METHODS AND THEORETICAL CONCEPTS

The economic literature suggests two main conceptual approaches to deal with the depletion of natural resources. Both aim at measuring the impacts of resource depletion on long run human welfare. The two approaches are conditions, which must be met if a country's population is to be as economically well off in the future as in the current period.

The first approach, often referred to as the depreciation approach, is to treat natural capital in the same way as human-made capital is treated in conventional accounting and estimate the value of the net change in the total capital stock (broadly defined). The value of the net change in total capital stock is given by equation 1:

The condition is then that net investment must be greater than or equal to zero. If investment equals zero, then a country just maintains its total capital and can sustain its current consumption levels. This result is referred to as "Hartwick's Rule", after Hartwick (1977, 1990). If INt >0, then an increase in consumption is possible. Therefore, in this approach depreciation associated with all forms of capital is netted out. Investments in human-made capital to match the drawing down of natural capital fits the criterion for weak sustainability described by Pearce et. al. (1989).

The second approach uses the Net National Product (NNP) alternatively called net domestic product (NDP) or domestic product. It can be shown that NNP is equal to a constant level of product whose present value equals the present value of consumption along an efficient path for a competitive economy (Maler, 1991; Hamilton et. al. 1994). To sustain economic welfare, net domestic product (NDP) should remain constant or increase from one period to the next (Dasgupta et al 1996). NDP differs from GDP in that it represents net investment after deducting depreciation. Unlike conventional NDP in national income accounts however, with natural resource accounting, NNP adjusts all forms of capital, not just physical capital (equations 2 & 3).

A country can evaluate whether its long-term welfare is rising, falling or remaining constant by examining the change in NDP. An increase in long-run welfare is only possible if dNDPt/dt>0.

There are two direct methods to estimate economic depreciation in natural resource accounting. The first method is commonly referred to as the net price method. This approach multiplies the net price of the resource (gross price (p) less the marginal cost of extraction (c')), by the physical quantity extracted (q(t)) to get depreciation (equation 4).

As discussed by Vincent and Hartwick (1997), it is important to use marginal net price whenever the cost function is non-linear. The reason is that use of average cost computes total resource rent, which often exceeds economic depreciation. A major obstacle in applied analysis however, is the fact that data on marginal costs are typically not available. Average costs are fairly simple to derive while marginal costs could require extensive and expensive data collection.

To circumvent this problem, the approach suggested in Vincent and Hartwick (1997) is followed to utilise average cost figures and the elasticity of the marginal cost curve (percent change in marginal cost per one percent change in quantity extracted). The following expression then yields the net price method (equation 5).

The second direct estimation approach, often referred to as the El Serafy method (El Serafy 1989), multiplies total resource rent by a conversion factor involving the discount rate, the number of years until the resource is exhausted (T-t) and the marginal cost elasticity⁴ (equation 6).

Vincent and Hartwick (1997) argue that this expression is reliable only when b equals infinity. To convert total rent (TR) to Hotelling Rent (HR), Vincent (1996) assumes that the real price of a tonne of an extracted resource is constant over time and the discount rate is given by i. If the remaining stock at the beginning of the period is denoted by St, then one can approximate the number of years until terminal time by St/qt-1. The ratio of Hotelling rent to total resource rent (HR/TR) becomes⁵ (equation 7):