- Email: [email protected]

Economics

38 (1992) 147-163.

‘

ai

9

University of Oslo, Oslo 3, Norway Received November

1989, final version received September

l!I!M

We consider a developing country with a two-period horizon, which possesses a natural resource that can be extracted with or without extraction costs. A donor can affect extraction through aid which is either unconditional or conditional on resource extraction, and has a preference for extraction to be postponed, indefinitely or at least until period 2. We show that shifting unconditional aid from period 2 to period 1 can lead to postponement of extraction to period 2 given that the country chooses an internal solution with respect to extraction, and faces a binding resource constraint over the two periods. Aid conditional on resource saving in period 1 can, however, have greater effects, and be effective also when ;he country initially extracts all of the resource in period 1 or does not face a resource constraint. We also discuss the effects of capital accumulation and donor investment subsidies on the extraction profile; these are shown to be largely negative in our model, by promoting early extraction.

Many issues concerning environmental and resource manage developing countries are likely to have a substa 1 impact on environment over the long term, and should thus the rich countries as well. This applies to probl desertification and dest adverse climate changes trolled increases in pollut and other effects; and the destruction that may lead to a reduction in diversity.’ A main prsbl valuation of environmental impr may be of much s community as a whole.

the

wdd

148

J. Strand, Foreign aid, capital accumulation,

and resource

extraction

This raises the issue of designing effective implementation schemes for developing country resource conservation One potential type of solutions could involve bargaining between rich and poor countries, where such conservation is part of the resulting bargaining outcome.2 More practically, the rich world may influence developing country resource management, through the structure of economic assistance and lending policies toward the latter countries, on either a bilateral or multilateral (through international aid and lending organization) basis. Some practical schemes which have been proposed in this context are the so-called structural adjustment programs, administered by the International Monetary Fund or the World Bank, where lending (possibly on terms very favorable for the receiver) is made conditional on certain environmental conservation measures in the receiving country,3 and so-called ‘debt-for-nature swaps’, where private institutions or governments in developed countries take over debt held by developing countries, possibly at substantial discounts, in return for e4ronmental favors by the respective developing countries.4 In the present paper we will discuss some such conservation issues, within a model where some donor gives aid to a particular developing country. We will study both the case where this aid is fully concessional (‘untied’), and that where the amount of aid given can be made to depend on particular conservation measures undertaken by the country in question. The resource alloca:ion of a developing country is assumed to be controlled by the incumbent government, whose horizon is two periods. The country is assumed to be shut off from international capital markets, but may receive aid in both periods. It possesses a natural resource R, of size R9 which it can exploit, for domestic use in period 1 and/or period 2. costsof cxploitation may be zero or positive. Except in cases with positive exploit .&ion costs and great resource abundance, the resource will in the model always be exhausted by the end of period 2. The main issue studied is thus the rather limited one of making the recipient country postpone its exploitation of the resource from period 1 to period 2. The donor countries may have a positive (perhaps substantial) willingness to pay for this, however, if exploitation in period 1 yields considerable negative externalities in period 2, or when such a postponement may provide ‘breathing space’ for effective conservational measures to be taken in the rich countries themselves, The issue of sustainable development in the recipient country itself is not directly addressed in this paper.5 ‘See e g Kowbud and Daly (1984) and Woe1 ( 1989, 1990) for attempts ailon ‘Fo; k&w&n of the principles and possible impacts of structural adjust 1984): ‘Vries f 1987) and Hansen ( 1988). enting d~~~=f~~~~~~~~~ swaps arc mrai d;~~~~~~~~of the issue of debta r..&* rR

ixy s

J. Strand, Foreign aid, capital accumulation. and resource extraction

549

In section 2 we present the basic two-period intertemporal optimization problem for the government, and the general solution to this problem. Section 3 discusses this solution when there are no resource extraction costs. ‘I’he developing country will then always exploit the entire resource over the two periods. If the amount of the resource now is small, the country is likely to be at a corner solution where it exploits the entire resource in one of the two periods only, and in period 1 given that the country’s discount rate is higher than the resource growth rate. In such a case a limited amount of unconditional aid will have no effect on resource extraction. Aid tied to resource extraction will, however, have such an effect, if the ‘tying parameter’ t is sufficiently high. Potentially, then, the entire resource use may be postponed from period 1 to 2, and tied aid much more effective that untied aid, for resource postponement purposes. If R is larger, part of it will reasonably be consumed in both periods. We then find that shifting aid from period 2 to period 1 will induce a roughly equal shift in the value of resource consumption, from period 1 to period 2. Tied aid may lead to additional such shifting, e.g., when a donor leaves total period 2 aid constant but ties more of it. In this case both tied and untied aid consequently have favorable effects on the resource extraction profile. In section 4 we extend the model to the case where marginal extraction costs are positive and increasing in extraction in each period. When the resource stock is very small, we may still have a corner solution where untied aid is ineffective. Implementing at least some resource postponement through tied aid is, however, now made cheaper for the donor, in the sense that the necessary t is lower. A small resource stock may now instead imply that some of it is always extracted in both periods, but still that the entire resource is extracted over the two periods. In such cases the effects of untied aid on extraction are roughly the same as with a large stock in section 3; increases in first- and decreases in second-period aid, as well as (corn sated) marginal increases in t, all lead to increased postponement of extraction. Finally, we consider a case whe large that it is never optimal for the n then as a rule nev periods, in the presence of exploitati affect second-period extraction, an extraction either. Only tied ai

150

J. Strand, Foreign aid, capital accumulation, and resource extraction

path over time. Tied aid in addition implies that first-period resource consumption becomes more expensive and shifts the consumption profile, toward more later consumption. Note one important difference in the effects of untied aid, between the cases of zero and positive extraction costs. With no extraction costs untied aid often has no effect on extraction when the amount of the resource is small, and possibly a large effect when it is large. With extraction costs, there can be effects of untied aid when the resource is small, but no effect when it is large (and the resource constraint not binding). We find a general tendency for period 1 investment to induce an increase in first-period resource consumption and thus extraction. In section 3 and partly section 4, this can be countered somewhat by an increase in period 2 resource demand, induced by a possible complementarity between capital and resources in production. With a large resource in section 4, however, such a factor will affect second-period resource use only, and thus tend to increase aggregate resource use over the two periods. In our model, the effects of increased capital accumulation on the extraction profile are thus largely negative. This paper apparently provides the first analytical discussion of the effects of foreign aid on environmental and resource strategies of a developing country. Our results may thus help to form a tentative analytical basis for the conclusion that ‘structural adjustment programs’ or similar schemes which resemble our conditional aid scheme, may be instrumental to the promotion of environmental causes, and indicate how such schemes are likely to work? Our analysis is much simplified on a number 9%accounts, some of which are discussed in the final section 5. We there also indicate possibilities for future research in this area. 2. The basic model Consider a small developing country whose government has a horizon of two periods. At the start of period 1 it possesses a natural resource R in the amount R which can be exploited in either of the two periods. With a constant growth rate g of the resource,

R&l

+g)(R-R,),

where Ri is resource exploitation in period i. If R is a biological resource, g can be interpreted as biologicai growth for a given level of care for the resource; if R is a mineral, g could be relative growth in valuation of the ‘Note, however, that structural adjustment n IenEing and not aid. This issue is auscher (1989) for a related analysis o

pr

Y d”

J. Strand, Foreign aid, capital accumulation, and resource extraction

i5P

resource, by the country itself and the world community. e assume that there may be extraction costs Hi in each period i. If Hi >O, it is given by Hi=h(Ri)zO,

h’ 20,

h"

SO,

h?(O) =O.

(2)

In section 3 below we will generally assume that HiEO, and come back to the case of Hi>0 in section 4. Total net output of the country in period i is given by Xi=f(Ki,

Ri)-Hi,

3)

where Ki is the capital stock of the COY. ry at the start of the period. We are thus abstracting from labor in production and assuming that capital and the resource affect output, j& f&O, fKKCO, fRR50, subscripts denoting derivatives. There are thus decreasing returns to capital, decreasing or constant returns to resource use, and K and R may be complementary, neutral or alternative in production. We assume that the country must use the resource domestically, and that it is cut off from international capital and credit markets.‘* 8 Assume also that the country receives transfers ?;: from abroad in each of the periods, which must be spent in the same periods as those in which they are received? T. is an unconditionai transfer, whiie -rmay be made conditional on the amount of resources remaining in period 2, and on its rate of investment, K2 - K,:

T;=t+h(l

+g)(~-Rl)+~Z(K2-Kl)r

(4

where t is the (positive or negative) untied component of T,, while t, and f, are respective ‘subsidy rates’. 7’1can then not be made conditional on the ‘No exporting of the resource in question can be defended if it has relatively little value as an export good (e.g. it is a rain forest where the net export value of the timber is relatively low), or (since the country is cut off from international credit markets) the value of the resource used domestically is approximately the same as the current value of possible export income from selling it abroad In some relevant cases, where R is a tradeable good and r is substantially below one, the assumption might be less easy to defend, since the vitae of current export into from the resource could be much higher than the value of ‘ts domestic use. A possible defense could be that when the country is cut off from international credit ~11 pay back its foreign debts, it might (or fear of such export income to service its debts. I when this would be more pro fkK=O would be equivalent to W being freely and co export value being the same), ‘The assumption that the international borrowing can be heavy; see the related an 9T might here possi

152

J. ~mnd, Foreign aid, capitd accudation, asd resource extraction

behavior of the developing country in any of the periods (e.g. it is awarded at the beginning of period l), while T2 can be made conditional on behavior in period 1 but not period 2. This implies that a donor has no way of directly affecting resource exploitation in period 2. In the absence of extraction costs, it is then clear that the country will always extract the entire remaining resource in period 2. The main issue dealt with in the paper is then how the country distributes its resource extraction over the two periods. Only in the case of positive extraction costs and a sufficiently low marginal utility of the resource (studied toward the end of the paper) can permanent saving of the resource be affected by donor policies. Total net spending of the country in period i is now given by l$=Xii_

T,

i= 1,2,

(5)

which consists of consumption C1 and investment K 2-K, (assuming no capita! depreciation) in period 1, and only consumption in period 2:

Yl=c1 +K,-K,,

(6)

The preferences of the country can be expressed by W=u(C,)+Su(C,),

(8)

where Ui> 0, uii

-~~CC2-S(K2,Rl)$h(R2)-t-tl(l +i,(Ki-Ki)*

j=,p -+-E,,R,+&[(l

*g)(R-R,)-r,&--K,)] +g)(R-R,)-

where Al--E,,are nonnegative Lagrange multipliers, A, and i,, associate I08 may here in addition to standard avcrnment will not remain in power

discountin

(9 ith

J. Strand, Foreign aid, capital accumulation, and resource extraction

is3

the budget constraints in the two periods, &--& with the constraints and RizO, and i., with the natural resource constraint. The fi conditions for this problem are u1

4,

w

= 0,

-A, + i,,(f,, + tr) + ii, =0, 3’JfRl -h’(R,)]-j.2t1(1-+g)+i,,-&(l

in addition to the Kuhn-Tucker

3 +g)=O,

conditions

&(K2-K1)=O,

AJ-(1+gj(R-R,)-R,]=O. _ This is a concave programming problem that yields, together with budget constraints, 11 equations that solve uniquely for the 11 vari Ri, K2 and the nonnegative multipliers i.,-i.,. Some pro solution are immediate and obvious. (lo)+ 11) yield u,/6u, = i.,/i.,, where 2, and j-1 can be inter

(13)

(19

154

J. Strand, Foreign aid, capital accumulation, and resource extraction

3. Solutions with zero extraction costs In this section we will discuss the solution in the special case where h(R,) ~0, i.e. no costs of extraction, and study the effects of changes in the donor parameters T’, t, tl and tt, on R1 and RZ. Note immediately that in this case we must have A6>O at an optimal solution for the country, i.e., it will always exploit its entire resource over the two periods. Since the only relevant issue for a donor here is whether or not to postpone extraction from period 1 to 2, we can focus on the effects on R, only. In the following in this section we will distinguish between two main cases: (a) the case where the amount of the resource is ‘small’ so that the country will exploit all of it in one of the periods; and (b) the case where it is ‘large’ and the country generally will exploit some of it in both periods. In most of the discussion we will assume A3>O and thus no capital accumulation, and come back to the case of Kz > K 1 at the end of the section. (a) R small, K2= K,.

Here we will assume that the entire resource is initially exploited in either period 1 or period 2, and that the levels of ul, u2, fR1 and fR2 are only marginally affected by whether R is consumed in period 1 or 2. We can then treat these as fixed parameters, with fRI = fR2 = f’. The condition under which the entire resource will be exploited in period 1 is then that &= 0, A5~4, at the solution to (10)--(18). This implies, from (I%o4)9

(20)

ut

Consider first t1 =0, i.e. all aid is unconditional. If now S; = t ( = T’J, = u2 and (20) holds if and only if r >g. The entire resource will then be

exploited in period I (2), if the government’s rate of discount is higher (lower) than the resource growth rate.

Assume now small changes in T” and/or t, that leave u1 and IS%,and thus ;i, and A2, constant. Then (20) remains unchanged, and thus the criterion for exploiting R is not affected. This implies that R1 will not be aJ&cted by small changes in TI and/or t in this case.

Intuitively, in this case, the country is not able to attain an intertemporally optimal allocation of consumption across the two periods, and feeis itself constrained in period 1. Its best strategy is then to exploit the entire resource in period t.

J. Strand, Foreign aid, capital accumulation, and resource extraction

can be tied to the amount of R spared in period 1. From (20), setting Rz ~0 will be beneficial for the country given that +g)

A1-&(l

&(l+g) fRg

Gz

(21)

With inequality in (21) the entire resource will now be saved for this case resource extraction may be affected by even very small aid, since postponement of extraction of one unit of the reso requires tI units of money in period 2. Conditional aid is thus more effective than unconditional aid, in general in this case. (b) R large, K2 = K1.

We now assume that the suficiently large that the country attains an consumption over the two periods, with some of two periods, implying Aa=A5 =O. From (IO), (ll), derive

amount of the resource is optimal allocation of its R extracted in each of the (13) and (14) we can now

(22) u,(G,)f,,(K,,R,)=(lt-g)Gu,(C,)[fR,(K,,R,)+t,]. Differentiating this condition together with the budget constraints for the two periods now yields

dRl -=-

ul lfR1

QT,

D

dR1 -=---

ii

423

’ +g)du22(fR2+tl)>o

9

D

dt

dR1

dR

(1 +g)Su2

&-=R2dt 1

D

’

where D= --lalI(sRA2-(~

+g)‘~u22

(23

J. Strand, Foreign aid, capital accumulation, and resource extraction

156

Assume now that ‘; is roughly constant for the relevant variation in R1 and R2, and that the country exhibits constant absolute risk aversion, i.e., uii/ui is a constant. Then with good approximation, dRljdT1 = -dR,/dt= - 1/2f,, and thus

‘$

(27)

(dT, = dt) = 0, 1

dR1 WT = -dt)=f. dT,

’

(28)

R

In this case, an equally great change in unconditional aid in both periods has no effect on resource extraction. Secondly, note that l/fR can be interpreted as the necessary resource input to produce one unit of the consumer good. An increase in first-period aid, accompanied by an equally large decrease in second-period aid, then leads to a decrease in first-period resource extraction so as to leave first-period consumption unchanged.

The conclusion is thus that increasing the unconditional aid in both periods has no effect on the extraction profile, while shifting the unconditional aid from the second to the first period has a large effect. In the latter case, since consumption over the two periods remains the same, an intertemporally optimal allocation of consumption for the country must imply that it exactly offsets the change in the aid profile, by changes in resource extraction. Note that for these results to hold exactly, fR must be unaffected by RI over the relevant ranges for changes in RI and RZ. T2 rlnust be known -with certainty by the receiving country, i.e., the donor is known to be fully committed to its promises about future aid. Consider next countries with internal solutions with respect to R, but with different degrees of abundance of the resource, greater abundant lower f& Since the derived effects are inversely proportional t abundance implies greater effec,ts of untied aid. Intuitively, with greater abundance, the marginal value of a unit of the resource, in terms of consumption, is lower. It then takes a greater change in resource use, to establish a new intertemporal equilibrium of consumption after a change in d/or t. wider now the effec in opposite directions: an inc e effect of increased seco which tends to i ok that when

J. Strand, Foreign aid, capital accumulation, and resource extraction

unchanged,

i.e.setsdt =

157

- R2 dt,, thyy h--n . ....me effect will drop 0uP 1 In both

cases dR,/dt, ~0. A donor may now consequently induce a reduction in R, even when total

aid in each period is the same, by in period 2 switchingfiom untied aid, to aid tied to resource extraction. At an internal solution for the receiver,

%(I u2

+g)(+R;+t’. Rl

(29

An increase in t 1 then leads to an increase in u,/u,, and thus a shift in consumption from period 1 to period 2. First-period consumption is then made relatively more expensive, since the country by assum consumes out of the resource in period f (R, Al), and t1 implies an extra cost of this consumption. We will now consider modifications of the above conclusions, when the optimal solution for the country instead implies capital accumulation, and thus & = 0. This again implies, from (I2),

(4

K,>K,*

Since the corner solution R2 -0 is of less interest here, we will concentrate on case (b) above. First, assume away all aid, i.e., Ti = Tz =O. Then if, fR I = fRz9 the main effect of K 2 > K 1 k to increase first-period exploitation Of the resource, by a suficient amount to keep total consumption roughly constant. In that sense increased capital accumulatio

in period 1”

greater immediate pressure on the resource, for early consumption. A factor countering this could, however, stem from complementarity of and R in production. Increased K would then raise fR2, thus raising t productivity of period 2 resource use and thereby this use itsel interpretation of such an effect could be that more capital eq processing and utilizing of the resource more efficient. If this e fRz/fRl could increase and EL2/E,, ni~cantly, in t C2 relative to Cr when Kz increases. While unconditional aid has no majo changing the conditional ai impact. We find from ( 12

J. Strand, Foreign aid, capital accumulation, and resource extraction

158

fK2’(l

+g)

f$+tl - tp

(30)

Rl

Conditional aid can thus have a neutral effect on investment only when (1 +g)tl/fR1 = t2, given & =&= A5=O. While t2 > 0 obviously increases investment by making it cheaper for the country, t, >O reduces it, by making first-period spending in general (also that for investment) more expensive. Consider then an increase in t 1 while t2 =O. When A3=0, this will lower K2, and thereby have an additional negative effect on R1 and a positive effect on RZ, in addition to the effects of t, already noted in case (b) above. The effect on resource extraction is thus enhanced when also capital accumulation responds (in a negative way) to such aid.

.

Solutions with extraction costs

We will now introduce resource extraction costs into the model, in the simple way represented by eq. (2). Extraction costs there take a somewhat unrealistic form by only depending on extraction in any ghen period and not on accumulated extraction. Our formulation will still capture some important aspects of the basic problem. We will in section 5 below come back to consequences for the model, of extraction costs instead depending on accumulated extraction. (a) i? small, R2= 0 given no conditional aid. This case is equivalent to case (a) in section 3 above, given that t 1= t2 =O. This implies that the country in section 3 would have incentives to set R2 = 0, and that h’(W) is sufficiently

small to affect this choice. In this case the analysis is basically the same as in section 3 above. The only main difference is that the condition on t1 under which conditional aid is effective for implementing at least some resource postponement, now is different, namely t1=

_d%-_[fRl

-fR2+j.2(l *g)

_h’(R)1.

(31)

We find that the level of t, solving (31) is reduced when h’( Extraction costs thus make it less expensive for a donor to implement at least some resource postpone;nent through conditional aid in this case, (6) icpsmall, R,, R,>O.

by the distribution

J. Strand, Foreign aid, capital accumulation, and resource extraction

A, rO at the optimal solution. The constraint on total resource use is consequently still binding (i.e., the utility of the country would increase wit a higher initial resource stock R). Consider also now first Aa> 0, i.e., Kz = K 1. ( 13) and ( 14) then yield

4 CfRl-wR,)I=j~,cl +g)[fRZ--h’(R2)+t1]*

(32)

Eq. (32) together with (lo), (1 I), (18) and the two budget constraints now solve for AI, AZ, the Ci and the Ri as functions of T;, t and tl. The effects o these parameters on R1 can now be calculated, in a fashion quite analogs to (23)-(25) (noting that fR1 =fR2 = SR is assumed constant), as

dR1 w.k-h,)<() ___----=-------------dTl 4

(33)

9

+g)~~ZZ(fR+fl -M,O dR1 __ = - (1 _~__________~_ dt

DI

dR1 dt_ =

dR,

R2 ~_~~ _ _

9

(1 +g)Su, ______

1

4

(35) ’

where now D, =

--~22~fR-M2-(lm2&2(fR+fl -h2)2+u,h,l +( 1 +g)2SU2h22

>@,

and hi and hii are the first and second deriv:“ives of h in period i. effects on RI of marginal changes in Tl and b, in increa:;es in

and

t

will /eme

(36

160

J. Strand, Foreign aid, capital accumulation, and resource extraction

(25): the added substitl&n effect makes first-period aid more expensive, leading the country to choose a lower R1, thus restoring equilibrium through a marginal extraction cost which is lower in period 1 and higher in period 2. Note that when we assume R2 =O in the absence of extraction costs for this case [i.e., case (a) in section 31, T1= t and t1 =0, RI > R2 with extraction costs; how much greater depends on the shape of the extraction cost function. Giving relatively more aid in period 1 and/or conditional aid in period 2 will help to shift more of the extraction to period 2, but by assumption [by h’(R) being sufficiently large] never all of it. Investments and investment subsidies here have effects on the extraction profile which are similar to those in case (b), section 3. When AS= 0, (12), (13) and ( 14) yield

-wwl=(l UK2+ tZKfR1

+&Kfiw-h’(R2)+~11.

(37)

A high fK2 (and/or tz) at equilibrium here tends to make h’(R1 ), and thus R,, relatively higher. Consequently, resource extraction will be speeded up also in this case. By how much now, however, depends on the shape of the h function. If h’ is strongly increasing around the level of R1 optimal for Kz = K 1, R, will now not be much affected. In such cases we also find that Kz -K1 is reduced beyond the case of no extraction costs: such costs make increased first-period spending out of the resource at the margin (for investment or consumption) more expensive, and thus raise the required returns to investment. (c) R large. We interpret this to mean that R is sufTlciently large for the constraint (18) not to be binding, i.e., A, =0 at the optimal solution. ‘Ike entire resource will then generally not be exploited over t&z two periods. We find the following simple solutions from (13)-( 14):

Assuming K, = Kz, R2 is here determined uniquely from (39). I?: is generally determined t/zðer with Cl, C2, A, and A, from (38), (lO)--(11) and the two budget constraints. When tl =0, i.e., no conditional aid, (38) alone determines R 1 uniquely. In this case, con ditional aid alone has no efect

whatsoever on resource extra&m.

and R, are determined by marginal productivit

J. Strand, Foreign aid, capital accumulation, amd resource extraction

dR1 -----= -(l +g)6 FLO, dt

2

d$=(l

+g)(W-R,)d$

1

au2

41 +g)D’

2

where

We now find that the effects of TI and t are proportional to tl but else much the same as in previous cases. When tl > 0, RI is in (38) set to opti consumption profile over the two periods. 7” and t then have into as in the cases dealt with above. t1 as before has opposing income and substitution effects on R1. When cl, is small initially, the negative substitution effect will now, however, always dominate. The main conclusions are that with a large resource and positive extraction costs, implying that the resource constraint does not bind, R2 is never afJ;ected by untied aid or aid conditimal on resource extraction, and never by untied aid alone, Only with conditional aid can R1 be aflected, a

then in much the same way as in the cases dealt with above. Since R2 is never affected, a reduction in R, implies a permanent saving of the resource, not just a postponement of extraction. benefit to a policy to reduce R1 in this case, relative to previous cases studied. Consider here the implications When t 1=0, R1 is independent ( K2 - K 1), and thus aggreg When t 1 >O, higher (K2 period consumption and ma R to re-establish an optimal consum Increased capital accu increase in exploitation, from two s pressure for consu maki

162

J. Strand, Foreign aid, capital accumulation, and resource extraction

complementary. There thus appears to be an even clearer controversy between the objective of a rapid capital accumulation and that of resource conservation, here than in section 3 above. Admittedly, vve are ignoring important potential factors that may work in the opposite direction; some of these will be mentioned in the following final section. xtensions and final comments In this final section we wi!l limit ourselves to discussing implications of changing some of the strong and sometimes unrealistic assumptions made above, and outline some potential directions for future research. (I) In our analysis the growth rate g of the resource was assumed exogenou-,. In the case of a renewable resource, such as a forest or an animal population, investment can be made in care for the population, thus possibly increasing g. If part of the capital accumulation in period 1 goes into such purposes, this of course makes investment more favorable as a conservation measure, than in our original analysis. (2) Alternatively, the resource could largely serve as an input for investment, of the form Kz--K,=g(R&, where R,, is the part of R1 being ‘invested’.14 Such a relationship should imply a greater tendency toward extracting the resource in period 1, in cases where returns to investment are high. The exact form in which resource extraction affects investment is likely to vary from case to case and should be an interesting topic for research. (3) Extraction costs could in practice be a more complicated function of resource extraction, and could depend on accumulated and not only sir+period extraction. Higher first-period extraction will then generaily increase marginal extraction costs in period 2, implying ? :more general dependence between RI and R2 than that found in section 4 of our paper. In particular, we would now have such a dependence even in the case of an abundant resource, in case (c). (4) Part of the investment in period 1 could a&o be for improvcmegts i, the resource extraction iechnology and thus tend to lower marginal extraction costs. This would imply a tendency for investment to shl!r extraction, from period 1 to period 2 (provided that the entire resource in extracted), but also to increase aggregate extraction when the resource constraint does not bind. (5) Investment ieac9rg to development of the receiving country could, however, also have many other effects on net resource extraction, some of which may be favorable. First, it may tend to lower the implicit discount rate of the country and thus the pressure for early consumption. Secondly, it may increase the efficiency of a given amount of domestic reso se. ly, it

J. Strand, Foreign aid, capital accumulation. and resource extraction

163

may stimulate the degree to which proper care is taken for the resource by the population (related to point 1 above). Such points, which have been much stressed in recent literature about developing country resource problems,’ ’ should tend to modify our so far largely negative conclusions, about the possible effects of investment and investpent subsidies on resource conservation. Clearly, this is a very important research topic, both theoretically and empirically. l&e a now quite large literature on this, e.g. Anderson (1987), Barnes and Ohvares ( 1988), Southgate (1988), as well as Repetto (1987) and Turner (1988).

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