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Evaluating Projects in a Dynamic Economy: Some New Envelope Results


  • Chuan-Zhong Li
  • Karl-Gustaf Löfgren


This paper deals with the modern theory of social cost-benefit analysis in a dynamic economy. The theory emphasizes the role of a comprehensive, forward-looking, dynamic welfare index within the period of the project rather than that of a project's long-term consequences. However, what constitutes such a welfare index remains controversial in the recent literature. In this paper, we attempt to shed light on the issue by deriving three equivalent cost-benefit rules for evaluating a small project. In particular, we show that the direct change in a net national product (NNP) qualifies as a convenient welfare index without involving any other induced side effects. The project evaluation criterion thus becomes the present discounted value of the direct changes in NNP over the project period. We also illustrate the application of this theory in a few stylized examples. Copyright Verein für Socialpolitik and Blackwell Publishing Ltd. 2008.

Suggested Citation

  • Chuan-Zhong Li & Karl-Gustaf Löfgren, 2008. "Evaluating Projects in a Dynamic Economy: Some New Envelope Results," German Economic Review, Verein für Socialpolitik, vol. 9, pages 1-16, February.
  • Handle: RePEc:bla:germec:v:9:y:2008:i::p:1-16

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    References listed on IDEAS

    1. Avinash Dixit & Peter Hammond & Michael Hoel, 1980. "On Hartwick's Rule for Regular Maximin Paths of Capital Accumulation and Resource Depletion," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 551-556.
    2. Robin W. Boadway, 1975. "Cost-benefit Rules in General Equilibrium," Review of Economic Studies, Oxford University Press, vol. 42(3), pages 361-374.
    3. Kenneth Arrow & Partha Dasgupta & Karl-Göran Mäler, 2003. "Evaluating Projects and Assessing Sustainable Development in Imperfect Economies," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(4), pages 647-685, December.
    4. Thomas Aronsson & Karl-Gustaf Löfgren, 1998. "Green Accounting in Imperfect Market Economies," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 11(3), pages 273-287, April.
    5. Asheim, Geir B., 2000. "Green national accounting: why and how?," Environment and Development Economics, Cambridge University Press, vol. 5(01), pages 25-48, February.
    6. Caputo, Michael R., 1990. "How to do comparative dynamics on the back of an envelope in optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 14(3-4), pages 655-683, October.
    7. Dreze, Jean & Stern, Nicholas, 1987. "The theory of cost-benefit analysis," Handbook of Public Economics,in: A. J. Auerbach & M. Feldstein (ed.), Handbook of Public Economics, edition 1, volume 2, chapter 14, pages 909-989 Elsevier.
    8. Per-Olov Johansson & Karl-Gustaf Löfgren, 1996. "On the interpretation of ‘green’ NNP measures as cost-benefit rules," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 7(3), pages 243-250, April.
    9. Aronsson, Thomas & Lofgren, Karl-Gustaf, 1999. "Welfare equivalent NNP under distributional objectives," Economics Letters, Elsevier, vol. 63(2), pages 239-243, May.
    10. Dasgupta, Partha & M Ler, Karl-G Ran, 2000. "Net national product, wealth, and social well-being," Environment and Development Economics, Cambridge University Press, vol. 5(01), pages 69-93, February.
    11. Dasgupta, Partha, 2001. "Valuing Objects and Evaluating Policies in Imperfect Economies," Economic Journal, Royal Economic Society, vol. 111(471), pages 1-29, May.
    12. Weitzman, Martin L, 2001. " A Contribution to the Theory of Welfare Accounting," Scandinavian Journal of Economics, Wiley Blackwell, vol. 103(1), pages 1-23, March.
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    Cited by:

    1. Li, Chuan-Zhong & Isacsson, Gunnar, 2009. "Valuing urban accessibility and air quality in Sweden: A regional welfare analysis," Working Paper Series 2009:2, Uppsala University, Department of Economics.
    2. Li, Chuan-Zhong & Löfgren, Karl-Gustaf, 2010. "Dynamic cost-benefit analysis of large projects: The role of capital cost," Economics Letters, Elsevier, vol. 109(2), pages 128-130, November.
    3. Chuan-Zhong Li & Gunnar Isacsson, 2012. "Valuing urban accessibility and air quality in Sweden," Empirical Economics, Springer, vol. 42(3), pages 881-898, June.
    4. Löfgren, Karl-Gustaf, 2011. "On Envelope Theorems in Economics: Inspired by a Revival of a Forgotten Lecture," Umeå Economic Studies 830, Umeå University, Department of Economics.

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    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis


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