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Investment Rules and Time Invariance under Population Growth

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  • Geir B. Asheim
  • John M. Hartwick
  • Tapan Mitra

Abstract

We propose an adaptation of Hartwick’s investment rule to models with population growth and show that following Hartwick’s rule is equivalent to a time-invariant real per capita net national product. In the so-called DHSS model of capital accumulation and resource depletion the proposed Hartwick’s rule equates the accumulation of per capita capital, net of the capital dilution effect of population growth, to the value of the depletion of the resource, gross of the capital dilution effect. We investigate why this asymmetry arises by analyzing a general model with multiple capital goods, in which we obtain a formulation of Hartwick’s investment rule where capital gains play a role if population growth is positive. Since capital gains accrue only to the resource but not to capital, we get the apparent asymmetry in the DHSS model. In both models we obtain as a corollary that keeping the value of net investments equal to zero leads to constant consumption if population is constant.

Suggested Citation

  • Geir B. Asheim & John M. Hartwick & Tapan Mitra, 2020. "Investment Rules and Time Invariance under Population Growth," CESifo Working Paper Series 8513, CESifo.
  • Handle: RePEc:ces:ceswps:_8513
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    More about this item

    Keywords

    sustainable development; population growth; intergenerational equity;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development

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