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Savings growth and the path of utility


  • Kirk Hamilton
  • Cees Withagen


We derive an expression relating the change in instantaneous utility to the growth of net (genuine) saving in an economy with multiple stocks and externalities that maximizes welfare in the utilitarian sense. This result is then shown to hold for decentralized competitive efficient economies as well, to yield an extension of the Hartwick rule: instantaneous utility is non-declining along a development path if genuine saving is decreasing. By way of example the rule is applied as a constant genuine saving rate rule in a simple Dasgupta-Heal-Solow-Stiglitz economy. The rule yields a path with unbounded consumption and higher wealth than on the standard Hartwick constant consumption path.

Suggested Citation

  • Kirk Hamilton & Cees Withagen, 2007. "Savings growth and the path of utility," Canadian Journal of Economics, Canadian Economics Association, vol. 40(2), pages 703-713, May.
  • Handle: RePEc:cje:issued:v:40:y:2007:i:2:p:703-713

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    References listed on IDEAS

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    JEL classification:

    • Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development
    • Q56 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environment and Development; Environment and Trade; Sustainability; Environmental Accounts and Accounting; Environmental Equity; Population Growth
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products


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