Natural Resources: Curse or Blessing?

Substituting the rates of decline of E and R into the resource depletion equation, using the
marginal factor productivity conditions, and integrating over time gives two equations relating
E(0) and R(0) to S(0):

E(0) + ^{(1 α ββ r (0)} = ₅ (0) and r (0)^-(i-^α -^{β )}
εr(1 - α)r

Hence, a resource bonanza (higher S(0)) lifts the declining paths of resource use and resource
exports up (higher R(0) and E(0)), also lifts the declining paths of capital and production, and
depresses the price trajectory (higher Q(0)). Since the optimum production in this small open
economy depends only on world prices, the optimal trajectories of E, R, K, and Y are
independent of consumer preferences (σ and ρ). Substituting these together with the Euler
equation into the present-value national wealth constraint, one gets initial consumption:

_r            (      ( 1 - α - β Y Y(0)       ^λ∣ Q(0)E(0) ^λ∣

C (0) = [(1 - σ ) r + σp]l A (0) + l------- Il ɪK (0) I+^^v7 ʊ I,

V V 1 - α )V r ) εr )

where Y(0), K(0) and Q(0) directly follow from E(0) and R(0). Since Y(0)-rK(0) equals
W(0)+(1-1∕ε)Q(0)E(0) and the wage W grows at the same rate as output, households consume
a constant fraction of the sum of financial, human and natural resource wealth. Clearly, a
higher σ or lower ρ boosts consumption growth, but lowers C(0). The expression for initial
consumption holds for all instants of time. Natural resource wealth (QE∕rε) declines over time
at the rate (ε-1)r and human wealth declines at the rate βr/(1-α-β). Hence, supposing that
r=ρ, a constant level of consumption can be sustained by accumulating sufficient foreign
assets, A, to compensate for the continually declining levels of natural resource and human
wealth. It is easy to extend the results to a return that declines with the level of foreign
investment, e.g, r = r(A-K), r'<0, or to allow for some uncertain date in the future at which
prices fall due to invention of some new alternative technology or source of resources
(Dasgupta et al., 1978).

These pioneering insights on optimally converting natural resources into financial
assets have not yet been extended to take account of resource windfalls harming
competitiveness, provoking corruption, rent seeking and other distortions.¹⁵ But analysis of a
basic Dutch disease model without capital accumulation albeit with learning by doing

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