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Social optimality with resource depletion: an investment project valuation model.

JEL D61 . Q51 . D21

The core objective of this research is to arrive at the optimal social extraction path on an investment project level reaching dynamic social optimality with resource depletion, in contrast to the traditional benefit-cost criterion of project feasibility. The focal argument is that marginal social benefits, at equilibrium, must strictly exceed marginal social cost, at equilibrium, in order to correct for historical failures and expected cumulative environmental disturbances away from the optimum social extraction path.

A dynamic optimization model is proposed based on maximizing the generation of social capital for a given transversal-free project cycle whereby social surplus includes environmental factors related to resource depletion and environmental sustainability. This is based on upper-bound and lower-bound system failure of environmental sustainability constraints, in addition to private financial payoffs from a given supply of capital.

The main assumption is that social surplus can be formulated as an aggregate likelihood function for private financial returns augmented to produce additively-separable social utility levels pertaining to the micro-sustainability of physical capital resources at an investment project level. An upper sustainability constraint on resource depletion ensures lack of resource over-depletion beyond the socially efficient rate, and a lower sustainability constraint ensures availability of critically needed input resources for an efficient production level. Both constraints are treated in dynamic optimality with the objective of maximizing the social surplus from an investment project.

Based on the value-added social welfare optimization problem proposed, the dynamic conditions for social optimality conclude the following major propositions:

Proposition I: Society's production capacity for maximum social welfare can only be attained if both static and dynamic resource depletion arguments are sustainable.

Proposition II: Social re-investments, as a shadow price for resource depletion, are dependent on society's current efforts for value-added output in addition to society's historical system failures deviating from an optimal resource depletion path.

Proposition III: Systematic expected short-run system failures within a social cycle may reveal actual environmental instability in the long run.

Proposition IV: The rate of social re-investments dictate to society an optimal rate of consumption of social capital which basically follows the slack value of the resource depletion constraint.

Proposition V: Most importantly, and contrary to the classical theory of environmental economics, dynamic optimality requires social reinvestments to generate marginal social benefits, at equilibrium, strictly exceeding marginal social cost to society due to resource extraction, in order to arrive at an efficient allocation of resources.

In retrospect, environmental sustainability could be viewed as cumulative disturbances of non-optimal deviations from a long-run social extraction path corrected by social re-investments that carry social capital returns exceeding marginal social cost.

Formally, Proposition V can be summarized based on the following:


The left hand side denotes the dynamic rate of the shadow price of long run sustainability of the value of an investment project based on social optimality, whereas the first term on the right hand side denotes the dynamic rate of the shadow price of short-run private rents from resource depletion. The second term on the right hand side is an inverse function of the cumulative effects of changes in efficient investment valuation based on social optimality relative to changes in actual production levels, given a timeline horizon of an investment project for N years.

At equilibrium, using dynamic optimization, it is derived from the above condition for social optimality to occur with resource depletion that the marginal social benefits of an investment project has to strictly exceed marginal social costs, the latter including private marginal cost of production and marginal external costs to society. This MSB> MSC condition is a pivotal finding in the research, binding along the optimal social extraction path for an investment project, with a relational determination given by:


It should be noted from the above that the traditional MSB=MSC condition is still valid as a special case of the model, in the event that the production output of an investment project, [Q.sup.t], converge towards the efficient production level from resource depletion at social optimality, [Q.sup.E]. Additionally, the above relation is not in absolute value, hence giving rise to: (1)MSB>MSC for over-utilization of resources, and (2) MSB< MSC for under-utilization of resources, with both of these conditions yielding social optimality.

DOI 10.1007/s11293-010-9227-1

Published online: 16 May 2010

T. H. Selim ([mail])

The American University in Cairo, New Cairo, Egypt

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Title Annotation:ANTHOLOGY
Author:Selim, Tarek H.
Publication:Atlantic Economic Journal
Geographic Code:1USA
Date:Sep 1, 2010
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