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.
Highlights
Hartwick’s investment rule prescribes reinvesting resource rents in reproducible capital, keeping the value of net investments equal to zero, in order to keep consumption constant
One example is the model of capital accumulation and reource depletion, the so-called Dasgupta-Heal-Solow-Stiglitz model, that Solow (1974) and Hartwick (1977) used to analyze constant consumption paths in the presence of resource constraints
We show that following this rule is equivalent to constant real per capita net national product, where net national product is equal to production minus resource rents in this model
Summary
Hartwick’s investment rule prescribes reinvesting resource rents in reproducible capital, keeping the value of net investments equal to zero, in order to keep consumption constant. In this paper we formulate an interpretable definition of Hartwick’s investment rule to the population growth setting that can be applied for any exogenously given population growth function and any technology We obtain this result by focusing, not on constant per capita consumption, but on constant per capita net national product, defined as the maximized per capita value of the flows of goods and services that are produced by the productive assets. With population growth the relationship between an appropriately defined Hartwick’s rule and the constancy of per capita net national product can be established as an interpretable equivalence result without restrictive assumptions on population growth and technology. In the general model with multiple capital goods, we obtain as a corollary that keeping the value of net investments equal to zero leads to constant consumption if population is constant. We show how the suggested adaptation of Hartwick’s rule to the population growth setting can be interpreted, including the role that capital gains play in our proposed rule
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