John M. Hartwick

Natural resources, national accounting and economic depreciation

The current value Hamiltonian in an aggregate optimal growth problem with heterogeneous capital stocks including exhaustible, renewable and environmental stocks is the NNP function. Routine substitutions reveal that the using up of natural resource stocks is representable as an easy-to-interpret economic depreciation magnitudes. We obtain true NNP inclusive of natural resource stock diminution.

Substitution Among Exhaustible Resources and Intergenerational Equity

In Hartwick [3], it was shown that implicit in Solows [10] model of intergenerational equity and exhaustible resources was the savings-investment rule: society should invest in reproducible capital precisely the current returns from the use of flows of exhaustible resources in order to maintain per capita consumption constant. Population was assumed to remain constant. In Solow [10] and Hartwick [3] it was assumed that there was only one exhaustible resource. Beckmann [1] & [2] has investigated optimal growth in models with many exhaustible resources. In this paper we consider the case of many exhaustible resources and derive results on substitution among resources and on the nature of paths of development. One of Beckrmanns results on substitution is analysed. Our approach is first to analyse efficient paths under the assumption of general savings functions and then to analyse efficient paths under the assumption of the special savings function referred to above. Our results indicate the Solows existence theorem remains valid for the case of many exhaustible resources and some light is shed on the existence of paths for production functions not of the Cobb-Douglas form.

Investing returns from depleting renewable resource stocks and intergenerational equity

We demonstrate the following result: if along dynamically efficient development paths, the net current value of the diminution in natural resources stocks, renewable and non-renewable, is invested in reproducible capital, per capita consumption will remain constant over time in a world of unchanging technology and population. This is an extension of an earlier proposition covering only non-renewable or exhaustible resources.

Efficient Resource Allocation in a Multinucleated City with Intermediate Goods

I. The resource allocation problem, 341. — II. Commodity flow equilibrium, 344. — III. Transportation sector and land constraints, 345. — IV. The dual problem and producer and consumer equilibrium, 346. — V. A numerical example, 347. — VI. Concluding remarks, 350. — Appendix, 351.

Set-up costs and theory of exhaustible resources

This paper discusses the traditional specification problem from a geometric viewpoint. While the traditional emphasis is on the properties of estimators, the geometric approach also allows an easy development of corresponding results for inference. Errors arising from artificial inclusion or exclusion of variables are considered in terms of augmentations or restrictions on a given maintained hypothesis, and this allows a corresponding interpretation of tests based upon the Wald and Lagrange Multiplier Principles. It is demonstrated that biases arising from incorrect exclusion of variables do not invalidate the traditional F-test.

Deforestation and national accounting

We construct a first best growing economy in which land is being switched continuously from use in forestry to an alternative use. We find that implicitly for such activity to take place there must be no net loss to land owners. This implies no deduction in the national accounts for deforestation. With soil erosion on deforested land, Pigovian taxes must be levied to sustain a first best. We also observe an optimal tax on households for their implicit use of forests as oxygenation sinks.

Degradation of environmental capital and national accounting procedures

Abstract The capital theoretic approach to the environment as a wastable stock, a stock with a flow of abatement services, is explored in a simple Ricardo-like model involving wheat production and pollution production as an essential by-product. We then turn to how the national accounts are implicit in growth or capital theory models and how formulae emerge for accounting for the wasting of environmental capital (airsheds and watersheds) from ‘excessive’ use.

Constant Consumption and the Economic Depreciation of Natural Capital: The Nonautonomous Case

We investigate economic depreciation of natural capital for cases of non-stationary output prices, technology, and interest rates. For the former two cases (exogenous movements in prices and technology), constant consumption emerges under a strategy of investing to cover off economic depreciation. The interest rate case requires a modified sinking fund strategy.

Notes on Economic Depreciation of Natural Resource Stocks and National Accounting

In Hartwick [1990] I presented a methodology and formulas for incorporating changes in values of natural resource stocks in an economy’s national accounts. The aim was to account for the depletion of stocks from extraction (e.g., oil), from “overuse” (e.g., fishing) and from degradation (e.g., pollution). Essential to the analysis was the assumption that (a) prices reflected true scarcity (perfect competition or optimal planning) (b) property rights were well defined and universal (this is related to (a) via the notion of market failure or departures from perfect competition) and (c) technological progress was, in possibly a statistical sense of averaging, correctly anticipated.

Endogenous growth with public education

Abstract We investigate balanced aggregate growth in a model in which new knowledge is produced as an intermediate input and becomes embodied in all workers. Knowledge is a public input in the public goods sense. We examine the institutional arrangement of taxing all labor income to pay for new knowledge production. An optimal tax rate is characterized.