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The purpose of this paper is to show that in a general equilibrium framework it is not always optimal to exploit resources in strict sequence, beginning with the lowest cost deposit, even if it is possible to accumulate productive capital. Indeed if there is an exogenous upper bound on the flow of the substitute, it is always optimal to consume it simultaneously with a lower cost stock. Moreover, it may be optimal to consume the high-cost substitute before using a lower cost resource.

Kemp and Long (1980) are the first to question the “folk theorem” that low-cost natural resource stocks should be exhausted before using a high-cost substitute,1 when agents discount the future. They show that in a general equilibrium framework if the marginal cost of extraction and of using the substitute are both constant then it may be optimal to use the high-cost substitute before exhausting a low-cost natural resource. Simultaneously extracting a resource and using a high-cost substitute smooths the utility path. More recently, Amigues et al. (1998) show that it may be optimal to exploit a high-cost substitute strictly before using a lower cost exhaustible resource, if the flow capacity of the high-cost substitute is limited. They suppose that the marginal utility of this limited substitute is strictly positive at the steady state, when the stocks have been exhausted. So the flow of the substitute is scarce and since this flow is unstorable, delaying the start of the exhaustible resource exploitation is a method of saving. Lewis (1982) modifies Kemp and Long's model by allowing the extracted resource and high-cost substitute to be costlessly converted into capital. He finds that a sufficient condition for restoring the folk theorem in this model is that capital has a positive rate of return. In his conclusion he conjectures that in a general equilibrium analysis, it is optimal to use the least cost energy sources first whenever the extracted resource can be converted into productive capital. If Lewis’ conjecture holds, then the inclusion of productive capital in the Amigues et al. model would restore the folk theorem. The latter paper claims that the inability to save implies the failure of the folk theorem. I will show below that Lewis’ conjecture does not hold when the flow of substitute is bounded and scarce in the sense described above. It is always optimal to consume simultaneously the high-cost substitute and one of the stocks. Moreover, it may be optimal to use the high-cost substitute before beginning to extract from a lower cost stock. Since the Amigues et al. result holds even if the economy can accumulate productive capital, their explanation for the result (based on the desire to save) is incomplete. In fact, extending their model by including the possibility of capital accumulation decreases but does not suppress the incentive to use the high-cost substitute before exhausting lower cost stocks. The critical assumption is that the substitute is scarce, i.e. at the steady state the capacity constraint on the flow of the substitute is binding. The shadow value of this constraint is thus positive. The decision maker reduces the cost of this constraint (i.e. chooses its optimal shadow value) by investing and does so by using the low-cost stock early in the program and delaying the date at which he uses the substitute. The ability to invest in productive capital provides an additional means of reducing the cost of the constraint. By extracting the low-cost stock, and investing some of the output, the decision maker increases future consumption possibilities: he reduces the shadow value of the constraint on the high-cost flow. Note that an upper bound on the flow of substitute need not be due to the labor scarcity at the steady state. In fact, an upper bound on this flow may coexist with a zero shadow price for labor. For example, energy produced by wind mills may be bounded above because of lack of sufficient wind, not because of lack of wind mills, or lack of labor. In this paper I assume that labor is abundant at the steady state. If too much resource is extracted, the time at which some labor will become redundant (due to upper bound on the substitute flow) will arrive too quickly. As the shadow value of labor at the steady state is equal to zero (abundance), the decision maker has an incentive to delay extraction on the low-cost stock in order to keep future opportunities to work. The best way to cope with both the substitute flow constraint and the labor constraint is to produce the substitute in the early stage, and save part of this output in the form of capital accumulation. Then, by using the high-cost substitute early in the program, the decision maker prolongs the phase in which labor is fully used and, at the same time, delays the date at which he must rely exclusively on the substitute. Contrary to both Lewis’ conjecture and to the explanation in Amigues et al., the folk theorem may fail even in a general equilibrium model with opportunities to invest in productive capital. The model I present does not explicitly include disutility of labor. Including individual valuation of leisure would not alter the results. In such a general model, the shadow value of the constraint on the high-cost flow would equal the difference between the marginal utility of consumption and of leisure. In the steady state the agent would like to transform leisure into consumption, but would be unable to do so because of the constraint on the flow of the substitute. The decision maker has to perform a similar trade-off in the model without disutility of labor. I present the model and the results in the next section. The last section gives the main conclusions.

When the high-cost substitute is scarce it is not always optimal to exhaust low-cost resource stocks before making use of the substitute, even if the population can accumulate productive capital. Accumulating capital increases the future availability of consumption. When the population accumulates capital simultaneously it ‘saves leisure’. There is a trade off between accumulating capital as quickly as possible by extracting only the least cost stock and working as much and as long as possible by exploiting the substitute. This trade off implies my results. In my model the value of leisure is zero when the population consumes only the substitute, but of course it is easy to generalize this feature by allowing an endogenous value of leisure.