Hydroelectric rent and precipitation variability

Hydroelectric rent and precipitation variability The case of Norway Eirik S. Amundsen and Sigve Tjetta

Norway is about to reorganize its electricity production sector from a predominantly administered one to one which is based on market prices and principles of eficiency. The objective of this paper is to model the energy sector and to measure the size of hydro rent before and after the reorganization. We construct a regionally diversified and integrated equilibrium model of production, transmission and distribution of hydroelectricity. Particular attention is paid to the role of precipitation variability for the size and regional variation of hydro rent. We consider alternative routes for assessing the size of hydro rent in a long-run perspective. Keywords

: Energy modelling ; Hydroelectric rent ; Precipitation variability

local authorities) to the various users of electricity and in particular to large energy-intensive industries (Bye and Strom [7]). With the introduction of market prices, hydroelectric rent (or abbreviated : hydro rent) will be made commonly observable and it will show up where Nature’s scarcity exists, ie at the production site. Here, we set out to measure the size of the hydro rent before and after the reorganization of the electricity sector. In so doing we construct a regionally diversified and integrated equilibrium model of production, transmission and distribution of hydroelectricity along the same lines as the model ELNET developed by Mathiesen (Mathiesen [ 111, Bjorndalen and Tjotta [6]). In addition to installed production infrastructure, the main factor determining electricity production is precipitation. This varies both annually and regionally, and precipitation variability may result in a production discrepancy of up to 15-20% on either side of the national mean. Compared to existing literature in this field (eg Bernard [3] ; Bernard, Bridges and Scott [4] ; Jenkins [lo] ; Bernard and Cairns [ 51; Hartman and Lindblom [ 93 ; Amundsen, Andersen and Sannarnes [2]), this paper diverges in that it takes account of the influence that the annual and regional variation in precipitation has on the generation of hydro rent.

Like many other countries (eg New Zealand and Great Britain), Norway is about to reorganize its electricity sector from a predominantly administered one to one which is based on market prices and principles of efficiency in production, transmission and distribution.’ Along with the price changes that are bound to result from this reorganization, there will also be changes in economic rent generated in hydropower production. Hydropower is particularly important in Norway as it accounts for about 99% of total electricity production. Until now a fallacious principle of ‘no-rent’ pricing has resulted in a considerable dissipation of economic rent away from producers (mainly the state and the Eirik Schrsder Amundsen is with the Department of Economics, The University of Bergen, and Centre for Research in Economics and Business Administration, Jonas Reinsgt. 19, N-5008, Bergen, Norway. Sigve Tjertta is with The Norwegian School of Economics and Business Administration and Centre for Research in Economics and Business Sandviken,

Administration,

Helleveien

30,

5035

Bergen-

Norway.

Final manuscript

received

9 October

1992.

Financial support from NORAS and the Ministry of Finance is gratefully acknowledged. We are indebted to Lars Mathiesen and colleagues for valuable comments and to Jorgen Bjorndalen for research assistance. The paper benefited from a presentation at the XXXIItme Colloque International de I’ Association d’Economttrie applique,‘Modelisation des Marches internationaux de L’Energy, Montpellier, France, October 1991.

0140/9883/93/020081-11

0

1993 Butterworth-Heinemann

‘Cf The Ministry of Oil and Energy, ‘Law on production, transformation, transmission, sale, and distribution of energy’, Parliamentary Bill (St.prp.) No 43 1989/1990, Oslo, May 1990.

Ltd

81

Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjotta

Model and gains from reorganization The current organization of the Norwegian electricity sector is characterized by fixed and discriminating price regimes. For instance, while the power-intensive industry, which accounts for approximately a third of total domestic demand, paid on average 110 NOK/MWh in 1989, the residential and household sectors paid about 330 NOK/MWh. The big power-intensive companies (eg in wood and aluminium processing) normally purchase electricity directly on the wholesale markets on long-term contracts, fixed in price and quantity. The terms of these contracts are not determined by the market, but are influenced by various political considerations. The contracts are not renegotiable, and are generally not subject to secondhand trade. The other groups of domestic end-users purchase the power from distribution companies, which in their turn purchase the power on the wholesale markets. Also, for these groups prices are administered so as to attain the non-profit/no-loss objective of public utilities. Quantities are, however, not subject to regulation. At the wholesale level, derived demand from these groups of end-users may, therefore, be seen as determined by contracts fixed in price but not in quantity. Wholesale power supplied to satisfy end-use demand on contract terms (ie both for power-intensive companies and other end-users) will be referred to as fixed power. Around 90% of all hydropower is supplied in this way. The remaining wholesale supply is dealt with through a flexible market, and consists of deliveries of interruptible or occasional power and of exports. Here prices are determined by the market. In dry years imports of power may occur to fullfill the obligations to the customers in the contract markets. In wet years, exports may take place. The intention of the new market organization of the electricity sector is to put competitive pressure on the wholesale markets so as to promote efficient pricing. Here the guiding principle is that price differences for electricity should only reflect variation in quality (ie probability of delivery shortfall) and transmission costs. Model structure

In the following we model the electricity sector at the level of the wholesale markets. This is done both for the current organization and for the proposed new organization of the markets. We consider nine geographically diversified producer regions i (i E I) supplying electricity via a transmission network to four geographically distinct wholesale markets m (rn~M). (Names of producer regions and wholesale markets are reported in the tables and in Appendix

82

PKGdUCXr

Transmission

\I\lholesde markets

Distribution

Ed-USS segments

Figure 1. Structure of the model. 1). In each of these wholesale markets demand is derived from the demand in the various end-use segments (see Figure 1). Each producer region has a production capacity ti depending upon installed infrastructure and precipitation. A total production level qi is chosen such that 0 < qi < &. Variable production cost is given by Ci(qi) = uiqi, where vi is a strictly positive constant. Only the variable production cost enters directly into the models presented below, but in order to calculate hydro rent, data on capital costs are also necessary. Here, capital costs of power generation are annuitized using standard procedures.2 The cost structure (fixed and variable costs) is summarized in industry cost curves (or Salter diagrams) for each producer region, showing the relationship between annuitized cost per MWh and production capacity. These cost curves are based on average precipitation. When precipitation deviates from its average value, the cost curves change. The change in these curves is determined in such a way that the total cost (per unit annuity multiplied by production) in each cost category remains constant as precipitation changes. 2The present value of real investment and operating costs for a power plant are calculated and distributed as an annuity per MWh over the expected life of the power plant at the relevant real discount rate. Our investment cost data are based on each of 42 geographically dispersed power plants covering some one third of the total Norwegian electricity generation. The cost annuity is evaluated per l/7 1988 with an assumed life of 60 years and a real discount rate of 7% which is the rate proposed by the Ministry of Finance for public investment projects. These unit costs are applied with other information to construct the industry cost curves.

ENERGY

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Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjotta

The transmission network is defined by a set of sale-activities, S(i), for each producer region. Here, we use the same network formulation as Mathiesen [ 121, which allows us to identify each region’s sale to each wholesale market. The set, S(i) is determined by the location of the producer region in the transmission network and by the specific wholesale markets served by the producer region. Denoting quantity sold in a given sale-activity by X,, we have by definition :

exceeds or is equal to total demand in each market segment, and that all quantities are non-negative. We write : Y.

Max L = C jeJ w)~,s,lY),d

Pj( Y)dY

- C

(vitsj

+

t,)X,

SSS

s 0

such that:

ssS(i)

ssS( i)

C (l-sS)xS-

The electricity lost in transmission is assumed to be a constant fraction r, of the quantity sold in a given sale-activity. Also, there is a constant unit tariff t, for using the transmission network. Wholesale demand is derived from end-use demand. We denote by J, the total set of geographically specified end-use segments j, which, in each region, comprise all or some of the following demand segments : residential and agricultural, services, power-intensive metallurgical industry, wood-processing industry, other industry, occasional power and net exports. The wholesale demand stemming from segment j is denoted by Yj. Assuming that a fraction yj of electricity is lost in distribution from the wholesale market to the end-use segment j, this segment receives only (1 - rj) Yj of the quantity delivered from the wholesale market. We assume that demand in each end-use segment, j is characterized by a constant elastic demand function, yj = Aj#, where yj is the end-use demand, pj is the end-use price, sj is the own-price elasticity, and Aj is a constant. Aj is determined by calibration in such a way that observed end-use price corresponds to observed end-use quantity with the given price elasticities. The inverse demand function in end-use segment j is denoted pj = gj(yj). To arrive at the inverse derived demand function stemming from segment j at the wholesale level, we add a constant expenditure term, cj, which includes distribution tariffs and taxes paid at the end-use level. Thus, we have Pj( Yj) = ( 1 - yj)[gj( (1 - yj) Yj) - cj], where Pj denotes price of electricity at the wholesale level for delivery to end-use segment j. The reorganized

x,

3 0,

yj 3 0,

yj20,

VmEM

VSES VjgJ

(1)

The current system

To model the current system, the set of end-use segments is separated into two distinct subsets ; F and V. The subset F contains the contract or fixed market segments, where prices are administered and given. Since we do not consider any uncertainty or other variation of the demand functions ; fixed end-use prices imply fixed quantities demanded, Yj. In this way, demand in subset F is fixed and prices and quantities demanded are unconnected with the state of precipitation realized. The subset I/ represents the two variable market segments: occasional power and net exports. Here prices and quantities demanded are dependent upon precipitation. Compared to problem ( 1 ), the objective function now reads : yj pj(y)dy&V IS

1

Cvi(s)

+

ts)Xs

SC.3 0

and we add the following rj-

yjao,

constraints:

VjJ’EF

The basic model is calibrated for 1988, and relies on data for observed end-use quantities, end-use prices, production costs, transport costs and taxes.3 The data are presented in Appendix 1. The price elasticities in end-use consumption are given in Table 1. Table 2 provides data for the variation of precipitation for each region.

system

For clarity of exposition, we first present the model for a competitive organization of the wholesale markets (ie after reorganization). The objective is to maximize social surplus under the constraints that production capacity is greater than or equal to the total production for each producer, that total supply

ENERGY

1

kJ(m)

&i(m)

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April 1993

Comparison

In Table 3 we compare calculated prices and quantities in end-use

national average consumption at

3The data set is provided by the Central Bureau of Statistics the Norwegian Water Resources and Electricity Board.

and

83

Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjetta Table 1. Price elasticities (constant) applied in the model for the end-use segments; residential and agricultural (R), service (S), industry (I), power intensive industry (PII), wood-processing industry (WPI), occasional power (OP) and net export (NE). End-use segments R

S

I

PI1

WPI

OP

NE

-0.2

-0.3

-0.3

-0.1

-0.4

-2.0

-3.0

Table 2. The variation of production capacity depending upon precipitation for each region (TWh). The producer regions are 1: Glomma; 2: Bstlandet; 3: Snrlandet; 4: !&r-Vest; 5 : Midt-Vest; 6: Midt-Norge; 7: Helgeland; 8: Troms; and 9: Finnmark. (The data set is provided by The Norwegian Electric Power Research Institute.)

Probability 1 2 3 4 5 6 7 8

1

2

3

4

5

6

7

Mean

0.06 9.17 15.39 13.35 13.35 10.23 11.60 9.49 8.44 1.23 92.2

0.08 11.56 18.96 14.21 14.08 11.21 11.46 8.58 5.01 1.54 96.6

0.22 8.86 16.58 14.77 18.18 12.51 10.37 8.48 8.84 1.52 100.1

0.32 10.90 21.19 14.73 16.01 11.81 13.14 8.68 7.14 1.91 105.5

0.14 11.57 21.83 18.20 17.84 12.94 10.27 8.03 7.05 1.63 109.4

0.12 11.80 21.33 16.44 18.51 14.19 13.68 9.57 6.09 1.55 113.2

0.06 12.58 25.62 20.94 19.90 14.26 11.51 7.78 5.71 1.23 119.5

10.70 20.02 15.68 16.96 12.41 11.87 8.64 7.20 1.63 105.1

Table 3. Prices (NOK/MWh) precipitation.

and quantities (TWh) before and after the reorganization

of the hydropower market calculated at mean annual

After reorganization

Before reorganization

Residential and agricultural Service Industry Power intensive industry Wood-processing industry Occasional power National weighted average

Quantity

Price

Quantity

Price

30.9 17.5 7.9 29.6 4.5 3.2 93.5

414 370 318 103 139 136 277

33.4 20.5 8.9 28.9 4.5 4.5 98.2

280 215 215 131 140 170 208

Table 4. Increases in net consumer surplus (NOK x 106) going from the current to the reorganized market system of hydropower for various levels of precipitation. Precipitation

Increases

in net consumer

surplus

1

2

3

4

5

6

7

Mean

250

370

500

720

960

1200

1470

750

the average precipitation level before and after reorganization. Table 4 reports the gains in social surplus of reorganizing the wholesale markets, conditional on precipitation. It is observed that a reorganization leads to lower electricity prices for the residential and agricultural segements, the service segment and the industry segment, but higher prices for the power-intensive segments (with a corresponding inverse effect on quantities). The national average price of electricity falls. Also, it is seen that there is a

84

general increase in consumer surplus for all ievels of precipitation, in the switch from the current system to a system of efficient pricing. This is, of course, in line with what theory claims. The situation after reorganization is also illustrated by the Salter diagram in Figure.2. This diagram gives the annuitized unit (capital and operation) cost structure (ie the industry cost curves) for total national hydropower generation and average efficient electricity price, calculated at the average precipitation level. It

ENERGY

ECONOMICS

April 1993

Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjotta Annuity costs (NOwMwl)

ZOCK-

500 208 0

0

20%

40%

50%

80%

100%

Percent of mean prodUCtiOn

Figure 2. Salter diagram for the existing Norwegian hydropower production capacity calculated at mean average precipitation after reorganization.

is clear from the diagram that the unit cost at the optimal (short-run) production level is well above average price ; thus indicating a significant excess production capacity. In fact, this is true for all levels of precipitation.

The hydro rent concept and short-run surpluses Economic rent in hydro power generation is a result of Nature’s annual services of precipitation and water seepage in a limited number of topographically suitable production sites. The sites may vary in quality (ie development cost per kWh) and in proximity to the market (implying differential transmission power losses). Thus, hydro rent belongs to the class of Ricardian differential rent4 which, generally speaking, is the payment made to a production factor of a certain quality in excess of what is necessary to attract it to the productive process.5 It is important to remember .that economic rent is a long-run efficient equilibrium concept, and that the total surplus gained in the productive process can be partitioned into (pure ) economic rent and quasi-rent. In a long-run efficient equilibrium, quasi-rent exactly covers normal remuneration to capital. Any deviation from such an equilibrium results in quasi-rent that is either insufficient or more than sufficient to cover normal renumeration to capital. 4It is interesting to note, however, that hydro rent also possesses one of the characteristics of resource rent since water contained as storage in a dam is seasonally scarce capital and, thus is regulated according to its ‘water value’, ie a positive marginal user cost which is normally associated with resource rent. 5For discussion of the hydro rent concept, see also Bernard, Bridges and Scott 141.

ENERGY

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April 1993

Here we seek to evaluate hydro rent on the basis of the annual surpluses generated in the models presented above.6 In determining hydro rent, electricity should be evaluated at its opportunity cost which in a long-run efficient equilibrium would be equal to the marginal cost of obtaining additional electricity (for instance from new hydropower plants, from gas power plants, imports etc). However, as shown in the preceding paragraph there has been a significant overinvestment in infrastructure for all levels of precipitation, such that the marginal social value of electricity at the existing capacity is far below long-run marginal cost.7 Still, the common sunk cost argument dictates that all existing infrastructure should be in production since calculated efficient prices cover marginal short-run costs for all existing infrastructure. As illustrated in Figure 2, it is clear that total annual (capital and operation) costs are higher than total revenue evaluated at average efficient price. This means that there is a deficit, not a surplus in terms of economic rent. Hence, since the electricity system is out of long-run equilibrium, pure hydro rent can not be easily assessed from the present market situation. We will return to the relevant long-run pure rent concept later. Here, we consider the relationship between precipitation and the contribution to fixed costs and rent (ie revenue less variable cost) in the power plants in the current and in the reorganized system.’ This surplus concept constitutes an essential element for tax authorities in calculating taxable income from the power plants. Later in this paragraph we shall assess this size of (maximal) taxable income for the current system but first we report the findings related to the total contribution to fixed costs and rent in the Norwegian electricity system. Results are reported in Table 5. Four observations may be made. First, for all levels of precipitation, the contribution to fixed costs and rent falls when reorganizing the system. This is what 6We follow Bernard, Bridges and Scott (141, pp 11-12) in observing that prices obtained in a competitive auction bidding for hydro sites would represent a proper measure of the present value of all future annual hydro rents. However, such data are not available in Canada or Norway. ‘Export price could be a relevant measure of true opportunity cost. However, up until now free exports have not been allowed by the regulating authorities. Prices obtained by the existing, regulated, small-scale exports are presumably well below prices in a free export market. *The per unit electricity duty included in the model distorts allocation and influences the value of the contribution to fixed costs and rent. The rationale of this electricity duty is partly to capture some of the hydro rent for the central government. However, it is levied on end use distribution, which means that the hydro rent is ‘dragged downstream’ before it is captured. Furthermore, this duty is levied on (almost) all electricity generated irrespective of whether the electricity is produced in supermarginal or submarginal power plants.

85

Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjotta Table 5. Contribution to fixed costs and rent, and calculated maximum taxable income (NOK x 109) under various precipitation levels. Precipitation

Contribution to fixed costs and rent Existing system Reorganized system Calculated maximum taxable income, existing system

1

2

3

4

5

6

7

Mean

14.1 10.8

14.9 9.7

15.1 9.1

15.6 8.7

15.7 8.9

15.7 7.3

15.9 5.5

15.4 8.6

1.6

2.1

1.9

2.1

2.1

2.1

2.1

2.0

theory states : a more efficient allocation of electricity reduces scarcity and therefore the contribution to fixed costs and rent. Second, with efficient pricing, the contribution to fixed costs and rent tends to fall with increasing precipitation. This result depends upon own price elasticities and upon the industry cost curves which are derived conditional on precipitation. For segments with elasticities less than one, increased precipitation and hydropower delivered lead to reduced total revenue. For segments with elasticities greater than one (ie the occasional power and the net-export segments), increased precipitation and power generation leads to increased revenue. But, since most demand segements (accounting for some 85-90% of total demand) have own-price elasticities less than one, the aggregate effect of reduced revenue turns out to dominate the counteracting effects such that the contribution to fixed costs and rent actually falls with increased precipitation. Third, with the current hydropower system, an increase in precipitation tends to increase the contribution to fixed costs and rent. The reason for this result is mainly that revenue from the dominant demand segments remains constant, since these are fixed price markets in the existing system. Thus the effect on total contribution to fixed costs and rent is determined by the change of revenue in the flexible markets. Since price elasticities here are greater than one, increased precipitation leads to an increased contribution to fixed costs and rent. Fourth, although the precipitation data are organized in such a way that precipitation increases at a national level from category 1 to 7, there are regional variations. For instance, as reported in Table 2, precipitation in region number 7 (Helgeland) and number 8 (Troms) tends to be negatively correlated with precipitation at a national level. For the efficiently organized market system, this implies that these regions get a relatively high contribution to fixed costs and rent due to regional water abundance when precipitation is scarce on a national level, and a relatively low contribution to fixed costs and rent when precipitation is abundant for the country as a

86

whole. Thus, the regions of Helgeland and Troms have a larger coefficient of variation of the contribution to fixed costs and rent than the regions that are positively correlated with total national precipitation (eg region number 3, Sorlandet). In order to try to assess the maximal taxable income in the existing market system, we concentrate on reporting the contribution to fixed costs and rent from ‘supermarginal’ production plants, ie the plants that do have a surplus above annuitized costs. Except for the Bstlandet region, only 5-10% (depending upon the level of precipitation) of installed production infrastructure has a surplus above total annuitized cost. The Bstlandet region has a higher proportion due to early and low cost construction of power-generating infrastructure. The surpluses thus calculated give the maximal amount of taxable income. There are two reasons for this. First, the taxation unit is the company and a company may in addition to owning ‘supermarginal’ power plants also own ‘submarginal’ power plants from which it can deduct deficits. Second, no depreciation allowances are included in the assessed amount9 The reason for this is lack of information on the sizes of these allowances. A conclusion to be drawn from this assessment is, however, that the taxable income from power plants in the current situation of excess capacity is really not very high, even though it may be potentially high for an electricity system in long-run equilibrium.

Hydro rent under long-run equilibrium In order to evaluate hydro rent in a long-run efficient equilibrium two hypothetical experiments are performed. These are assumed to assess upper and lower boundaries on hydro rent. First, assuming demand functions remain invariant with respect to time and are equal to current demand, existing capacities are reduced until they correspond to optimal capacities in a long-run efficient equilibrium. ‘Presumably, many of the profitable power plants are old power plants with small amounts of depreciation allowances left.

ENERGY

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Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjgtta

Second, assuming existing capacities to remain constant over time, current demand functions are shifted outwards until existing capacities become optimal under the assumption that demand remains time-invariant at this higher level. In the following it is assumed that per unit annuities of capital costs (at the expected precipitation level), remain constant over long stretches of time within each cost class of the existing power plants. This assumption would be appropriate if, for instance, repetitive reinvestments in identical production infrastructure at a cost equal to initial investment costs were made each time a power plant became obsolete. However, extention of the economic life of an existing power plant by maintenance and renewals so as to maintain production performance, can probably be done at a relatively lower cost than initial investment reinvestments in generators, cost. Furthermore, pipelines, dams and the like, will benefit from technological progress and probably lead to lower unit capital cost and increased capacities in existing plants. The partial effect of such technological progress in a long-run model is to reduce economic rent. However, since it is difficult to determine the extent to which, the cost reducing factors are at work, we are content with the assumption of constancy of capital cost annuities. Also, possibilities exist for electricity generation on new hydropower sites, as well as for a massive increase in electricity generation based on natural gas. The long-run marginal costs of these alternatives are rather uncertain since they rely on imputed costs from negative environmental external effects (ie distortion of the natural environment on new hydropower sites and emission of CO, from electricity generation based on natural gas.)” However, it seems clear that some of the existing power plants have higher unit capital costs than these alternatives. The reason for this is that most power plants are built by the state and local authorities, and that a thorough and proper investment analysis was not always carried out before the decision was made to construct a power plant.”

‘%I addition, for gas power plants, the opportunity costs of natural gas (ie in exports or for use in petrochemical industry) are not easily assessed. “This is probably due to several factors such as the non-profit objective of public utilities, a low degree of cost-consciousness in the public sector and (up until now) a lack of a proper accounting system for assessing the real cost of a project. For this reason some high cost power plants have also been constructed. Since most of these power plants also, in effect, constitute local monopolies, electricity prices could be raised such that even these power plants could attain their non-profit objective. Otherwise, a considerable implicit transfer from low-cost power plants to high-cost power plants has taken place among power plants owned by the same local authority or by the state.

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Constant demand and reduction

of capacity

Assuming risk neutrality (or alternatively a risk adjusted discount rate), it can be shown that the relevant long-run optimality condition for capacity construction under the assumption of variable precipitation is that marginal expected revenue should be equal to marginal cost at the level of expected precipitation in each region considered. (See Appendix 2.) In the present experiment we therefore reduce capacities until this condition is simultaneously fulfilled for all producer regions. The idea of this experiment is illustrated in Figure 3, where we for illustrative simplicity use expected prices instead of expected marginal revenue. Since industry cost curves vary from region to region, optimal reductions are also regionally diversified, ranging from approximately 6% reduction in the Bstlandet region to 43% in the Helgeland region, and about 20% at a national average. Table 6 shows hydro rent conditional on precipitation. Here it is assumed that precipitation varies but that production infrastructure stays constant at the new calculated optimal value. Again we observe that hydro rent falls with precipitation. Since demand and cost functions are assumed time-invariant and since precipitation is independent

H \

\

4

L\

\

Figure 3. Annual hydro rent in the long run. Symbols : EE, existing demand, LL, necessary demand for long-run equilibrium with the existing production capacity if the low back-stop price, P, prevails. HH, Necessary demand for long-run equilibrium with the existing production capacity if the high back-stop price, P, prevails. X,, existing capacity. P,, existing price. Xi, sufficient production capacity for a long-run equilibrium at constant demand if the high back-stop price prevails. The corresponding price is Pf. Xk, sufficient production capacity for a long-run equilibrium prevails.

at constant

demand

if the low back-stop

price

87

Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjotta Table 6. Annual hydro rent (NOK x 109) in the long run assuming constant demand and reduced production capacity (expected average price NOK 420 per MWb, and mean production capacity) (Experiment 1). Precipitation

Calculated

hydro

rent

1

2

3

4

5

6

7

Mean

14

13

12

13

I

4

-2

10

Table 7. Annual bydro rent (NOK x 109) in the long run assuming constant production capacity and increased demand (Experiment

Calculated hydro rent, Low back-stop price (350 NOK/MWh) High back-stop price (450 NOK/MWh)

1

2

3

26

17

11

41

28

20

from one year to another, annual hydro rent at expected precipitation will be constant over the years and equal to NOK 10 billion. Assuming that hydro rent represents an infinite annuity, the expected net present value of all future hydro rent can be estimated at NOK 143 billion, at a real discount rate equal to 7%. Constant capacity and increasing

demand

With rising demand, the sunk cost argument dictates that all existing power plants continue to produce, including high-cost power plants. However, since alternative electricity projects will enter when prices reach a certain level, and thus stabilize prices at this level, prices will probably not reach a level that could make the most expensive power plants ex ante optimal. In this second experiment we will, therefore, not let prices rise above a certain price level. Since the long-run marginal cost of generating electricity from other sources than the existing plants is rather uncertain, we consider two scenarios of ‘back-stop prices ’ ; a low scenario (NOK 350/MWh) and a high scenario (NOK 450/MWh). It is assumed that large quantities of electricity can be supplied at these prices (ie infinite supply price elasticity). Demand is now increased in all segments until the expected price at the existing capacity becomes equal to the back-stop price. Using the historical growth rate of electricity demand in Norway (ie 2.4%/year), it may take a couple of decades before demand has risen sufficiently to warrant new investment in production capacity. However, this depends critically upon whether the ongoing efforts to initiate large-scale electricity exports to other North European countries are successful or not. For the high scenario the expected annual hydro

88

4

2).

5

6

7

6

4

3

2

8

12

8

5

3

15

Mean

rent is equal to NOK 15 billion and is, thus, higher than our appraisal in the previous section (NOK 10 billion). This is as expected since demand is higher in the present experiment and since the average equilibrium price in the previous section (ie NOK 420/MWh) is below the high scenario back-stop price (see Figure 3). Hence, if the high scenario is realized, expected annual hydro rent will be NOK lo- 15 billion. In the low scenario, the annual hydro rent is equal to NOK 8 billion. This is lower than the hydro rent estimated in the previous section. The reason for this is that the average equilibrium price earlier is higher than the low scenario back-stop price. However, imposing the low back-stop price for the capacity reduction experiment, it is clear that the equilibrium price could not remain at NOK 420/MWh. This is so since the back-stop technology would be introduced from the moment the electricity price tended to rise above the back-stop price. The price could not therefore rise above the back-stop price, and the hydro rent calculated in the previous section is clearly overestimated. Taking account of this effect and observing that annual hydro rent will not increase with a further demand increase (due to the infinite supply price elasticity) once the back-stop price is reached, the two experiments would in fact give the same result, ie an annual rent of NOK 8 billion, Hence, at a back-stop price equal to NOK 350/kWh, both experiments give the same result with respect to equilibrium price and expected hydro rent. Only quantities delivered would differ (see Figure 3).

Conclusions Applying

data from the Norwegian

ENERGY

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April 1993

Hydroelectric

rent and precipitation

a regionalized model has been compiled to analyse the social gains and the effects on hydro rent of going from the current administered (and socially erroneous) system to an efficient market system of the hydropower sector. The social gains are shown to be significant. Also, the paper focuses on the importance of precipitation variability for the appraisal of hydro rent. However, since there exists a considerable excess production capacity pure hydro rent is not easily assessed. In the short run we therefore concentrate on calculating the surplus in terms of the contribution to fixed costs and rent. For the reorganized market system, extreme but periodically observed precipitation levels give rise to a surplus that on an annual basis may deviate by more than 20% compared to the mean value of the surplus at the national level. The general effect on the surplus of going from the current organization to an efficient market system, is that the surplus falls for every precipitation category. This result is due to the more efficient use of the power and the consequent reduction in scarcity. For the reorganized marked system it is shown that the surplus tends to fall with increasing water abundance. This result hinges on the characteristics of the demand functions (price elasticities less than one) and of the marginal cost function applied (as given by Salter diagrams based on full cost annuities). However, for the current system, the surplus tends to increase with increased water abundance. This result is due to the fixed price regimes of the current system. It is also shown that some producer regions are fortunate to have precipitation negatively correlated with the general national precipitation; thus capturing huge hydro rent when water abundance is generally low for the nation as a whole and prices are high. These regions thus have a larger coefficient of variation of generated hydro rent than the rest of the country. The paper also assesses the maximum size of taxable income from the power plants in the existing system. Pure (long-run) hydro rent is assessed by performing two experiments, ie first assuming time-invariant demand, reducing capacities until long-run equilibrium is attained and second, assuming constant capacity (equal to existing capacity), increasing demand until long-run equilibrium is attained. This appraisal gives an annual expected hydro rent somewhere in the bracket NOK 8 billion to NOK 15 billion. Assuming this to be an infinite annuity the present value of expected hydro rent would, at a real discount rate of 7%, range from NOK 120 billion to NOK 210 billion. However, it should be observed that these higher surpluses cannot be

variability:

the case of Norway:

E. S. Amundsen and S. Tjotta

captured right away, since demand has to increase before the market reaches a long-run equilibrium and also since other market adaptions will have to take place. In particular, a significant number of non-renegotiable low-price long-run contracts still exist, and these may stay in effect for as long as 20 years. (Bye and Johnsen [S]). However, by changing the current policy in this field, for instance by allowing large-scale exports and second-hand trade in contracts, the surpluses could be realized and captured at an earlier stage.

References 1 2

3

4

5

6

E. S. Amundsen, ‘Thtorie des ressources tpuisables et rente pktroliere’, Economica, Paris, 1992. E. S. Amundsen, C. Andersen and J. G. Sannarnes, ‘Rent taxes on Norwegian hydro power generation’, The Energy Journal, Vol 13, No 1, 1992, pp 97-116. J.-T. Bernard, ‘Le financement de la conf&dCration : La rente des ressources naturelles’, Canadian Public Policy - Analyse De Politiques, Vol VIII, No 3, 1982, pp 297-299. J.-T. Bernard, G. E. Bridges and A. Scott, An Evaluation of Potential Canadian Hydro Electric Rents, University of British Columbia, Resources Paper No 78, 1982. J.-T. Bernard and R. D. Cairns, ‘On public utility pricing and foregone economic benefits’, Canadian Journal of Economics, Vol 10, 1988, pp 152-163. J. Bjerrndalen and S. Tj&ta ELNET - En model1 au det norske

krqftmarkedet.

Beskrivelse

og dokumentasjon

(ELNET - A model of the Norwegian power market : description and documentation), Working paper 38/91, Centre for Applied Research, Bergen, 1991. 7

8

9

10

11

12

13

T. Bye and S. Stream, ‘Kraftpriser og kraftforbruk’ (Power prices and power consumption), Sosialokonomen, Vol II, No 4, 1987. T. Bye and T. A. Johnsen, ‘Effektivisering av kraftmarkedet

Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjotta

Appendix 1

Appendix 2

Model data

Marginal investment in hydro power

The data applied in the models are summarized in Tables Al-A4. The end-use segments are: residential and agricultural (R), service (S), industry (I), power-intensive industry (PII), wood-processing industry (WPI), occasional power (OP) and net power (NE). Production cost, up = 5 NOK/MWh for all producer regions.

Consider, a marginal plant with a capital cost equal to I. We assume that the plant generates production X in infinite time periods and that production X is stochastic due to variation in precipitation. We scale investment such that E(X) = 1, ie the expected production is 1 in each period. The producer price of electricity, P, is uncertain due to

Table Al. Observed end-use quantities (TWh) in 1988.

East West Middle North c

R

S

I

PI1

WPI

OP

NE

z;

15.019 7.065 5.054 3.756 30.844

8.856 3.767 2.662 2.161 17.446

3.791 1.930 1.318 0.870 7.909

4.605 10.499 8.947 5.554 29.605

2.803 0.307 1.367 _ 4.477

3.201 0.693 0.407 0.181 4.482

3.358 2.260

38.275 24.261 19.755 12.522 94.813

Table A2. Observed end-use prices (NOK/MWh)

East West Middle North

5.618

in 1988.

R

S

I

PII

WPI

OP

NE

352 336 368 388

371 351 394 370

318 302 367 278

127 103 106 80

147 130 126

103 127 139 201

89 84

Table A3. End-use segment data.

Elastisity (E) Loss share (T) Distribution cost (NOK/MWh) VAT (NOK/MWh) Special tax (NOK/MWh)

R

S

I

PI1

WPI

OP

NE

-0.2 0.13 68

-0.3 0.08 68

-0.3 0.08 68

-0.1 0.00 0

-0.4 0.00 0

-2.0 0.08 22.5

-3.0 0 0

58 36

0 36

0 36

0 32

0 36

0 36

0 0

Table A4. Sales activities data, t = tax for using the transmission network (NOK/MWb), and T = loss fraction. The reducer regions are 1: Glomma, 2 : Bstlandet, 3 : Serlandet, 4 : &w-Vest, 5 : Midt-Vest, 6 : Midt-Norge, 7 : Helgeland, 8 : Troms and 9 : Finnmark. Producers

Markets East

1

t

2

:

3

:

4

t

5

5

6

t

7

5

8

:

9

r

90

12.0 0.015 8.0 0.01 16.0 0.02 16.0 0.02 24.0 0.03 24.0 0.03 40.0 0.049 64.0 0.078 96.0 0.115

West

Middle

North

9.6 0.012 8.0 0.01 16.0 0.02 40.0 0.049 72.0 0.087

24.0 0.03 12.0 0.015 12.0 0.015 12.0 0.015

8.0 0.01 8.0 0.01

ENERGY

ECONOMICS

April

1993

Hydroelectric rent and precipitation variability: the case of Norway: E. S. Amundsen and S. Tjotta variation in precipitation (and therefore supply) and due to demand fluctuations. We assume the same probability distribution on price P independently for each period. For simplicity we also assume that variable costs are equal to zero. For such a marginal project, net present value is equal to zero ; ie -I+

f

/l’E(PX)=O

r=0

where p is a risk-adjusted discount factor. annuitinzed capital cost (marginal cost) as

ENERGY

ECONOMICS

April

1993

Defining

and rearranging a = E(PX)

terms in the above condition, = E(P)

+ cov(P,

we arrive at

X)

This optimality condition simply states that expected marginal revenue should be equal to marginal cost. However, observe that expected marginal revenue can be separated into two terms; the expected price E(P) and a covariance term, cov(P, X), between price and production. Hence, for a specific producer, if price and production are independent such that cov(P, X) = 0, then a = E(P). This is the standard case of traditional investment analysis. Furthermore, if cov( P, X) < 0, we have a < E(P), ie marginal cost should be less than expected price. And, finally if cov( P, X) > 0, then a > E(P); ie marginal cost should be greater than expected price.

91