RDP 2013-14: Reserves of Natural Resources in a Small Open Economy Appendix B: Discussion of the Firms' Resource Problem

One important distinction between the dynamic program we describe in Section 3 and the approach described in Bohn and Deacon (2000) is the absence of a finite upper bound on the cumulative level of resources that can be discovered. This abstraction is important for our analysis since it implies that the policy functions that solve our problem are time invariant and admit a stationary (detrended) non-stochastic steady state. Intuitively, our approach implies that firm decisions concerning investment, exploration and production are not substantively affected by the existence of a known finite level of reserves yet to be discovered. This appears to be a reasonable assumption, at least in the Australian context. It is a different problem, however, from that in which a natural resource firm simply chooses its allocations of labour, capital and production to optimally extract from a pre-defined resource stock over time (whether exploration is required or not).

Although we abstract from a known finite bound on the remaining stock of undiscovered reserves, we do not entirely abstract from the concept of resource scarcity. As an alternative, we assume that the costs associated with exploration activity are increasing in the quantity of previously accumulated aggregate reserves. Specifically, we assume that the cost function is increasing in both exploration and aggregate reserves, ; that the derivative of the marginal cost of exploration is increasing in the level of exploration, ; and that this same derivative is sufficiently large that it outweighs any reduction in the marginal costs of exploration that could be associated with greater existing reserves . Finally, we assume that exploration costs tend to infinity as the stock of accumulated reserves becomes large, .

Together, these assumptions are consistent with many of the approaches adopted in the natural resource literature including Pindyck (1978), Reiss (1990), Heal (1993) and Sweeney (1993). Although this literature covers a wider range of cases, and the quantitative implications may well be different depending on the precise structure used, our own view is that the above assumptions capture the essence of a resource firms' problem. An appealing feature of our approach, and indeed our main motivation, is that it can be directly integrated into a SOE DSGE model. This is important as it allows us to study how endogenous reserves affect the propagation of resource price shocks in general equilibrium.