45
growth, fully determined by the share of employment in the traded sector LT. The production
functions of the two sectors in extensive and intensive form are thus given by:
X=F(LH,K,R) and X =G(LH,K) with H =(1+θL 1)H1 ,θ>0 and
TTTT NNN t Tt-1 t-1
Xt = Xt / LtH = F(1, kτ, Гт) ≡ f(kτ, r ) and xt = Xn / LnH = G(1,kN) ≡ g(kN).
The zero profit conditions are 1 = cW(W,r,Q)W + cr(W,r,Q)r + cQ(W,r,Q)Q and dW(W,r)W +
dr(W,r)r = P, where W indicates the wage, r the exogenous world interest rate, and c(.) and
d(.) are the unit-cost functions homogenous of degree one associated with the CRTS
production functions G(.) and F(.). They give the price of non-traded goods P and the wage W
in terms of the world interest rate r and the world resource price Q. Capital market
equilibrium demands Pg(kN) = f(kT,rT) = r and gives, together with the condition fr(kT,rT)=Q,
kN, kτ and rτ in terms of r and P (or Q). We obtain (suppressing r) that rτ=rT(Q), rτ'<0 and:
W = W( Q ), P = P( Q ), kN = kN( Q ) with P' = dwW' = -Cq/Cw < 0 and kN’ = - g 'Pq / g '' < 0.
Along the factor price frontier, the wage and the price of non-traded goods decrease if the
world priCe of natural resourCes inCreases. The latter induCes a fall in Capital intensity of the
non-traded seCtor. Overlapping households with logarithmiC utility and disCount faCtor
1/(1+p)<1 enjoy wage w when young and receive a natural resource dividend per effective
worker of e. It follows that aggregate Consumption per effeCtive young worker is given by:
Wt + Q,e, +1---LLdJ---I( w + Qe )
=(1 -Lτ,)g(kN(Q,)),
t t (1 + P)(1 + LT,-ɪ) JV t t-1
where μ indicates the relative utility weight (and budget share) of non-traded consumption.
The factor (1+LNt-1) is necessary to convert from old to young workers, the factor (1-LNt) is to
convert output per worker to output per young worker in the non-traded sector, and the labour
market equilibrium condition Lτt + LNt = 1 has been used. This condition for non-traded goods
market equilibrium can be written as a stable difference equation Lτt=Ω(Lτt-1,et,et-1,Qt,Qt-1)
with 0<Ω1<1, Ωi<0, i=2,3,4,5. An increase in resource dividend induces a gradual shift of
employment from the non-traded to the traded sector (Lτ falls), so there is less learning by
doing and the growth rate is permanently lowered ((Ht-Ht-1 )/Ht-1 falls). In this setup the
resource dividend cannot affect relative productivity. If this dividend is driven by a higher
world price of resources, depreciation of the real exchange rate and the lower capital intensity
in production of non-traded goods lead to even bigger falls in traded sector employment,
learning by doing and the rate of growth. GDP is given by Qe + WH + r(Kτ+KN) = QE +
(W+r)H[kN+Lτ(kτ-kN)]. Hence, GDP grows at the rate ξθLτ where the non-resource share of
GDP is ξ. Non-resource GDP falls on impact after a shock in Qe1 if the traded sector is
capital-intensive, that is dGDP/d( Qe1 )=1+( W+ r)H1 (∂Lτ1 /∂( Qe1 ))( kτ-kN)<1) as ∂Lτ1 /∂( Qe1 )<0.
Appendix 3: Hartwick rule for reinvesting natural resource rents in a closed economy
Does exhaustibility of natural resources constrain the growth potential if resources are
essential in production? The answer depends on the ease with which reproducible inputs can
be substituted for exhaustible natural resources. Utilitarian social welfare implies that
consumption first rises and then vanishes in the long run (e.g., Dasgupta and Heal, 1979). It is
difficult to defend from an ethical point of view that the consumption level of future