Exploration of non renewable resources a dynamic approach

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Exploration of non renewable resources a dynamic approach

Fuks, Saul

Abstract Arrow studies a model of exploration of non renewable natural resources, in continuous time (see |4|), where, the quantity of resources, to be found is a random variable. In our model there is a T planning period to go. If society consumes, in oen period, an amount c of non renewable resource, it receives a utility u(c). New resources can be found through exploration, α reflecting the effort applied to get them, spending p per unit of effort. The number of units found when effort α is employed is given by a random variable wα, having a Poisson distribution with parameter λα. Society is then faced with the problem of maximizing the descounted total utility: $$V^T \left( y \right) = Max\left[ {u\left( \alpha \right) - p\alpha + \delta {\rm E}V^{T - 1} \left( {y - 1c + W_\alpha } \right)} \right]$$ Subject to: 0≤c≤y, α≥0 where y is the stock of resources available at the begining of the initial period and δ is the discount factor. The new fact in the above problem, in relation with similar ones in literature, is that the probability distribution is defined by choice variable. Concavity plays a major role in thes kind of model, it can be proved that, under some conditions [related to decreasing risk aversion for u′(c) and u″(c)], V(y) is a concave function. The main result is that there exists y such that for y>y, α=0 (there is no exploration).