Gas power production, surplus concepts and the transformation of hydro electric rent into resource rent

4"

,

l~i

RESOURCE

and ENERGY ELSEVIER

ECONOMICS Resource and Energy Economics 19 (1997) 241-259

Gas power production, surplus concepts and the transformation of hydro electric rent into resource rent Eirik S. Amundsen Department of Economics, University of Bergen, Fosswinckelsgt. 6, N-5007 Bergen, Norway

Received 7 February 1994; accepted 16 September 1996

Abstract The paper considers the effects of introducing large scale gas power production capacity into an electricity sector based on hydropower. In this process the economic rent is transmitted from the hydro power sector to the resource rent in the gas power sector, but is along the way intermingled with ordinary producer surplus and quasi-rent stemming from increasing cost conditions in the production infrastructure and capacity constraints. The net effect on total rent generated depends on development in demand, demand elasticities, costs saved from delaying hydropower projects and the existence of producer surplus in gas power generation. The paper closes with a discussion of possible tax base changes following from the introduction of a thermal power system based on natural gas. © 1997 Elsevier Science B.V. JEL classification: Q30; Q32; Q40 Keywords." Thermal power; Hydropower; Economic rent

1. Introduction In many countries the share of natural gas as a fuel in electricity generation has been increasing as compared to oil, coal, nuclear and hydropower. This development can be attributed to several factors, e.g. extensive off-oil programs following in the aftermath of the oil price shocks of the 1970s, cost lowering technological progress, the flexibility of natural gas in combined heat and power generation (CHP) and the prospects of sizable future CO2-taxes favoring natural gas as 0928-7655/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0928-7655(96)00018-8

242

E.S. Amundsen/Resource and Energy Economics 19 (1997) 241-259

compared to coal and oil (Guldman, 1991; Lafrance and Perron, 1993). The trend towards increased use of natural gas is also present in some of the 'hydropower countries' which are fortunate enough to be endowed with reservoirs of natural gas. For instance, this is the case for both Canada and Argentina, where the use of natural gas for electricity generation is expected to increase its relative share into the next century (EMRC, 1991, and Camevali and Su~ez, 1993). While this development is still in its infancy in Norway large scale development programs for thermal power are being contemplated, using offshore gas reservoirs along the western coast. The general effect of large scale, low cost electricity generation from natural gas is to lower price and to relegate new development projects of hydropower to the future. An interesting aspect of this development is the effect it has on the generation of economic rent. Since both reservoirs of natural gas and topographical and hydrological conditions suited for water power production are gifts of Nature, both sectors generate rent. But the rents generated are of somewhat different kinds. The hydroelectric rent (or 'hydro rent' for short) is of the Ricardian kind, which under constant demand and cost conditions could be generated eternally. The rent stemming from the extraction of natural gas, however, is a resource rent of limited durability based on a scarcity which is ever-increasing along with extraction. 1 The resource rent is, thus, associated with the concept of user-cost or inter-temporal alternative cost (see, for example, Bernard et al., 1982, and Amundsen and Tjctta, 1993). Along with the introduction of low cost thermal power based on natural gas (or 'gas power' for short) we would expect the hydro rent to decline, while the resource rent will be generated in the gas power sector. Thus, in a sense, surplus is transmitted from the hydro sector to the gas sector. Along the way, however, it is intermingled with ordinary producer surplus and the quasi-rent stemming from increasing cost conditions in the production infrastructure and capacity constraints. In this paper we set out to identify the various surplus concepts attached to a joint large scale development of capacities for gas power production and extraction from a gas reservoir of no alternative use. In particular, we seek to verify how the surplus concepts are composed of pure rent and producer surplus and how the surplus is transmitted through prices. Furthermore, we seek to determine the extent to which reduced hydro rent is compensated for by an increased resource rent. This is a question that may be important from a taxation point of view since the introduction of gas power may lead to a change of the tax base. But not only may the total tax take change; there may also be changes in the time-profile of taxes captured, as the expansion of electricity production and the development of price

1It is interesting to note, however, that the hydro rent also possesses one of the characteristics of resource rent since water contained as storage in a dam is a seasonally scarce capital and, thus, is regulated according to its "watervalue', i.e. a positive marginal user cost.

E.S. Amundsen/Resource and Energy Economics 19 (1997) 241-259

243

may be different with and without gas power. Finally, tax changes may come about since surpluses are transmitted to the petroleum sector, which normally will have a harsher tax regime than the hydropower sector. We shall return to these questions in the latter part of the paper. 2. The model: cost structure and demand

We consider the joint construction of a gas power plant and gas extraction infrastructure (i.e. production units and pipelines) furnishing the power plant with natural gas. Gas power production is assumed to be introduced 2 at some date, 0, and comes in addition to a base level production of hydropower. From this date on follows a period of simultaneous hydro- and gas power production until some date, T, when gas extraction and gas power production are terminated. Thereafter, hydropower is the only source of electricity production. However, it may be optimal to expand the capacity for hydropower production and this may take place both during the period of joint gas power and hydropower production, as well as during the period where hydropower is the sole source of electricity generation. Hence, three productive activities are involved: the extraction of natural gas, the generation of gas power and the generation of hydropower. For this reason, we are in need of an economic structure for each of these activities, as well as a precise description of the relationship between them. Since we wish to study surplus concepts attached to these activities, we shall have to consider the various cost elements which are essential in electricity production, e.g. set-up costs, flow fixed costs, short run marginal cost, and capacity costs. This necessitates a somewhat lengthy model description involving many symbols. However, the various cost assumptions allow us to disentangle otherwise intermingled surplus concepts attached to these activities. For the sake of simplicity, we shall assume that the hydropower plants are infinitesimally small, with infinite life, and are installed in order of increasing cost. Since, in real life, the cost of installing new hydropower generation capacity is primarily composed of irreversible capital cost, we will assume that the short run marginal production cost is equal to zero. A sunk-cost argument, then, dictates that all hydropower production capacity be utilized once installed. Formally, a distinction is made between hydropower production capacity and hydropower production. Hydropower production capacity at date t is denoted ~th, while hydropower production at date t is denoted xth. Due to the sunk-cost argument we

2 We do not consider the problem of optimal start-up of the power plant since it has no particular relevance for the problem considered. Optimal start-up depends upon assumptions of the investment structure of gas power capacity (i.e. whether capacity is constructed instantaneously or is built up over time) and upon the development of demand over time. The question of optimal start-up is dealt with elsewhere. (For the case of hydropower projects, see Rodseth, 1982, and for the case of petroleum extraction capacity, see Amundsen, 1992).

244

E.S. Amundsen / Resource and Energy Economics 19 (1997) 241-259

have x h = ~h, at all dates. Furthermore, we assume no depreciation of capacity such that one capacity unit is capable of producing one power unit at each instant of time into infinity. Also, it is assumed that an initial level of hydropower production capacity, 2h exists at the date when the heat power plant is introduced. New hydropower production capacity, zt, may be added to the existing hydropower production capacity at any date t. To avoid solutions of exploding investments we put boundaries on the investments, i.e. we assume 0 < zt < Zmax. The constraint, z . . . . may be viewed as being determined by the hydropower industry's capacity to invest at any point in time. Since we assume no depreciation of production capacity, we have ( d ~ h / d t ) = zt > 0. The cost of new capacity at date t is assumed to be an increasing function both of the size of the physical investment, zt, and of the level of capacity installed at the date considered, ~h. Here we shall assume a linear version of such a function (see below). To summarize, we assume the following functional structure of production and cost for the hydropower sector Production: x h = Ych. Capacity construction cost: a(~rh)z/, with d > 0, 3 and d' > 0. Marginal production cost: equal to zero. For gas power production we consider a large scale gas power plant fueled by natural gas. Gas power production at date t is denoted x g and the input of natural gas at date t is denoted Yt. The plant is assumed to have a maximum, endogenously determined, production capacity, ~g. We assume the following functional structure of production and cost for the gas power plant: Production: x~ =f(Yt), with f ' > O, f " < O. Capacity construction c o s t : J(.~g) -~- B, with J ' > O, J" > O, B is a positive constant. Flow-fixed operating cost: b(2g), with b' > O, b" > O. For natural gas we consider a single reservoir with no other use than to be applied in gas power production. There is a maximum, endogenously determined, extraction capacity, ~. The initial stock of in situ natural gas is denoted Y and the remaining stock at date t is denoted 11,. We assume the following cost structure for gas extraction: Capacity construction cost: K( p) + C, with K' > O, K" > O, C is a positive constant. Flow-fixed operating cost: c(p) with c' > 0 and c" > O. Marginal cost: equal to zero. It should be noted at the outset that since no storage facilities are assumed for natural gas, the time-path of gas input into gas power production corresponds to the gas supply from the gas reservoir. We shall assume that this is a one-to-one

3 For a one-variable function g(s), we occasionally apply the standard notation ( d g / d s ) = g' (or

g'(s)) and (d2g/ds 2) = g" (or g"(s)).

E.S. Amundsen~Resource and Energy Economics 19 (1997) 241-259

245

correspondence such that: xgt =f(Yt), always. Also, in time intervals where extraction capacity is binding, the production of gas power will be constant, and conversely, in time intervals where the capacity of gas power production is binding, the extraction of natural gas will be constant. From the point of view of a social planner, excess capacity in either gas extraction or gas production is clearly suboptimal. Thus, we shall assume that the capacity constraints in extraction and in gas power generation correspond such that: ~g = f ( ~ ) . Furthermore, it follows that the length of the extraction period for natural gas is equal to the length of the period of gas power production. The demand for electricity is assumed to be characterized by a downward sloping demand curve with non-negative shift over time. Denoting total electricity production at date t by x t = x~ + xgt, we assume Demand function (inverse form): p = p(x;t) with (Op/Ox) < 0 and (Op/Ot) >_

O. 3. Optimal joint production of gas power and hydropower To arrive at the joint optimal solution of gas and hydropower production, we shall proceed in two steps. The first step involves the assumptions that extraction capacity ~ and the gas power generation capacity .~g (in addition to the hydropower production capacity :~h at date 0) are exogenously given. In the second step we relax these assumptions and determine the optimal capacities. We return to the second step later. In order to proceed with the first step, we define the following maximum function:

S(T, YChT) =

J;[J:

]

p( s , t ) d s - a( £h" ) .~t* e-r(t T)dt,

where the asterisk denotes optimal values. Hence, this function expresses the maximum future social surplus of additional hydropower production capacity evaluated at date T, as a function of terminal time for gas power production and of the level of hydropower production capacity, ~ at date T. The constrained joint maximization problem of gas- and hydropower production is

fr[f +

max Jo t J'~ho Y,,z,,T

Xgtp ( s , t ) d s

+ S(T, Ychr)e-rr subject to ~h = ~h (d2h/dt) = zt

zt>_O

-- a( ~fh)z, --

]

b(x g) - c( y ) e-rtdt

E.S. Amundsen / Resource and Energy Economics 19 (1997) 241-259

246

Z t ~ Zmaz

Yo= Y (dY,/dt) -y, frytdt < Y Yt
~h, 2g and ~ assumed given The corresponding Hamiltonian with Lagrangian slackness conditions reads

H i = [~;h' + f(Y')p( s , t ) d s - a( 2h )zt - b( 2g) - c( Y)le-r' + Atz, + ( p~t - tot)zt - %Yt - flt(f(Yt) - 2 g ) - ~'t(Yt - Y ) , where At denotes the adjoint variable for 2th and where /x t and tot are variables taking care of dual slackness in the equalities zt >-- 0 and zt < Zmax, respectively. For 0 < zt < z . . . . we, thus, have /xt = tot = 0. Likewise, Yt denotes the adjoint variable for ~, and e t and fit are variables taking care of dual slackness in the inequalities Yt < Y and f ( y t ) -< xg, respectively. We find

oil

= At + (/x, - w,) - a ( ~ h ) e - ~ t = O,

(1)

--

(2)

Oz.t

oi-/, o~,~

)t t = [ p ( x h + x g , t ) - d ( x

h) z,ll e - r t ,

0/4, Oyt = P( xh + xgt, t ) f ' ( Y t ) e-rt - Yt - et - [3tf'(Y,) = O,

(3)

o/4, or,

-

~'t =

(4)

O,

O[S(r,~r)e -rr] = At,

HT=

[f~+f(yr)p(s,T)ds-

(5) a(2h)Zr-b(~

g) - c ( ~ ) ] e - r r

+ ArZr + (/Xr - tot) zr - "/r Yr - f l r ( f ( Y r )

- xg) - e r ( Y r

O[S(T, 2~)e-r~] -Y)

+

OT

= O.

(6)

3.1. Expansion of hydropower production capacity and production The Maximum Principle states that a control at any date t should be set such that H t is maximized at that date. However, considering condition (1), it is clear that we in fact are dealing with a control problem which is linear in zt (i.e.

E.S. Amundsen//Resource and Energy Economics 19 (1997) 241-259

247

(OHt/az) does not contain zt). Hence, the optimal control zt is a 'bang-bang' control in cases where the value of the state variable 2 h does not coincide with the so-called singular solution (see, for example, Seierstad and Syds~eter, 1987, pp. 165-166). The singular solution is characterized b y / z t = tot = 0, which means that the constraints zt = 0 and zt = Zmax are not binding (see Clark and Munro, 1975, pp 103-105). Otherwise, if these constraints are binding, there will be a 'most rapid approach policy' in the sense that the control variable takes on values such that production capacity is driven to its optimal level as rapidly as possible. Hence, if /xt > 0 and tot = 0, then the optimal control is zt* = 0, and if /z t = 0 and tot > 0, then the optimal control is z t = Zmax" Considering the case of a gradual expansion of hydropower production capacity (in which case ~-£t= tot = 0 , i.e. the singular solution), we arrive at the following condition by taking the time derivative of (1) and inserting it into (2):

p(x~ + xgt,t)= ra(2h).

(7)

Condition (7) says that the singular control should be so adjusted that the marginal investment cost of additional hydropower production capacity, a(~h), is equal to an infinite annuity of the marginal social value of electricity at the date considered, p(x h + x g, t)/r. The economic rationale for this condition is that new capacity constructed is durable (has infinite life), and for that reason also future gains should be taken into account. In the model it is assumed that the hydropower production capacity is optimal at date 0, i.e. that p(~h, 0 ) = ra(~0h) = ra(~h). The question is then: Will new hydropower production capacity will be built up during the period (0, T) in which there is a joint production of hydropower and gas power? To answer this question observe that as long as p ( $ h + Xg, t ) < p ( ~ h , 0), the optimal solution is to keep the capacity equal to Sh (i.e. the optimal control is to put zt = 0). But clearly, if the demand function remains constant over time we must have p(~h +X g, t) < p(~h, 0), as long as x g > 0 (i.e. there is an immediate price drop at date 0 when gas power production is introduced). This implies that hydropower capacity will not be expanded within the interval (0, T) for the case of time-invariant demand (and neither will it be expanded after date T). With a gradual increase of demand over time, i.e. Op(x)/Ot > 0 for all t, investment in hydropower production capacity may be resumed. The date at which this will take place can be identified as that date t' for which p(~h +X g, t) =p(.~h, 0). 4 It will be shown later that the price path will have to increase

4 It should be noted that the investment decision here, as in many other linear optimal control problems, only depends upon current price. This builds upon the assumption of a gradual increase of demand, such that we avoid the problems of so-called 'blocked intervals' following from the irreversibility of investment (see Arrow, 1964, 1968). If demand also was allowed to decrease over time for shorter periods, then it would be desirable but not possible to actually decrease capacity. In that case the investment decision would depend upon the total price path over the blocked interval.

248

E.S. Amundsen/Resource and Energy Economics 19 (1997) 241-259

according to the Hotelling rule. This implies that hydropower production capacity will be built up gradually and this process will continue also after date T as long as demand continues to increase. 3.2. Gas extraction and gas p o w e r production

The optimal gas extraction and gas power production is determined by conditions (3), (4), (5) and (6). Starting with the adjoint equation for Yt (condition (4)) this states that Yt, in fact, is time invariant and equal to a constant 3' (i.e. there are no stock effects). Also, it must be the case that yrY~ = 0, such that Yr = 0 if TT > 0. Condition (3) implies a version of the Hotelling rule for gas extraction in the case of capacity constraints. To interpret this, consider first the case where extraction and production capacities are not binding ( e t =/3 t = 0). In this case we have Y err = P t f ' ( Y t * )

(8)

= qt,

where qt denotes the marginal social value of (extracted) natural gas, which also corresponds to the price at which natural gas can be traded between the resource owner and the gas power producer in a competitively organized market. Optimally, the marginal social value of natural gas at date t, qt, is equal to the current marginal social user cost (Te rt) and it increases at a rate equal to the discount rate. However, qt is also equal to the social value of the marginal product in gas power generation. If Pt were time-invariant, the marginal product would have to increase at a rate equal to r (implying falling production), and if Pt increases at a rate equal to r, then the marginal product would have to be constant (implying constant production). Also, if P, increases at a rate less than r, then marginal productivity would also increase at a rate less than r. However, the relationship between Pt and marginal productivity is determined by the demand side of the market. Under the assumption that the gas power plant provides total residual supply, a time-invariant demand function (coupled with (8)) would imply that both Pt and the marginal productivity increase at a rate less than r. Next, consider the case where the capacity constraints are binding. In this case the gas extraction and the gas power production are constant, and the marginal social value of (extracted) natural gas qt is equal to q, = (pt - / 3 e " ) f ' ( y )

= ( y + e,)e r'.

(9)

From (9), we see that qt is equal to the net value of the marginal product, where the net value is equal to the social value of a marginal unit of electricity less a marginal producer surplus to cover capital and flow-fixed costs for the power plant, ~t err (i.e. a marginal quasi-rent). However, q, is also equal to current marginal user cost of in situ natural gas plus a marginal contribution to cover capital and flow-fixed cost for the installed extraction capacity, e,. Alternatively (9) can be transformed to y = (pt e-r' - ~t)f'(~)

- e t.

E.S. Amundsen/Resource and Energy Economics 19 (1997) 241-259

249

pof' (y)

p0f' (Yo)

~

y

t=O

p0f'(y)

pof' (Yo)

~y ptf' (y)

0
ptf' (Yt)

~y "~
,~y t=T Fig. 1. The relationship between gas prices, electricity prices and shadow prices at four different stages of gas power generation. This condition shows how the marginal user cost of in situ natural gas is 'composed' when capacity constraints are binding. The in-situ value of the marginal unit of natural gas is equal to the net social value of its marginal product (i.e. after deduction of a marginal quasi-rent to the gas power infrastructure) less a marginal quasi-rent to the extraction infrastructure. For an illustration, see Fig. 1. 3.3. Date o f transition

Date T is the shutdown date for the gas power plant and the date of transition from a combined gas p o w e r / h y d r o p o w e r system to a pure hydropower system.

250

E.S. Amundsen/Resource and Energy Economics 19 (1997) 241-259 X

t

xh+~

"c

t'

T

t

Fig. 2. A possible case of transition from gas power to hydropower generation assuming increasing demand.

C o n d i t i o n (5) is a necessary transversality condition w h e n there is a 'scrap-value f u n c t i o n ' present (see Seierstad and Sydsaeter, 1987, pp. 1 8 1 - 1 8 5 ) . It essentially says that ~h should be so determined that the marginal cost of n e w investments at date T (i.e. Ar ) should be equal to the reduction in future additional social surplus. Thus, it has the nature of a c o s t - m i n i m i z i n g condition. C o n d i t i o n (6) is (in addition to condition (5)) the transversality condition for free terminal time with a scrap-value function. This condition states that the optimal controls, YT and Zr, should have values such that the H a m i l t o n i a n evaluated at the optimal shut-down date be equal to the time-derivative of the scrap-value function. 5 In the case of strictly positive d e m a n d shifts over time, the time derivative of the scrap-value function is negative since a marginal p o s t p o n e m e n t of terminal time T in essence m e a n s a reduction of future social surplus. In fact, we find

a[S(Z, xh)e -rT] 8T

= - rS(T, Ych)e -rT -- [ f X ; p ( s ' Z ) d s

--d(YC~)ZT]

This then calls for a strictly positive value of the Hamiltonian at the shut down date T to counteract the negative influence of the value of the scrap-value function.

5 If, however, the demand function is constant over time, then the scrap-value function will be equal to zero and so will zr. Hence, the complexity of condition (5) is significantly reduced, and even more so if the gas power production capacities are assumed not to be binding at the shutdown date due to the reduction in gas power production as dictated by the Hotelling rule (i.e. et = fit = 0). It is then easily seen that condition (6) says that gas power production should be halted when the social surplus from gas power production (consumer surplus at the optimal production level less production cost) becomes equal to zero.

E.S. Amundsen/Resource and EnergyEconomics 19 (1997) 241-259

251

Assuming the existence of flow-fixed costs in gas power production, a strictly positive amount of gas power (i.e. x g > 0) will have to be abruptly replaced by a strictly positive amount of new hydropower capacity at the transition date. Here the upper boundary, Zmax may become binding and the 'most rapid approach' policy dictates that that additional hydropower capacity investments be made at this maximum speed until the optimal level of additional hydropower production capacity has been reached (see, for example, Clark, 1976, pp. 80-82). For an illustration see Fig. 2.

4. Optimal capacities for gas extraction and gas power production In order to determine the optimal capacity of extraction and the optimal capacity of gas power generation, we proceed to the second step of the optimization problem. Here we shall assume that demand is constant or weakly monotonic increasing over time (i.e. (Ox/Ot)>_ O, for all t) in such a way that the unconstrained extraction path for natural gas and the production path for gas power are decreasing over time. This assumption implies that there is an interval [0, ~-] in the first part of the total extraction period where the capacities are binding and where gas extraction and gas power production are constant (i.e. y, = ~ and ~g = f ( ~ ) ) . In the latter period, [z, T] gas extraction and power production are decreasing. To determine the optimal capacities, we define a maximum function V(~) as the value of the objective function evaluated for the optimal plan, conditional on the fixed capacities, i.e. such that

v(

= fo -TY

;" dt +

T

x~ +f(y:)p(s,t)ds_a(ycht,)Z, - b ( f ( y ) )

-- c( y') )e -rt - Tyt* ]dt + S(T, Yc~)e -rr. Also we let

M = V(~)-J(f(5:)) -B-K(~)-C and choose ~ (and therefore also ~g = f ( ~ ) ) , such that M is maximized. That is

oM

or(y)

O~

a~

J'(~g)f'(~)

-- K ' ( ~ ) = O.

(10)

252

E.S. Amundsen/Resource and Energy Economics 19 (1997) 241-259

Upon utilizing (10) we find

r

[

f'(Y)fo p(2g+xht*'t)e-rtdt=f'(~) J'(xg)

+ b'(2g)

+ K'(y) + c'(y)

(1 --e-rT) ] "7

(1 - - e -rT ) F

+ fT. (11)

The LHS of (11) gives the marginal gain of simultaneously increasing extraction and production capacity such that one more unit of electricity can be produced in the time interval where capacities are binding (i.e. in the period 0 to r). The RHS gives the marginal cost of such an expansion. We observe that the marginal user cost of in situ natural gas enters as a cost element, since an expansion of the use of in situ natural gas in the capacity constraining interval is at the expense of future utilization.

5. Producer surplus and resource rent in the gas power sector

The introduction of gas power production based on natural gas implies that a part of the hydro rent otherwise generated in the electricity sector is now captured by the gas power sector. This surplus is then split between the gas power plant and the gas extraction unit. A part of this surplus is transformed to a resource rent of limited duration and a part pops up as producer surplus in the two activities involved. To see more precisely the nature of the surplus generated and the split between the two activities involved, we consider the surplus in each of the two activities. The surplus in the gas power plant is

foTptYt * { [ f ( Yt* )/Yt* ] --f'( Yt* )} e-rtdt + {x*[ J ' ( f ' ( -B} +

Y* ) Y*/X* )

-

-e-rr/r))}.

(12)

The surplus in the extraction of natural gas is yY+{~'(K'-[K/~*)]-C} --e-rT)/r]}.

+ {~'[c' - (c/~')][(1 (13)

The first term in (12) expresses the (accumulated) producer surplus from power generation. This is strictly positive since f(y) is assumed strictly concave (which

E.S. Amundsen~Resource and Energy Economics 19 (1997) 241-259

253

implies that average product ( f ( y,* )/Yt* ) is higher than marginal product f'(y,* )). The second term in braces is a producer surplus due to increasing marginal construction cost in the gas power plant. Even though the marginal construction cost J ' is higher than average construction cost J/Tf g *, the expression in the braces is not necessarily positive since J ' is multiplied by a correction factor less than one (i.e. marginal product divided by average product). Also, the fixed construction cost element B must be covered. The third term in braces is (accumulated) producer surplus due to increasing marginal flow fixed costs. As above, this element is not necessarily positive since marginal cost, b', is multiplied by a factor less than one and this may become smaller than average cost, b/Yc g*. The first term of condition (13) gives the accumulated value of user cost for in-situ stock of natural gas. 6 This is often referred to as resource rent. The second term in braces is an expression for the producer surplus due to the increasing marginal construction cost of the extraction infrastructure. Even though the first part of this expression is positive (since K' > K / ~ * ), the total expression is not necessarily positive, since there is also a fixed cost element. The last term in braces gives (accumulated) producer surplus due to increasing marginal flow-fixed cost. This element is positive. The many surplus concepts are due to the assumption of large scale developments in a single production and extraction unit. It may be illuminating to relax this assumption. Thus, assume that total gas power production is supplied by a plethora of infinitesimally small power plants served by a single large scale extraction unit, such that we in effect have a constant cost gas power industry. Each and every gas power plant would then have a surplus of the kind given by (12). But since each has an infinitesimally small production, average production is equal to marginal production, marginal construction cost is equal to average construction cost, marginal flow-fixed operating cost is equal to average flow-fixed operating cost and the 'correction factor' is equal to one. 7 Consequently, all surplus disappears in the gas power industry. A similar assumption in the extraction sector, i.e. a plethora of extraction units, each extracting an infinitesimally small amount of natural gas, would imply that the producer surplus element in the extraction sector vanished. Only the resource rent would remain. 8 The total

6 The expression for the accumulated value of user-cost depends critically on the assumption that there are no stock-cost effects. 7 We abstract from the fixed cost element B; otherwise no production would take place. Also, it is assumed that for all functions g(s) we have

g(s)

lim - s~O

= g'(O).

S

8 In this case, we would have yY = PrYf'(y~. )e ft.

254

E.S. Amundsen/Resource and Energy Economics 19 (1997) 241-259

social surplus from gas power production would then consist of consumer surplus and the resource rent. Thus, even though the gas power industry is a low cost industry compared to marginal hydropower plants, no surplus would remain in the gas power industry. This illustrates the dictum that replicable man-made capital will not have a remuneration above the normal rate of return and that all surplus ends up at the level of Nature's scarce resources. However, with capacity constraints and increasing cost conditions present, ordinary producer surplus and the quasi-rent will pop up also in the gas extraction industry. From a taxation point of view there is an immediate observation to be made here, namely that since not all surplus generated in the extraction of natural gas (or any other non-renewable resource for that matter) constitutes a proper resource rent, it is not correct to subject all surplus in this industry to harsh rent taxation. This is a point which is more or less recognized in practice. At least there exist different tax arrangements around the world that allow a certain amount of positive profit before the specific rent tax applies (e.g. the special 'tax allowance' in the Norwegian petroleum taxation system, the 'uplift' and 'oil allowance' in the British system, the 'carbon allowance' in the Danish system, and the 'uplift' in the taxation system for Canada 'Land'). However, the rationale for having such tax arrangements is not always clearly expressed, and may range from arguments such as favoring of a just distribution of the tax burden, stimulating interest in marginal petroleum projects, and ensuring neutrality of taxation (i.e. neutralizing the tax effect of differences in the composition and timing of investment and operation cost between projects).

6. Transformation of hydroelectric rent into resource rent

While the total social surplus following from the introduction of low cost gas power must be expected to increase due to falling prices and larger consumer surplus, the producer surplus and the economic rent generated may well decrease. The question of how the economic rent and the producer surplus are affected is an important one from a taxation point of view. Indeed, the introduction of a gas power sector may influence governmental tax take in three ways. First, the size of the surplus subject to taxation may change. Secondly, the time-profile of surplus generated may be altered and therefore also the time-profile of taxes. Thirdly, as the surplus is transformed to a sector with a different tax system, the size of the tax revenue captured may be affected. To address the question of the extent to which the reduced hydro rent is offset by resource rent and producer surplus by the introduction of a gas power sector, we consider a hydro rent with and without gas power production. In the case considered it is assumed that gas power production is terminated at date T and that the time-profile of hydropower capacity construction is identical with and without

255

E.S. Amundsen~Resource and Energy Economics 19 (1997) 241-259

gas power production from this date on. 9 Thus the hydro rent generated after date T will also be identical in the two situations. Denoting hydropower production without gas power production by x h', we find that the difference in surplus generated with and without a gas power sector is equal to

fo Y [ p ( x h • +X~ • ; t ) ( x , h, + X g , ) _ p ( X th, , t ) ( x h ' ) ] e - r t d t - { [ b ( x +c(~*)][(1 +

--e-rr)/r]

foa(xh,)z;e-r,dt_

g*)

-- J ( 2 g * ) - B - K ( ~ * ) - C}

r r a ("x t h* Jr'

)zt*e-rt"

(14)

If the demand elasticity is less than one in absolute terms (i.e. inelastic demand), as is normally found in empirical studies of electricity demand (see, for example, Atkinson and Manning, 1994), then the gross revenue term of (14) is negative. This must be so, since we know that total electricity production with a gas power sector is larger than without such a sector. Hence, with inelastic demand gross revenue generated must fall with the introduction of gas power production. This result holds even if the demand elasticity varies over time, as long as it is always less than one. The second term of (14) (in braces) is negative and gives the construction and operating costs of gas reservoir infrastructure and gas power production. The net value of the last two terms is, however, non-negative and gives the present value effects of the differing timing of hydropower production capacity construction. If demand is increasing over time, then the expression is positive and represents the reduced cost in present value terms of delaying the build-up of optimal hydropower production capacity to be utilized at date T. Without gas power production, the build-up of additional hydropower production capacity takes place during the entire time-interval [0, T], whereas with gas power production the build-up is done during a restricted later interval It', T]. Thus, since we assume a cost function for additional production capacity which is linear in physical investment, there will be no extra cost of doing the build-up more intensively and the present value of postponed build-up must, therefore, be lower. If demand is time-invariant, however, the last two terms dissappear, since no additional hydropower production capacity will be built up, in any case. Thus with time-invariant demand and a price elasticity within the normal range,

9 This, assumption involves a potential problem in that the flow-fixed costs in the gas power sector may lead to a downward jump of gas power production at the transistion date (see Section 3.3). This reduction will be compensated by an abrupt increase of hydropower production capacity which may be restricted by the upper boundary of investment (the 'bang-bang' control). If this is the case, then the time-profiles of hydropower capacity construction will not be identical with and without gas power production. To avoid this complication, we allow for a so-called 'impulse control' (see Clark, 1976, p. 58) which, in this setting, essentially means that there is sufficient construction capacity to allow a discontinuous jump in the construction of new hydropower production capacity.

256

E.S. Amundsen/Resource and Energy Economics 19 (1997) 241-259

there will be a reduction of total economic rent generated, i.e. the increase in resource rent (and producer surplus due to large scale construction of infrastructure) is not sufficient to make up for the reduction of hydro rent. An intuitive explanation of this result is simply that the scarcity of Nature's (low cost) production factors for electricity decreases when natural gas is introduced as a production factor in addition to hydropower. For the same reason, total economic rent generated must fall. With increasing demand, the cost saving of postponed hydropower capacity construction could, in principle, outweigh the two other negative effects such that there will be an increase in total rent and producer surplus with gas power production. However, if the investment and operation costs of the gas power sector outweigh the gain from delayed hydropower construction, then economic rent and producer surplus will definitely fall under the assumption of demand elasticities within the normal range. But, not only can the goverment lose a tax base due to reduced rent through the introduction of a gas power sector, it can suffer an unfavorable tilt of the time-profile of taxes. Without a gas power sector the nominal value of rent generated at each instant of time will increase over time provided there are positive shifts of demand over time. This is the classic picture of the development of the Ricardian differential rent as the extensive margin is expanded due to increases in demand. However, with the introduction of gas power based on a non-renewable resource, the Hotelling rule dictates a certain pace of price increases over time and therefore also reductions of production over time (assuming constant or moderately increasing demand). The introduction of a gas power sector may, thus, imply an abrupt reduction of price and rent generated at date 0, followed by a more rapid increase of rent over time as compared to the case without a gas power sector. This change may then have an adverse effect on the tax take of a government favoring stability of taxes, as it tilts the time-profile of taxable surplus away from the present to the future. This effect is easily seen for the case of time-invariant demand. With inelastic demand there is obviously a drop of rent and producer surplus at the date of the introduction of gas power (production is expanded, price drops and deductible expenses on the gas power infrastructure are introduced). From this date there is fairly rapid increase of surplus due to the Hotelling rule (i.e. after the period of constant gas power production). This is seen by taking the time derivative of the Dr, between rent and producer surplus with and without gas power production. Assuming constant depreciation allowances and cost deduction, and denoting demand elasticity by 77, we get

difference,

[ l] "Yert

b,=kf* 1 -

I'(Y,*)

>0.

Inspection of signs shows that this expression is positive, which means that the discrepancy between surplus with and without gas power production is decreasing over time (i.e. from date r on).

E.S. Amundsen~Resource and Energy Economics 19 (1997) 241-259

257

The case of increasing demand is not equally clear-cut. That is, there must obviously also be a drop of rent and producer surplus at date 0, due to the expansion of production and the introduction of investment and operating cost for gas power production. But the difference in the expansion of surplus with and without a gas power sector is not necessarily monotone. Taking the time-derivative of the difference D t between the rent and producer surplus with and without gas power production, we find (assuming constant elastic demand less than 1)

[)t = [ Jct Pt * _.~,tp~][1

1 ] _i_ Op( x,* ) x t

+ [d(xh*)z, * --d(xh')z;

cgP( X't)

+ a ( x h * ) ~ , * -- a ( x h ' ) ~ ; ] .

The first element of this expression is clearly positive since electricity production is falling over time (after date ~-) when gas power production is involved, while electricity production is increasing when only hydropower production is present. However, the second element is indeterminate and depends upon the precise assumption of the positive demand drift over time. The same is true for the last element in parentheses. Thus, the sign of the total expression is indeterminate. However, an assumption that the demand drift is only 'moderate' (i.e. that (Op/Ot) takes low values everywhere) seems sufficient to render the second and third elements negligible. If this is the case, then there will be a monotone tilt of the time-profile of rent and producer surplus away from the present to the future. Finally, it should be observed that since the composition of total rent in the electricity sector changes from pure hydro rent to a combination of hydro rent and resource rent, there may be an effect on the overall level of taxation of electricity production. While the oil and gas sectors in many countries are subject to rent taxation, i.e. a level of taxation above the normal taxation level, the hydropower sector is normally not. 10 Hence, a fair conclusion is that the tax revenue from introducing a significant amount of gas power based on the country's own endowments of natural gas may actually increase even though there is no change in the total rent generated. This is then a partial effect which works in the opposite direction of the two effects discussed above, which may have a negative influence on the governmental tax take.

7. Conclusions The introduction of low cost gas power generation into a system of electricity generation based on hydropower leads to a transformation of hydro rent into

m Canada and Norway may seem like possible exceptions to this general picture since both countries have a specific excise tax on hydro electricity generation. However, these taxes do not constitute any appropriate and harsh rent tax comparable to the rent tax elements of the petroleum taxation system.

258

E.S. Amundsen~Resource and Energy Economics 19 (1997) 241-259

resource rent. In this process the surplus from gas power generation does not remain in the power generating sector itself, but is forwarded to the gas extraction industry by way of appropriately set gas prices (though after some allowance for remuneration to installed capacity, i.e. quasi-rent and some ordinary producer surplus due to increasing cost). This only confirms the old Ricardian dictum that man-made capital warrants no economic rent. In a socially optimally organized production sector, economic rent turns up at the level of Nature's scarce resources. While the introduction of low cost gas power based on natural gas leads to increased social surplus, the effect on govermental tax take may be negative. Total rent (hydro rent and resource rent) might increase due to the changed production structure, or it might not. Assuming constant demand over time and a constant elastic demand with a price elasticity less than one, total rent will definitely decrease. The explanation for this result is simply that the scarcity of Nature's (low cost) production factors for electricity decreases when natural gas is introduced as a production factor in addition to hydropower. For this reason the total economic rent generated must fall, and the tax base for the government is consequently reduced. However, if demand is increasing over time, then the total surplus from introducing low cost gas power may well increase, provided that costs saved from postponed hydropower construction are sufficiently high. The introduction of gas power production may also tilt the time-profile of taxes away from the present and to the future. This may be considered an adverse effect from the point of view of a government favoring stability of taxes. On the other hand, the changed composition of economic rent from a pure hydro rent to a combination of hydro and resource rents may actually imply an increase of tax revenue due to the harsher taxation in the petroleum sector.

Acknowledgements This paper was prepared during a sabbatical visit to Energiewirtschaftliches Institut, University of Cologne, Germany, and at the Department of Economics, University of Copenhagen, Denmark. Financial support from Ruhrgas, NorFa and Statoil, is gratefully acknowledged. I would like to express my gratitude to an ananymous referee for valuable criticism and comments. I am also indebted to colleagues at the above-mentioned universities and at the University of Bergen for helpful comments. The usual disclaimer applies.

References Amundsen, E.S., 1992, Th6ode des Ressources l~puisables et Rente P6troli~re (Economica, Paris). Amundsen, E.S. and S. Tjctta, 1993, Hydroelectric rent and precipitation variability, Energy Economics 15, 81-91.

E.S. Amundsen / Resource and Energy Economics 19 (1997) 241-259

259

Arrow, K.J., 1964, Optimal capital policy, the cost of capital, and myopic decision rules, Annals of the Institute of Statistical Mathematics 16, 20-21 Arrow, K.J., 1968, Optimal capital policy with irreversible investment, in: J.N. Wolfe, ed., Value, capital and growth, Papers in honour of Sir John Hicks (Edinburgh University Press) 1-20. Atkinson, J. and N. Manning, 1994, A survey of international energy elasticities, in: T. Barker et al., eds., Global warming and energy demand (Routledge, London). Bernard, J.-T., G.E. Bridges and A. Scott, 1982, An evaluation of potential Canadian hydro electric rents, University of British Columbia. Resources Paper No. 78. Carnevali, D. and C. Suftrez, 1993, Electricity and the environment: Air pollutant emissions in Argentina, Energy Policy 21, 68-72. Clark, C.W., 1976, Mathematical bioeconomics: The optimal management of renewable resources (John Wiley and Sons, New York). Clark, C.W. and G. Munro, 1975, The economics of fishing and modern capital theory: A simplified approach, Journal of Environmental Economics and Management 2, 92-106. EMRC, 1991, Electric power in Canada 1990 (Energy, Mines and Resources Canada, Minister of Supply and Services Canada). Guldman, J.-M., 1991, Natural gas market expansion and delivery infrastructure costs, Resources and Energy 13, 57-94. Lafrance, G. and D. Perron, 1993, Energy demand impact of incentive programmes, Energy Economics 15,226-231. R0dseth, A, 1982, Optimal timing and dimensioning of hydropower projects, in: O. Bjerkholt et al., eds., Analysis of supply and demand of electricity in the Norwegian economy (Central Bureau of Statistics of Norway, Oslo) 304-330. Seierstad, A. and K. Syds~eter, 1987, Optimal control theory with economic applications (North-Holland, Amsterdam).