Natural Resources: Curse or Blessing?

34

^∞

S = -E, S(0) = S₀  or ∫ E(t)dt = S₀.

0

There are two efficiency conditions:

d [ Q (1 - ε-¹ )- TC'( E )] /dt
Q (1 - ε-¹ )- TC'( E )

The first one states that the marginal product of capital is set to the interest charge. The
second requires that the marginal resource rents must increase at a rate equal to the world
interest rate. An anticipated positive rate of increase in the world resource price or in the rate

of technical progress in extraction technology thus induces resource depletion to be postponed:

AC'(E)              E EC"(E)

μ ≡ —₇----——----> 0 and ε ≡---— > 0.

Q(1-ε^-1)-AC'(E)              C'(E)

With exogenous continual improvements in extraction technology (τ > 0), it pays to delay
depletion of reserves to reap the benefits of technical progress. The rate of increase in the
price of resources and the rate of change in resource depletion are then reduced even further.
Now consider the case π* ≡ Q* / Q* > 0 . This pushes up the rate of increase in the price of
resources charged by the country and postpones resource depletion. We assume r - π* > μ
(π*+τ), so π > π* and reserves are not exhausted in finite time. With a constant r* and π* and
no costs of extraction, one has E(0) =ε(π-π*)S₀=ε(r-π*)S₀. Reserves are exhausted
relatively slowly if the world interest rate is low and the world rate of increase in the world
price is high. In general, this is also true if the rate of technical improvements in exploration
technology is high. Sustaining the max-min level of constant consumption requires:

A (t) = [ Q (t) (1 - ε ^- )- A (t)C '( E (t))] E (t)

-∫ exp(-∫ r(v)dv)[r(s)T(s)C(E(s)) + π(s)Q(s)E(s) + rⁱ(s)(A(s) - K(s))]ds.

for the closed economy first has per-capita consumption rising and then falling and vanishing
asymptotically; the first phase may not occur (Dasgupta and Heal, 1979; chapter 10 and appendix 3).

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