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Efficient pricing of natural gas
Journal
of Public
Economics
36 (1988) 1777196.
EFFICIENT
PRICING
North-Holland
OF NATURAL
GAS
A Case Study of Egypt
Ricardo MARTIN Development Research Department, World Bank, Washington, DC 20433, USA
S. VAN WIJNBERGEN* Development Research Department, World Bank, Washington, DC 20433, USA, CEPR and NBER Received
July
1984, revised
version
received
September
1987
1. Introduction
If natural gas is freely traded across international borders, its appropriate shadow price is the international or fuel oil equivalent price net of transport costs.’ However, in many countries this condition does not apply. Exports are often subject to long-term contractual arrangements specifying quantities which, if they are binding, make gas effectively into a non-traded commodity on the margin. Moreover, exporting natural gas involves substantial fixed costs: either a pipeline has to be laid or a liquefaction plant plus special harbor facilities need to be constructed. Such outlays on start up costs are only justifiable economically if gas reserves are large enough. There is, however, an increasing number of countries where gas reserves are too low to justify the large fixed costs involved in setting up such export facilities. But when natural gas is not a tradable commodity, world prices cannot be used as reference price. This is especially true if substitution possibilities with fuel oil are limited on the margin (otherwise the fuel oil equivalent price would once again apply). The standard procedure for solving the ensuing pricing problems consists of the following steps: (a) Assume a ‘plausible’ but arbitrary implied exhaustion date. *Helpful discussions with Kermal Dervis ‘This is strictly true for producer prices Mirrlees (1974). Final consumer prices will the government has only distortionary tax from such second-best problems. In any intermediate use.
0047-2727/88/$3.50
0
1988, Elsevier
extraction
path and calculate
the
are gratefully acknowledged. only, under assumptions spelled out in Little and in general differ from producer prices, if for example instruments to meet its revenue needs. We abstract case, the bulk of natural gas production is for
Science
Publishers
B.V. (North-Holland)
178
R. Martin and S. van Wijnbergen, Efficient pricing
ofnatural gas
(b) Assume, as efficiency requires, that the last unit extracted is priced at the fuel oil equivalent price prevailing at the extraction date. (c) Calculate the implied rent to unit reserves by subtracting marginal extraction costs; then calculate the rental value in each preceding period by applying Hotelling’s rule. This rule states that intertemporal efficiency requires rental values that rise over time at the capital market interest rate. Applying this rule requires an assumption about the appropriate discount rate. (d) Finally, calculate a time path of prices by adding these rental values to the corresponding marginal extraction costs each period. One problem with this procedure is the need to arbitrarily assume an extraction path, rather than derive it from the optimizing principles underlythis procedure cannot incorporate ing the Hotelling rule. Furthermore, extraction costs that are a function of the amount of reserves remaining, and it cannot determine the rent accruing to factors constraining supply, a potentially important component of the shadow prices of gas. In this paper we show how to solve the gas pricing problem incorporating all these issues. We present an intertemporal model endogenously determining optimal extraction patterns and shadow prices, and implement this approach by analyzing gas pricing in Egypt. Egypt has far too few reserves to consider incurring the fixed costs involved in exporting, but will in the near future produce too much for all the gas to be absorbed domestically with low efficiency losses, such as by switching electricity generation from oil to gas. The pricing issue is therefore relevant and non-trivial. In section 2 we discuss the economics of efficient gas pricing, using a simple diagrammatic exposition. Section 3 presents the model used, while section 4 discusses the results. Section 5 has some conclusions and suggestions for extensions. 2. Efficient pricing of natural gas: A diagrammatical
exposition
If natural gas is freely traded across international borders, its shadow price should be its international price net of transportation costs to the ‘burner tip’. However, in many countries international trade is not a relevant alternative for natural gas, mainly because reserves are too small to justify the substantial fixed costs of a liquefaction plant or a pipeline. This is clearly the situation in Egypt. In that case, gas should still be priced at its international fuel oil equivalent price if on the margin it substitutes perfectly for fuel oil (always a traded commodity). This will be the case if, because of the size of reserves or supply constraints, gas output is so low that substitution possibilities and the level of energy demand do not restrict demand on the margin when fuel price equivalence is maintained in pricing gas.
179
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
On the other hand, for higher levels of output (which, of course, is not an exogenous variable), one usually does not face an infinitely elastic demand for gas: as more is produced it has to substitute for other sources of energy in uses where gas is progressively less efficient. Consider first the case where there are no supply constraints on production and distribution of natural gas (fig. 1). If there is a finite amount of gas that will be exhausted, say at time IT;the price of gas has only two components if there are no supply constraints: marginal extraction costs MC, and rent to reserves. Efficient exploitation of the natural gas resource will lead to a rental component rising at the relevant rate of discount, with the price of natural gas reaching its fuel oil equivalent at the moment of exhaustion [Hotelling (1931)]. Which discount rate is relevant depends among other things on the numeraire in which the price of gas is expressed; this is one of course only an issue when relative prices in the rest of the economy are changing over time. The gas price path so derived will provide a floor for the price of gas when Price
Fuel Oil Equivalent Price
Rent pet Unit to Gas Reserves
Unit Extraction Cbsts f
I I
~ T
Time
WorldBank - 41801 1
Fig.
1. Pricing
of natural
gas when use is demand-constrained.
R. Martin and S. van Wijnbergen,
180
Eflcient
pricing of natural gas
supply constraints become binding. In that case the shadow price of gas incorporates a third component: rent to the factors constraining supply. The fuel oil equivalent price will provide a ceiling (see fig. 2). We can thus distinguish three stages in the demand for gas. If supply or distribution constraints limit output to below QA (see fig. 2), substitution possibilities on the demand side have yet to start declining. Substitution of oil by gas in the production of power will typically take place in this first region (0, QA). On the other hand, for output beyond QB, the inverse demand curve implies a price for gas which is actually below the price floor P, set by marginal extraction costs and unit rent to reserves; in that range supply constraints would earn zero rent and will accordingly cease to be binding. That implies we are again in the situation of fig. 1, where marginal extraction costs and unit rent to reserves are the sole components of the efficient gas price. Price of Gas
I
\
Demand for Gas
Domestlc Demand for Gas
PO.
'G PF
PE
1 0
I QA
Fig. 2. The value of natural gas. Notes: AE is a linking total energy use E to its price P. ACBE gas, taking account of the fact that substitution share of gas in total energy increases. PO is reserves plus extraction costs and P, is
I %
I QB
) Quantity of Gas
segment of the inverse demand curve for energy, is the derived inverse demand curv for natural of fuel oil by gas is increasingly difficult as the the fuel oil price equivalent, P, is the rent to the revenue (per unit) from gas exports.
R. Martin and S. uan Wijnbergen, Eflicient pricing of natural gas
181
If the ceiling on output set by constraints on production and distribution of natural gas is at an intermediate value, say Qc, the price will be in between its ceiling PO and its floor PF. As a consequence, a rent RCG, accrues to the supply constraint equal to:
RCGt=PG,-PF,, where PG,= &(QC);& is the inverse demand curve for gas. PF,,the price floor, equals marginal extraction costs plus unit rent to reserves. Note that RCG, could be used in shadow pricing projects that expand distribution facilities (e.g. pipelines) or otherwise increase the availability of gas to users. As time goes on, demand for gas will increase while supply constraints will be relaxed; accordingly, the ratio PGJPO, may go through several phases before it eventually reaches unity. The pricing decision becomes difficult in the stages where this ratio is below one - but also more important since many projects may or may not be justifiable according to which price between PO and PF is used in evaluating gas inputs. In what follows we present and numerically implement a procedure that not only solves this pricing problem, but also determines when such stages begin and end.
3. A long-run optimizing
model
Table 1 contains the basic equations of the model. The non-oil/gas economy consists of two goods (traded and non-traded) and two primary factors of production (labor and capital), plus partially competitive imports. Labor is assumed to be mobile between sectors, while existing capital cannot be shifted once installed in one sector. New capital, on the other hand, is completely malleable. However, in a perfect foresight model like this, the non-malleability of installed capital is binding only at the very beginning of the planning period. The model is optimized over 20 successive units of time: each unit is calibrated to represent 2 years. There are several sets of constraints. First, for each good, the material balance equations [eq. (l)] (equation numbers refer to the numbers in table 1) limit total demand for intermediate use, consumption, investment and export (the latter for traded goods only) to the available supply. The main assumption incorporated in (1) is that new capital uses traded goods, nontraded goods and non-competitive imports in constant proportions. Eq. (2) is the balance of payment constraint. External borrowing, remittances and income from the Suez Canal are exogenous (variable Ft), so that (2) limits the amount by which total imports (for intermediate use, consumption and investment) can exceed export revenues (from oil and traded goods). The international prices of oil and of other imports are exogenous, but the price
R. Martin and S. van Wijnbergen,
182
Table Equations Eq. no.
Dual variables
(da) (4b)
CW IPBOP,l [PO,1 IPGNJ CPGI
(5)
[PVi.]
(1)
(2) (3)
(10) (11) (12.a)
IPK,I CPGI CPWI [PW CPKi,l [PI,1 CPU,1
(1W
Max
(7)
(8) (9)
gas
1
of the model.
Equations ~ja,jQj,+Ci,+sil,+Xi,~Qi,,
i=N,T
Cj a,,@, + CM, + sml, 5 rtO,XO, + n7;(X7; - C7;) + F, EN, + E7; + X0, i QO, + QG, ENG, 5 I(I&Nr
QG,-ENGS,(I/,,ET Qi,~~A(a,,Ei~SL’+(l-aaEi)Vi;SE’)~’~SEi, with
(6)
Efficient pricing of natural
i=N,T
Vi, =(a,iLi;SY’+a,iKi;SY3_‘ISYI i=O,G
Qi, 5 aKiKi,, Qi, 5 Hi,,
i=O,G
1 Li, 5 f;, = L,( 1.05)’ Ri,zRi,_,-Qi,,
i=O,G
Ki,sKi,_,DEP+li,_,, CIi,j
i=N,T,G
=r,=Io(l.O55)’
U,= [a,CN~~sC+(l-a,)(a,CM;ST+(l-a,)CT;Sr)sC~sT]~L~SC x U;pF’
Notes: 1. See table 3 for a list of variables. 2. The associated dual variables are shown
in square
brackets.
received from exports of traded goods (nT) falls with increases in export volume. That is, non-oil exports can be expanded beyond a trend only at the cost of declining terms of trade. Eq. (3) imposes a balance between total use of energy and its supply: production of oil and gas. As discussed in the previous section, only a certain proportion of the demand for energy can use gas or oil products with equal efficiency. The model dramatizes that fact by assuming zero effkiency for gas beyond a share rjN, It/r in each sector [eqs. (4a) and (4b)]. Those shares are assumed to gradually increase over time,2 to reflect the fact that there is more room for fuel substitution before equipment using it has been installed. Total output in each sector is related to primary factors and energy use via a two-level CES production function [eq. (5)]: labor and capital combine to produce value-added, which can, in turn, be combined with different proportions of energy to produce final output. For a given sectoral allocation of primary factors, the sectoral demand for energy has elasticity qEi= -cEi/( 1 -a,,), where uEi is the share of energy in the value of output and crEi= l/( 1 + SEl’) is the elasticity of substitution between energy and value21n 9 periods they sectors, respectively.
go from
0.5 in both
sectors
to 0.8 and
0.55 in non-traded
and
traded
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
183
added. The elasticity of the aggregate demand for energy is larger than the weighted average of the sectoral elasticities, since both sectors differ in their energy intensity and sectoral demand are price responsive; thus an increase in the price of oil reduces energy use not only by substituting with primary factors (if a,>O), but also by changing the composition of total output towards a lower energy intensive mix. There are also capital requirements for the production of oil and gas (although we ignore their direct use of labor), as shown in eq. (6). In addition, production may be constrained by output limits as well [eq. (7)]. These capacity constraints will play an important role later on. We view them as arising from two different sources. First, it takes some time to put a given reservoir into production and to create the infrastructure for transporting the gas from the field to the users. This is more important at the initial stages of gas development. Therefore we expect this type of capacity constraint to be binding, if at all, at the begining of the planning period only. The second source of constraints on the rate at which reserves can be extracted is an upper limit given by the technical characteristics of the reservoir (e.g. gas pressure). It is not entirely a technical constraint, of course, since it depends on the number of wells drilled, their location, etc.; it gives an upper bound, and one that may be binding even when significant reserves are still available. Note that eqs. (6) and (7) assume that oil and gas output can be separately controlled. Some of the natural gas produced comes from wells in which oil is the main output (associated gas), but in fact all we need, of course, is that there is enough dry gas (i.e. gas not associated with oil) for it to constitute the marginal source of supply at least during most of the planning period. Eq. (8) gives the overall labor availability; the labor force grows at 2.7 percent per year (i.e. at 5 percent per period). Next are the stock-updating equations [eqs. (9) and (lo)]: oil and gas reserves are depleted by extraction (all future discoveries are already included in the initial stocks RO,, RG,), and the capital stock increases by new investment and decreases by depreciation. Total investment is exogenous; it is assumed to grow at 5.5 percent per year. See Dervis, Martin and van Wijnbergen (1985) for a discussion of optimal investment paths with and without foreign borrowing. The assumption of exogenous investment considerably simplifies the numerical solution of the model; its principal effect on the solution is to reduce the flexibility of the economy to adjust to alternative reserve and price scenarios. Changes in investment would affect gas shadow prices through (i) changes in the demand for energy, and (ii) changes in the social rate of discount; neither of them affect the qualitative nature of the results. The above set of constraints defines the intertemporal production possibility set for the economy. As mentioned above, out time horizon is 20 periods. Each represents two calendar years. This is large enough to allow complete exhaustion of oil and gas reserves. As these are the only endogenous stocks
184
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
in the economy, no terminal constraint is required to force the model to account for future generations. The model selects the path for production and consumption which maximizes the discounted sum of utility of consumption [eq. (12)]. The basic parameters defining social objectives are: substitution in consumption between non-traded and traded (imported and domestically produced) goods, SC and S7; elasticity of the marginal utility of real consumption (#J- l), and pure rate of time preference (6- 1). As part of the optimal solution we obtain shadow prices for all constraints of the model. Those shadow prices must satisfy a set of conditions (table 2), which make them equivalent to the market prices that would obtain in competitive markets with perfect foresight. However, given our focus on the pricing of natural gas, we will discuss only those equations relevant for that issue. The basic equation is (D.3), which must hold whenever there is positive production of gas. The right-hand side gives the value of one additional unit of natural gas (PC). There are two possible regimes: ‘expensive’ or ‘cheap’ gas, with the price of gas at or below the oil equivalent price, respectively.3 The first regime obtains when gas output is below the maximum allowed by the energy substitution possibilities, so that eq. (4) is not binding and PGT is zero. With binding demand constraints, on the other hand, gas should be cheaper; of course, the economy should use more energy-intensive processes under this regime [eq. (D.S)].” The left-hand side of (D.3) decomposes the price of gas into cost of extraction (PVG+~iPiai,) plus rent to output constraint (PCG),and rent to reserves (PRG).The latter component changes over time according to the Hotelling rule (D.9): in utility numeraire it grows at the pure rate of time preference, 6- 1; in terms of a more conventional numeraire, such as real consumption (whose utility price is PV),it would grow at the consumption rate of interest, which is an endogenous variable in the model. But even with good estimates of the social rate of discount, we cannot determine PC without also simultaneously determining the optimal extraction path. This is for two reasons: first, we need to know the period in which reserves are exhausted to determine the rent to reserves via, the Hotelling equation. (At this moment neither production nor demand constraints would be binding, so that PG=PO and PRG is everything in excess of the cost of extraction.) Second, the residual between the price of oil and the cost of gas extraction plus gas rental value must be assigned between the capacity constraint (PCG) and reduced price to gas users (PGT,PGN). This trade-off clearly depends on the output level, hence the additional importance of the extraction path. sThe price of oil is of course given by the international price, since it is fully tradable [eq. (D.6)]. The price of gas can never be above the oil price equivalent, since oil is assumed to be at least as efficient as gas in all uses. 4The treatment of the premia of oil over gas in each sector, PGT and PGN, is only apparently asymmetric; it can never be optimal to be demand-constrained in only one sector, since gas is assumed to be freely transportable between sectors. And indeed (D.4) forces PGN = PGT
R. Martin
and S. van Wijnbergen,
Efficient pricing of natural gas
Table
185
2
Dual equations.
Ea. no.
P.1) (D.2) (D.3) (D.4) (D.5)
(D.6) (D.7)
(D.8) (D.9) (D.lO) (D.11) (D.12)
Primal variables
lQ_J [QQI lQG1 IENGI CEil lx01 [XT1 [K&l I&l C&l [Lil [Gil
Dual eauations x,Pia,+PVjLPj,
j=N,T
xi Pia,, + PVO + PC0 + PRO 2 PO xiPiaic+PVG+PCG+PRG=PO-PGT=PG PGN-PGT=O PVi dQi/dEi= PO - $,PGi,
i = N, T
PO = PBOPnO PT=PBOPd(nTXT)/3XT PKi,=d(PKi,+
,DEP-
VPi,+I SQijaKi)
PRi, = GPRi, + 1 PI, = 6PKi,+, PW=PVidQi/dLi, Pi=PU,dU/aCi,
i=N,T i=N,T,M
Notes: 1. See table 3 for definitions of the variables. 2. The associated primal variables are shown in square 3. The time subindexes are omitted when all variables same period.
4. Discussion
brackets. refer to the
of the results
We first present a ‘base case’. There, size of reserves, technology of oil and gas substitution, structure of extraction costs and so on reflect what is known about natural gas in Egypt in the base year, 1981. The resulting intertemporal pattern of shadow prices for natural gas and the corresponding components of those prices is given in fig. 3. We than present a sensitivity analysis of the structure of gas prices. Specifically, we look at the impact of changes in: (a) higher output capacity; (b) the share of total energy demand that can be satisfied through natural gas before the marginal rate of substitution starts to decline; (c) the size of natural gas reserves; (d) the substitution elasticity between energy and non-energy factors of production; (e) oil prices. For the base case, we find a window of natural gas is less valuable to the economy products (see fig. 3). During that period the about 80 percent of its oil equivalent price, infrastructure for production and distribution
about 10 years during which than caloric equivalent oil shadow price of gas drops to starting around 1980, as the of gas expands to a level that
R. Martin and S. van Wijnbergen, Efjicient pricing of natural gas
186 80
70
60
50
I; 2
40
2
30
20 ,’
,’
-PO
,’ ,’
-----
pG
._._ ____.
pReserves
-‘-‘-.
P Resaves & Capoclty
,’ ,’
,_,’
10
0 1980
I
I
I
19GU
I
I
2m
I
I
2010
2020
Time World Bank -
Fig. 3. Decomposition
41801 3
of price of gas
allows substituting oil products in essentially all uses in which gas is equally efficient. Later on, the aggregate economy expands, and with it the demand for energy; gas output then becomes again constrained by capacity limits, which now reflect the maximum flow of gas obtainable from the known reservoirs. Therefore, the price of gas again becomes equal to the oil equivalent price.
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
187
As fig. 3 indicates, only at the peak of the excess supply period is the price of gas equal to just cost of extraction plus rent to reserves. In all other periods production is at capacity. Both capacity and demand constraints are binding simultaneously in those other periods; this is possible because of the energy elasticity of aggregate demand. This energy elasticity results from induced changes in the composition of output and from direct substitution with other primary factors, as discussed in section 3. In fact, the whole window period is one of constant energy use, since the output constraint on gas is fixed during that period; this can only be implemented in a growing economy by rapidly increasing energy prices. The opposite case of almost never binding output capacity is presented in fig. 4. In that run we assume a considerably higher flow output capacity. As a result, from period 4 onwards production of gas is only limited by total available reserves. This clearly represents an extreme case. Under this scenario, thk price of gas equals marginal cost of extraction plus rent to reserves. Accordingly, there is a long period during which the shadow price falls below the fuel oil equivalent price. Interestingly, the maximum and average gaps are smaller than in the base case, as no sharp drop and subsequent steep increase in the price is needed to maintain a constant level of demand, as in the base scenario. Table 4 and figs. 5-9 summarize the results obtained by changing some critical parameters in the model itself. Consider first the coefftcients Icli, the maximum share of energy that can be satisfied with gas instead of oil products without loss of efficiency. In the base run, this share starts at 50 percent for both sectors and then increases gradually over the next 15-20 years (reflecting delays in retiring equipment, diffusion of knowledge, etc.). If the initial value is reduced to 40 percent (but follows the same relative increase over time as before), the effect on PC is significant: the window period expands to 20 years, with an average gap of almost 30 percent. But 40 percent is an unrealistically low estimate of the range within which gas is a good substitute for other energy products. The other case, in which 60 percent is the limit below which oil and gas are perfect substitutes, results in almost complete elimination of the window period (fig. 5). The total level of gas reserves is not a very important determinant of the price of gas unless it is associated with changes in output capacity. This is demonstrated in fig. 6. The low reserves scenario assumes 400 million tons of oil equivalent, that is 30 percent lower than the base case level of 570 million tons. The effect is to reduce the average gap between the prices of oil and gas from 19 to 12 percent (table 3), but keeping the same period of cheap gas as before. The rent to reserves is significantly larger in this case, representing all of the residual between the price of gas and the cost of extraction. Large reserves (840 million tons of oil equivalent, or 47 percent more than the base case) have almost no effect on the value of gas if the base scenario for output capacity is left unchanged: under those conditions they only increase further
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
188
1 70 -
60
-
50
-
=‘ g v) 2
40-
30
-
01 1980
I
I 1990
I
I
-
PO
-----
PGmse
--~------
PG HluhCapoclty
I
I
2030
I
2010
2020
Ttme World Bank -
Fig. 4. Price of oil and gas. Gas output
41801 4
capacity.
the rent that accrues to that constraint while reducing the depletion premium, with no net effect on PG. With a larger, non-binding, output constraint the results are more dramatic (fig. 6): we obtain the extended window characteristic of unconstrained output together with the low depletion premium associated with large reserves; the average gap is now close to 30 percent and lasts for essentially the whole planning period.
R. Martin and S. van Wijnbergen, Table
Eflicient pricing of natural gas
189
3
List of variables. (a) Primal Qcf I
Ii Xi Ei ENG Ki, Li Ri (b) Dual Pi PVi PCi PRi PGi rri PKi PI PW PBOP (c) Parameters rri aij
si ahi SEi, S Vi aN, aT SC,ST DEP F, Hi, *it 4 ****** The sectors
=Gross output, i=N,T,O,G = Consumption, i=N,M,T =Total investment =Investment in sector i, i=N,T,G = Exports, i = T, 0 = Energy use in sector i, i=N,T =Natural gas used in the non-traded sector =Capital, labor, used in sector i, i= N,T,G =Stock of reserves at the end of the period, = Price of good i, i = N, T, 0, G = Unit value added, i = N, T, 0, G =Rent to output constraint, i=O,G = Rent to reserves, i = 0, G = Premium of oil over gas as source of energy = World prices, i = 0, T = Value of installed capital, i = N, T, G =Value of new capital = Wages = Price of foreign exchange
i=O,G
in sector
i, i = N, T
= World prices of oil and traded goods, i=O, T = Unit input of good i in the production of good j, i = N, T, M, j=N,T,O,G = Unit requirement of good i in new capital goods, i = N, T, M = Share coefficients in production functions, h = E, L, K, i = N, T = Elasticity parameters in production functions, i = N, T =Share coefficients in utility function = Substitution parameters in utility function = Depreciation factor for capital goods (1 -depreciation rate) = Exogenous inflows of foreign exchange (workers remittances, revenue from Suez Canal, aid) = Production capacity for oil and gas, i = 0, G =Share of energy that can be satisfied with natural gas or oil producers with equal efficiency, i=N,T =Elasticity of the marginal utility of real income = Pure time preference factor (1 + rate of time preference) are: N = non-traded;
T = traded;
0 = oil; G = gas; M = imports.
Next we present the effects of changing the ease with which energy and other primary inputs can substitute for each other in production. As discussed in section 3, we postulate a production function which is separable in energy and other factors or production. The relevant parameters are the elasticities of substitution ~~~~ which together with the energy shares define the elasticities of the sectoral demand for energy (see above). In the base scenario, oET = oEN = 0.8. That implies sectoral demand functions with elasticities between 0.9 and 1. For the high elasticity simulation we increase gET to 1.4. That gives considerably more flexibility to the economy, increasing the window period to 14 years; the effect comes via a lower rate of growth of the
R. Martin and S. van Wijnbergen, Efficient pricing o/ natural gas
190
Table 4 Sensitivity
analysis
of the gas-oil
Number of period with PG
4. Elasticity of substitution between energy and primary factors: (a) Low (uET = cEN = 0.4) (b) High (u ET= 1.4, CEN0.8) reserves Low (400) High (840) High reserves and large production capacity
6. Price of oil (a) Constant price (b) Low growth (2%) (c) High growth (3%) Note: Each year represents
.w
11
[Gl]
11
35
WI
1
4
fS31 CSll
3 7
27 31
19 19
fR21 IR41
5 5
[R4A]
15
16 36 40
12 20 28
0
0 17 17
5
3. Maximum share of energy demand that can be satisfied with gas: (a) Low (40%) (b) High (60%)
Average
[Cl]
1. Base 2. Large gas production capacity
Maximum
gap (%I 30 25
Case
5. Gas (a) (b) (c)
price gap.
CPll 0 cp21 3 CP31 6 two calendar
26 19
(%I
38 4
10 17
_
years.
overall demand for energy due to increasing real prices; this in turn makes the output constraints on gas non-binding during a longer period. The opposite effect is obtained with low substitution elasticities (fig. 7): a window of just 6 years, with an average oil-gas price differential of 19 percent, as the demand for energy grows at almost the same rate as the economy, despite increasing prices for natural gas. The final set of scenarios explores the sensitivity of the results to present and future oil prices; see fig. 8. Clearly, the price of oil is an important variable for the valuation of gas, in whatever way the latter is calculated. The main reason is again the impact on the aggregate demand for energy. This impact comes through two channels: first, from factoral substitution and variations in the composition of output and, second, from a smaller rate of growth of the economy, as future oil prices increase more rapidly. When the real price of oil grows slowly or not at all, the demand for energy increases via those two effects. This also increases the demand for gas, with the result that the oil-gas substitution penalty (i.e. the difference in their prices) becomes smaller (when PO grows at 2 percent), or is eliminated entirely (when PO is constant).
R. Martin and S. van Wijnbergen, Efjicient pricing
of natural gas
191
80
70
60
50
2 >
40
2
30
20
-FO
10
0
L
1980
I
I
I
1990
I
----
FGEKlse(50%)
---------._._
FGLOW(40%)
I
2000
FG High (80%)
I
I
2010
2020
Time World Bank -
Fig. 5. Price of oil and gas. Maximum
share
of energy
demand
that can be satisfied
41801 5
with gas.
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
192
80
70
60
50
2 > 5
40
30
20
-PO -----
FG Bose
--------10
-
--
------
FGLowReserves --
FG Loi@z Reserves PG Large Resaves&Capac~ty
0 1980
1990
2000
2010
2020
Time
World Bank - 418016
Fig. 6. Price of oil and gas. Gas reserves.
R. Martin
and S. van Wijnbergen, Efficient pricing of natural gas
8o-
7
0
o-
o-
5t 3-
is> 4cI3
30
20
-PO -------------
IO
0
FGEase
193
R. Martin and S. van Wijnbergen, Efficient pricing
194
of natural
gas
11
09
08
07
04
03
02
PG/PO Base
_--_
PCjPG
--_------
PO/PG3%Grow+hPO
-.-.-
PO/PG’Z%GrowthPO
Constant 011 Price
01
0
I
I 1990
1980
I
I
I
2000
I
I
2020
2010
TIm0
World Bank -
Fig. 8. Ratio
of price of gas to price of oil. Different
price scenarios.
41801 8
195
R. Martin and S. van Wijnbergen, Efjicient pricing of natural gas
80 ,’
r’ ,’
I’ ,’ >’ ,’
70
r’ #’ #’ 3’ ,’
60
50 ,’
3 2 2
1’ >’ 8’
,’
40
/ i’
,.’
PG Bose PG
_._______ FG -.-.F’S
1980
1990
2000
Constant 011 Price 3% Growth PO 2% Growth PO
2020
2010
Time World Bank -
Fig. 9. Price of gas. Different price scenarios.
418019
196
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
5. Conclusions
Standard procedures to compute the shadow price of gas cannot handle output supply constraints or reserve-dependent extraction costs satisfactorily. In this paper we set up a methodology that can incorporate such factors; and present an application to the case of Egypt. Implementing this procedure calls for solving a non-linear intertemporal optimization problem, which was done numerically. The solution clearly demonstrates the importance of those cost components and hence the usefulness of our methodology. The most salient feature of the solution is that under almost all scenarios there is a significant period during which gas should be priced below its fuel oil equivalent price. This is clearly very important for projects where large use of natural gas is contemplated, such as steel mill construction and so on. We provide an extensive analysis of the sensitivity of the size and duration of this gap with respect to oil prices, structure of energy demand, size of gas reserves and ‘tightness’ of supply constraints. This study has established both the feasibility and the usefulness of the intertemporal optimization procedures outlined and implemented in the previous sections. Simplifications, moreover, are clearly possible, especially in modelling total energy demand; to use a multisector general equilibrium model (even if it is a small one like the one used here) to generate an aggregate demand curve for energy is probably overly cumbersome. Furthermore, practical extensions and improvements could be made, especially in modelling substitution between gas and other sources of energy and in the structure of extraction costs. Finally, a difficult but important extension would be the explicit incorporation of uncertainty about future oil prices and size of gas reserves.
References Dervis, K., R. Martin and S. van Wijnbergen, 1985, Policy analysis of shadow pricing, foreign borrowing and resource extraction in Egypt, World Bank Staff Working paper no. 622 (World Bank, Washington). Diamond, P. and J. Mirrlees, 1971, Optimal taxation and public production, American Economic Review, 61, 261-278. Hotelling, H., 1931, The economics of exhaustible resources, Journal of Political Economy, 39, 137-175. Little, I.M.D. and J. Mirrlees, 1974, Project appraisal and planning for developing countries (Heinemann Educational Books, London). Neary, J.P. and S. van Wijnbergen 1986, Natural Resources and the Macroeconomy (MIT Press, Cambridge, MA).
of Public
Economics
36 (1988) 1777196.
EFFICIENT
PRICING
North-Holland
OF NATURAL
GAS
A Case Study of Egypt
Ricardo MARTIN Development Research Department, World Bank, Washington, DC 20433, USA
S. VAN WIJNBERGEN* Development Research Department, World Bank, Washington, DC 20433, USA, CEPR and NBER Received
July
1984, revised
version
received
September
1987
1. Introduction
If natural gas is freely traded across international borders, its appropriate shadow price is the international or fuel oil equivalent price net of transport costs.’ However, in many countries this condition does not apply. Exports are often subject to long-term contractual arrangements specifying quantities which, if they are binding, make gas effectively into a non-traded commodity on the margin. Moreover, exporting natural gas involves substantial fixed costs: either a pipeline has to be laid or a liquefaction plant plus special harbor facilities need to be constructed. Such outlays on start up costs are only justifiable economically if gas reserves are large enough. There is, however, an increasing number of countries where gas reserves are too low to justify the large fixed costs involved in setting up such export facilities. But when natural gas is not a tradable commodity, world prices cannot be used as reference price. This is especially true if substitution possibilities with fuel oil are limited on the margin (otherwise the fuel oil equivalent price would once again apply). The standard procedure for solving the ensuing pricing problems consists of the following steps: (a) Assume a ‘plausible’ but arbitrary implied exhaustion date. *Helpful discussions with Kermal Dervis ‘This is strictly true for producer prices Mirrlees (1974). Final consumer prices will the government has only distortionary tax from such second-best problems. In any intermediate use.
0047-2727/88/$3.50
0
1988, Elsevier
extraction
path and calculate
the
are gratefully acknowledged. only, under assumptions spelled out in Little and in general differ from producer prices, if for example instruments to meet its revenue needs. We abstract case, the bulk of natural gas production is for
Science
Publishers
B.V. (North-Holland)
178
R. Martin and S. van Wijnbergen, Efficient pricing
ofnatural gas
(b) Assume, as efficiency requires, that the last unit extracted is priced at the fuel oil equivalent price prevailing at the extraction date. (c) Calculate the implied rent to unit reserves by subtracting marginal extraction costs; then calculate the rental value in each preceding period by applying Hotelling’s rule. This rule states that intertemporal efficiency requires rental values that rise over time at the capital market interest rate. Applying this rule requires an assumption about the appropriate discount rate. (d) Finally, calculate a time path of prices by adding these rental values to the corresponding marginal extraction costs each period. One problem with this procedure is the need to arbitrarily assume an extraction path, rather than derive it from the optimizing principles underlythis procedure cannot incorporate ing the Hotelling rule. Furthermore, extraction costs that are a function of the amount of reserves remaining, and it cannot determine the rent accruing to factors constraining supply, a potentially important component of the shadow prices of gas. In this paper we show how to solve the gas pricing problem incorporating all these issues. We present an intertemporal model endogenously determining optimal extraction patterns and shadow prices, and implement this approach by analyzing gas pricing in Egypt. Egypt has far too few reserves to consider incurring the fixed costs involved in exporting, but will in the near future produce too much for all the gas to be absorbed domestically with low efficiency losses, such as by switching electricity generation from oil to gas. The pricing issue is therefore relevant and non-trivial. In section 2 we discuss the economics of efficient gas pricing, using a simple diagrammatic exposition. Section 3 presents the model used, while section 4 discusses the results. Section 5 has some conclusions and suggestions for extensions. 2. Efficient pricing of natural gas: A diagrammatical
exposition
If natural gas is freely traded across international borders, its shadow price should be its international price net of transportation costs to the ‘burner tip’. However, in many countries international trade is not a relevant alternative for natural gas, mainly because reserves are too small to justify the substantial fixed costs of a liquefaction plant or a pipeline. This is clearly the situation in Egypt. In that case, gas should still be priced at its international fuel oil equivalent price if on the margin it substitutes perfectly for fuel oil (always a traded commodity). This will be the case if, because of the size of reserves or supply constraints, gas output is so low that substitution possibilities and the level of energy demand do not restrict demand on the margin when fuel price equivalence is maintained in pricing gas.
179
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
On the other hand, for higher levels of output (which, of course, is not an exogenous variable), one usually does not face an infinitely elastic demand for gas: as more is produced it has to substitute for other sources of energy in uses where gas is progressively less efficient. Consider first the case where there are no supply constraints on production and distribution of natural gas (fig. 1). If there is a finite amount of gas that will be exhausted, say at time IT;the price of gas has only two components if there are no supply constraints: marginal extraction costs MC, and rent to reserves. Efficient exploitation of the natural gas resource will lead to a rental component rising at the relevant rate of discount, with the price of natural gas reaching its fuel oil equivalent at the moment of exhaustion [Hotelling (1931)]. Which discount rate is relevant depends among other things on the numeraire in which the price of gas is expressed; this is one of course only an issue when relative prices in the rest of the economy are changing over time. The gas price path so derived will provide a floor for the price of gas when Price
Fuel Oil Equivalent Price
Rent pet Unit to Gas Reserves
Unit Extraction Cbsts f
I I
~ T
Time
WorldBank - 41801 1
Fig.
1. Pricing
of natural
gas when use is demand-constrained.
R. Martin and S. van Wijnbergen,
180
Eflcient
pricing of natural gas
supply constraints become binding. In that case the shadow price of gas incorporates a third component: rent to the factors constraining supply. The fuel oil equivalent price will provide a ceiling (see fig. 2). We can thus distinguish three stages in the demand for gas. If supply or distribution constraints limit output to below QA (see fig. 2), substitution possibilities on the demand side have yet to start declining. Substitution of oil by gas in the production of power will typically take place in this first region (0, QA). On the other hand, for output beyond QB, the inverse demand curve implies a price for gas which is actually below the price floor P, set by marginal extraction costs and unit rent to reserves; in that range supply constraints would earn zero rent and will accordingly cease to be binding. That implies we are again in the situation of fig. 1, where marginal extraction costs and unit rent to reserves are the sole components of the efficient gas price. Price of Gas
I
\
Demand for Gas
Domestlc Demand for Gas
PO.
'G PF
PE
1 0
I QA
Fig. 2. The value of natural gas. Notes: AE is a linking total energy use E to its price P. ACBE gas, taking account of the fact that substitution share of gas in total energy increases. PO is reserves plus extraction costs and P, is
I %
I QB
) Quantity of Gas
segment of the inverse demand curve for energy, is the derived inverse demand curv for natural of fuel oil by gas is increasingly difficult as the the fuel oil price equivalent, P, is the rent to the revenue (per unit) from gas exports.
R. Martin and S. uan Wijnbergen, Eflicient pricing of natural gas
181
If the ceiling on output set by constraints on production and distribution of natural gas is at an intermediate value, say Qc, the price will be in between its ceiling PO and its floor PF. As a consequence, a rent RCG, accrues to the supply constraint equal to:
RCGt=PG,-PF,, where PG,= &(QC);& is the inverse demand curve for gas. PF,,the price floor, equals marginal extraction costs plus unit rent to reserves. Note that RCG, could be used in shadow pricing projects that expand distribution facilities (e.g. pipelines) or otherwise increase the availability of gas to users. As time goes on, demand for gas will increase while supply constraints will be relaxed; accordingly, the ratio PGJPO, may go through several phases before it eventually reaches unity. The pricing decision becomes difficult in the stages where this ratio is below one - but also more important since many projects may or may not be justifiable according to which price between PO and PF is used in evaluating gas inputs. In what follows we present and numerically implement a procedure that not only solves this pricing problem, but also determines when such stages begin and end.
3. A long-run optimizing
model
Table 1 contains the basic equations of the model. The non-oil/gas economy consists of two goods (traded and non-traded) and two primary factors of production (labor and capital), plus partially competitive imports. Labor is assumed to be mobile between sectors, while existing capital cannot be shifted once installed in one sector. New capital, on the other hand, is completely malleable. However, in a perfect foresight model like this, the non-malleability of installed capital is binding only at the very beginning of the planning period. The model is optimized over 20 successive units of time: each unit is calibrated to represent 2 years. There are several sets of constraints. First, for each good, the material balance equations [eq. (l)] (equation numbers refer to the numbers in table 1) limit total demand for intermediate use, consumption, investment and export (the latter for traded goods only) to the available supply. The main assumption incorporated in (1) is that new capital uses traded goods, nontraded goods and non-competitive imports in constant proportions. Eq. (2) is the balance of payment constraint. External borrowing, remittances and income from the Suez Canal are exogenous (variable Ft), so that (2) limits the amount by which total imports (for intermediate use, consumption and investment) can exceed export revenues (from oil and traded goods). The international prices of oil and of other imports are exogenous, but the price
R. Martin and S. van Wijnbergen,
182
Table Equations Eq. no.
Dual variables
(da) (4b)
CW IPBOP,l [PO,1 IPGNJ CPGI
(5)
[PVi.]
(1)
(2) (3)
(10) (11) (12.a)
IPK,I CPGI CPWI [PW CPKi,l [PI,1 CPU,1
(1W
Max
(7)
(8) (9)
gas
1
of the model.
Equations ~ja,jQj,+Ci,+sil,+Xi,~Qi,,
i=N,T
Cj a,,@, + CM, + sml, 5 rtO,XO, + n7;(X7; - C7;) + F, EN, + E7; + X0, i QO, + QG, ENG, 5 I(I&Nr
QG,-ENGS,(I/,,ET Qi,~~A(a,,Ei~SL’+(l-aaEi)Vi;SE’)~’~SEi, with
(6)
Efficient pricing of natural
i=N,T
Vi, =(a,iLi;SY’+a,iKi;SY3_‘ISYI i=O,G
Qi, 5 aKiKi,, Qi, 5 Hi,,
i=O,G
1 Li, 5 f;, = L,( 1.05)’ Ri,zRi,_,-Qi,,
i=O,G
Ki,sKi,_,DEP+li,_,, CIi,j
i=N,T,G
=r,=Io(l.O55)’
U,= [a,CN~~sC+(l-a,)(a,CM;ST+(l-a,)CT;Sr)sC~sT]~L~SC x U;pF’
Notes: 1. See table 3 for a list of variables. 2. The associated dual variables are shown
in square
brackets.
received from exports of traded goods (nT) falls with increases in export volume. That is, non-oil exports can be expanded beyond a trend only at the cost of declining terms of trade. Eq. (3) imposes a balance between total use of energy and its supply: production of oil and gas. As discussed in the previous section, only a certain proportion of the demand for energy can use gas or oil products with equal efficiency. The model dramatizes that fact by assuming zero effkiency for gas beyond a share rjN, It/r in each sector [eqs. (4a) and (4b)]. Those shares are assumed to gradually increase over time,2 to reflect the fact that there is more room for fuel substitution before equipment using it has been installed. Total output in each sector is related to primary factors and energy use via a two-level CES production function [eq. (5)]: labor and capital combine to produce value-added, which can, in turn, be combined with different proportions of energy to produce final output. For a given sectoral allocation of primary factors, the sectoral demand for energy has elasticity qEi= -cEi/( 1 -a,,), where uEi is the share of energy in the value of output and crEi= l/( 1 + SEl’) is the elasticity of substitution between energy and value21n 9 periods they sectors, respectively.
go from
0.5 in both
sectors
to 0.8 and
0.55 in non-traded
and
traded
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
183
added. The elasticity of the aggregate demand for energy is larger than the weighted average of the sectoral elasticities, since both sectors differ in their energy intensity and sectoral demand are price responsive; thus an increase in the price of oil reduces energy use not only by substituting with primary factors (if a,>O), but also by changing the composition of total output towards a lower energy intensive mix. There are also capital requirements for the production of oil and gas (although we ignore their direct use of labor), as shown in eq. (6). In addition, production may be constrained by output limits as well [eq. (7)]. These capacity constraints will play an important role later on. We view them as arising from two different sources. First, it takes some time to put a given reservoir into production and to create the infrastructure for transporting the gas from the field to the users. This is more important at the initial stages of gas development. Therefore we expect this type of capacity constraint to be binding, if at all, at the begining of the planning period only. The second source of constraints on the rate at which reserves can be extracted is an upper limit given by the technical characteristics of the reservoir (e.g. gas pressure). It is not entirely a technical constraint, of course, since it depends on the number of wells drilled, their location, etc.; it gives an upper bound, and one that may be binding even when significant reserves are still available. Note that eqs. (6) and (7) assume that oil and gas output can be separately controlled. Some of the natural gas produced comes from wells in which oil is the main output (associated gas), but in fact all we need, of course, is that there is enough dry gas (i.e. gas not associated with oil) for it to constitute the marginal source of supply at least during most of the planning period. Eq. (8) gives the overall labor availability; the labor force grows at 2.7 percent per year (i.e. at 5 percent per period). Next are the stock-updating equations [eqs. (9) and (lo)]: oil and gas reserves are depleted by extraction (all future discoveries are already included in the initial stocks RO,, RG,), and the capital stock increases by new investment and decreases by depreciation. Total investment is exogenous; it is assumed to grow at 5.5 percent per year. See Dervis, Martin and van Wijnbergen (1985) for a discussion of optimal investment paths with and without foreign borrowing. The assumption of exogenous investment considerably simplifies the numerical solution of the model; its principal effect on the solution is to reduce the flexibility of the economy to adjust to alternative reserve and price scenarios. Changes in investment would affect gas shadow prices through (i) changes in the demand for energy, and (ii) changes in the social rate of discount; neither of them affect the qualitative nature of the results. The above set of constraints defines the intertemporal production possibility set for the economy. As mentioned above, out time horizon is 20 periods. Each represents two calendar years. This is large enough to allow complete exhaustion of oil and gas reserves. As these are the only endogenous stocks
184
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
in the economy, no terminal constraint is required to force the model to account for future generations. The model selects the path for production and consumption which maximizes the discounted sum of utility of consumption [eq. (12)]. The basic parameters defining social objectives are: substitution in consumption between non-traded and traded (imported and domestically produced) goods, SC and S7; elasticity of the marginal utility of real consumption (#J- l), and pure rate of time preference (6- 1). As part of the optimal solution we obtain shadow prices for all constraints of the model. Those shadow prices must satisfy a set of conditions (table 2), which make them equivalent to the market prices that would obtain in competitive markets with perfect foresight. However, given our focus on the pricing of natural gas, we will discuss only those equations relevant for that issue. The basic equation is (D.3), which must hold whenever there is positive production of gas. The right-hand side gives the value of one additional unit of natural gas (PC). There are two possible regimes: ‘expensive’ or ‘cheap’ gas, with the price of gas at or below the oil equivalent price, respectively.3 The first regime obtains when gas output is below the maximum allowed by the energy substitution possibilities, so that eq. (4) is not binding and PGT is zero. With binding demand constraints, on the other hand, gas should be cheaper; of course, the economy should use more energy-intensive processes under this regime [eq. (D.S)].” The left-hand side of (D.3) decomposes the price of gas into cost of extraction (PVG+~iPiai,) plus rent to output constraint (PCG),and rent to reserves (PRG).The latter component changes over time according to the Hotelling rule (D.9): in utility numeraire it grows at the pure rate of time preference, 6- 1; in terms of a more conventional numeraire, such as real consumption (whose utility price is PV),it would grow at the consumption rate of interest, which is an endogenous variable in the model. But even with good estimates of the social rate of discount, we cannot determine PC without also simultaneously determining the optimal extraction path. This is for two reasons: first, we need to know the period in which reserves are exhausted to determine the rent to reserves via, the Hotelling equation. (At this moment neither production nor demand constraints would be binding, so that PG=PO and PRG is everything in excess of the cost of extraction.) Second, the residual between the price of oil and the cost of gas extraction plus gas rental value must be assigned between the capacity constraint (PCG) and reduced price to gas users (PGT,PGN). This trade-off clearly depends on the output level, hence the additional importance of the extraction path. sThe price of oil is of course given by the international price, since it is fully tradable [eq. (D.6)]. The price of gas can never be above the oil price equivalent, since oil is assumed to be at least as efficient as gas in all uses. 4The treatment of the premia of oil over gas in each sector, PGT and PGN, is only apparently asymmetric; it can never be optimal to be demand-constrained in only one sector, since gas is assumed to be freely transportable between sectors. And indeed (D.4) forces PGN = PGT
R. Martin
and S. van Wijnbergen,
Efficient pricing of natural gas
Table
185
2
Dual equations.
Ea. no.
P.1) (D.2) (D.3) (D.4) (D.5)
(D.6) (D.7)
(D.8) (D.9) (D.lO) (D.11) (D.12)
Primal variables
lQ_J [QQI lQG1 IENGI CEil lx01 [XT1 [K&l I&l C&l [Lil [Gil
Dual eauations x,Pia,+PVjLPj,
j=N,T
xi Pia,, + PVO + PC0 + PRO 2 PO xiPiaic+PVG+PCG+PRG=PO-PGT=PG PGN-PGT=O PVi dQi/dEi= PO - $,PGi,
i = N, T
PO = PBOPnO PT=PBOPd(nTXT)/3XT PKi,=d(PKi,+
,DEP-
VPi,+I SQijaKi)
PRi, = GPRi, + 1 PI, = 6PKi,+, PW=PVidQi/dLi, Pi=PU,dU/aCi,
i=N,T i=N,T,M
Notes: 1. See table 3 for definitions of the variables. 2. The associated primal variables are shown in square 3. The time subindexes are omitted when all variables same period.
4. Discussion
brackets. refer to the
of the results
We first present a ‘base case’. There, size of reserves, technology of oil and gas substitution, structure of extraction costs and so on reflect what is known about natural gas in Egypt in the base year, 1981. The resulting intertemporal pattern of shadow prices for natural gas and the corresponding components of those prices is given in fig. 3. We than present a sensitivity analysis of the structure of gas prices. Specifically, we look at the impact of changes in: (a) higher output capacity; (b) the share of total energy demand that can be satisfied through natural gas before the marginal rate of substitution starts to decline; (c) the size of natural gas reserves; (d) the substitution elasticity between energy and non-energy factors of production; (e) oil prices. For the base case, we find a window of natural gas is less valuable to the economy products (see fig. 3). During that period the about 80 percent of its oil equivalent price, infrastructure for production and distribution
about 10 years during which than caloric equivalent oil shadow price of gas drops to starting around 1980, as the of gas expands to a level that
R. Martin and S. van Wijnbergen, Efjicient pricing of natural gas
186 80
70
60
50
I; 2
40
2
30
20 ,’
,’
-PO
,’ ,’
-----
pG
._._ ____.
pReserves
-‘-‘-.
P Resaves & Capoclty
,’ ,’
,_,’
10
0 1980
I
I
I
19GU
I
I
2m
I
I
2010
2020
Time World Bank -
Fig. 3. Decomposition
41801 3
of price of gas
allows substituting oil products in essentially all uses in which gas is equally efficient. Later on, the aggregate economy expands, and with it the demand for energy; gas output then becomes again constrained by capacity limits, which now reflect the maximum flow of gas obtainable from the known reservoirs. Therefore, the price of gas again becomes equal to the oil equivalent price.
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
187
As fig. 3 indicates, only at the peak of the excess supply period is the price of gas equal to just cost of extraction plus rent to reserves. In all other periods production is at capacity. Both capacity and demand constraints are binding simultaneously in those other periods; this is possible because of the energy elasticity of aggregate demand. This energy elasticity results from induced changes in the composition of output and from direct substitution with other primary factors, as discussed in section 3. In fact, the whole window period is one of constant energy use, since the output constraint on gas is fixed during that period; this can only be implemented in a growing economy by rapidly increasing energy prices. The opposite case of almost never binding output capacity is presented in fig. 4. In that run we assume a considerably higher flow output capacity. As a result, from period 4 onwards production of gas is only limited by total available reserves. This clearly represents an extreme case. Under this scenario, thk price of gas equals marginal cost of extraction plus rent to reserves. Accordingly, there is a long period during which the shadow price falls below the fuel oil equivalent price. Interestingly, the maximum and average gaps are smaller than in the base case, as no sharp drop and subsequent steep increase in the price is needed to maintain a constant level of demand, as in the base scenario. Table 4 and figs. 5-9 summarize the results obtained by changing some critical parameters in the model itself. Consider first the coefftcients Icli, the maximum share of energy that can be satisfied with gas instead of oil products without loss of efficiency. In the base run, this share starts at 50 percent for both sectors and then increases gradually over the next 15-20 years (reflecting delays in retiring equipment, diffusion of knowledge, etc.). If the initial value is reduced to 40 percent (but follows the same relative increase over time as before), the effect on PC is significant: the window period expands to 20 years, with an average gap of almost 30 percent. But 40 percent is an unrealistically low estimate of the range within which gas is a good substitute for other energy products. The other case, in which 60 percent is the limit below which oil and gas are perfect substitutes, results in almost complete elimination of the window period (fig. 5). The total level of gas reserves is not a very important determinant of the price of gas unless it is associated with changes in output capacity. This is demonstrated in fig. 6. The low reserves scenario assumes 400 million tons of oil equivalent, that is 30 percent lower than the base case level of 570 million tons. The effect is to reduce the average gap between the prices of oil and gas from 19 to 12 percent (table 3), but keeping the same period of cheap gas as before. The rent to reserves is significantly larger in this case, representing all of the residual between the price of gas and the cost of extraction. Large reserves (840 million tons of oil equivalent, or 47 percent more than the base case) have almost no effect on the value of gas if the base scenario for output capacity is left unchanged: under those conditions they only increase further
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
188
1 70 -
60
-
50
-
=‘ g v) 2
40-
30
-
01 1980
I
I 1990
I
I
-
PO
-----
PGmse
--~------
PG HluhCapoclty
I
I
2030
I
2010
2020
Ttme World Bank -
Fig. 4. Price of oil and gas. Gas output
41801 4
capacity.
the rent that accrues to that constraint while reducing the depletion premium, with no net effect on PG. With a larger, non-binding, output constraint the results are more dramatic (fig. 6): we obtain the extended window characteristic of unconstrained output together with the low depletion premium associated with large reserves; the average gap is now close to 30 percent and lasts for essentially the whole planning period.
R. Martin and S. van Wijnbergen, Table
Eflicient pricing of natural gas
189
3
List of variables. (a) Primal Qcf I
Ii Xi Ei ENG Ki, Li Ri (b) Dual Pi PVi PCi PRi PGi rri PKi PI PW PBOP (c) Parameters rri aij
si ahi SEi, S Vi aN, aT SC,ST DEP F, Hi, *it 4 ****** The sectors
=Gross output, i=N,T,O,G = Consumption, i=N,M,T =Total investment =Investment in sector i, i=N,T,G = Exports, i = T, 0 = Energy use in sector i, i=N,T =Natural gas used in the non-traded sector =Capital, labor, used in sector i, i= N,T,G =Stock of reserves at the end of the period, = Price of good i, i = N, T, 0, G = Unit value added, i = N, T, 0, G =Rent to output constraint, i=O,G = Rent to reserves, i = 0, G = Premium of oil over gas as source of energy = World prices, i = 0, T = Value of installed capital, i = N, T, G =Value of new capital = Wages = Price of foreign exchange
i=O,G
in sector
i, i = N, T
= World prices of oil and traded goods, i=O, T = Unit input of good i in the production of good j, i = N, T, M, j=N,T,O,G = Unit requirement of good i in new capital goods, i = N, T, M = Share coefficients in production functions, h = E, L, K, i = N, T = Elasticity parameters in production functions, i = N, T =Share coefficients in utility function = Substitution parameters in utility function = Depreciation factor for capital goods (1 -depreciation rate) = Exogenous inflows of foreign exchange (workers remittances, revenue from Suez Canal, aid) = Production capacity for oil and gas, i = 0, G =Share of energy that can be satisfied with natural gas or oil producers with equal efficiency, i=N,T =Elasticity of the marginal utility of real income = Pure time preference factor (1 + rate of time preference) are: N = non-traded;
T = traded;
0 = oil; G = gas; M = imports.
Next we present the effects of changing the ease with which energy and other primary inputs can substitute for each other in production. As discussed in section 3, we postulate a production function which is separable in energy and other factors or production. The relevant parameters are the elasticities of substitution ~~~~ which together with the energy shares define the elasticities of the sectoral demand for energy (see above). In the base scenario, oET = oEN = 0.8. That implies sectoral demand functions with elasticities between 0.9 and 1. For the high elasticity simulation we increase gET to 1.4. That gives considerably more flexibility to the economy, increasing the window period to 14 years; the effect comes via a lower rate of growth of the
R. Martin and S. van Wijnbergen, Efficient pricing o/ natural gas
190
Table 4 Sensitivity
analysis
of the gas-oil
Number of period with PG
4. Elasticity of substitution between energy and primary factors: (a) Low (uET = cEN = 0.4) (b) High (u ET= 1.4, CEN0.8) reserves Low (400) High (840) High reserves and large production capacity
6. Price of oil (a) Constant price (b) Low growth (2%) (c) High growth (3%) Note: Each year represents
.w
11
[Gl]
11
35
WI
1
4
fS31 CSll
3 7
27 31
19 19
fR21 IR41
5 5
[R4A]
15
16 36 40
12 20 28
0
0 17 17
5
3. Maximum share of energy demand that can be satisfied with gas: (a) Low (40%) (b) High (60%)
Average
[Cl]
1. Base 2. Large gas production capacity
Maximum
gap (%I 30 25
Case
5. Gas (a) (b) (c)
price gap.
CPll 0 cp21 3 CP31 6 two calendar
26 19
(%I
38 4
10 17
_
years.
overall demand for energy due to increasing real prices; this in turn makes the output constraints on gas non-binding during a longer period. The opposite effect is obtained with low substitution elasticities (fig. 7): a window of just 6 years, with an average oil-gas price differential of 19 percent, as the demand for energy grows at almost the same rate as the economy, despite increasing prices for natural gas. The final set of scenarios explores the sensitivity of the results to present and future oil prices; see fig. 8. Clearly, the price of oil is an important variable for the valuation of gas, in whatever way the latter is calculated. The main reason is again the impact on the aggregate demand for energy. This impact comes through two channels: first, from factoral substitution and variations in the composition of output and, second, from a smaller rate of growth of the economy, as future oil prices increase more rapidly. When the real price of oil grows slowly or not at all, the demand for energy increases via those two effects. This also increases the demand for gas, with the result that the oil-gas substitution penalty (i.e. the difference in their prices) becomes smaller (when PO grows at 2 percent), or is eliminated entirely (when PO is constant).
R. Martin and S. van Wijnbergen, Efjicient pricing
of natural gas
191
80
70
60
50
2 >
40
2
30
20
-FO
10
0
L
1980
I
I
I
1990
I
----
FGEKlse(50%)
---------._._
FGLOW(40%)
I
2000
FG High (80%)
I
I
2010
2020
Time World Bank -
Fig. 5. Price of oil and gas. Maximum
share
of energy
demand
that can be satisfied
41801 5
with gas.
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
192
80
70
60
50
2 > 5
40
30
20
-PO -----
FG Bose
--------10
-
--
------
FGLowReserves --
FG Loi@z Reserves PG Large Resaves&Capac~ty
0 1980
1990
2000
2010
2020
Time
World Bank - 418016
Fig. 6. Price of oil and gas. Gas reserves.
R. Martin
and S. van Wijnbergen, Efficient pricing of natural gas
8o-
7
0
o-
o-
5t 3-
is> 4cI3
30
20
-PO -------------
IO
0
FGEase
193
R. Martin and S. van Wijnbergen, Efficient pricing
194
of natural
gas
11
09
08
07
04
03
02
PG/PO Base
_--_
PCjPG
--_------
PO/PG3%Grow+hPO
-.-.-
PO/PG’Z%GrowthPO
Constant 011 Price
01
0
I
I 1990
1980
I
I
I
2000
I
I
2020
2010
TIm0
World Bank -
Fig. 8. Ratio
of price of gas to price of oil. Different
price scenarios.
41801 8
195
R. Martin and S. van Wijnbergen, Efjicient pricing of natural gas
80 ,’
r’ ,’
I’ ,’ >’ ,’
70
r’ #’ #’ 3’ ,’
60
50 ,’
3 2 2
1’ >’ 8’
,’
40
/ i’
,.’
PG Bose PG
_._______ FG -.-.F’S
1980
1990
2000
Constant 011 Price 3% Growth PO 2% Growth PO
2020
2010
Time World Bank -
Fig. 9. Price of gas. Different price scenarios.
418019
196
R. Martin and S. van Wijnbergen, Efficient pricing of natural gas
5. Conclusions
Standard procedures to compute the shadow price of gas cannot handle output supply constraints or reserve-dependent extraction costs satisfactorily. In this paper we set up a methodology that can incorporate such factors; and present an application to the case of Egypt. Implementing this procedure calls for solving a non-linear intertemporal optimization problem, which was done numerically. The solution clearly demonstrates the importance of those cost components and hence the usefulness of our methodology. The most salient feature of the solution is that under almost all scenarios there is a significant period during which gas should be priced below its fuel oil equivalent price. This is clearly very important for projects where large use of natural gas is contemplated, such as steel mill construction and so on. We provide an extensive analysis of the sensitivity of the size and duration of this gap with respect to oil prices, structure of energy demand, size of gas reserves and ‘tightness’ of supply constraints. This study has established both the feasibility and the usefulness of the intertemporal optimization procedures outlined and implemented in the previous sections. Simplifications, moreover, are clearly possible, especially in modelling total energy demand; to use a multisector general equilibrium model (even if it is a small one like the one used here) to generate an aggregate demand curve for energy is probably overly cumbersome. Furthermore, practical extensions and improvements could be made, especially in modelling substitution between gas and other sources of energy and in the structure of extraction costs. Finally, a difficult but important extension would be the explicit incorporation of uncertainty about future oil prices and size of gas reserves.
References Dervis, K., R. Martin and S. van Wijnbergen, 1985, Policy analysis of shadow pricing, foreign borrowing and resource extraction in Egypt, World Bank Staff Working paper no. 622 (World Bank, Washington). Diamond, P. and J. Mirrlees, 1971, Optimal taxation and public production, American Economic Review, 61, 261-278. Hotelling, H., 1931, The economics of exhaustible resources, Journal of Political Economy, 39, 137-175. Little, I.M.D. and J. Mirrlees, 1974, Project appraisal and planning for developing countries (Heinemann Educational Books, London). Neary, J.P. and S. van Wijnbergen 1986, Natural Resources and the Macroeconomy (MIT Press, Cambridge, MA).