A closed form solution to Stollery's global warming problem with temperature in utility

Stollery (1998) studied a polluting oil extracting economy governed by the constant utility criterion. The pollution caused the growth of temperature, negatively affecting production and utility. Stollery provided a closed form solution for the case with the Cobb-Douglas production function and temperature affecting only production. This paper offers a closed form solution to a non-trivial example of this economy with utility affected by temperature.essential nonrenewable resource; polluting economy; sustainable development; special function representation

The dependence of the potential sustainability of a resource economy on the initial state: a comparison of models using the example of Russian oil extraction

The studies of the International Monetary Fund offer a model for recommending sustainable budget policy to oil-exporting countries including Russia. The model does not contain any resource as a factor of production and assumes that Russian oil reserves will be exhausted by the middle of the 21st century. The current paper examines the sustainability of open and closed models, which are calibrated on Russia's data and include a resource as a factor of production. The open-model case shows that monotonic economic growth is impossible given the current state of the Russian economy. This paper offers an approach for estimating changes that improve long-term sustainability.nonrenewable resource; weak sustainability; open imperfect economy; Russian oil extraction

Investment and current utility change in dynamically inefficient economies

An extensive literature shows the importance of investment policy for sustainability of resource-based economies by examining the role of investment in current utility change (CUC) for a competitive optimizing economy. This paper extends some of these results by analysing the dependence of CUC on genuine investment (GI), expressed in marginal resource productivity, under dynamic inefficiency. The inefficiency arises when a social planner, due to imperfection in knowledge or in institutions, does not take into account deviations of real economy from a theoretical model. These deviations or distortions, connected with the resource extraction, can influence utility, production, the balance equation, and the dynamics of the reserve. The analysis of this natural discrepancy between theory and real life implies that: first, institutional and resource policies in inefficient economies may be more important for CUC than investment policy; and secondly, under uncertainties in production possibilities and in damages from economic activities, sustainability requires a more cautious resource policy than is advised by a theory. The paper also suggests that the indicators GI, expressed in accounting prices and in marginal resource productivity, can complement each other in sustainability evaluation.nonrenewable resource; dynamic inefficiency; genuine investment; resource policy; sustainable development

Sustainable growth: Compatibility between criterion and the initial state

There is a large body of research devoted to our understanding of sustainable growth in resource based economies. Some of this research is inapplicable to the real economy. This is a result of inconsistency between the commonly used criteria and the initial state of the real economy. The inconsistency can lead to either inferior, unsustainable, or nonexistent optimal paths of consumption per capita if the criterion is not linked to the initial state. We demonstrate this in a model of the Dasgupta-Heal-Solow-Stiglitz variety with the constant consumption per capita as a benchmark criterion. Our results show that the inconsistency in this case can imply Pareto inferior paths of consumption per capita.essential nonrenewable resource; sustainable extraction; criterion inconsistency; Hartwick Rule

Switching to a sustainable efficient extraction path

The economy depends on the essential nonrenewable resource and the path of extraction is nondecreasing and inefficient. At some point the government gradually switches to a sustainable (in sense of nondecreasing consumption over time) pattern of the resource use. Technical restrictions do not allow to switch to the efficient extraction instantly. Transition curves calibrated to the current pattern of world oil production are used as the extraction paths in the "intermediate" period. However, there is no solution in finite time for the "smooth" switching from the optimal "transition" to the optimal efficient path, constructed with respect to the same welfare criterion. We analyze numerically two approaches for the approximate solution: "epsilon-smooth" switching and "epsilon-optimal" transition curve with smooth switching. Both cases give the unexpected result: the consumption path along the "inefficient" transition curve is always superior to the constant which we obtain after switching to the "efficient" Hartwick's curve. The result implies that for the correct switching to the efficient curve in finite time the saving rule must be adjusted. We estimate the importance of following the efficient path by comparing the consumption along the plausible transition path and the efficient pattern of the resource use. For simplicity we use in our examples the constant per capita consumption as a welfare criterion and the Hartwick rule as the benchmark of investment rule.Essential nonrenewable resource; Sustainable extraction; Hartwick rule; Transition to efficient path

Maximin-optimal sustainable growth with nonrenewable resource and externalities

I offer an approach linking a welfare criterion to the "sustainable development potential" of the economy. This implies a dependence of a criterion on the information about the current state. I consider the problem for the Dasgupta-Heal-Solow-Stiglitz model with externalities. The economy-linked criterion is constructed on an example of the maximin principle applied to a hybrid level-growth measure. This measure includes as special cases the conventional measures of consumption level and percent change as a measure of growth. The hybrid measure or geometrically weighted percent can be used for measuring sustainable growth as an alternative to percent. The closed form solutions are obtained for the optimal paths including the paths, dynamically consistent with the information updates.essential nonrenewable resource, modified Hotelling Rule, economy-linked criterion; geometrically weighted percent; normative resource peak

Decreasing of Oil Extraction: Consumption behavior along transition paths

A normative analysis of the problem of optimal extraction of a non-renewable resource is considered. The economy depends on the essential non-renewable resource and the rate of the resource extraction increases over time. At some instant the government gradually switches to a sustainable (in sense of non-decreasing consumption over time) pattern of the resource extraction. Different approaches are offered for the construction some curves of switching to decreasing paths of the resource depletion. Consumption paths have diverse behavior patterns along these curves, including a path of unlimited growth. A new approach to the Rawlsian maximin criterion which allows for growth of consumption is offered.Non-renewable resource; Intergenerational justice; Hartwick rule; Optimal path of extraction; Generalized Rawlsian criterion

Sustainable growth: The extraction-saving relationship

The paper presents two new results for the Dasgupta-Heal-Solow-Stiglitz model with an essential nonrenewable resource: (1) the pattern of resource extraction can be more important for sustainable growth than the pattern of saving when the Hotelling Rule modifier is not small enough; (2) the qualitative behavior of the long-run per capita consumption can be examined along any smooth enough path of extraction using the "sustainability functional" introduced in the paper.sustainable growth; modified Hotelling Rule; sustainability number; Hubbert curve consumption

Maximin-optimal sustainable growth with nonrenewable resource and externalities

I offer an approach linking a welfare criterion to the “sustainable development opportunities” of the economy. This implies a dependence of a criterion on the information about the current state. I consider the problem for the Dasgupta-Heal-Solow-Stiglitz model with externalities. The economy-linked criterion is constructed on an example of the maximin principle applied to a hybrid level-growth measure. This measure includes as special cases the conventional measures of consumption level and percent change as a measure of growth. The hybrid measure or geometrically weighted percent can be used for measuring sustainable growth as an alternative to percent. The closed form solutions are obtained for the optimal paths including the paths, dynamically consistent with the updates in reserve estimates.Essential nonrenewable resource, modified Hotelling Rule, economy-linked criterion, geometrically weighted percent, normative resource peak.

A constant-utility criterion linked to an imperfect economy affected by irreversible global warming

The question of formulation of a social planner criterion for an imperfect economy is examined using an example of a polluting economy negatively affected by growing temperature. Imperfection of the economy is expressed here in deviations from the optimal initial state. It is shown that a criterion not linked to a specific initial state almost always implies either unsustainable or inefficient paths in the economy. In this paper, I link the constant-utility criterion to the initial amount of the resource reserve. This criterion implies efficient resource use and the paths of utility asymptotically approaching some constants, which depend on the parameters of the temperature function. The criterion can be formulated for the cases when the reserve estimate changes over time and when the high level of temperature can cause extinction.Essential nonrenewable resource, imperfect polluting economy, economy-linked criterion, semisustainable development, semiefficient extraction.