Hartwick's Rule Research Articles

Sustainable development with stock pollution

ABSTRACTOptimal pollution control is an important challenge for sustainable development with three distinct cases. First, the situation where nature's assimilative capacity is completely destroyed involves normative problems that require further research. Second, environmental restoration with initial pollution above the steady-state stock requires an economy to initially allocate a relatively high share of its resources to cleaning-up activities. In return, this generally results in an intertemporally efficient development path that is both environmentally and economically sustainable. Third, optimal trajectories in situations with initial stocks of pollution below the long-term optimum generally imply an increase in pollution and a decline of optimal consumption. In this case, the investment of the environmental rents accruing from nature's assimilative capacity into man-made capital is required in analogy to the famous Hartwick rule to maintain a constant flow of instantaneous welfare. This would facilitate growth in consumption sufficient to compensate for the rising disutility of pollution.

Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value

Taux d’escompte nul et sentiers optimaux d’extractiond’une ressource épuisable ayant une valeur d’aménité Nous étudions les sentiers optimaux du modèle canonique de Dasgupta-Heal-Solow,dans le cas où le taux d’escompte est nul et où le niveau du stock de capital naturelintervient dans la fonction d’utilité. Nous utilisons une règle de Keynes-Ramsey quipermet de généraliser la règle de Hartwick : si la société a un taux d’escompte nul maisaccepte une substitution intertemporelle entre niveaux d’utilité, l’investissement net nedoit plus être zéro, comme dans le cas maximin, mais doit être positif et être fixé à unniveau qui dépend de la distance entre le niveau d’utilité de court terme et le niveau defélicité atteint à long terme. Nous caractérisons les solutions optimales dans le cas oùl’utilité et la production sont Cobb-Douglas et nous analysons l’influence de l’élasticitéintertemporelle de substitution sur le profil temporel du sentier optimal. Nous montrons aussi que, dans ce cas Cobb-Douglas, la valeur relative des stocks de ressource etde capital reste constante sur le sentier optimal, à un niveau qui ne dépend pas desconditions initiales.

Hartwick's rule and maximin paths when the exhaustible resource has an amenity value

This paper studies the maximin paths of the canonical Dasgupta–Heal–Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. Hartwick's rule then appears as an efficient tool to characterize solutions in a variety of settings. We start with the case without technical progress. We obtain an explicit solution of the maximin problem in the case where production and utility are Cobb–Douglas. When the utility function is CES with a low elasticity of substitution between consumption and natural capital, we show that it is optimal to preserve forever a critical level of natural capital, determined endogeneously. We then study how technical progress affects the optimal maximin paths, in the Cobb–Douglas utility case. On the long run path of the economy capital, production and consumption grow at a common constant rate, while the resource stock decreases at a constant rate and is therefore completely depleted in the very long run. A higher amenity value of the resource stock leads to faster economic growth, but to a lower long run rate of depletion. We then develop a complete analysis of the dynamics of the maximin problem when the sole source of well-being is consumption, and provide a numerical resolution of the model with resource amenity. The economy consumes, produces and invests less in the short run if the resource has an amenity value than if it does not, whereas it is the contrary in the medium and long runs. However, and without surprise, the resource stock remains for ever higher with resource amenity than without.

On competitive equitable paths under exhaustible resource constraints: The case of a growing population

The paper examines the nature of competitive paths in an exhaustible resource model, which allows for a growing population. For competitive paths that are equitable in the sense that the per capita consumption level is constant over time, the implicit investment rule is derived. This is seen to be a generalization of Hartwick's rule, obtained in the case of a stationary population. It is also shown that the existence of a competitive equitable path implies that a population can experience at most quasi‐arithmetic growth.

A step beside the maximin path: Can we sustain the economy by following Hartwick's investment rule?

If sustainability is interpreted as the requirement to sustain consumption or utility at an optimal level, a maximin objective appears to be relevant. The sustained economy is characterized by an optimal investment following Hartwick's investment rule. This paper examines how the sustainability of a production–consumption economy with a non-renewable resource is modified in the neighborhood of the maximin path, i.e. when the consumption and the resource price are not optimal. A Sustainable Consumption Indicator is introduced in order to characterize the sustainability of constant consumption paths, defined as deviations from the maximin path. We describe how an over-consumption jeopardizes future sustainability.

Savings growth and the path of utility

Abstract. 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.

On accounting for sustainable development and accounting for the environment

Economic sustainability or intergenerational equity entails maintaining social well-being by decisions about investments in different types of assets. Under certain conditions, consumption can be sustained by depleting resources, or various kinds of natural capital, while building up other kinds of capital. Theoretically, the choices involve the use of a set of accounting prices. The question becomes one of finding and implementing accounting prices that express the roles of the various capital goods in achieving the objective of the economy. Hartwick's rule holds that an economy can be sustained if the value of the total, net investment in the economy, evaluated at those accounting prices, is zero. The rule applies to a special, abstract economic model which expresses a social objective different from the discounted-utilitarian objective on which national accounting is based. Different objectives give rise to different accounting prices. Because the prices may not be right, the zero net-investment rule using available national-accounting prices cannot generate a condition for sustaining an economy. Still, environmental accounting is a tool which, used prudently, can make an important contribution to social decision-making. This paper expands upon these ideas by discussing the incorporation of natural resource and intangible environmental costs and benefits into green accounting at the firm as well as the economy level. Common techniques of mine valuation and standard corporate accounting are the bases for this extension to the valuation of and accounting for decisions concerning the environment.

WEAK AND STRONG SUSTAINABILITY, ENVIRONMENTAL CONSERVATION AND ECONOMIC GROWTH

ABSTRACT. To investigate the role of explicit and implicit assumptions in different models of weak and strong sustain‐ability, the Solow/Hartwick model of intergenerational equity with nonrenewable resources is gradually extended to include renewable resources, endogenous technical progress, and stock pollution. This reveals the fundamental role of endogenous technical progress for sustainable development, the inconsistency of implicit sustainability assumptions in various models, as well as the existence of a Hartwick rule for Daly's steady‐state economy. Moreover, it shows that the concepts of Solow sustainability and strong sustainability coincide as a special case of weak sustainability. The latter integrates economic and environmental concerns and aims at maintaining the welfare potential of an economy over time. It does not rule out economic growth by assumption. Rather, the analysis shows that environmental conservation and economic growth can be compatible with each other, without jeopardizing social welfare. Finally, the analysis shows that the discussion of sustain‐ability models cannot be restricted to the explicit differences that are usually pointed out by their authors and commentators. Rather, implicit assumptions must be made explicit.

Capital Accumulation and Resource Depletion: A Hartwick Rule Counterfactual

How rich would resource-abundant countries be if they had actually followed the Hartwick Rule (invest resource rents in other assets) over the past 30 years? The authors use time series data on investments and rents on exhaustible resource extraction for 70 countries to answer this question. The results are striking: Gabon, Trinidad and Tobago, and Venezuela would all be as wealthy as the Republic of Korea, while Nigeria would be five times as well off as it is currently. The authors also derive a more general rule for sustainability-maintain positive constant genuine investment-and use this to draw further empirical results.

Maximin: a direct approach to sustainability

We solve directly a general maximin (sustainment, intergenerational-equity) problem. Because the shadow values of a maximin problem do not correspond to the shadow values from a general discounted-utility solution, they correspond to the prices of only a very special competitive economy. Virtual discount factors for the economy arise. They do not correspond to hyperbolic discount factors. Hartwick's rule is derived and generalized naturally to take into account non-autonomous and non-deterministic features of the economy. Under uncertainty, Hartwick's rule is the analytic expression of a form of precautionary principle. Hotelling's rule is a necessary condition, but may be more complex than has been appreciated in simple models. Some interpretations of strong sustainment are special cases of weak sustainment but, paradoxically, may be more difficult to solve.

Intertemporal Equity and Hartwick's Rule in an Exhaustible Resource Model*

AbstractIn a standard exhaustible resource model, it is known that if, along a competitive path, investment in the augmentable capital good equals the rents on the exhaustible resource (known as Hartwick's rule), then the path is equitable in the sense that the consumption level is constant over time. In this paper, we show the converse of this result: if a competitive path is equitable, then it must satisfy Hartwick's rule.

RENEWABLE NATURAL RESOURCES AND ENDOGENOUS GROWTH

We study the sustainability of long-run growth in a two-sector economy where a renewable natural resource is exploited under private property rights. We obtain short- and long-run growth trajectories in closed form, examine transitional dynamics, and characterize convergence properties. We find conditions for sustainable long-run growth, which depend on the harvesting rate, and show that the speed of convergence decreases during transition. We identify a stronger version of Hartwick's rule and analyze parameter dependences for endogenous variables. Economic growth relies less on abundance or scarcity of natural resources than on the way they are managed.

ON THE SUSTAINABLE PROGRAM IN SOLOW'S MODEL

ABSTRACT. We show that our general result (Withagen and Asheim [1998]) on the converse of Hartwick's rule also applies for the special case of Solow's model with one capital good and one exhaustible resource. Hence, the criticism by Cairns and Yang [2000] of our paper is unfounded.

Sustainable farm income in the presence of soil erosion: an agricultural Hartwick rule

Soil erosion is a physical and economic problem of natural capital degradation. Even along an intertemporally efficient trajectory, one can have in a loss of soil fertility and a continuous decline of agricultural net revenue. Moreover, soil erosion is a major source of surface water pollution in rural areas. Erosion control is thus a challenge for sustainable resource management and internalizing external effects. To sustain the level of farm income, an ‘agricultural Hartwick rule’ is proposed which addresses both on-farm and off-farm effects of soil erosion. First, it requires the investment of the soil rents into alternative capital. Second, additional measures are required to comply with an ambient quality target. A charge-subsidy scheme proves the most adequate from a perspective of cost-effectiveness and sustainability, if effluent charge revenues are earmarked to subsidize cropland retirement at the watershed scale. In combination with the investment of soil rents this enables to maintain the level of farm income constant over time while respecting the ambient quality target. Altogether, this fulfills the requirements of efficiency and sustainability.

The Hartwick Rule: Myths and Facts

We shed light on the Hartwick rule for capital accumulation and resource depletion by providing semantic clarifications and investigating the implications and relevance of this rule. We extend earlier results by establishing that the Hartwick rule does not indicate sustainability and does not require substitutability between man-made and naturalcapital. We use a new class of simple counterexamples (i) to obtain the novel finding that a negative value of net investments need not entail that utility is unsustainable, and (ii) to point out deficiencies in the literature.

Intertemporal Equity and Efficient Allocation of Resources

Competitive paths which are efficient are shown to satisfy a terminal cost minimization condition, thereby providing a continuous-time counterpart to the discrete-time result due to Malinvaud. Using this result, competitive paths which are equitable and efficient are shown to satisfy Hartwick's investment rule, which states that the value of net investment is zero at each date. Our result indicates that Hartwick's rule can help to signal inefficiency of competitive equitable paths. Journal of Economic Literature Classification Numbers: C61, D90, O41.

Hartwick's rule and economic conservation laws

This paper examines two policy rules for intergenerational equity in a model of optimal capital accumulation and resource extraction. First, we introduce Hartwick's rule (1977. American Economic Review 66, 972–974) for a constant consumption path and also consider relationships between Hartwick's rule and conservation laws. Second, by using conservation laws, we investigate another rule for a constant utility. This paper also attempts to derive the investment rule for Benthamite utility maximization.

THE CONVERSE OF HARTWICK'S RULE AND UNIQUENESS OF THE SUSTAINABLE PATH

ABSTRACT. We provide a constructive proof of the converse of Hartwick's rule for a generalization of Solow's model with one capital good and one exhaustible resource. We also show that the sustainable path is unique.

Sustainability accounting and green accounting

Theoretical issues arising in maximin and utilitarian programs are considered in order to shed light on the merits of various concepts of income and types of environmental accounting as guides for environmental policy. The accounting prices for sustaining an economy obey Hartwick's rule but are inconsistent with the principles of national accounting. Moreover, they would be formidably difficult to calculate. Green net national product is an approximate index of welfare in a utilitarian economy which maximises future discounted utility flows. These conclusions hold even if underlying conditions are non-autonomous.JEL Codes: Q3, E2

The Hartwick Rule: Myths and Facts

We consider the Hartwick rule for capital accumulation and resource depletion, provide semantic clarifications and investigate whether this rule indicates sustainability and requires substitutability between manmade and natural capital. In addition to shedding light on the meaning of the Hartwick rule by reviewing established results, we establish the following novel finding: The value of net investments being negative does not imply that utility is unsustainable. Throughout we make the assumption of a constant technology, without which the Hartwick rule does not apply.