World Oil: The Growing Case for International Policy

NEHA KHANNA [*] Can the economic theory of depletion be reconciled with low petroleum prices? This article uses a revision of the theory, which reflects demand functions that rise in response to increasing world population and income. The magnitude of producers' and consumers' surplus is estimated under both competitive and monopolistic assumptions; the result indicates a present value comparable to or in excess of today's gross world economic product. Game theory suggests a framework that explains the interaction between oil pricing and military policy, and the economic incentives that result in a general pattern of recent market equilibrium crude oil prices often fluctuating within a $15-20 per barrel range. The analysis concludes that the economic incentives for political instability in the Persian Gulf will increase, and more formal methods of setting the international framework for Persian Gulf oil may be expected. (JEL C61, Q32, Q41, Q43, Q48) 1. ECONOMIC THEORY AND DEPLETION The theory of depletion is generally excluded from applied analyses of petroleum geopolitics. Generally, the theory is perceived as being counterfactual in several important ways. As usually discussed, the theory assumes constant price or constant demand functions, and projects monotonically declining output and rising prices. These predictions for price and quantity arise from both monopolistic and competitive versions of the theory. However, the theory can be extended to reflect upwardly shifting demand functions rising in response to growing income and population, and constant, increasing, or declining extraction cost. With these two extensions, depletion theory projects market equilibria where output rises, peaks, and then declines. The price trajectory may decline, stay constant, or rise with the latter part of the path always increasing. With these modifications, the theory can be used to calculate the magnitudes of producer and consumer surplus that may arise from future use of world oil resources. Equation (1) separates the competitive equilibrium trajectory for production and use into two components: (1) QE(t) = QC(t) - [e.sup.rt] *SF, where t is the time subscript, QE is the market equilibrium quantity of production and consumption, QC is the quantity that would have been demanded in a competitive market without resource limitations, r is the real discount rate, and SF is a scarcity factor reflecting the amount by which unconstrained production exceeds remaining stock (see Appendix for details). The associated price path is (2) P(t) = MC(t) + [e.sup.rt] *SF*B1, where MC is marginal cost, P is price, SF is the scarcity factor again, and B1 is a coefficient. Equations (1) and (2) simplify the results of an optimal control solution to the problem of finding maximum producer and consumer surplus in competitive and monopolistic markets where demand curves shift upward as population and incomes rise, and remaining petroleum stock is finite. In addition, the marginal extraction cost may change over time in response to technological or environmental conditions, but remains unaffected by the declining stock of remaining resources. The full problem and solution are summarized in the Appendix, [1] showing the basis for these equations. Note that in Equation (1) the equilibrium quantity QE would equal the market solution QC if there were no resource limitation, making the scarcity factor SF equal zero. Similarly, in Equation (2), price equals marginal cost if there is no scarcity. Furthermore, if in the presence of scarcity the marginal cost of extraction were declining over time, the optimal price trajectory may initially decline before ultimately rising. Figures 1 and 2 show stages of the solution. Figure 1 represents market equilibria with shifting demand and supply functions, and no resource limitation. This trajectory is also shown in Figure 2, as the sequence of triangles. …