Natural Resources: Curse or Blessing?

37

consumption for the faction in power or higher public spending of the type that primarily
benefits those in power.

There are no studies available yet, which attempt to apply these political economy
insights to a formal model addressing the optimal depletion of natural resources. This is an
interesting area for further research and some of these issues are discussed in section 5 which
deals with optimal harnessing of given natural resource windfalls. Here we offer as a first step
a simple analysis of how common-pool problems induce competing factions to use a discount
rate greater than the interest rate in the Hotelling rule which in turn leads to voracious natural
resource depletion, excessive investment rates, less build-up of foreign assets and lower
consumption than is socially optimal for the small open economy of section 4.3.^{19 20} This
analysis also allows us to illustrate how natural resources are gradually transformed into
foreign assets. Although we do not offer a full political economy analysis, we do clarify some
conceptual issues to do with measuring genuine saving in non-competitive environments and
suggest that World Bank figures may under-estimate genuine saving.

The dynamics of the stock of natural resources owned by each faction i is given by
.S'_i = -Ei +∑ξ(Ej -Ei), Si(0) = Si₀.Here ξ > 0 indicates the speed by which oil, gas or
j≠i

water seeps from one field to another or the degree of imperfection of property rights on
natural resources (van der Ploeg, 2010a). No seepage (as is the case for gold, silver or
diamonds) or perfect property rights corresponds to ξ = 0. In general, we have ξ > 0. As in
Lane and Tornell (1996) and Tornell and Lane (1999), we make a distinction between
uncontested stocks of foreign assets (bonds and capital) and contested stocks of natural
resources.²¹ Furthermore, extraction costs are zero, the production function of each group is
given by f ( Ki ) = K“ (1/ N )^α, Q(.) = E^-1(.), and the saving equation of each faction equals

( ⅛N, ʌl            _         .           ...

A. = r(A. - K. ) + QI ∑ E IE + f(K ) - C.. Resources of each competing faction are perfect
^{i i}            ∖ j1 j ) ^{i              i}

substitutes in demand. A homogenous society with perfect property rights has the usual
Hotelling rule Q / Q = r. The Hotelling rule under fractionalization (N > 1) becomes
Q / Q = r + ξ( N -1) > r ,so resource prices rise faster than the rate of interest if there are
factions contesting resource rents, seepage is strong, or property rights imperfect. As a

¹⁹ With a max-min specification of social welfare (σ = 0), consumption of each faction will be constant
over time. With a positive elasticity of intertemporal substitution (σ > 0), short-sighted factions induce
excessive resource extraction and less accumulation of foreign assets which will lead to a bias towards
higher consumption in the short run and lower consumption in the long run.

²⁰ This can also be shown for a closed economy with capital accumulation where the subgame-perfect
Nash equilibrium yields a suboptimally low level of sustainable consumption (van der Ploeg, 2010c).

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