38
consequence of the higher discount rate used by competing factions, resource extraction is
more voracious and the rate of decline of natural resource revenues,
.
(QE)/(QE) =-(ε-1)[r +ξ(N -1)], is higher in more fractionalized societies. Although
fractionalized societies save a greater fraction of their natural resource
revenues,---= 1 +
QE L
ξ(N-1)
εr+(ε-1)ξ(N-1)
1 — I ≥ 1 —, they end up with less wealth in the
ε ) ε
long
run.
Hence, SWF ≡ lim A(t) - A0 = 1 +
t→∞
ξ(N-1)
εr+(ε-1)ξ(N-1)
Q(ε(r +ξ(N -1)))S0<Q(εr)S0if N>1,
especially if N is large and world demand for resources is more elastic. The sustainable level
of consumption equals interest on initial foreign assets plus wage income plus interest on
accumulated wealth, C = rA 0 + (1 - α )(α / r )α/(1-a ) + rSWF ,and is thus lower in fractionalized
societies where resources suffer from weak property rights and seepage. It is thus optimal to
gradually transform natural resource reserves into interest-earning foreign assets. The wealth
of the state, i.e., sovereign wealth, gradually grows from A0 to A0+SWF. The final level of
accumulated foreign assets in a fractionalized society is less than in a homogenous society
despite the lower initial price of natural resources. Also, the speed of transformation is faster
in a fractionalized society. It is the interest earned on sovereign wealth that makes up for
dissipating resource revenues and thus makes it possible to sustain constant consumption as
resources are depleted. Comparing the market with the socially optimal outcome suggests that
benevolent governments redistribute from the lucky cohort that discovers resources to later
cohorts by bequeathing them a large stock of foreign assets.
If there is an imperfect mechanism for resource allocation, one must use the true
accounting prices Qa when calculating genuine saving (Dasgupta and Maler, 2000; Dasgupta,
2001b; Arrow et al., 2003). These are the effect of a marginal increase in the initial stock of
resources on social welfare divided by the effect of a marginal increase in initial foreign
assets on social welfare. In the present context, this amounts to:
1 -1 IQ (0) ≤ Qa (O) ≡
ε)
∂C/ ∂S0 ∂SWF
∂ C / ∂A0 ∂S0
ε[r + ξ(N -1)]
εr+(ε-1)ξ(N-1)
1 -1 IQ (0) ≤ Q (0).
In societies that are homogenous or have perfect property rights the accounting price equals
marginal resource revenue. In fractionalized societies with insecure property rights, however,
the accounting price is higher and is closer to the world price of resources. Estimates of
21
21 The Keynes-Ramsey rule is again C/ C=σ(r-ρ), so that the rate of growth in consumption is not