<1> Edward B Barbier is Reader at the Department of Environmental Economics and Environmental Management, University of York, UK. Thomas Homer-Dixon is Director of the Trudeau Centre for Peace and Conflict Studies and Assistant Professor in the Department of Political Science at the University of Toronto, Canada.

<2> R.E. Lucas, "On the Mechanics of Economic Development." Journal of Monetary Economics, Vol. 22 (1988), pp. 3-42; S. Rebelo, "Long-Run Policy Analysis and Long-Run Growth." Journal of Political Economy, Vol. 99, No. 3 (1991), pp. 500-521; P. Romer, "Increasing Returns and Long-Run Growth," Journal of Political Economy, Vol. 94, No. 5 (1986), pp. 1002-1037; P. Romer, "Endogenous Technological Change," Journal of Political Economy, Vol. 98, No. 5 (1990), pp. S71-S102.

<3> An endogenous variable is a dependent variable within an economic model. An exogenous variable is independent.

<4> R.J. Barro and X Sala-I-Martin, Economic Growth (New York: McGraw-Hill, 1995).

<5> Barro and Sala-I-Martin, Economic Growth; N.G. Mankiw, D. Romer, and D.N. Weil, "A Contribution to the Empirics of Economic Growth," Quarterly Journal of Economics, Vol. 107 (1992), pp. 407-437; H. Pack, "Endogenous Growth Theory: Intellectual Appeal and Empirical Shortcomings," Journal of Economic Perspectives, Vol. 8, No. 1 (1994), pp. 55-72; P. Romer, "The Origins of Endogenous Growth," Journal of Economic Perspectives, Vol. 8, No. 1 (1994), pp. 3-22.

<6> P. Romer, "Two Strategies for Economic Development: Using Ideas and Producing Ideas," in World Bank, Proceedings of the World Bank Annual Conference on Development Economics, 1992 (Washington, D.C.: The World Bank, 1993), pp. 63-91.

<7> Pack, "Endogenous Growth Theory."

<8> E.B. Barbier, "Natural Capital and the Economics of Environment and Development," in A.M. Jansson, M. Hammer, C. Folke, and R. Costanza (eds.), Investing in Natural Capital: The Ecological Economics Approach to Sustainability (Washington, D.C.: Island Press, 1994).

<9> Recent efforts to extend endogenous growth models to incorporate environmental considerations have generally focused on the short- and long-run implications of pollution and its disutility. See A. Bovenberg and S. Smulders, "Environmental Quality and Pollution-Augmenting Technological Change in a Two-Sector Endogenous Growth Model," Journal of Public Economics, Vol. 57 (1995), pp. 369-391; I. Musu, "Transitional Dynamics to Optimal Sustainable Growth," Paper presented at the 6th Annual European Association of Environmental and Resource Economics Conference, Umeå, Sweden, 24-26 June, 1995; I. Musu and M. Lines, "Endogenos Growth and Environmental Preservation," in G. Boero and A. Silberston (eds.), Environmental Economics: Proceedings of European Economic Associations at Oxford, 1993 (London: St. Martins Press, 1995); and N. Vellinga, "Short Run Analysis of Endogenous Environmental Growth," Paper presented at the 6th Annual European Association of Environmental and Resource Economics Conference, Umeå, Sweden, 24-26 June, 1995.

<10> P.S. Dasgupta and G. E. Heal, The Economics of Exhaustible Resources (Cambridge, UK: University Press, 1979); J.E. Stiglitz, "Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths," Review of Economic Studies, Symposium on the Economics of Exhaustible Resources (1974), 123-138.

<11> Stiglitz, "Growth with Exhaustible Natural Resources."

<12> E.B. Barbier, Endogenous Growth and Natural Resource Scarcity, EEEM Discussion Paper 9601, Department of Environmental Economics and Environmental Management (York, UK: University of York, 1996).

<13> Stiglitz, "Growth with Exhaustible Natural Resources"; Romer, "Endogenous Technological Change."

<14> For example, in the standard neoclassical model with exhaustible resources and exogenous technical change, the expression for production of aggregate output, Q, would be written as Q = K^a1L^a2R^a3e^Tt, where K is the stock of physical capital, L is labour, R the resource input and T is the constant rate of technological progress. As shown by Stiglitz (1974), this expression can be re-written as Q = K^a1L^a2(Re^(T/a3)t)^a3, where T/a₃ is the (exogenous) rate of resource-augmenting technical progress. In the Romer-Stiglitz model developed by Barbier (1996) the production function becomes Q = n^(p-1)A^p-K^a1L^a2R^a3(H - H_A)^a4 , where the additional terms include n, which is the amount of foregone capital necessary to create one unit of durable goods, A, the stock of "ideas" or technical designs, H, the total stock of human capital, H_A the amount of human capital allocated to innovation, and the parameter p = (1 - a₁) = a₂ + a₃ + a₄ . Assuming n is constant, this expression can be rewritten as Q = n^(p-1)(A^(p/a3)R)^a3K^a1L^a2(H - H_A)^a4 where A^(p/a3) represents resource-augmenting endogenous technological progress.

<15> T.F. Homer-Dixon, "The Ingenuity Gap: Can Poor Countries Adapt to Resource Scarcity," Population and Development Review, Vol. 21, No. 3 (1995), pp. 587-612.

<16> If increasing resource scarcity is reflected in market prices, than the value of the depleted scarce resource will rise relative to the costs of depletion. The result is that increasing scarcity generates higher economic profits, or rents. If property rights are well-defined and maintained, and in particular if the resource is under sole ownership, then economic theory suggests that the resource will be depleted to maximize long-term economic rents, and thus generally "conserved" for as long as possible. However, these conditions rarely hold in developing countries for scarce resources; often there is competitive rent-seeking by many powerful interest groups to extract maximum rent in the short run through resource depletion. As noted by a recent article in The Economist, even countries with large resource endowments are not immune to this problem, particular if commodity price booms increase the windfall gains from scarce resources: "A natural-resource endowment gives rise to what economists call 'rent' - the difference between what is actually paid to the producer and the minimum price that he would have demanded to produce the stuff in the first place. For many countries that have enjoyed booming natural-resource incomes in the past few decades, especially those that have sudden windfalls, these rents have been staggeringly large . . . . The upshot is routinely an outbreak of competitive rent-seeking. The power centres in any resource-rich country soon notice that the profits from capturing a slice of the rent from the natural resources beat those from any possible alternatives; and they act accordingly." See The Economist, "The Natural Resources Myth: Ungenerous Endowments," 23 December 1995 - 5 January 1996, pp. 107-109.

<17> T.F. Homer-Dixon, "Environmental Scarcities and Violent Conflict: Evidence from Cases," International Security, Vol. 19, No. 1 (1994), pp. 5-40; Homer-Dixon, "The Ingenuity Gap"; T.F. Homer-Dixon, J.H. Boutwell, and G.W. Rathjens, "Environmental Change and Violent Conflict," Scientific American (February 1993), pp. 38-45.

<18> Romer, "Endogenous Technological Change."

<19> United Nations Population Fund, The State of the World Population 1994 (New York: UNFPA, 1994).

<20> J. Boyce, Agrarian Impasse in Bengal: Institutional Constraints to Technological Change (Oxford: Oxford University Press, 1987).

<21> F. Golleti, The Changing Public Role in A Rice Economy Approaching Self-Sufficiency: The Case of Bangladesh, IFPRI Research Report 98 (Washington, D.C.: International Food Policy Research Institute, 1994).

<22> P. Wallich, "The Analytical Economist: The Wages of Haiti's Dictatorship." Scientific American, Vol. 271, No. 6 (1994). p. 36.

<23> R.T. Deacon, "Deforestation and the Rule of Law in a Cross-Section of Countries," Land Economics, Vol. 70, No. 4 (November 1995), pp. 414-430.

<24> Barbier, "Endogenous Growth and Natural Resource Scarcity."

<25> A third possible scenario of "negative" innovation is ruled out in the models developed by Barbier, because it is assumed that "decumulation" of the stock of ideas is not feasible; that is, resource scarcity may disrupt the social conditions and institutions necessary to generate new innovations, but once created, technical designs or other forms of technological knowledge do not simply disappear. Some may argue, however, that this is an unnecessarily restrictive condition and that the actual process of innovation in an economy is more complex. For example, Homer-Dixon distinguishes between the generation of ingenuity and its dissemination or implementation. (See Homer-Dixon, "The Ingenuity Gap.) If this distinction is valid then, although the generated ideas themselves may be hard to lose or "decumulate," their implementation may be affected to the point that the stock of ideas is no longer functional in the broader economic and social system. In this sense, the stock of ingenuity in society may for all intents and purposes appear to "decumulate."

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