and then falls and capital is accumulated. The price of nonrenewables first falls and then rises.

References
Aghion, P. and P. Howitt (1998). Endogenous Growth Theory. : Cambridge, MA: MIT Press.
Barbier, E.B. (1999), ‘Endogenous growth and natural resource scarcity’, Environmental and Resource Economics 14: 51–74.
Bretschger, L. (2005), ‘Economics of technological change and the natural environment: how effective are innovations as a remedy for resource scarcity?’ Ecological Economics 54: 148–163.
di Maria, C. and S. Valente (2008) Hicks meets Hotelling: the direction of technical change in capital–resource economies, Environment and Development Economics 13: 691–717.
Grimaud, A. and L. Roug (2003), ‘Non-renewable resources and growth with vertical innovations: optimum, equilibrium and economic policy’, Journal of Environmental Economics and Management 45: 433–453.
Groth, C. and P. Schou (2002), ‘Can non-renewable resources alleviate the knife-edge character of endogenous growth?’ Oxford Economic Papers 54: 386–411.
Scholz, C. and G. Ziemes (1999), ‘Exhaustible resources, monopolistic competition, and endogenous growth’, Environmental and Resource Economics 13: 169–185.
Smulders, S. (1999). “Endogenous growth theory and the environment.” in J. C. J. M. van den Bergh (ed.), Handbook of Environmental and Resource Economics, Edward Elgar, Cheltenham, 89-108.
Smulders, S. (2005). “Endogenous technical change, natural resources and growth.” In: R. Ayres, D. Simpson, and M. Toman (eds.), Scarcity and Growth in the New Millennium. Washington, DC: Resources for the Future.
Smulders, S. and M. de Nooij (2003). “The impact of energy conservation on technology and economic growth.” Resource and Energy Economics, 25: 59–79.
Solow, R. M. (1974). “Intergenerational equity and exhaustible resources.” Review of Economic Studies, Symposium on the Economics of Exhaustible Resources: 29-46.
Stiglitz, J. E. (1974a). “Growth with exhaustible natural resources: efficient and optimal growth paths.” Review of Economic Studies, Symposium on the Economics of Exhaustible Resources: 123-138.
Tahvonen, O. and S. Salo (2001). “Economic growth and transitions between renewable and nonrenewable energy resources.” European Economic Review 45: 1379-1398.