"Contemplation of the world's disappearing supplies of minerals, forests, and other exhaustible assets has led to demands for regulation of their exploitation. The feeling that these products are now too cheap for the good of future generations, that they are being selfishly exploited at too rapid a rate, and that in consequence of their excessive cheapness they are being produced and consumed wastefully has given rise to the conservation movement" (Hotelling 1931, 139).
Already in 1931 Hotelling described aptly the problem concerning sustainable management of resources in order to ensure intergenerational equity. More than 80 years later the problem still has not been solved but a lot of work has been done in order to
nd a remedy. One major contributor is John Hartwick with his rule concerning how to keep consumption constant if the economy runs partially on exhaustible resources. This paper starts with a short introduction to three different concepts of sustainability. It continues to give an overview of relevant research prior to Hartwick. The main part consists of the original Hartwick rule which is discussed in some depth. In the following priority is given to adaptations to the rule done by Hartwick himself over those by other economists. Obviously, it is not possible to cover every work in this regard. Rather, the work chosen tackles those aspects that are viewed most critically and were fairly close in time to release to the original Hartwick rule.
Table of Contents
1 Introduction
2 Sustainability
3 The Foundations of the Hartwick Rule
4 The Hartwick Rule
4.1 The basic Model
4.2 Extensions to the basic Model by Hartwick
4.3 Extensions to the basic Model by other Economists
5 Conclusion
6 References
Objectives and Research Focus
The main objective of this seminar paper is to examine the Hartwick Rule within the context of sustainability and intergenerational equity. The research questions center on how constant consumption can be maintained in an economy that relies on exhaustible resources, how the original model has been adapted over time, and whether the underlying neoclassical assumptions remain valid under different economic conditions.
- Theoretical exploration of sustainability concepts (weak, strong, and environmental).
- Foundational analysis of resource economics models by Hotelling, Solow, Stiglitz, and Dasgupta & Heal.
- Detailed examination of the original Hartwick Rule and its mathematical derivation.
- Review of subsequent extensions to the Hartwick model, including multiple capital stocks and population growth.
- Critical reflection on the limitations of the Hartwick Rule regarding neoclassical assumptions.
Excerpt from the Book
4.1 The basic Model
In the discourse of intergenerational equity and exhaustible resources Hartwick looked at the following problem: ”if society invests all rents from exhaustible resources in reproducible capital goods, and invests only this amount, i.e., consumes the remainder of the product given population constant, will output rise, remain constant, or fall over time?” (Hartwick 1977, 972). Under the assumption of a one-commodity economy he employed a Cobb-Douglas production function for the reason that each input is essential. The production function depends on the reproducible capital k(t), the flow from the exhaustible resource y(t) and labour. Since he assumed constant population labour is set to one. Consumption c(t) and output x(t), just like k(t) and y(t), are per capita terms. Further, constant returns to scale and thus homogeneity of degree one, is assumed for f (k(t), y(t),1). (4.1.1)
Further he assumed marginal productivities ∂ f/∂ k (=ˆ fk) and ∂ f/∂ y (=ˆ fy) to be positive and ∂2 f/∂ k2 (=ˆ fkk) as well as ∂2 f/∂ y2 (=ˆ fyy) to be negative. The output depends to every point in time on x(t) = c(t) + ˙k +ay(t) (4.1.2) with ˙k being the time derivative of k, a the costs of extracting one unit of the exhaustible resource and thus ay(t) describing the extraction costs. From this, the savings-/investment function ˙k = (fy −a)y(t) (4.1.3) is gained. Applying the Hotelling Rule, the efficient extraction of the exhaustible resource is fk = d log dt (fy −a). (4.1.4)
Note that the dynamic of the economy can be described with the savings rule (4.1.3) and the efficient extraction path (4.1.4) (Hartwick 1977, 972 & 973).
Chapter Summaries
1 Introduction: This chapter introduces the problem of intergenerational equity in the context of exhaustible resources and provides an overview of the scope of the paper.
2 Sustainability: This section defines the core concepts of weak, strong, and environmental sustainability, establishing the discourse for the subsequent economic analysis.
3 The Foundations of the Hartwick Rule: This chapter reviews seminal work by Hotelling, Solow, Stiglitz, and Dasgupta & Heal, which provides the necessary neoclassical background for the Hartwick Rule.
4 The Hartwick Rule: This main section details the derivation of the Hartwick Rule, discusses its mathematical components, and examines extensions concerning multiple resources, capital depreciation, and population growth.
5 Conclusion: This chapter synthesizes the findings, reiterating the importance of the Hartwick Rule while acknowledging the need for more complex models to reach environmental sustainability.
6 References: This section lists all academic sources and literature cited throughout the paper.
Keywords
Hartwick Rule, Sustainability, Intergenerational Equity, Exhaustible Resources, Resource Economics, Cobb-Douglas Function, Capital Accumulation, Technical Progress, Weak Sustainability, Neoclassical Economics, Net Investment, Economic Depreciation, CES Production Function, Consumption, Natural Capital
Frequently Asked Questions
What is the core subject of this paper?
The paper fundamentally investigates the "Hartwick Rule" and its implications for sustainable development, specifically how an economy can maintain constant consumption while utilizing finite exhaustible resources.
What are the central themes discussed?
The central themes include intergenerational equity, the substitutability between natural and man-made capital, the role of technical progress, and the mathematical modeling of resource extraction.
What is the primary research goal?
The primary goal is to analyze the original Hartwick Rule and track its evolution through various extensions, evaluating whether these models effectively address the challenge of infinite growth with finite resources.
Which scientific methodology is applied?
The paper employs a literature-based analysis of neoclassical growth models, focusing on mathematical production functions like Cobb-Douglas and general CES functions to derive economic paths.
What is covered in the main part of the document?
The main part provides the mathematical foundations of the Hartwick Rule, followed by adaptations by Hartwick himself and other economists to account for real-world factors like extraction costs, depreciation, and population growth.
How would you characterize this work with keywords?
Key terms defining the work are Hartwick Rule, Weak Sustainability, Intergenerational Equity, Exhaustible Resources, and Capital Accumulation.
How does the author define the difference between weak and strong sustainability?
The author distinguishes them based on the elasticity of substitution between natural and physical capital: weak sustainability allows for full substitution, while strong sustainability views natural capital as critical and limited in substitutability.
Why are the models of Dixit et al. and Okuguchi important?
They are important because they relax highly implausible assumptions from earlier models, such as constant population and a one-commodity economy, thereby creating more realistic frameworks for sustainability.
What is the significance of the Hotelling Rule in this context?
The Hotelling Rule is the foundation for the Hartwick Rule, as it defines the efficient extraction path for exhaustible resources by linking the growth rate of resource prices to the interest rate.
- Citar trabajo
- B.A., B.Sc. Esther Schuch (Autor), 2014, The Hartwick Rule and Sustainability. An Ongoing Development, Múnich, GRIN Verlag, https://www.grin.com/document/273700
