The genuine savings criterion and the value of population |
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Authors: | Kenneth J Arrow Partha Dasgupta Karl-Göran Mäler |
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Institution: | (1) Department of Economics, Stanford University, Stanford, CA 94305-6072, USA (e-mail: arrow@stanford.edu) , US;(2) Faculty of Economics and Politics, University of Cambridge, Cambridge CB3 9DE, UK (e-mail: partha.dasgupta@econ.cam.ac.uk) , GB;(3) Stockholm School of Economics and Beijer International Institute for Ecological Economics, Royal Academy of Sciences, Box 50005, 10691 Stockholm, SWEDEN (e-mai: Karl@Beijer.kva.se) , SE |
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Abstract: | Summary. In any dynamic model of the economy with changing population, the latter should properly be one of the state variables of
the system. It enters both in the maximand, at least under total utilitarianism, and into the production function in one way
or another. If population growth is exponential and constant returns prevails, then a simple transformation to per capita variables can be used to eliminate one state variable, but this ceases to be true if growth is not exponential, as it obviously
is not and cannot be. If the growth of population is exogenous, then introducing it into the system does not affect the optimal
policy. However, if one asks whether the system is sustainable, in the sense of at least maintaining total welfare (integral
of discounted utilities), then the criterion is that that the value of the rates of change of the state variables is non-negative,
so that the shadow price of population becomes relevant. In this paper, we derive explicit formulas in a simple model, showing
that the rate of growth of per capita capital is not the correct formula but must have another terms added to it. We also study the question under an alternative
criterion of long-run average utilitarianism.
Received: June 1, 2002; revised version: September 27, 2002
RID="*"
ID="*"Research support was provided by the William and Flora Hewlett Foundation. An earlier version of this paper was presented
at a celebration of Mordecai Kurz's 66th birthday at Stanford University, 1–3 August 2002.
Correspondence to: K.J. Arrow |
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Keywords: | and Phrases: Optimal control Population Genuine savings Accounting prices |
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