Natural Resources: Curse or Blessing?

46

generations vanishes asymptotically. Hence, the normative focus in the literature on natural
resources has been on max-min egalitarianism which leads to a constant level of per capita
consumption. Non-decreasing per capita consumption is infeasible under exponential
population growth if resources are essential inputs in production and there is no technical
progress (Dasgupta and Heal, 1974; Solow, 1974; Stiglitz, 1974), but feasible with quasi-
arithmetic population growth (Mitra, 1983; Asheim, et. al., 2007). The so-called Hartwick
rule states that natural resource rents should be fully reinvested in reproducible capital under
max-min social welfare. This entails in the absence of population growth a constant savings
rate equal to the constant functional share of resource inputs (Hartwick, 1977). With no
population growth and no technical progress, the economy features constant consumption and
is thus a max-min optimum. If there is positive population growth, a max-min optimum
requires constant consumption per head. If consumption per head were rising (falling) over
time, welfare could be raised if earlier (later) generations saved and invested less or consume
capital at the expense of later (earlier) generations. A max-min optimum then requires that
investment in reproducible capital exceeds natural resource rents.

Consider a closed economy with resource depletion ∫^∞ R(t)dt = S₀ , zero depreciation,
0⁰

savings rate s ≡ K/Y, Cobb-Douglas production Y = F(K,R) = K^αR^βL^1-α-β, and population
growth rate equal to η. Firms set marginal products to factor prices, that is FR = Q and FK = r.

The Hotelling rule in absence of extraction costs is  F_i /FR = Y/ Y - R/ R = FK = αY / K. The

following saving rate sustains a stable income per capita:

^..(s-β)r-αη

Y/ Y - η = sr - αη + β(Y/ Y - η - r) =------------= 0 ⇒ s = β + (α / r)η ≡ s *.

1-β

If there is no population growth (η = 0), all resource rents must be invested in capital to
sustain a constant income per capita (i.e., QR = sY or s = β). This is the well-known Hartwick
rule and holds for general production functions.²³ It corresponds to a max-min optimum, since
it sustains constant consumption per capita. With population growth (η > 0), the country must
invest more than the resource rents to sustain constant income and constant consumption per
capita (s* > β). The interest rate then declines while the capital-output ratio rises with time, so
the saving rate rises over time. The steady-state depletion rate is r-η, so societies with fast
growing populations should deplete their resources less rapidly.

Without population growth and technical progress, the Hartwick rule also results in a
max-min optimum in economies with many consumption goods, heterogeneous capital goods
and endogenous labour supplies provided there is free disposal and stock reversal (Dixit et al.,
1980). The conditions under which a max-min optimum implies adherence to the Hartwick
rule are also known (e.g., Withagen and Asheim, 1998; Mitra, 2002).

The Hartwick rule is related to the Hicksian definition of real income, that is “the
maximum amount a man can spend and still be as well off at the end of the week as at the
beginning”. The general equilibrium features of such a Hicksian definition of real income,

²³ Differentiating K =F(K,R,L) -C=F_RR and using the Hotelling and Hartwick rules K = F_RR
..                                     .                                 .                  .                            .                                                                         .                  .                      ..                  .                              .

yields K =FK+FR-C=(F/F)FR+FR-C=K-C,so C =0.
KR   RRRR

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