Constant-utility paths in a resource-based economy

Bazhanov, Andrei (2010): Constant-utility paths in a resource-based economy.

Abstract

This paper analyzes a social planner's solution in a resource-based economy under a constant-utility criterion. The utility function includes social progress in a multiplicative form. The resulting paths of consumption include the patterns of growth that are conventionally used in the literature. This approach extends conventional link between the utilitarian criterion and the maximin for the cases with finite elasticity of marginal utility. The closed form solutions, derived for the Dasgupta-Heal-Solow-Stiglitz (DHSS) model, include the result of Solow (1974) and Hartwick (1977) as a specific case. The approach is applied to an example of a distorted resource-extracting economy under the requirement for smoothness of the paths with respect to historical data.

• Item Type: MPRA Paper
• Language: English
• Keywords: essential nonrenewable resource; sustainable growth; geometrically weighted percent; distorted economy
• Subjects: Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q3 - Nonrenewable Resources and Conservation > Q32 - Exhaustible Resources and Economic Development; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q3 - Nonrenewable Resources and Conservation > Q38 - Government Policy; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O47 - Empirical Studies of Economic Growth ; Aggregate Productivity ; Cross-Country Output Convergence; O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O13 - Agriculture ; Natural Resources ; Energy ; Environment ; Other Primary Products

References

Alvarez-Cuadrado, F., Long, N.V., 2009. A mixed Bentham-Rawls criterion for intergenerational equity: theory and implications. Journal of Environmental Economics and Management 58(2), 154--168.

Arrow, K.J., 1973. Rawls's principle of just saving. Swedish Journal of Economics 75(4), 323--335.

Arrow, K.J., Dasgupta, P., Mäler, K.G., 2003. Evaluating projects and assessing sustainable development in imperfect economies. Environmental and Resource Economics 26, 647--685.

Asheim, G.B., 1988. Rawlsian intergenerational justice as a Markov-perfect equilibrium in a resource technology. Review of Economic Studies, 55(3), 469--483.

Asheim, G.B., 2005. Intergenerational ethics under resource constraints. Swiss Journal of Economics and Statistics 141(3), 313--330.

Asheim, G.B., Buchholz, W., Hartwick, J.M., Mitra, T., Withagen, C., 2007. Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints. Journal of Environmental Economics and Management 53, 213--229.

Bazhanov, A.V., 2008. Sustainable growth in a resource-based economy: the extraction-saving relationship. MPRA Paper No. 12350.

Bazhanov, A.V., 2010. Sustainable growth: Compatibility between a plausible growth criterion and the initial state. Resources Policy 35(2), 116--125.

Bazhanov, A.V., 2011. A closed-form solution to Stollery's problem with damage in utility. Computational Economics (in print), DOI: 10.1007/s10614-010-9249-4.

Becken, W., Schmelcher, P., 2000. The analytic continuation of the Gaussian hypergeometric function 2F1(a,b;c;z) for arbitrary parameters. Journal of Computational and Applied Mathematics 126, 449--478.

Calvo, G., 1978. Some notes on time inconsistency and Rawls' maximin criterion. Review of Economic Studies, 45(1), 97--102.

CERA, 2006. Why the peak oil theory falls down: myths, legends, and the future of oil resources. (November 10, 2006), http://www.cera.com/aspx/cda/client/report/reportpreview.aspx? CID=8437&KID= . Accessed 25 December 2007.

Dasgupta, P., 1974. On some alternative criteria for justice between generations. Journal of Public Economics 3, 405--423.

Dasgupta, P., Heal, G., 1974. The optimal depletion of exhaustible resources. Review of Economic Studies 41, 3--28.

Dasgupta, P., Heal, G., 1979. Economic Theory and Exhaustible Resources. Cambridge University Press, Cambridge, England.

Elster, J., 1989. Solomonic judgements: studies in the limitations of rationality. Cambridge University Press, Cambridge, England.

Fleurbaey, M., 2007. Intergenerational fairness, in: Roemer, J.E., Suzumura K. (Eds.), Intergenerational equity and sustainability. Palgrave Macmillan, New York, pp. 155--175.

Foley, D., 1967. Resource allocation and the public sector. Yale Economic Essays 7, 45--98.

Gaudet, G., 2007. Natural resource economics under the rule of Hotelling. Canadian Journal of Economics 40(4), 1033--1059.

Griffin, J.M., Gregory, P.R., 1976. An intercountry translog model of energy substitution responses. American Economic Review 66, 845--857.

Groth, C., Koch, K.J., Steger, T.M., 2006. Rethinking the concept of long-run economic growth. CESifo Working Paper N 1701.

Hadamard, J., 1902. Sur les problemes aux derivees partielles et leur signification physique. Princeton University Bulletin 13, 49--52.

Hamilton, K., 1994. The Hartwick rule in a greenhouse world. Ch. 4, in: Sustainable development and green national accounts. Ph.D. Thesis, University College, London.

Hamilton, K., Ruta, G., Tajibaeva, L., 2006. Capital accumulation and resource depletion: a Hartwick Rule counterfactual. Environmental and Resource Economics 34, 517--533.

Hartwick, J.M., 1977. Intergenerational equity and the investing of rents from exhaustible resources. American Economic Review 67, 972--974.

Hotelling, H., 1931. The economics of exhaustible resources. The Journal of Political Economy 39(2), 137--175.

Hubbert, M.K., 1956. Nuclear energy and the fossil fuels. American Petroleum Institute, Drilling and Production Practice. Proceedings of Spring Meeting, San Antonio, Texas, pp. 7--25.

Kahneman, D., Varey, C., 1991. Notes on the psychology of utility, in: Elster, J., Roemer J.E. (Eds.), Interpersonal comparisons of well-being. Cambridge University Press, New York, pp. 127--163.

Kolm, S.C., 1997. Justice and Equity. MIT Press, Cambridge, MA.

Koopmans, T.C., 1964. On flexibility of future preference, in: Bryan, G. L., Shelly, M. W. II (Eds.), Human judgments and optimality. John Wiley, New York, pp. 243--254.

Lecomber, R., 1979. The Economics of Natural Resources. John Wiley & Sons, New York.

Leininger, W., 1985. Rawls' maximin criterion and time-consistency: further results. Review of Economic Studies 52(3), 505--513.

Levhari, D., Liviatan, N., 1977. Notes on Hotelling's economics of exhaustible resources. Canadian Journal of Economics 10, 177--192.

Long, N. V., 1975. Resource extraction under the uncertainty about possible nationalization. Journal of Economic Theory 10, 42--53.

Long, N.V., 2007. Toward a just savings principle, in: Roemer, J.E., Suzumura K. (Eds.), Intergenerational equity and sustainability. Palgrave Macmillan, New York, pp. 291--319.

Luke, Y.L., 1969. The Special Functions and their Approximations, Vol. 1, Academic Press, New York, 1969.

Malinvaud, E., 1953. Capital accumulation and efficient allocation of resources. Econometrica 21 (2), 233--268.

Martinet, V., 2007. A step beside the maximin path: Can we sustain the economy by following Hartwick's investment rule? Ecological Economics 64, 103--108.

Mitra, T., 1978. Efficient growth with exhaustible resources in a neoclassical model. Journal of Economic Theory 17, 114--129.

Mitra, T., 1983. Limits on population growth under exhaustible resource constraints. International Economic Review 24, 155--168.

Nordhaus, W.D., Boyer, J., 2000. Warming the World: Economic Models of Global Warming. MIT Press, Cambridge.

Pezzey, J.C.V., 2004. Exact measures of income in a hyperbolic economy. Environment and Development Economics 9, 473--484.

Phelps, E. S., Riley, J. G., 1978. Rawlsian growth: dynamic programming of capital and wealth for intergeneration "maximin" justice. Review of Economic Studies, 45(1), 103--120.

Pindyck, R.S., 1979. Interfuel substitution and the demand for energy: an international comparison. Review of Economics and Statistics 61, 169--179.

Radler, M., 2006. Oil production, reserves increase slightly in 2006. Oil and Gas Journal 104(47), 20--23.

Rawls, J., 1971. A Theory of Justice. Belknap Press of Harvard University Press, Cambridge.

Scanlon, T.M., 1991. The moral basis of interpersonal comparisons, in: Elster, J., Roemer, J.E. (Eds.), Interpersonal comparisons of well-being. Cambridge University Press, New York, pp. 17--44.

Solow, R.M., 1974. Intergenerational equity and exhaustible resources. Review of Economic Studies 41, 29--45.

Stiglitz, J., 1974. Growth with exhaustible natural resources: efficient and optimal growth paths. Review of Economic Studies 41, 123--137.

Stollery, K.R., 1998. Constant utility paths and irreversible global warming. Canadian Journal of Economics 31(3), 730--742.

UN, 2004. World Population to 2300. United Nations, New York.

World Commission, 1987. World Commission on Environment and Development. Our Common Future. Oxford University Press, Oxford/New York.

World Oil, 2009. Worldwide look at reserves and production. Oil & Gas Journal 107(47), 20--21.