## Resources for the Future

Krautkraemer and Toman

Empirically, since the resource price should reflect both the marginal extraction cost and the scarcity rent, one generally would expect from (3) that the price of a nonrenewable resource would be increasing over time. However, there has not been a persistent increase in prices of fossil fuels (or other nonrenewable resources), but rather fluctuations over various time periods. Fossil fuel prices fell over much of the twentieth century, peaked dramatically in the 1970s and early 1980s, and have generally fallen since then—see Figures 1–3. This further illustrates the need for a richer theory to capture observed behavior.

# 3. A More General Theory of Economically Efficient Depletable Resource Supply

A more useful general theory must take into account the stylized facts noted above—that resources are heterogeneous, with extraction costs that vary systematically over time with depletion of resource deposits; and that resources can be augmented through exploration and development. Moreover, a complete theory must account for the high degree of capital intensity of the extractive sector and the implications of this in terms of potential constraints on productive capacity.

# 3.1 Resource Extraction

Let us first address generalization of the Hotelling extraction model to deal with resource heterogeneity. Among the many good papers to deal with this case, Pindyck (1978) and Heal (1976) are particularly noteworthy. To examine this part of the problem, we continue to treat reserves as fixed for the moment, and we ignore capacity constraints.

# The cost of extraction is assumed to be given by some function, C(q_{t }, R_{t }) , where R_{t }is the

stock of resource that has not yet been depleted. Incorporating this “stock effect” into extraction cost is a simple if somewhat imprecise way to introduce resource heterogeneity into the extraction cost relationship. The relationship is relatively straightforward if we focus on a single energy resource development: as the resource in this development declines, cost is assumed to rise (deeper pits to be dug, more waste material to be removed, weaker reservoir pressure). It is less straightforward if we are attempting to describe heterogeneity among resource deposits, as discussed below.

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