ENVIRONMENTAL MODELLING

Environmental Modelling



Abstract

This paper systematizes main results on economic models concerning renewable and nonrenewable capital goods where the criterion is to sustain the utility on some minimal level over whole time horizon. Using the framework of the multidimensional Dasgupta- Heal-Solow model, it sheds light on the relation of two different approaches: the discounted utility approach with sustainability constraint, which is historically older and the maximin approach which has been introduced only recently. In both approaches, we deal especially with the Hartwick's rule and formulate assumptions when this rule (or its generalized version) constitutes either necessary or sufficient condition for constant utility.

Environmental Modelling

Introduction

Solow (1974) was the first to discover the maximin benchmark inside the context of a neoclassical development form with an “exhaustible” or nonrenewable resource. Solow's form was a continuous-time form and examined the intergenerational share of utilisation, capital, and asset extraction over an infinite horizon. Early forms often characterised the utility of the lifetime living at instant t as a function of per capita consumption; in order that U(t) = U(C(t) L(t)) = U(c(t)) , where C(t) is the grade of utilisation at instant t , L(t) is the dimensions of the community at instant t , c(t) = C(t) L(t) is utilisation per capita, and U(•) is a firmly concave utility function. The centered inquiry was if a nonrenewable asset, absolutely crucial for affirmative output, would permit for sustainable utility over an infinite horizon.

 

 

In Solow's form, yield was very resolute by a output function with capital, work, and the rate of extraction from a nonrenewable asset as inputs. A piece of that yield would be identically spent by the community while the residual piece would be utilised to boost the supply of capital. Solow examined versions of the form with a unchanging or increasing community and with none or affirmative technological progress. Adopting the maximin benchmark may lead to unchanging utilisation per capita in each lifetime, and therefore to unchanging utility. This could be accomplished supplied the elasticity of substitution between extractive flows from the nonrenewable asset and a sub-function of capital and work in the output of the constructed good, was not less than one. The Solow output function can be in writing as Y(t) = F(K(t),L(t))q(t)h , where Y(t) is aggregate yield made at instant t , and F(K(t),L(t)) is the sub-function that aggregates capital, K(t) , and work, L(t) , and it is presumed to be homogeneous of stage (1! h) , where 1 > h > 0 .

The general function F(K(t),L(t))q(t)h is a Cobb-Douglas pattern with unitary elasticity of substitution, between q(t) and the sub-function F(•) . Over time, the capital-labor aggregate has to alternate for extraction from the nonrenewable asset to depart utilisation per capita and utility unchanging over time. The primary supplies of capital and the nonrenewable asset are significant in working out the greatest utilisation per capita and utility that could be maintained indefinitely. Solow considers the maximin benchmark as a sensible benchmark for intertemporal designing “except for ...