Export efficiency of large projects

Export efficiency of large projects The case of aluminium smelters

Paul van Moeseke

We draw attention to a number of key factors in the evaluation of major projects, such as smelters, which are highly capital- and energy-intensive as well as export-orientated. The practice of justifying such projects by upvaluing foreign exchange is considered, as is the cost of distortion. Export efficiency is introduced as the key criterion: the efficiency of some recent smelter proposals in Oceania was between 36 and 50 cents in the dollar. A correct power price is essential: hydropower (in contrast with hydroenergy) should be priced as a depletable resource. Keywords:

Exports; Efficiency; Aluminium

Paul van Moeseke is Professor and Head of the Department of Economics, Massey University, New Zealand. Research was initiated during the author’s tenure of the Professorial Fellowship in Economic Policy of the Reserve Bank of Australia, whose generous support is gratefully acknowledged. He is indebted to Anthony Bird Associates (Kingston upon Thames) and to Drs F. Vande Ginste (Brussels) for research data on current electricity prices to smelters; and to Professor M. Kemp (Sydney) for discussions on depletion theory. He owes several helpful suggestions to the referee. ‘P. van Moeseke, ‘Aluminium smelting in New Zealand (The First Report)‘, fconomic Discussion Paper, No 8008, 1980, Otago University, New Zealand. ‘P. van Moeseke, ‘Aluminium and power (The Second Report)‘. Economic Discussion Paper, No ‘8105; 1981, Otago University, New Zealand. 3P. van Moeseke, ‘Aluminium and power: continued on p 111

110

The main thrust of this article is that the worldwide reallocation of smelter capacity ought to be coordinated in view of the serious planning errors made in the recent past, leading to the scrapping or mothballing of five planned smelters in Oceania alone (Aramoana in New Zealand; Bunbury, Bundaberg, Lochinvar and Portland in Australia). Since adequate information is the prime prerequisite of the competitive market this coordination can be left to market forces if location is based on correct energy costing. Remembering that aluminium is essentially solid electricity, I proposed in an address to the World Aluminium Congress in Monte Carlo that an international agency like UNIDO or the World Bank start listing independent estimates of the long-run marginal cost of power in all potential host countries. This would save both them and the companies concerned risk and expense, relieve pressure on governments to negotiate uneconomic deals for political reasons and promote efficient worldwide smelter location. The proposed measure is purely indicative, rather than coercive, and therefore entirely consonant with free competition. The measure would further constitute the first concrete step towards the New International Economic Order within a major commodity market. As well as the long-run marginal cost of the supposedly cheap power prospective host nations have to offer, relocation will have to take into account their point of view in determining the export efficiency of smelters (net foreign earnings per dollar’s worth of domestic resources absorbed). It is already apparent that correct economic analysis puts the industrial nations and classical producers at a lesser comparative disadvantage than was thought. The severe cutbacks in planned smelter capacity in Australasia, for instance, are at least partly due to economic reappraisals, such as the author’s smelter reports,‘-3 written from the national, rather than the corporate, point of view, and which evaluated the net benefits of a multinational enterprise requiring huge investment in power plant by the host country. If the industry majors are to avoid expensive relocation mistakes they will have to make sure planned greenfield smelters stand up to economic analysis.

0301-4207/85/0201

lo-09$03.00

@ 1985 Butterworth

& Co (Publishers)

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Export efficiency of large projects

Relocation plans, in the wake of the oil crisis, from the industrial to the peripheral nations, essentially marked a trade-off between cheap power and market distance, the cost of stricter environmental controls in industrial areas being a subsidiary factor. On the local level, in the absence of overall economic impact studies, feasibility reports commissioned both by companies and local governments stressed regional employment and gross earnings from electricity payments. The real cost of reallocating smelter capacity has been vastly underestimated, and the net benefit overestimated. Specifically, and summarizing the main points to be discussed in the article:

0

0

a

0

0

continued from p 110 the host nation’s export efficiency’, Metal Bulletin, Proceedings of the Second International Aluminium Congress, 1983, pp 81-7. %ee P. van Moeseke, ‘Depletion pricing of hydropower: the case of smelters’, Natural Resources Forum (UN), Vol7, 1985 (forthcoming).

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The amount of gross foreign earnings, normally the chief, if not the sole, objective of smelter projects in the ‘new’ locations, is by itself meaningless. The relevant criterion is export efficiency, ie net foreign earnings per unit of domestic value added. Low export efficiency has been justified by the practice of ‘upweighting’ foreign exchange, ie valuing foreign earnings considerably above par (by 100% and more). We show that this operation normally involves a logical error and runs counter to the scarce-factor propositions of the theory of international trade: advocating large, capital-intensive projects in developing economies with surplus labour strains commonsense, accelerates inflation and can be shown to be inefficient. Standard cost-benefit analysis at given prices, while appropriate for evaluating, say, a new road bypass or hospital, is simplistic in the case of projects, such as smelters, that are large relative to a small economy and affect the nation’s electricity and capital supply, as well as their relative prices, significantly. It is shown how the magnitude of the cost of distortion can be approximated. Several basic theoretical errors have repeatedly been made in estimating the economic welfare cost of power to the nation. It is erroneous, inter alia, to cost extra capacity for a giant baseloader, to be supplied on top of present peak demands, at standard concessionary rates. Furthermore, in the case of hydropower plants, it is essential to know that hydroelectricity is a twin resource, namely hydroenergy, which is renewable as long as it rains, and hydropower, which is depleted as the remaining suitable river valleys get dammed and the corresponding power blocks auctioned off in very long-term contracts. What a smelter really buys is precisely hydropower since its hydroenergy cost, essentially distribution cost per unit, is very small. As hydropower is depletable it is subject to depletion pricing, ie efficient allocation implies that its price, like that of any depletable resource, be subject to a secular rise at the social rate of discount (so-called Hotelling rule). In any case competition with fossil fuels, as well as substitution at the margin, subjects power to depletion pricing. Other factors determining the rising long-run marginal cost of power are summed up in the final section of the paper.4

On a more practical level, regarding specifically the relocation and expansion of the aluminium industry in the author’s part of the world, Australasia, it is obvious that New Zealand possesses none of the relevant comparative advantages (bauxite, cheap power, industrial and capital markets, environmental tolerance): no aluminium company

111

Export

efficiency of large projects

would locate in New Zealand if it had to generate its own power. While the existing Comalco smelter at Tiwai Point has consistently posted reasonable results and expanded its capacity this was possible only because its secret power price is known to be a fraction of the current long-run marginal cost of New Zealand hydropower. Indeed I showed in my report’ that a second smelter, to be viable, would, on long-run price trends, need to have its power heavily subsidized. Australia possesses all the above-mentioned comparative advantages to some extent although, again as forecast in my report6, the euphoric projections of a fourfold capacity expansion to more than 1.5 m tonnes have since been cut back to some 975 000 tonnes’ following the cancellations already referred to. (The fate of the Portland smelter is still in the balance at the time of writing, February 1985.) Australia’s abundant supplies of both bauxite and steaming coal assure it a significant role in aluminium production: at 45c/lb (mid-1984 US cents) its production costs compare very favourably, according to Anthony Bird’s’ recent figures, with those in the USA (64~) and Japan (64~); only Quebec’s (43~) are slightly lower.

Export effkiency

and exchange premium

We define the annual positive fraction E = Net Foreign

export

Earnings

efficiency

(NFE)lDomestic

which measures the efficiency (ideally are traded. If one puts q = l/E the net annual (l-q)

5P. van Moeseke, op cif, Ref 1. 6P. van Moeseke, op tit, Ref 1. 7J.A. Cook, ‘Australia’s aluminium expansion - a look at progress and thoughts for the future’, Metal Bulletin, Proceedings of the Second international Aluminium Congress, 1983, pp l-8. production ‘Anthony Bird, ‘Aluminium costs’, Third International Aluminium Conference, Munich, September 1984 (unpublished).

112

of an export

Value

operation

Added

2 1) at which domestic social benefit

NFE = NFE - DVA

as the

(DVA) resources

of the project

is (1)

which is, of course, negative if the project is inefficient (E < 1). If Equation (1) is negative q measures the shadow price of foreign exchange required, ceteris paribus, to make the project break even; equivalently, q-l is then the required premium on foreign exchange. The ceteris paribus clause is essential as pointed out below. For concrete examples of the measurement and use of those concepts the reader may refer to my reports ‘I 2 on two smelter projects - since cancelled - in New Zealand with estimated efficiencies of E = 35.6% (q = 2.8), respectively E = 50% (q = 2). This means that, under then prevailing conditions, domestic resources earned, dollar for dollar, nearly thrice, respectively twice, as much foreign exchange in traditional export activities, or that, at the then rate of exchange, $2.80, respectively $2, of domestic inputs were required per dollar of foreign exchange earned. It is pointed out in the next section that upweighting of foreign exchange in this case involves a logical error. Computing the export efficiency E is straightforward when practically the entire smelter output is to be exported as is the case for new smelters in Australasia, where existing and committed capacity already far exceeds local demand. Let exports of value y > 0 absorb II different inputs of value Xj > 0 (j = 1, . . . , n with foreign content mj (0 2 mi ‘1, all j) where mj =l if all of input j is imported and is zero if it is a purely domestic factor. In particular if i refers to capital then mj is the fraction of return on capital

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Export efficiency of large projects

paid overseas. Further, foreign-owned fraction to be in equilibrium.

if Xj is depreciation then mj corresponds to the of equity capital. The exchange rate is assumed

Define Net Foreign Earnings (NFE) = y - Cmyj Domestic Value Added (DVA) = X(1-mi)xj The concept E = 0, -

of export

efficiency used in this paper

XmFj)lC(l-mj)xj

is

= NFEIDVA

where it is assumed, trivially, that NFE 2 0, DVA > 0 value informs Clearly E $1 according as y z Xx, so that market efficiency, which equals at least 1 or (100%) if the operation at least breaks even. The formula is, of course, more involved if part of the output is sold in the home market.

Upweighting ment

‘P. Dasgupta, S. Marglin and A. Sen, Guidelines for Project Evaluation, UN IDO (Vienna), United Nations, New York, 1972. “‘G Irvin, Modern Cost-Benefit Methods, Macmillan, London, ,1978. “I.M.D. Little and J.A. Mirrlees, frojecf Appraisal and Planning for Developing C&ntries, Heinemann, London, 1974: _ “OECD. Manual of industrial Proiect Analysis; Vols I and II, Paris, 1968. ’ 130ECD, Memo& of Project Appraisal in Developing Countries, Paris, 1973. 14L. Squire and H. van der Tak, Economic Analysis of Projects, Published for the World Sank, Johns Hopkins University Press, 1975. 15E. Eisenberg, ‘Duality in homogeneous programming’, Proceedings of the American Mathematical Society, Vol 12, 1963, pp 783-787. “P. van Moeseke, ‘Duality theorem for convex homogeneous programming’, Metroeconomica, Vol 16, 1964, pp 32-40. “P. van Moeseke, ‘Saddlepoint in homogeneous programming without Slater condition’, Econometrica, Vol 42, No 3, 1974, pp 593596. ‘*G. Leblanc and P. van Moeseke, ‘The Le Chatelier principle in convex programming’, Review of Economic Studies, Vol 43, No 1, 1976, pp 143-147. igP. van Moeseke, op cif, Ref 1. *OP. van Moeseke, op cif, Ref 2. ” The Economist, 15 March, 1980.

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foreign exchange and capital intensive develop-

Note that the shadow price of foreign exchange is determined ex post, and is a notion very different from an ex ante and arbitrary premium often advocated by planning officials. Given existing trade restrictions the true shadow price might, in the UNIDO and LMST approaches,%14 be estimated ex ante by the weighted domestic-to-border price ratios of tradables in the marginal trade bill under a number of assumptions including given relative commodity prices. But a major project affects relative resource prices so that naive shadow pricing involves a logical error. This is easily demonstrated, given the official objective of maximizing the project’s net foreign earnings. Upvaluing the latter by a factor q implies that prices of domestic inputs should be upvalued by the same factor q so that the operation is nugatory since both numerator and denominator in E are multiplied by q. This is easily demonstrated. Denote aluminium production by a, NFE by n(a), and the mtuple of resources used by R. As a and n(u) are proportional to the amount of resources used, by the duality theorem of homogeneous the optimal output a* satisfies n(a*) = v*R, where v* programming’sP17 is the mtuple of resource shadow prices (rents). It follows at once that upvaluing iz by a factor q yields qn(a*) = (qv*)R. While this observation is immaterial for redundant factors it definitely applies to electricity; and the DVA of this factor alone is of the same order of magnitude as total NFE. This is an illustration of one of the two main scarce-factor propositions in trade theory, namely the StolperSamuelson theorem, which implies that an increase in the price of (or imputation of a premium or subsidy to) a commodity (aluminium) increases the value of the factors intensively used in its production (electricity). The theorem is an early instance of the Le Chatelier effectls in economics. The duality theorem, however, allows us to quantify this purely qualitative statement with precision. By any standard aluminium smelting is one of the most capital- and energy-intensive major industries and hence among the least labourintensive. Investment was about $lm per employee in 1979-8019,20 or some 27 times the $36 252 average for 19 major British industries.” Even this 113

Export efficiency of large projects

figure underestimates total investment by excluding public funding of roading and harbour facilities (quite apart, of course, from the required additional electric capacity). It is noteworthy that gross sales per job, for instance, are about 13 times higher than for the US aerospace industry,22 which one would think of as particularly capital-intensive. The standard complaint about developing nations’ overvalued exchange rates cum investment incentives is the distortion induced by thus subsidizing capital costs relative to labour costs. Upweighting foreign exchange, hence capital cost, is designed precisely to counteract this effect in favour of less capital-intensive projects, contrary to common official practice. Advocating large, capital-intensive projects while simultaneously upweighting borrowed capital, as has often been done to justify major projects, in an economy with surplus labour, strains commonsense, accelerates inflation and runs counter to both neoclassical production theory and scarce-factor propositions. Indeed under standard assumptions about the Net National Product as a production function in terms of the factors labour and capital, it can readily be shown2” that, if the return on capital is given in the world market (so-called ‘small country’ assumption), capital-intensive development is efficient only if the real wage is upvalued. At constant real wages, on the contrary, a capital-intensive move to a higher income level is shown to be inflationary as well as inefficient (isocost cuts isoquant): the same income level may be realized by employing more labour and borrowing less capital. Clearly, it is the labour-intensive move that reflects the relative upweighting of foreign exchange and downweighting of labour. This conclusion is an illustration of the second scarce-factor proposition, the Rybczynski theorem, whereby overendowment of one factor (labour surplus) ought to expand the industry that absorbs it relatively intensively. It has received strong empirical support in findings by, inter ah, the World Bank24.2” and the NBER,26, which have warned repeatedly against overemphasis on vast capital-intensive projects, so-called white elephants, in developing countries. The 1979 World Development Report2’ rightly complains that:

=P. van Moeseke, op tit, Ref 2. 23P. van Moeseke, op cif, Ref 2. 24A. Mashayekhi, Shadow Prices for Project Appraisal in Turkey, Staff Working Paper No 392, World Bank, Washington DC, 1980. 25World Development Report, World Bank, Washington DC, 1979. ‘Alternative =A.O. trade Krueger, strategies and employment in LDCs’, American Economic Review (Papers and Proceedings), Vol68, No 2, May 1978, pp 264-283. 2700 cit. Fief 25. 28BrPhiipott and A. Stroombergen, Unemploiment and Structural Change, Project on Economic Planning Occasional Paper No 41, Victoria University, August, 1980.

114

Despite their obvious abundance of labour, many developing countries have encouraged capital-intensive industrialization. . .by artificially lowering the price of capital to the modern private sector. Subsidized interest rates, allowances for accelerated depreciation, tax holidays, overvalued exchange rates, and facilities for duty-free imports of capital have enhanced the profitability of capital-intensive investments and often encouraged enterprises to economize on labour rather than on capital. In New Zealand that the 1980-85 if anything,

Philpott and Stroombergen’s2s major energy projects may,

[be] deleterious

to employment

PEP model

indicated

[because of their] very low labour

intensity

and high import intensity and the fact that the substantial block of investment involved, reduced resources available for other and more employment creating types of investment.

Distortion: income effect or deadweight loss Comparing two alternatives by straightforward cost-benefit analysis at given prices is acceptable for investment plans that are small relative to the economy (construction of a road bypass, say) but simplistic in the

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1985

Export efficiency of large projects

case of major projects. The latter imply a considerable shift along the opportunity frontier (from position 1 to position 2 in Figure 1) and, under standard assumptions, a corresponding drop in real income at present prices. (Unless the frontier expands - but if there is a net loss as in the low-efficiency examples given earlier the reverse holds.) The figure graphically illustrates the frontier in the space of inputs x (electricity) and y (real index of all other inputs), where Ax represents the increase in electricity cost Ay the corresponding drop in real National Income (iVZ) at current factor prices. This cost is a ‘pure’ distortion and is apart from, and in addition to, subsidy S which supplements payments C at the low rate (dotted slope) charged to the smelter consortium. It prescinds the higher marginal cost (slope of frontier in 2) that ‘should’ prevail in position 2 or the possibility that through inefficient reallocation the distortion is even greater through contraction of the opportunity frontier (position 2’), as in the examples earlier. If one solves y = g(x) from the transformation curve f(x,y) = 0 of Figure 2 the magnitude of Ay can be approximated by the second term,

l/2( Ax)‘g”(xO)

29P. van Moeseke, op tit, Ref 2. 30R.H. Court, ‘Defective energy planning and the need for more public information’, New Zealand Economic Papers, Vol 13, 1979, p 24-35.

(2)

of a Taylor series, where g” is the rate of change of marginal cost (MC) in cents/unit2 (cents per unit-squared). Since we face a rising average cost (AC) curve the increase in the MC of electricity due to smelter expansion rises even faster (twice as fast, in linear approximation). In the New Zealand context2” for example, if the cost increases by II cents for a production increase Ax of some 4500m units (or kWh) per annum then, by Equation (2), Ay = 22.5 n (in $m) or $22Sm ($45m) for a lc (2~) increase in MC (corresponding roughly to a V2c (lc) increase in AC). These amounts may be compared to the $50m per annum deadweight loss Court3’ arrives at for a 500 MW capacity increase (which, in his article, refers to errors in power forecasts), or roughly the

Ax

Expansion

Ay Deadweight loss S

Subsidy

C

Payment by consortium

NI

f(x,Y) = 0

National income

/

f

II 5.

INI \

\i

2’Y\ Ax Figure 1. Cost of distortion.

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I \

’

x=GWhpa

115

Export efficiency of large projects

immediate requirement for new capacity, namely a third potline at the existing smelter, plus a second smelter, had the latter gone ahead.

Risk allowance The vast commitment of resources to just one primary product, a volatile metal at that, is a great risk, particularly for a small economy. The risk is compounded by the high energy content of the inputs. To omit the risk allowance from the quantitative appraisal of projects of this size is unacceptable. Risk-efficient decisions are guided not just by expected value, which has been the sole criterion so far but by a weighting of, for instance, both expectation and standard deviation of net returns (truncated minimax31 Markowitz efficiency). Relative weights in the range 0.5 1.5 for the itandard deviation appear reasonable on both theoretical and empirical grounds.32T” A coefficient of variation of average annual aluminium prices of at least 7% around the trend line seems realistic statistically but margins on semis vary more widely. Even if one takes only this variation into account a conservative decision, attaching a unit weight to the standard deviation, would not be based on expected value but on a 7% risk discount, say, which by itself exceeds total labour cost, for instance. Actually, the covariances of all inputs and outputs ought to be included, in particular the risk of high levels of oil burning in dry years, given the often tight construction schedules of the required and the cost of blackouts in case of power failure due to hydrostations,34 the total inelasticity of a smelter’s power demand. The determination of these risk factors and their covariances evidently warrants a separate study. In the long run the gravest risk, perhaps, is the expected constancy, in real terms, of the aluminium price if the electricity charge is tied to it, while the energy-determined prices of imported materials, as well as the opportunity cost of power (below) rise exponentially.

The rising marginal cost of electricity

31P. van Moeseke, ‘Minimax-maximax solution to linear programming under risk’, Economefrica, Vol 31, October 1963, pp 749-750. 32P. van Moeseke, ‘Stochastic linear programming’, Yale Economic Essays, vol 5, Sorina 1965, DD 197-253. 3’P. tan MO&eke, ‘Towards a theory of efficiency’, In J. Quirk and A. Zarley, eds, Papers in Quantitative Economics, University Press of Kansas, 1968. %.f Electricity Division, Ministrv of Energy, Report of thk Electricity Sect& Planni%g Committee 7980, unpublished, Wellington, August, 1980.

116

The real marginal cost of electricity must rise significantly with any large-scale power addition, for at least four reasons. First, the Samuelson-Stolper theorem: if the world price for a traded commodity rises (or, equivalently, if the commodity is subsidized) the real price of a factor which it absorbs relatively intensively, in this case energy, increases. Second, since the LAC (long-run average cost) curve is rising it is axiomatic that the LMC (long-run marginal cost) curve rises even faster (Figure 2). Efficient allocation requires that all other consumers pay the higher price (‘extra payment’ in Figure 2) irrespective of smelter subsidy. If the smelter is subsidized beyond, say, average cost they should pay the further amount indicated as ‘subsidy’ in the figure. Researchers often underestimate the present value of electricity cost by charging periods rather than the (suitably prices a, b, c. . .in successive discounted) final LMC throughout, thereby ignoring the so-called producer surplus. The error is very significant: initial under-costing (typically at less than lc/unit until 1990) is decisive, while higher costs later on matter little because at discount rates of, say, lo%, discount factors beyond the first decade are very large.

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Export efficiency of large projects

LMC /

_--

/

___----------------

I I I Extra payment

.?i

1;’ Subsidy,/ I

I

i I

-5 Y

_--ZY;I-

/

(GWhpa)

I I I

I

I

Extra hydrocapacity

Figure 2. Long-run marginal

electricity cost: (LMC) and average (UC).

35For further information on subsidized power charges in Australia consult P.L. Swan, ‘Pricing of electricity to Alcoa at Portland’, Victoria, Department of Economics, Australian National University, 1981, (unpublished); H.W. Dick, ‘Aluminium smelters and the price of electricity’, In Socio-Economic Survey of the Hunter Region, Hunter Social Research Coop, 1980; and P. Crabb, ‘Hydroelectric power in Newfoundland, Tasmania and the South Island’, Three Nations Conference, Christchurch 1980 (unpublished). %ee F.H. Gruen and A.L. Hillman, ‘A review of issues pertinent to liquid fuel policy’, Economic Record, Vol 57, No 157, June 1981, pp 11 l-l 27. 37P. van Moeseke, ‘Depletion pricing and intergenerational allocation’, In H. Siebert, ed, Ersch@fbare Ressourcen. (Verhandlungen des Vereins fiir Socialpolitik, Mannheim, 1979), Duncker & Humblot, Berlin, 1980. 38P. van Moeseke, op tit, Ref 2.

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The above argument can be obviated only in the case of horizontal cost curves. These, however, are excluded by the Hotelling rule (below), even in the presence of a so-called backstop resource such as lignite coal: indeed, it is not the full extraction cost of lignite that ought to be charged but its opportunity cost, which must rise exponentially like that of oi1.3” The notion of expanding hydropower at constant LMC is simply a logical error, not an accounting matter. Third, without entering into a disquisition on the complex welfare calculus of peakload pricing, it is intuitively clear that rate reductions for large baseloaders within a system of given capacity cannot simply be extended, in general, to extra capacity for a baseloader who needs guaranteed constant power 24 hours a day, every day of the year, to be supplied on top of present peak demands. This follows at once from the observation that, in equilibrium, LMC 2 SMC. (Since the LAC curve is an envelope of SAC curves LMC < SMC would imply suboptimal hydrocapacity, where SMC, SAC denote the short-run curves.) Fourth, hydroenergy is evidently, to a considerable extent, a substitute for depletable fossil fuels.36 The key result of depletion pricing, the so-called Hotelling rule, implies that the real rent of a depletable resource rises exponentially over time at the (social) rate of discount: so, therefore, will, in dynamic equilibrium, the opportunity cost of existing hydropotential as well as the marginal value of hydroinvestment. Intuitively, the rising capital costs sunk in deeper and less accessible wells, offshore exploration and shale development imply, by substitution, a corresponding rise in the marginal value of investment in, inter aEiupower dams and coal mines. The validity of the Hotelling rule can be generalized to multi-resource depletion programming.37 I have argued elsewhere38 that hydropo wer, as distinct from hydroenergy, should be treated like a depletable resource. An immediate corollary of the rule is that the cost of electricity should not be discounted over time because the exponential rise exactly cancels

117

Export efficiency of large projects Table 1. Power cost of electricity (dkWh).

Notes: k: current power cost. h: equivalent constant cost (Hotelling value) over the 42%year smelter lifespan.

Discount rate

Upper Clutha (mid-1990 $)

Lower Waitaki (early-1960 $)

r (%)

k

h

k

h

4 5 6

1.33 1.54 1.76

2.76 3.71 4.08

1.51 1.75 2.00

3.13 4.22 5.54

the discount. Conversely, if the price of electricity is indexed by an aluminium price that is approximately constant over time in real terms, then the index base itself should be adjusted, by the Hotelling rule, for the increase in the opportunity cost of power over time. A possible alternative is to tie the power component of the electricity price, if not to oil, at least to the OECD GDP deflator or some such index.3y If k is the cost of one unit at time t = 0 its opportunity cost at time t equals ke” and the Present Discounted Value of one unit per annum over T years is T s

(ke”)e-”

dt = kT

0

Consequently, (in real terms) should satisfy

if the electricity over time then,

charge h were by contract to be constant in order to cover the opportunity cost, it

T

s

he-”

dt = kT

(3)

0

so that

h = rKT/(l--eprT)

3gH.J. Barnett, G. van Muiswinkel and M. Shechter, ‘Are minerals costing more?‘, HASA Working Paper 8120, Laxenburg, February, 1981. 4oP. van Moeseke, op cif, Ref 2. 4’New Zealand Press Association, 14 February, 1981.

118

(4)

The cost of the hydroelectricity consists of charges for hydroenergy (kWh) and hydropower (kW). Neglecting the former, which are relatively minor for a large baseloader, Table 1 lists, by way of illustration and for different values of r, the current power cost k and the much higher corresponding equivalent constant cost (or Hotelling value) h for the five Upper Clutha River stations and for the ten Lower Waitaki River stations in New Zealand. The Upper Clutha mid-1980 capital cost of $813m for 3 000 GWh per annum was derived in an earlier paper. 4o The ‘early-1980’ Lower Waitaki figure is $923m (about $1230m for 4000 GWh per annum according to the New Zealand Press Association).41 More generally, if the electricity charge is linked to the aluminium pricep(t), indexedp(0) = 1, by a formula h = h@(t)) then the left side of Equation (3) takes the value L[h(p(t))] ;f of the corresponding Laplace transform. If the charge is simply proportional to p(t) and the price trend is p(O)e”’ one substitutes (r-a) for r in Equations (3) and (4).

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