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The growth and distributional consequences of international trade in natural resources and capital goods: a neo-Austrian analysis
Ecological Economics 48 (2004) 83 – 91 www.elsevier.com/locate/ecolecon
ANALYSIS
The growth and distributional consequences of international trade in natural resources and capital goods: a neo-Austrian analysis John Proops * School of Politics, International Relations and the Environment, Keele University, Keele, Staffordshire, UK Received 19 November 2002; accepted 15 September 2003
Abstract The problem explored is the role of natural resources in economic growth. A neo-Austrian model is constructed which can represent either a single, autarchic country, or a pair of trading countries, one of which can export natural resources and the other can export manufactured capital. It is shown that under autarchy, the price of the natural resource has no effect on economic growth, while under conditions of trade, it has a significant influence. Falling natural resource prices slow the growth in the resource exporting country and stimulate it in the capital exporting country. Some policy implications of this finding are explored. D 2003 Elsevier B.V. All rights reserved. Keywords: Neo-Austrian analysis; International trade; Natural resources and capital goods
1. Introduction This paper looks at the relationship between economic growth and natural resources. In the literature, one finds two interesting strands of thought on this issue. Regarding the USA, Wright (1990) argues that the availability of plentiful, and therefore cheap, natural resources was a positive feature for 19th century growth of the US economy. However, with regard to the role of natural resources in the trading relations between the rich countries of the North and the poorer countries of the South, there seems to be a view that the trade in natural resources (from the South to the North) is one of the reasons countries in the South stay poor. In particular, the long-run fall in natural resource prices has been argued to be a * Tel.: +44-1782-583103. E-mail address: [email protected] (J. Proops). 0921-8009/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2003.09.002
cause of the slow rate of economic growth seen in many countries in the South. (The classic work on long-run natural resource prices is Barnett and Morse, 1963.) At this point, it is interesting to note that there is an extensive literature on trade and the environment, in terms of pollution (e.g. the special issue of Ecological Economics, 1994, and numerous more recent pieces). However, there is a very sparse literature on the relationships between trade and natural resources, with a recent exception being Liddle (2001). In this paper, I shall develop a neo-Austrian model of production, which can be equally applied to autarchy (as for the 19th century USA) or for trade (as for modern North – South relations). I shall use it to explore the role of natural resources in economic growth under autarchy, and will show that falling resource rents have no impact on a static measure of national income. However, falling labour costs of resource extraction and resource use do influence
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long-term economic growth. When the model is generalised to the case of two trading countries, characterised as one being ‘‘natural resource producing’’ (i.e. the South) and the other as ‘‘capital producing’’ (i.e. the North), then the resource rent is no longer ‘‘neutral’’, but has an effect on both the growth rate and the distribution of ‘‘global’’ national income between the North and the South. It will be shown that the model reproduces the observed bias of economic growth towards the North. This finding has strong policy consequences for North – South relations with regard to both natural resource extraction and the production of new capital, if present (and growing) transnational inequalities of per capita income are to be addressed. Finally, before proceeding to a presentation of the model, it may be worth noting that this paper represents something of a break in my attitude towards international trade. Like most people who have studied and taught economics, I was impressed by the standard analysis of the mutual benefits to trade, deriving from Ricardo’s notion of specialisation in production in which there is comparative advantage. Indeed, that simple argument still holds true, I believe. However, the vehemence of the recent anti-globalisation protests led me to wonder whether such a strong rejection of the modern international trading system was simply a rejection of modernity and global integration, or whether it was perhaps founded on insights into the potentially damaging structure of trade we find in the modern world. Reflecting on this issue, together with the well-established data on falling natural resource rents, led me to the model I present here.
sense that it allows for the production and accumulation of capital, allowing the ‘‘traverse’’ over time from a mainly labour intensive economy to one that is more capital intensive. In more detail, the model for this paper has four sectors, producing three commodities. Sectors 1 and 2 produce the consumption good (X), either via ‘‘artisan production’’ (Sector 1), using only labour (L) as an input, or by ‘‘industrial production’’, using labour, (produced) capital (K) and a natural resource (N) as (complementary) inputs. The (new) capital (DK) is produced in Sector 3, using only labour as an input, while the natural resource (R) is extracted in Sector 4, again using only labour as an input. Note that a distinction is made between the unextracted natural resource, R, and the extracted resource, N. This distinction is necessary to allow a differentiation between the resource rent, attributable to R (the resource ‘‘in the ground’’), and the resource price, associated with N (the resource in use). Of course, the resource rent is an element of the resource price, as will become apparent below. (It should also be noted that the natural resource can be considered as either renewable or nonrenewable; both types command a scarcity rent.) Algebraically, the sectors can be described as follows, using the standard notation: ‘‘!’’ means ‘‘transformed into’’; ‘‘P’’ means ‘‘combined with’’. We also introduce ‘‘technological coefficients’’ for each sector, indicating the necessary inputs per unit of output; (e.g. in Sector 1, l1 is the labour needed to produce one unit of the consumption good). We can then write: Sector 1 L1 ! X1 ;
where
2. Resource use under autarchy The model I shall develop in this section is based on the neo-Austrian approach (for comprehensive introductions, see Faber and Proops, 1998; Faber et al., 1999; this section draws especially upon Faber and Proops, 1993; Faber et al., 1999, Chapter 8). The neo-Austrian approach is multi-sectoral, with each sector producing an output with various inputs. It assumed that inputs are related to each other, and to outputs, in fixed ratios (i.e. all inputs to a sector are complements). The model is dynamic, in the
Sector 2 L2 PKPN ! X2 ;
L1 ¼ X1 : l2 where
L2 K N ¼ ¼ k 2 n2 l2
¼ X2 ðL; K and N are complementsÞ: Sector 3 L3 ! DK;
Sector 4 L4 PR ! N ;
where
L3 ¼ DK: l3
where
L4 ¼R l4
¼ N ðL and R are complementsÞ:
J. Proops / Ecological Economics 48 (2004) 83–91
As noted above, for Sector 4, R represents the resource ‘‘in the ground’’, while N represents the same quantity of resource which has been extracted, using the labour L4. The solution to the model’s dynamics is relatively straightforward. 1. The present stock of capital, K(t), determines the output of the consumption good from Sector 2, X(t), and the use in Sector 2 of the natural resource, N(t), and labour, L2(t). 2. This known use of the natural resource in Sector 2 determines the use of labour, L4(t), in Sector 4, to extract that amount of the resource. 3. Next, a choice needs to be made concerning the accumulation of new capital, by producing it in Sector 3. Once the amount of new capital, DK(t), is decided, that also determines the amount of labour, L3(t), needed in Sector 3. (In the analysis that follows, we assume that the value of capital accumulation in each period equals the value of savings. We also assume that savings is a fixed proportion of GDP; i.e. we assume a constant savings ratio, s.) 4. Finally, knowing the total amount of labour available, L, the remaining labour is used in Sector 1 (i.e. L1=LL2L3L4), allowing the calculation of the production of the consumption good in Sector 1, X1. (We assume that the labour available is always sufficient to ensure that L1>0.) For the next period, the previous period’s stock of capital is augmented by the new capital produced in the previous period; i.e. K(t+1)=K(t)+DK(t). Then the allocation of labour outlined above is repeated, thus giving the time paths of production of the consumption good, new capital and natural resource extraction. (For simplicity of exposition, we ignore capital deterioration. For a discussion of how capital deterioration can be treated in such models, see Faber et al., 1999, pp. 58 – 60).
3. Calculating the Prices As well as being able to calculate the dynamics of capital accumulation, resource use and production of the consumption good, the model can also be used to
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Table 1 Input – output representation of production under autarchy
1 2 3 4 L K R
1
2
3
4
Output
– – – – PLL1 – –
– – – PNN PLL2 PKK –
– – – – PLL3 – –
– – – – PLL4 – PR R
PXX1 PXX2 PDKDK –
calculate the prices in the economy, and consequently calculate the values of the various sectors’ outputs, as well as the total economy’s national income/product (i.e. its Gross Domestic Product, or GDP). The prices are most easily calculated by assuming that for each sector, and in each period, there is accounting balance (i.e. the values of inputs equal the values of corresponding outputs). This is most easily represented by introducing relevant prices and showing the values of the various flows in an input – output table (Table 1). (The price notation is self-explanatory.) So for Sector 1, there is a single (non-produced) input, labour, of value PLL1, giving rise to output of the consumption good of value PXX1. For Sector 2, there are three inputs: labour and capital, plus the extracted natural resource, of respective values PLL2, PKK and PNN, giving rise to output of the consumption good, of value PXX2. (NB PK is the price of capital in use; i.e. the rental rate of capital.) Sector 3 uses an input of labour, of value PLL3, to produce new capital, of value PDKDK. (NB PDK is the price of new capital, and differs from PK. For the relationship between these two prices of capital, see Faber et al. (1999), p. 84.) Finally, Sector 4 uses labour input, of value PLL4, and (non-extracted) natural resources, of value (‘‘in the ground’’) of PRR, to give an output of extracted natural resources, of value PNN. (As noted above, the price of the resource ‘‘in the ground’’, PR, corresponds to the resource rent.) These relationships can be expressed algebraically, as follows: Sector 1
PL L1 ¼ PX X1 ;
i:e: PL l1 ¼ PX :
Sector 2 PL L2 þ PK K þ PN N ¼ PX X2 ; i:e: PL l2þ PK k2 þ PN n2 ¼ PX
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J. Proops / Ecological Economics 48 (2004) 83–91
PL L3 ¼ PDK DK;
Sector 3
i:e: PL l3 ¼ PDK :
Sector 4 PL L4 þ PR R ¼ PN N ; i:e: PL l4 þ PR ¼ PN : (As noted above, from the above expression we see that the price of the extracted resource equals the resource rent plus the extraction cost.) If we take labour as the nume´raire, (i.e. take PL as fixed), and take PR as given exogenously (to be discussed further below), then we obtain the following for the other prices: PX ¼ l1 PL ; PK ¼
PDK ¼ l3 PL ;
PN ¼ l4 PL þ PR ;
ðl1 l2 l4 n2 ÞPL n2 PR : k2
As we have both the quantities and the prices for this model, we can define Gross Domestic Product (GDP, or Y) in the usual way, as the value of final outputs (i.e. of consumption plus investment), or the value of basic inputs (i.e. of labour, capital and natural resources). Note that the output of the natural resource does not count as part of GDP, as this is used as an intermediate input (i.e. for production in Sector 2). So the two representations of GDP are: Outputs : Inputs :
Y ¼ PX ðX1 þ X2 Þ þ PDk DK: Y ¼ PL ðL1 þ L2 þ L3 þ L4 Þ þ PK K þ PR R:
As L=L1+L2+L3+L4, and R=N=n2K/k2, and using the prices derived above, from the output GDP equation we get: ðl1 l2 l4 n2 ÞPL n2 PR n2 K Y ¼ PL L þ K þ PR k2 k2 ðl1 l2 l4 n2 Þ ¼ PL L þ PL K : k2 (The same equation can be derived, at greater length, from the input equation for GDP.) From this equation, we see that, surprisingly, the level of GDP is determined by the availability of labour (L) and capital (K), but not the availability of the natural resource. This is because the natural resource is a complement in production for capital,
so on its own it has no value. Indeed, that it needs to be extracted (l4>0) and used in manufacture (n2>0), actually reduces GDP (i.e. BY/B/4<0 and BY/Bn2<0). If new discovery of resources and technical progress allow l4 and n2 to reduce in size then, ceteris paribus, GDP increases. However, there is a distributional issue here related to the ownership of the natural resource. The natural resource attracts a rent ( PRR=PRn2K/k2) paid to its owners, and thereby leaves a smaller share of GDP to be paid to the owners of labour and capital. If PR is falling over time, reflecting reducing natural resource scarcity because of new discoveries, then the share of GDP paid to the resource owners will fall and that to capital owners will rise. (As labour is both the nume´raire and in fixed supply, payments to labour are constant, so for a growing GDP, this share also falls.) In conclusion, in this model, resource rents have no direct effect on GDP, but: (a) technical progress in resource extraction and use would increase GDP; and (b) a falling resource rent would increase the share of GDP going to capital. These results are consistent with the arguments of Wright (1990).
4. Resource use and trade In this extension of the above model, we move to a consideration of two producing countries, which trade with each other. In particular, we assume the two countries have different characteristics. Country A produces the consumption good with both techniques (i.e. Sectors 1 and 2), but cannot produce the capital good. However, it can produce the natural resource (Sector 4). Country B also has both Sectors 1 and 2, but while it can produce new capital (Sector 3), it cannot produce the natural resource. To be able to produce and to grow, each country needs access to both new capital and the natural resource, which each achieves by trading with the other. Here Country B has characteristics which we could term ‘‘Nothern’’, in that it produces and exports new
J. Proops / Ecological Economics 48 (2004) 83–91
capital, but imports raw materials. Conversely, Country A is ‘‘Southern’’ in character, needing to import new capital, but being able to export raw materials. (This approach follows that of Jo¨st, 1996; Faber et al., 1999, Chapter 5.) The dynamics of the model will be given by Country B investing a certain proportion of its GDP in new capital, which it produces. In using its total capital stock, it uses natural resources, which it imports from Country A. As Country A cannot produce new capital, we assume that its investment in new capital is limited by its access to foreign currency; so the value of its imported new capital equals the value of its exports of natural resources to Country B. (There is no trade in the other good, X.) We assume that the techniques of production in Sectors 1 and 2 are the same in the two countries. The full description of the techniques of production is: Country A LA 1 ¼ X1A ; l1 LA K A N A Sector 2 2 ¼ ¼ ¼ X2A ; l2 k2 n2 L4 Sector 4 ¼ R ¼ N ¼ N A þ N B: l4
Sector 1
Country B LB1 ¼ X2B ; l1 LB K B N B ¼ ¼ X2B ; Sector 2 2 ¼ l2 k2 n2 LB Sector 3 3 ¼ DK ¼ DK A þ DK B l3 Sector 1
If we introduce prices, we can represent the relations between these two economies as a pair of trade input – output tables, as in Table 2. (For a fuller discussion of the input –output representation of international trade, see Proops et al., 1993, pp. 131 –138.) Table 2 shows a pair of trade-linked input –output tables, for the two countries. Here PK and PDK are the same in the two countries, as the capital is produced only in Country B, and the two countries have the
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Table 2 Input – output representation of production under with trade A 1 A 1 2 4 L K R B 1 2 3 L K
– – – PLLA1 – – – – – – –
B 2 – – PNNA PLLA2 PKKA – – – – – –
4
DFD
1
2
3
DFD
– – – PLLA4 – PRR – – – – –
PXX1A PXX2A
– – – – – – – – – PLLB1 –
– – PNN B – – – – – – PLLB2 PKKB
– – – – – – – – – PLLB3 –
– – –
–
– – PDKDKA
PXX1B PXX2B PDKDKB
DFD stands for Domestic Final Demand.
same capital-using technique. Similarly, PL, PX, PN and PR are the same in the two countries, as they use identical techniques in Sectors 1 and 2. Considering first Country A, there are three productive sectors, A1, A2 and A4. Sector A1 uses an input of Country A labour, of value PLL1A, to produce consumption good for Country A, of value PXX1A. Sector A2 uses labour and capital from Country A, of values PLL2A and PKKA, respectively, plus extracted natural resource from Country A, of value PNNA to produce consumption good for Country A, of value PXX2A. Sector A4 uses labour and unextracted natural resource from Country A, of respective values PLL4Aand PR R, to produce extracted natural resources for Countries A and B, of respective values PNN2A and PNN B. Country B also has three productive sectors, B1, B2 and B3. Sector B1 uses an input of Country B labour, of value PLL1B, to produce consumption good for Country A, of value PXX1B. Sector B2 uses labour and capital from Country B, of values PLL2B and PKK B, respectively, plus extracted natural resource from Country A, of value PNN B, to produce consumption good for Country B, of value PXX2B. Finally, Sector B3 uses an input of Country B labour, of value PLL3B, to produce new capital for Country A, of value PDKDKA, and new capital for Country B, of valuePDKDKB.
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J. Proops / Ecological Economics 48 (2004) 83–91
We can express these relationships algebraically, to give: A1
A PL LA 1 ¼ PX X1 ;
A2
A A A PL LA 2 þ PK K þ PN N ¼ PX X2 ;
i:e: PL l1 ¼ PX :
i:e: PL l2 þ PK k2 þ PN n2 ¼ PX : PL LA 4 þ PR R ¼ PN N ;
A4
¼ N A þ N B; B1
Y B=PLLB+PKK B+PNN BPDKDK A, i.e. Y B=PLLB+PKK B. For Country A, we also know: R=N=N A+N B=(KA+KB)n2/k2.
here R ¼ N
i:e: PL l4 þ PR ¼ PN :
PL LB1 ¼ PX X1B ;
For Country B:
i:e: PL l1
¼ PX ðas for A1Þ:
Using this, and substituting for the prices, we obtain: PR K2B n2 A A A l1 l2 l4 n2 Y ¼ PL L þ K þ k2 k2 and
B2 PL LB2 þ PK K B þ PN N B ¼ PX X2B ; i:e: PL l2 þ PK k2 þ PN n2 ¼ PX ðas for A2Þ:
l1 l2 l4 n2 PR K2B n2 Y B ¼ PL LB þ K B : k2 k2
B3 PL LB3 ¼ PDK DK; i:e: : PL l3 ¼ PDK :
We note that if we set K=KA+KB and L=LA+LA and sum the two GDPS, we obtain the same expression as for the single country (autarchy) model. Further, the terms containing PR are of the same size but oppositely signed, showing that while the resource rent has no effect on the (static) global GDP, it does affect the GDPs for the separate trading countries; i.e. it influences the distribution of the (static) global GDP. (This is analogous to the distributional effect of resource rents on the owners of natural resources and capital, as noted under autarchy.) If PR declines then, ceteris paribus, YA decreases and YB increases correspondingly. Thus, if Country B saves (and accumulates capital) out of GDP, this further increases the savings out of GDP for Country B. In line with intuition, one can show by comparative static analysis (or by simulations) that the following holds. If the resource rent is falling, then there is a tendency for the rate of growth of Country A also to fall, while that of Country B tends to rise. Therefore, a combination of trading relations determined by the availability of the natural resource and the ability to manufacture capital, combined with a falling resource rent, generates precisely the pattern of development we have observed over the past half century; i.e. the rich countries seem to grow at the expense of poor countries.
here DK ¼ DK A þ DK B
Using labour as nume´raire, (i.e. holding PL constant), and taking PR as exogenous, these equations can be solved to give:
PX ¼ PL l1 ; PK ¼
PN ¼ PL l4 þ PR ;
PL ðl1 l2 l4 n2 Þ PR n2 ; k2
PDK ¼ PL l3 :
Using the above prices and quantities, we can calculate the GDP ( Y) for each country, as: GDP= Value Added+ImportsExports. For Country A: Y A=PLLA+PKKA+PRR+PDKDKAPNNB. If the investment constraint is in operation for Country A, then the value of new capital for that country equals the value of natural resource exports: PDKDKA=PNNB; i.e. Y A ¼ PL LA þ PK K A þ PR R:
J. Proops / Ecological Economics 48 (2004) 83–91
Details of the effects of resource rents on the rates of economic growth are derived in the appendices. In Appendix A, it is shown that for the autarchy case, the rate of GDP growth is independent of the behaviour of the natural resource rent, depending only on the savings ratio and the technical coefficients. In particular, the rate of GDP growth increases if the coefficients relating to the natural resource (in extraction and use) are falling, in line with Wright’s (1990) argument. In Appendix B, the trade case is explored, with a derivation of the GDP growth rates for Countries A and B. For both countries we find that the rate of GDP growth depends on both the level of the resource rent and the rate of growth of the resource rent. The effect of a falling resource rent is in line with intuition. For Country A, it contributes to reduced rates of GDP growth, while for Country B, it promotes GDP growth. The consequence of a falling resource rent, as has been observed for almost all natural resources over the past century, is that rates of growth of the North will be boosted, while for the South rates of growth will be diminished. The consequence is clear: a continuing and potentially increasing inequality of income per capita.1
5. Policy discussion The standard argument in favour of trade between the North and South is that it allows the South to accumulate capital and therefore to achieve improved growth rates, and the potential to reduce both internal poverty and also transnational inequalities. In this paper, I have tried to show that if, as seems always to be the case, trade asymmetry exists so that the North exports capital goods and the South exports raw materials, then the consequences of the (almost universally observed) falling resource rents is that trade will not diminish
1
I am indebted to Anthony Friend for pointing out that this trade model could also be applied to regional growth disparities between regions in a single country, such as between the USA precivil war Union and Confederate states.
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transnational inequality. What are the implications of this finding? First, price support for raw material exports by the South may be necessary. One effective method of achieving this would be the drastic reduction of price support (both explicit and implicit) for raw material production (including agriculture) in the North. This would have the effect of increasing raw material scarcity, and so driving up natural resource rents. Second, there needs to be concerted international efforts to allow the South to become a producer of capital goods. Standard ‘‘infant industry’’ protectionist arguments can be used here. However, probably even more important is the transfer of technology from the North to the South, together with appropriate labour training. In conclusion, it should be stressed that it is unlikely that unfettered free trade will produce ‘‘trickle down’’ effects for the South while natural resources are apparently becoming less scarce, and while the North maintains its present monopoly on the production of the means of production.
Acknowledgements For their perceptive comments on an earlier version of this paper, I am grateful to the participants at a seminar at the Interdisciplinary Institute of Environmental Economics, University of Heidelberg, in October 2002.
Appendix A . Rate of growth of GDP under autarchy We have seen that under autarchy, the model gives GDP as:
ðl1 l2 l4 n2 Þ Y ¼ PL L þ PL K : k2 We can represent the (continuous) GDP growth rate as: r = (dY/dt)(1/Y). Recalling that h in Y, only i K varies with time, we see PL that: r ¼ dK dt Y
ðl1 l2 l4 n2 Þ k2
. Now, we suppose that
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J. Proops / Ecological Economics 48 (2004) 83–91
savings is a fixed proportion of GDP, and all savings are invested in new capital. So we can write (in continuous time): PDK
dK dK sY sY ¼ sY ; i:e: ¼ ¼ : dt dt PDK PL l3
Substitution gives: r¼
sY PL ðl1 l2 l4 n2 Þ l 1 l 2 l 4 n2 ¼s : pL l 3 Y k2 l3 k2
We suppose that for Country B, savings are a fixed proportion (s) of GDP, and this is converted into new capital; i.e.: PDK(dK B/dt)=sY B; i.e. (dK B/dt)=((sY B)/ (PDK)). Recalling that: PDK=PLl3, we obtain: (dKB/dt)= ((sYB)/( PLl3)). Substitution for this in the expression for r B, followed by reorganisation, gives: rB ¼
sb sn2 PR n2 K B dPR : l3 l3 k2 PL k2 Y B dt
So the growth rate of GDP is independent of the behaviour of the natural resource rent. It depends only on the technical coefficients of production and the savings rate. (For an alternative derivation of this result, without natural resources, see Faber, 1978, p. 158.)
So the rate of GDP growth for Country B has three components. First, a constant, identical to the rate of growth under autarchy. Second, a component that varies with the resource rent. Third, a component that varies directly with the capital stock and the rate of change of the resource rent, and inversely with the GDP of Country B.
Appendix B . Rates of growth of GDP with Trade
B.2 . Growth rate of GDP for Country A
We have derived the following as the GDPs of the two trading countries:
We define the rate of growth for Country A as: r A=(dYA/dt)(1/YA). Differentiating the expression for Y A and substitution gives: 1 dK A n2 dK B dPR bþ þ KB PL PR rA ¼ : YA dt k2 dt dt
l 1 l 2 l 4 n2 PR K2B n2 Y A ¼ PL LA þ K A þ k2 k2 l 1 l 2 l 4 n2 PR K2B n2 Y B ¼ PL LB þ K B : k2 k2 4 n2 We define: bu l1 l2kl to give: 2
PR K2B n2 and Y A ¼ PL LA þ K A b þ k2
PR K2B n2 Y B ¼ PL LB þ K B b k2 B.1 . Growth rate of GDP for Country B We define the rate of growth for Country B as: rB=(dY B/dt)(1/Y B). Differentiating the expression for YB and substitution gives: 1 r ¼ B Y B
dK B n2 dK B B dPR PL b þK PR : dt k2 dt dt
We suppose that Country A investment is constrained by the value of natural resource exports; i.e.: PDK(dKA/dt)=( PNN B). Reorganisation and substitution gives: dK A ðPLA l4 þ PR ÞK B n2 ¼ : dt pA L l 3 k2 We have already derived above the expression for dKB/dt. Substituting these in the expression for rA, and reorganising, gives: rA ¼
n2 l4 bK B PLA n2 bK B PR n2 sY B PR þ þ k2 l 3 Y A k2 l3 Y A k2 l 3 Y A B n2 K dPR : þ k2 Y A dt
Here the rate of growth of GDP depends on four components; for each it varies inversely with the GDP
J. Proops / Ecological Economics 48 (2004) 83–91
of Country A. For the first component, it also varies directly with the capital stock in Country B. For the second, it again varies directly with the KB, but also with the resource rent. The third varies directly with YB and the resource rent, while the fourth varies directly with K B and the rate of change of the resource rent. References Barnett, H., Morse, C., 1963. Scarcity and Growth: The Economics of Resource Scarcity. Johns Hopkins Univ. Press, Baltimore, MD. Faber, M., 1978. Introduction to Modern Austrian Capital Theory. Springer, Heidelberg. Faber, M., Proops, J., 1993. Natural resource rents, economic dy-
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namics and structural change: a capital theoretic approach. Ecological Economics 8, 17 – 44. Faber, M., Proops, J., 1998. Evolution, Time, Production and the Environment, 3rd ed. Springer, Heidelberg. Faber, M., Proops, J., Speck, S., 1999. Capital and Time in Ecological Economics: Neo-Austrian Modelling. Edward Elgar, Cheltenham, UK. Jo¨st, F., 1996. Climate change and economic development: a neoAustrian approach. In: Faucheux, S., Pearce, D., Proops, J. (Eds.), Models of Sustainable Development. Edward Elgar, Cheltenham, UK, pp. 187 – 204. Liddle, B., 2001. Free trade and the environment – development system. Ecological Economics 39, 21 – 36. Proops, J., Faber, M., Wagenhals, G., 1993. Reducing CO2 Emissions: A Comparative Study for Germany and the UK. Springer, Heidelberg. Special Issue, 1994. Ecological Economics 9, 1 – 97. Wright, G., 1990. Origins of American industrial success, 1879 – 1940. American Economic Review 80, 657 – 668.
ANALYSIS
The growth and distributional consequences of international trade in natural resources and capital goods: a neo-Austrian analysis John Proops * School of Politics, International Relations and the Environment, Keele University, Keele, Staffordshire, UK Received 19 November 2002; accepted 15 September 2003
Abstract The problem explored is the role of natural resources in economic growth. A neo-Austrian model is constructed which can represent either a single, autarchic country, or a pair of trading countries, one of which can export natural resources and the other can export manufactured capital. It is shown that under autarchy, the price of the natural resource has no effect on economic growth, while under conditions of trade, it has a significant influence. Falling natural resource prices slow the growth in the resource exporting country and stimulate it in the capital exporting country. Some policy implications of this finding are explored. D 2003 Elsevier B.V. All rights reserved. Keywords: Neo-Austrian analysis; International trade; Natural resources and capital goods
1. Introduction This paper looks at the relationship between economic growth and natural resources. In the literature, one finds two interesting strands of thought on this issue. Regarding the USA, Wright (1990) argues that the availability of plentiful, and therefore cheap, natural resources was a positive feature for 19th century growth of the US economy. However, with regard to the role of natural resources in the trading relations between the rich countries of the North and the poorer countries of the South, there seems to be a view that the trade in natural resources (from the South to the North) is one of the reasons countries in the South stay poor. In particular, the long-run fall in natural resource prices has been argued to be a * Tel.: +44-1782-583103. E-mail address: [email protected] (J. Proops). 0921-8009/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2003.09.002
cause of the slow rate of economic growth seen in many countries in the South. (The classic work on long-run natural resource prices is Barnett and Morse, 1963.) At this point, it is interesting to note that there is an extensive literature on trade and the environment, in terms of pollution (e.g. the special issue of Ecological Economics, 1994, and numerous more recent pieces). However, there is a very sparse literature on the relationships between trade and natural resources, with a recent exception being Liddle (2001). In this paper, I shall develop a neo-Austrian model of production, which can be equally applied to autarchy (as for the 19th century USA) or for trade (as for modern North – South relations). I shall use it to explore the role of natural resources in economic growth under autarchy, and will show that falling resource rents have no impact on a static measure of national income. However, falling labour costs of resource extraction and resource use do influence
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long-term economic growth. When the model is generalised to the case of two trading countries, characterised as one being ‘‘natural resource producing’’ (i.e. the South) and the other as ‘‘capital producing’’ (i.e. the North), then the resource rent is no longer ‘‘neutral’’, but has an effect on both the growth rate and the distribution of ‘‘global’’ national income between the North and the South. It will be shown that the model reproduces the observed bias of economic growth towards the North. This finding has strong policy consequences for North – South relations with regard to both natural resource extraction and the production of new capital, if present (and growing) transnational inequalities of per capita income are to be addressed. Finally, before proceeding to a presentation of the model, it may be worth noting that this paper represents something of a break in my attitude towards international trade. Like most people who have studied and taught economics, I was impressed by the standard analysis of the mutual benefits to trade, deriving from Ricardo’s notion of specialisation in production in which there is comparative advantage. Indeed, that simple argument still holds true, I believe. However, the vehemence of the recent anti-globalisation protests led me to wonder whether such a strong rejection of the modern international trading system was simply a rejection of modernity and global integration, or whether it was perhaps founded on insights into the potentially damaging structure of trade we find in the modern world. Reflecting on this issue, together with the well-established data on falling natural resource rents, led me to the model I present here.
sense that it allows for the production and accumulation of capital, allowing the ‘‘traverse’’ over time from a mainly labour intensive economy to one that is more capital intensive. In more detail, the model for this paper has four sectors, producing three commodities. Sectors 1 and 2 produce the consumption good (X), either via ‘‘artisan production’’ (Sector 1), using only labour (L) as an input, or by ‘‘industrial production’’, using labour, (produced) capital (K) and a natural resource (N) as (complementary) inputs. The (new) capital (DK) is produced in Sector 3, using only labour as an input, while the natural resource (R) is extracted in Sector 4, again using only labour as an input. Note that a distinction is made between the unextracted natural resource, R, and the extracted resource, N. This distinction is necessary to allow a differentiation between the resource rent, attributable to R (the resource ‘‘in the ground’’), and the resource price, associated with N (the resource in use). Of course, the resource rent is an element of the resource price, as will become apparent below. (It should also be noted that the natural resource can be considered as either renewable or nonrenewable; both types command a scarcity rent.) Algebraically, the sectors can be described as follows, using the standard notation: ‘‘!’’ means ‘‘transformed into’’; ‘‘P’’ means ‘‘combined with’’. We also introduce ‘‘technological coefficients’’ for each sector, indicating the necessary inputs per unit of output; (e.g. in Sector 1, l1 is the labour needed to produce one unit of the consumption good). We can then write: Sector 1 L1 ! X1 ;
where
2. Resource use under autarchy The model I shall develop in this section is based on the neo-Austrian approach (for comprehensive introductions, see Faber and Proops, 1998; Faber et al., 1999; this section draws especially upon Faber and Proops, 1993; Faber et al., 1999, Chapter 8). The neo-Austrian approach is multi-sectoral, with each sector producing an output with various inputs. It assumed that inputs are related to each other, and to outputs, in fixed ratios (i.e. all inputs to a sector are complements). The model is dynamic, in the
Sector 2 L2 PKPN ! X2 ;
L1 ¼ X1 : l2 where
L2 K N ¼ ¼ k 2 n2 l2
¼ X2 ðL; K and N are complementsÞ: Sector 3 L3 ! DK;
Sector 4 L4 PR ! N ;
where
L3 ¼ DK: l3
where
L4 ¼R l4
¼ N ðL and R are complementsÞ:
J. Proops / Ecological Economics 48 (2004) 83–91
As noted above, for Sector 4, R represents the resource ‘‘in the ground’’, while N represents the same quantity of resource which has been extracted, using the labour L4. The solution to the model’s dynamics is relatively straightforward. 1. The present stock of capital, K(t), determines the output of the consumption good from Sector 2, X(t), and the use in Sector 2 of the natural resource, N(t), and labour, L2(t). 2. This known use of the natural resource in Sector 2 determines the use of labour, L4(t), in Sector 4, to extract that amount of the resource. 3. Next, a choice needs to be made concerning the accumulation of new capital, by producing it in Sector 3. Once the amount of new capital, DK(t), is decided, that also determines the amount of labour, L3(t), needed in Sector 3. (In the analysis that follows, we assume that the value of capital accumulation in each period equals the value of savings. We also assume that savings is a fixed proportion of GDP; i.e. we assume a constant savings ratio, s.) 4. Finally, knowing the total amount of labour available, L, the remaining labour is used in Sector 1 (i.e. L1=LL2L3L4), allowing the calculation of the production of the consumption good in Sector 1, X1. (We assume that the labour available is always sufficient to ensure that L1>0.) For the next period, the previous period’s stock of capital is augmented by the new capital produced in the previous period; i.e. K(t+1)=K(t)+DK(t). Then the allocation of labour outlined above is repeated, thus giving the time paths of production of the consumption good, new capital and natural resource extraction. (For simplicity of exposition, we ignore capital deterioration. For a discussion of how capital deterioration can be treated in such models, see Faber et al., 1999, pp. 58 – 60).
3. Calculating the Prices As well as being able to calculate the dynamics of capital accumulation, resource use and production of the consumption good, the model can also be used to
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Table 1 Input – output representation of production under autarchy
1 2 3 4 L K R
1
2
3
4
Output
– – – – PLL1 – –
– – – PNN PLL2 PKK –
– – – – PLL3 – –
– – – – PLL4 – PR R
PXX1 PXX2 PDKDK –
calculate the prices in the economy, and consequently calculate the values of the various sectors’ outputs, as well as the total economy’s national income/product (i.e. its Gross Domestic Product, or GDP). The prices are most easily calculated by assuming that for each sector, and in each period, there is accounting balance (i.e. the values of inputs equal the values of corresponding outputs). This is most easily represented by introducing relevant prices and showing the values of the various flows in an input – output table (Table 1). (The price notation is self-explanatory.) So for Sector 1, there is a single (non-produced) input, labour, of value PLL1, giving rise to output of the consumption good of value PXX1. For Sector 2, there are three inputs: labour and capital, plus the extracted natural resource, of respective values PLL2, PKK and PNN, giving rise to output of the consumption good, of value PXX2. (NB PK is the price of capital in use; i.e. the rental rate of capital.) Sector 3 uses an input of labour, of value PLL3, to produce new capital, of value PDKDK. (NB PDK is the price of new capital, and differs from PK. For the relationship between these two prices of capital, see Faber et al. (1999), p. 84.) Finally, Sector 4 uses labour input, of value PLL4, and (non-extracted) natural resources, of value (‘‘in the ground’’) of PRR, to give an output of extracted natural resources, of value PNN. (As noted above, the price of the resource ‘‘in the ground’’, PR, corresponds to the resource rent.) These relationships can be expressed algebraically, as follows: Sector 1
PL L1 ¼ PX X1 ;
i:e: PL l1 ¼ PX :
Sector 2 PL L2 þ PK K þ PN N ¼ PX X2 ; i:e: PL l2þ PK k2 þ PN n2 ¼ PX
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PL L3 ¼ PDK DK;
Sector 3
i:e: PL l3 ¼ PDK :
Sector 4 PL L4 þ PR R ¼ PN N ; i:e: PL l4 þ PR ¼ PN : (As noted above, from the above expression we see that the price of the extracted resource equals the resource rent plus the extraction cost.) If we take labour as the nume´raire, (i.e. take PL as fixed), and take PR as given exogenously (to be discussed further below), then we obtain the following for the other prices: PX ¼ l1 PL ; PK ¼
PDK ¼ l3 PL ;
PN ¼ l4 PL þ PR ;
ðl1 l2 l4 n2 ÞPL n2 PR : k2
As we have both the quantities and the prices for this model, we can define Gross Domestic Product (GDP, or Y) in the usual way, as the value of final outputs (i.e. of consumption plus investment), or the value of basic inputs (i.e. of labour, capital and natural resources). Note that the output of the natural resource does not count as part of GDP, as this is used as an intermediate input (i.e. for production in Sector 2). So the two representations of GDP are: Outputs : Inputs :
Y ¼ PX ðX1 þ X2 Þ þ PDk DK: Y ¼ PL ðL1 þ L2 þ L3 þ L4 Þ þ PK K þ PR R:
As L=L1+L2+L3+L4, and R=N=n2K/k2, and using the prices derived above, from the output GDP equation we get: ðl1 l2 l4 n2 ÞPL n2 PR n2 K Y ¼ PL L þ K þ PR k2 k2 ðl1 l2 l4 n2 Þ ¼ PL L þ PL K : k2 (The same equation can be derived, at greater length, from the input equation for GDP.) From this equation, we see that, surprisingly, the level of GDP is determined by the availability of labour (L) and capital (K), but not the availability of the natural resource. This is because the natural resource is a complement in production for capital,
so on its own it has no value. Indeed, that it needs to be extracted (l4>0) and used in manufacture (n2>0), actually reduces GDP (i.e. BY/B/4<0 and BY/Bn2<0). If new discovery of resources and technical progress allow l4 and n2 to reduce in size then, ceteris paribus, GDP increases. However, there is a distributional issue here related to the ownership of the natural resource. The natural resource attracts a rent ( PRR=PRn2K/k2) paid to its owners, and thereby leaves a smaller share of GDP to be paid to the owners of labour and capital. If PR is falling over time, reflecting reducing natural resource scarcity because of new discoveries, then the share of GDP paid to the resource owners will fall and that to capital owners will rise. (As labour is both the nume´raire and in fixed supply, payments to labour are constant, so for a growing GDP, this share also falls.) In conclusion, in this model, resource rents have no direct effect on GDP, but: (a) technical progress in resource extraction and use would increase GDP; and (b) a falling resource rent would increase the share of GDP going to capital. These results are consistent with the arguments of Wright (1990).
4. Resource use and trade In this extension of the above model, we move to a consideration of two producing countries, which trade with each other. In particular, we assume the two countries have different characteristics. Country A produces the consumption good with both techniques (i.e. Sectors 1 and 2), but cannot produce the capital good. However, it can produce the natural resource (Sector 4). Country B also has both Sectors 1 and 2, but while it can produce new capital (Sector 3), it cannot produce the natural resource. To be able to produce and to grow, each country needs access to both new capital and the natural resource, which each achieves by trading with the other. Here Country B has characteristics which we could term ‘‘Nothern’’, in that it produces and exports new
J. Proops / Ecological Economics 48 (2004) 83–91
capital, but imports raw materials. Conversely, Country A is ‘‘Southern’’ in character, needing to import new capital, but being able to export raw materials. (This approach follows that of Jo¨st, 1996; Faber et al., 1999, Chapter 5.) The dynamics of the model will be given by Country B investing a certain proportion of its GDP in new capital, which it produces. In using its total capital stock, it uses natural resources, which it imports from Country A. As Country A cannot produce new capital, we assume that its investment in new capital is limited by its access to foreign currency; so the value of its imported new capital equals the value of its exports of natural resources to Country B. (There is no trade in the other good, X.) We assume that the techniques of production in Sectors 1 and 2 are the same in the two countries. The full description of the techniques of production is: Country A LA 1 ¼ X1A ; l1 LA K A N A Sector 2 2 ¼ ¼ ¼ X2A ; l2 k2 n2 L4 Sector 4 ¼ R ¼ N ¼ N A þ N B: l4
Sector 1
Country B LB1 ¼ X2B ; l1 LB K B N B ¼ ¼ X2B ; Sector 2 2 ¼ l2 k2 n2 LB Sector 3 3 ¼ DK ¼ DK A þ DK B l3 Sector 1
If we introduce prices, we can represent the relations between these two economies as a pair of trade input – output tables, as in Table 2. (For a fuller discussion of the input –output representation of international trade, see Proops et al., 1993, pp. 131 –138.) Table 2 shows a pair of trade-linked input –output tables, for the two countries. Here PK and PDK are the same in the two countries, as the capital is produced only in Country B, and the two countries have the
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Table 2 Input – output representation of production under with trade A 1 A 1 2 4 L K R B 1 2 3 L K
– – – PLLA1 – – – – – – –
B 2 – – PNNA PLLA2 PKKA – – – – – –
4
DFD
1
2
3
DFD
– – – PLLA4 – PRR – – – – –
PXX1A PXX2A
– – – – – – – – – PLLB1 –
– – PNN B – – – – – – PLLB2 PKKB
– – – – – – – – – PLLB3 –
– – –
–
– – PDKDKA
PXX1B PXX2B PDKDKB
DFD stands for Domestic Final Demand.
same capital-using technique. Similarly, PL, PX, PN and PR are the same in the two countries, as they use identical techniques in Sectors 1 and 2. Considering first Country A, there are three productive sectors, A1, A2 and A4. Sector A1 uses an input of Country A labour, of value PLL1A, to produce consumption good for Country A, of value PXX1A. Sector A2 uses labour and capital from Country A, of values PLL2A and PKKA, respectively, plus extracted natural resource from Country A, of value PNNA to produce consumption good for Country A, of value PXX2A. Sector A4 uses labour and unextracted natural resource from Country A, of respective values PLL4Aand PR R, to produce extracted natural resources for Countries A and B, of respective values PNN2A and PNN B. Country B also has three productive sectors, B1, B2 and B3. Sector B1 uses an input of Country B labour, of value PLL1B, to produce consumption good for Country A, of value PXX1B. Sector B2 uses labour and capital from Country B, of values PLL2B and PKK B, respectively, plus extracted natural resource from Country A, of value PNN B, to produce consumption good for Country B, of value PXX2B. Finally, Sector B3 uses an input of Country B labour, of value PLL3B, to produce new capital for Country A, of value PDKDKA, and new capital for Country B, of valuePDKDKB.
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J. Proops / Ecological Economics 48 (2004) 83–91
We can express these relationships algebraically, to give: A1
A PL LA 1 ¼ PX X1 ;
A2
A A A PL LA 2 þ PK K þ PN N ¼ PX X2 ;
i:e: PL l1 ¼ PX :
i:e: PL l2 þ PK k2 þ PN n2 ¼ PX : PL LA 4 þ PR R ¼ PN N ;
A4
¼ N A þ N B; B1
Y B=PLLB+PKK B+PNN BPDKDK A, i.e. Y B=PLLB+PKK B. For Country A, we also know: R=N=N A+N B=(KA+KB)n2/k2.
here R ¼ N
i:e: PL l4 þ PR ¼ PN :
PL LB1 ¼ PX X1B ;
For Country B:
i:e: PL l1
¼ PX ðas for A1Þ:
Using this, and substituting for the prices, we obtain: PR K2B n2 A A A l1 l2 l4 n2 Y ¼ PL L þ K þ k2 k2 and
B2 PL LB2 þ PK K B þ PN N B ¼ PX X2B ; i:e: PL l2 þ PK k2 þ PN n2 ¼ PX ðas for A2Þ:
l1 l2 l4 n2 PR K2B n2 Y B ¼ PL LB þ K B : k2 k2
B3 PL LB3 ¼ PDK DK; i:e: : PL l3 ¼ PDK :
We note that if we set K=KA+KB and L=LA+LA and sum the two GDPS, we obtain the same expression as for the single country (autarchy) model. Further, the terms containing PR are of the same size but oppositely signed, showing that while the resource rent has no effect on the (static) global GDP, it does affect the GDPs for the separate trading countries; i.e. it influences the distribution of the (static) global GDP. (This is analogous to the distributional effect of resource rents on the owners of natural resources and capital, as noted under autarchy.) If PR declines then, ceteris paribus, YA decreases and YB increases correspondingly. Thus, if Country B saves (and accumulates capital) out of GDP, this further increases the savings out of GDP for Country B. In line with intuition, one can show by comparative static analysis (or by simulations) that the following holds. If the resource rent is falling, then there is a tendency for the rate of growth of Country A also to fall, while that of Country B tends to rise. Therefore, a combination of trading relations determined by the availability of the natural resource and the ability to manufacture capital, combined with a falling resource rent, generates precisely the pattern of development we have observed over the past half century; i.e. the rich countries seem to grow at the expense of poor countries.
here DK ¼ DK A þ DK B
Using labour as nume´raire, (i.e. holding PL constant), and taking PR as exogenous, these equations can be solved to give:
PX ¼ PL l1 ; PK ¼
PN ¼ PL l4 þ PR ;
PL ðl1 l2 l4 n2 Þ PR n2 ; k2
PDK ¼ PL l3 :
Using the above prices and quantities, we can calculate the GDP ( Y) for each country, as: GDP= Value Added+ImportsExports. For Country A: Y A=PLLA+PKKA+PRR+PDKDKAPNNB. If the investment constraint is in operation for Country A, then the value of new capital for that country equals the value of natural resource exports: PDKDKA=PNNB; i.e. Y A ¼ PL LA þ PK K A þ PR R:
J. Proops / Ecological Economics 48 (2004) 83–91
Details of the effects of resource rents on the rates of economic growth are derived in the appendices. In Appendix A, it is shown that for the autarchy case, the rate of GDP growth is independent of the behaviour of the natural resource rent, depending only on the savings ratio and the technical coefficients. In particular, the rate of GDP growth increases if the coefficients relating to the natural resource (in extraction and use) are falling, in line with Wright’s (1990) argument. In Appendix B, the trade case is explored, with a derivation of the GDP growth rates for Countries A and B. For both countries we find that the rate of GDP growth depends on both the level of the resource rent and the rate of growth of the resource rent. The effect of a falling resource rent is in line with intuition. For Country A, it contributes to reduced rates of GDP growth, while for Country B, it promotes GDP growth. The consequence of a falling resource rent, as has been observed for almost all natural resources over the past century, is that rates of growth of the North will be boosted, while for the South rates of growth will be diminished. The consequence is clear: a continuing and potentially increasing inequality of income per capita.1
5. Policy discussion The standard argument in favour of trade between the North and South is that it allows the South to accumulate capital and therefore to achieve improved growth rates, and the potential to reduce both internal poverty and also transnational inequalities. In this paper, I have tried to show that if, as seems always to be the case, trade asymmetry exists so that the North exports capital goods and the South exports raw materials, then the consequences of the (almost universally observed) falling resource rents is that trade will not diminish
1
I am indebted to Anthony Friend for pointing out that this trade model could also be applied to regional growth disparities between regions in a single country, such as between the USA precivil war Union and Confederate states.
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transnational inequality. What are the implications of this finding? First, price support for raw material exports by the South may be necessary. One effective method of achieving this would be the drastic reduction of price support (both explicit and implicit) for raw material production (including agriculture) in the North. This would have the effect of increasing raw material scarcity, and so driving up natural resource rents. Second, there needs to be concerted international efforts to allow the South to become a producer of capital goods. Standard ‘‘infant industry’’ protectionist arguments can be used here. However, probably even more important is the transfer of technology from the North to the South, together with appropriate labour training. In conclusion, it should be stressed that it is unlikely that unfettered free trade will produce ‘‘trickle down’’ effects for the South while natural resources are apparently becoming less scarce, and while the North maintains its present monopoly on the production of the means of production.
Acknowledgements For their perceptive comments on an earlier version of this paper, I am grateful to the participants at a seminar at the Interdisciplinary Institute of Environmental Economics, University of Heidelberg, in October 2002.
Appendix A . Rate of growth of GDP under autarchy We have seen that under autarchy, the model gives GDP as:
ðl1 l2 l4 n2 Þ Y ¼ PL L þ PL K : k2 We can represent the (continuous) GDP growth rate as: r = (dY/dt)(1/Y). Recalling that h in Y, only i K varies with time, we see PL that: r ¼ dK dt Y
ðl1 l2 l4 n2 Þ k2
. Now, we suppose that
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savings is a fixed proportion of GDP, and all savings are invested in new capital. So we can write (in continuous time): PDK
dK dK sY sY ¼ sY ; i:e: ¼ ¼ : dt dt PDK PL l3
Substitution gives: r¼
sY PL ðl1 l2 l4 n2 Þ l 1 l 2 l 4 n2 ¼s : pL l 3 Y k2 l3 k2
We suppose that for Country B, savings are a fixed proportion (s) of GDP, and this is converted into new capital; i.e.: PDK(dK B/dt)=sY B; i.e. (dK B/dt)=((sY B)/ (PDK)). Recalling that: PDK=PLl3, we obtain: (dKB/dt)= ((sYB)/( PLl3)). Substitution for this in the expression for r B, followed by reorganisation, gives: rB ¼
sb sn2 PR n2 K B dPR : l3 l3 k2 PL k2 Y B dt
So the growth rate of GDP is independent of the behaviour of the natural resource rent. It depends only on the technical coefficients of production and the savings rate. (For an alternative derivation of this result, without natural resources, see Faber, 1978, p. 158.)
So the rate of GDP growth for Country B has three components. First, a constant, identical to the rate of growth under autarchy. Second, a component that varies with the resource rent. Third, a component that varies directly with the capital stock and the rate of change of the resource rent, and inversely with the GDP of Country B.
Appendix B . Rates of growth of GDP with Trade
B.2 . Growth rate of GDP for Country A
We have derived the following as the GDPs of the two trading countries:
We define the rate of growth for Country A as: r A=(dYA/dt)(1/YA). Differentiating the expression for Y A and substitution gives: 1 dK A n2 dK B dPR bþ þ KB PL PR rA ¼ : YA dt k2 dt dt
l 1 l 2 l 4 n2 PR K2B n2 Y A ¼ PL LA þ K A þ k2 k2 l 1 l 2 l 4 n2 PR K2B n2 Y B ¼ PL LB þ K B : k2 k2 4 n2 We define: bu l1 l2kl to give: 2
PR K2B n2 and Y A ¼ PL LA þ K A b þ k2
PR K2B n2 Y B ¼ PL LB þ K B b k2 B.1 . Growth rate of GDP for Country B We define the rate of growth for Country B as: rB=(dY B/dt)(1/Y B). Differentiating the expression for YB and substitution gives: 1 r ¼ B Y B
dK B n2 dK B B dPR PL b þK PR : dt k2 dt dt
We suppose that Country A investment is constrained by the value of natural resource exports; i.e.: PDK(dKA/dt)=( PNN B). Reorganisation and substitution gives: dK A ðPLA l4 þ PR ÞK B n2 ¼ : dt pA L l 3 k2 We have already derived above the expression for dKB/dt. Substituting these in the expression for rA, and reorganising, gives: rA ¼
n2 l4 bK B PLA n2 bK B PR n2 sY B PR þ þ k2 l 3 Y A k2 l3 Y A k2 l 3 Y A B n2 K dPR : þ k2 Y A dt
Here the rate of growth of GDP depends on four components; for each it varies inversely with the GDP
J. Proops / Ecological Economics 48 (2004) 83–91
of Country A. For the first component, it also varies directly with the capital stock in Country B. For the second, it again varies directly with the KB, but also with the resource rent. The third varies directly with YB and the resource rent, while the fourth varies directly with K B and the rate of change of the resource rent. References Barnett, H., Morse, C., 1963. Scarcity and Growth: The Economics of Resource Scarcity. Johns Hopkins Univ. Press, Baltimore, MD. Faber, M., 1978. Introduction to Modern Austrian Capital Theory. Springer, Heidelberg. Faber, M., Proops, J., 1993. Natural resource rents, economic dy-
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namics and structural change: a capital theoretic approach. Ecological Economics 8, 17 – 44. Faber, M., Proops, J., 1998. Evolution, Time, Production and the Environment, 3rd ed. Springer, Heidelberg. Faber, M., Proops, J., Speck, S., 1999. Capital and Time in Ecological Economics: Neo-Austrian Modelling. Edward Elgar, Cheltenham, UK. Jo¨st, F., 1996. Climate change and economic development: a neoAustrian approach. In: Faucheux, S., Pearce, D., Proops, J. (Eds.), Models of Sustainable Development. Edward Elgar, Cheltenham, UK, pp. 187 – 204. Liddle, B., 2001. Free trade and the environment – development system. Ecological Economics 39, 21 – 36. Proops, J., Faber, M., Wagenhals, G., 1993. Reducing CO2 Emissions: A Comparative Study for Germany and the UK. Springer, Heidelberg. Special Issue, 1994. Ecological Economics 9, 1 – 97. Wright, G., 1990. Origins of American industrial success, 1879 – 1940. American Economic Review 80, 657 – 668.