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Oil pricing policies and macroeconomy for an oil-based economy
Oil pricing policies and macroeconomy for an oil-based economy Majid Ahmadian
This paper analyses the oil pricing policies for an oil-based economy within a national planning framework. It contains a total asset maximization problem in the non-oil sector and a macroeconomic model. The main conclusion is that Hotelling’s r-percent rule fails to apply for an oil-based nation if the minimum-import constraint becomes binding. Therefore, the diflerence between the marginal revenue growth rate and the yield on domestic investment turns down when the import constraint is binding and then it goes through several cycles before it turns up as the constraint is non-binding over the planning horizon. Keywords:
Oil; Pricing; Hotelling
rule
The theory of exhaustible resources was originated by Harold Hotelling [I], who first demonstrated that net marginal revenue grows at the rate of interest in the monopolistic market. This result is often called Hotelling’s r-percent rule in the exhaustible resources literature. Levhari and Pindyck [2] argued that this rpercent growth rule does not hold for a monopoly producer of durable extractable resources with rising extraction marginal cost.’ Moussavian and Samuelson [4] demonstrated that this r-percent path also fails to hold for a nondurable resource with a zero extraction cost.’ In these models, the traditional profit maximization principle is treated. The purpose of this paper is to analyse the pricing policies for oil in an oilbased economy by maximizing total assets over the life of the resource in the non-oil sector, rather than applying the profit maximization rule. It concludes that the r-percent growth rule breaks down for an oilbased nation as the required minimum-import constraint is imposed by the economy.
national planning framework. It is composed of a macroeconomic model and a total asset maximization problem in the non-oil sector. In the maximization problem, each oil-producing country chooses its oil pricing policy by maximizing its objective function subject to some constraints. An oilexporting country’s objective function is the sum oft he flows accumulated domestic investments in the non-oil sector over the life of the exhaustible resource. By assuming that a substantial percentage of revenue from oil exports is invested domestically by an oil producer in the non-oil sector. The constraints of the model are the required minimum-imports, resource exhaustion and export demand function for oil. This problem (P) is summarized as:
Model and notations
’ Indeed, they expand Stewart‘s [6] model by setting holding one unit of the resource stock in circulation marginal value of services from a unit of that stock. equalizing the resource price to the marpmal value. For
This section
presents
an oil pricing
model
within
a
The author may be contacted at 100 Edison Avenue, Buffalo, NY 14215, USA. The author is grateful to Professor Thomas Romans and Professor David Salant for their useful and helpful comments and suggestions. Final manuscript received 5 September 1985.
{qer3 and {p,,} maximize
C I,,( 1 + r)‘I -’ t=,
user cost of equal to the rather than more detail.
se-e Stewart [6]. ’ Their paperconcludes that with constant demand elasticity. a nondurable exhaustible resource monopolist expects the price to grow faster (slower) than the rate of interest as the initial stock ofcapital is large (small). In other words, the price of resource grows faster than (equal to) (slower than) the rate of interest as the saving rate is large (zero) (small).
0140-9883/86/040251-06 $03.00 0 1986 Butterworth & Co (Publishers) Ltd
251
pricing policies for an oil-based economy: M. Ahmadian
Oil
subject
to the required
M,,
demand
minimum-import
r=l,._.,
T
function
for oil
(1)
qel = qe(Pet), for t = 1, . . , T and the resource
depletion
constraint
(2)
constraint
Ro= 1 4et+ 1 qdt r-1
1=I
I,, is a proportion of revenue from oil exports and is assumed to be invested domestically in the non-oil sector. M, and M,, are actual imports and the required minimum-imports at time r. qer and qdr are the export and domestic production of oil. pet is the export price of oil at time t. r is the rate of return on domestic investment in the non-oil sector. T is the final exhaustion date of the resource. R, is the initial proven oil reserves. The macroeconomic model explains the basic of an oil-based structure and characteristics several definitional, includes economy.3 It behavioural, and structural relationships, such as: NNI, = 0, + 0, + At4
(4)
Or= Oe,+ Od,
(5)
o,=O(K,_ *)
(6)
K,=K,_,
(7)
+I,,
A,=A(F,-1)
(8)
Ft=Ft_l
(9)
+B,
t3, = E, - M, + NFI, - NKO,
(10)
E, = O,, + E,
(11)
3 For a comprehensive specification of a macroeconomic model related to an oil-based nation, see Motamen [3] and Razavi [S]. 4 The returns from the portfolio of assets held outside country A,, as a component of NNI,, are a recent characteristic of oil-based economies. Thischaracteristtc distinguishes them from the rest ofthe less developed countries. For example. the portfolios of foreign assets were generated for the Iranian and Saudi Arabian economies by the oil booms of November 1973 and January 1974. In these periods. these countries had balance-of-payments surpluses that enabled them to hold portfolios of foreign assets. Such portfolios were composed of deposits held by central banks and international financial institutions as well as funds paid for loans and investments abroad. A, in Equation (4) takes zero values for some OPEC nations like Algeria, Venezuela, Indonesia. etc. because they face serious balance-of-payments deficits.
252
(12)
NNP,=CI+I,,+G,+B,
(13)
ct=co*,
T
T
E,= &I,,)
o
1
(14)
Net national product Equation (4) consists of the incomes from the oil sector 0, and the non-oil sector 0, and also the returns from the portfolio of foreign assets A,. 0, in Equation (5) is equal to the net incomes from oil exports O,, and domestic oil consumption O,,. Equation (6) shows the net non-oil income as a positive function of the stock of domestic capital lagged one period K,_ 1, while K, is the sum of the previous period’s stock of domestic capital and the flow of internal investment Equation (7). The earnings from the portfolio of foreign assets are presented by a functional relationship in Equation (8) where F,_ 1 stands for the portfolio of foreign assets lagged one period. Equation (9) presents the sum of the previous period’s portfolio of foreign assets F,_ 1 and balanceof-payments surplus or deficit B,. B, in Equation (10) is defined as the sum of the net current balance E,- M,, net factor incomes from abroad NFI,, and net capital outflow NKO,. Equation (11) defines the value of total exports E, which is divided into the values of oil exports and non-oil exports E,. E, is assumed to be a positive function of domestic investment Equation (12). Finally, NNP is defined by Equation (13) where G, is total government expenditures and C, is private consumption expenditures. C, is related to the non-oil income by the average propensity to consume Equation (14). As explained before, the first constraint is concerned with the minimum-import requirement of the economy. To specify this constraint, M, is provided by Appendix 1 by utilizing the macroeconomic model as follows: M,=
-(l-c)ti(K,_,)+_&) (15)
-W’,-,)+O,,+S,
For the development needs in the non-oil sector, the economy needs the minimum imports. The required minimum-imports are defined as: M,, = bl,, + d6,,
O
and
O
(16)
It is assumed that a minimum percentage of the I,, should be imported from abroad bl,, and also a minimum percentage of the 0, should be spent for imports of raw materials do,. Substituting M, and M,, from Equations (15) and (16) into constraint (l), the
ENERGY
ECONOMICS
October
1986
Oil pricing policies for an oil-based economy: M. Ahmadiun
required
minimum-import
constraint
f(P,,,q,,;S,)=(~+d-c)~(~,-,)-~(~,,)
Here Q is the domestically.
+(ba-
l)O,,+A(F,-1)
-S,dO
fort=l,...,T
percentage
L,=R,-(17)
of 0,,
to
be
invested
Oil pricing policies The pricing policies for oil are determined problem (P). In doing this, the Lagrangean given by:
where Ly=qP,-qe(pe,),
L,=O,
is obtained:
by solving function is
i
t=1
get- i at=0
for all t
(21) (22)
1=1
q;, is the derivative
of qe, with respect to pet. f, and f, are the partial derivatives off‘@,,, qe,; S,) with respect to pet and qe, respectively (as shown in Appendix 2). Solving y, from Equation (19a) and substituting into Equation (18a), we can get per. Then, eliminating z between per and the lagged pe, + , , x, + 1 is given namely by: - 1 + L( 1 + x&z,) XI+1
=
H 1+1
(23)
where
L(p,,,
gel,
x,, Y,, z; 3
= 1 ~,,U+ dT-’
H,=
,=I
-,i1
and
X,f(P,,9 qe,; S,)
+
L=
c y,(q,,-q,(p,,)) R,-
:
get-
; r=l
r=1
qdt
where x,, y, and z are the multipliers associated with the minimum-import constraint, export demand function for oil and the resource depletion constraint, respectively. s includes all exogenous variables like S,, T, r, R, and a. The complementary slackness conditions are derived from the Lagrangean function as follows:5 q,, 2 0 but if qe, > 0, then Lq=ape,(l L,dO,
-x,f,+y,-z=O
+r)T-,
but if L&O,
then q,,=O
for all t
(18a) (18b)
pe, 2 0, but if per > 0, then
L,=aq,,(l L,
+r)‘-’
but if L,
-x,f,-~,4b,=O
M,, but if M,,<
U9a)
then per = 0 for all t (19b)
x, > 0, but if x, > 0, then M, = M,, M,,d
M,,
(2Oa)
then x, = 0, for all t (20b)
’
It
is important
ENERGY
to note that I,, = uO,, where 0,, = P,,q,,
ECONOMICS
October
MM1 + 4
for all t
MR,. I
r=1
+Z
&(l +r)‘-’
1986
Mb+ I denotes the marginal revenue from oil exports at time t + 1 and w is determined in Appendix 2. It follows from Equation (23) that the Lagrangean multipliers associated with minimum-import constraint x,s are interrelated over the exhaustion date of the resource. This interrelationship is useful for analysing the implications of Hotelling’s r-percent rule for an oil-based economy. This r-percent rule is investigated by parameter L in Equation (23) and by utilizing the values of the minimum-import multipliers determined due to the complementary slackness conditions (20). According to these conditions, x,s take positive or zero values. If x,>O, then the minimumimport constraint is binding; otherwise, the constraint is non-binding, ie x, = 0. This implies that the numerator of Equation (23) takes positive or zero values, while the denominator is strictly positive (see Appendix 2). Setting x,20 and x,+, 30, the numerator of Equation (23) is used to analyse the application of Hotelling’s r-percent rule in the different stages that the economy may follow. These stages are derived in Appendix 3 and represented in Table 1. Their economic implications are discussed as follows: 1. Consider the case in which the minimum-import constraint is non-binding in both the consecutive periods t and t + 1. This implies that the economy does not impose any limitation on its imports and purchases of any essential or non-essential foreign goods. In this
253
Oil pricing policies for an oil-based economy: M. Ahmadian
Table
I. Analysis and interrelationship
of the Lagrange
Stages
Characteristic of the Lagrange multiplier
I
x,=0 -Y +
2
multiplier of the minimum-import
Marginal revenue rate of oil export
growth
constraint in two consecutive periods.
Export price of oil growth rate with constant elasticity of demand ‘.-I
implication regarding the minimum-import constraint AI, > M ,,
ifR=r
-0
M,+,>lM,,+,
1 -
Y, = 0
M,’ M,, M t+,=JJfrt+,
iJ,
li4R0 3
M, = M,,
.Y,> 0 x, + * > 0
4
M
x, > 0
P&.>r
tiR>r \‘, + , --0
5
M,+,>M,,+,
x, = 0 x, + , = 0
Note that &fR is the marginal
growth
tiR=r
rate of the export
M, ’ M,, Mr+~>M,t+,
Pe=r
revenue
case an optimal oil pricing policy for an economy will be a monopoly price path. Therefore, without binding the minimum-import constraint, equalizing the growth rate of the marginal revenue from oil exports to the rate of return on domestic investment yields Hotelling’s r-percent rule as far as our maximization problem is concerned. 2. Suppose the import constraint becomes binding in the period t + 1, ie the economy keeps its imports at the minimum level at that date. Then the optimal oil pricing policy will be determined when the marginal revenue from oil exports grows at a lower rate than the yield on domestic non-oil investment. 3. When the minimum-import constraint is binding in the two periods t and t + 1, ie .x,> 0 and x,, 1 > 0. it implies that Hotelling’s r-percent growth rule fails to apply for an oil-based economy, because the lower marginal revenue growth rate from stage two continues to be lower and then it switches to a growth rate higher than the rate of return on internal investment. 4. This stage is quite the reverse of stage two, when the minimum-import constraint is binding in period t but non-binding in period t + 1. The economy will follow the optimal oil pricing policy only if the growth rate of marginal revenue from oil exports is higher than the rate of return on domestic investment. 5. By this stage the economy is back to a position in which the constraint is non-binding in both periods r and r + 1. In this case, an optimal oil pricing policy for a country resulted from the r-percent path. In the case of constant export demand elasticity, the growth rate of the export price of oil is compared with the rate of return on domestic investment over the above-mentioned stages. In this case, without binding the import constraint, the r-percent rule applies for an
254
-M.,+,
If,--
M, = M,,
from oil and i’e is the rate of growth
of the export
price of oil.
oil producer in both monopolistic and competitive markets. These stages are summarized as follows: 19xx
194’4
kR=r
&lR(r,
or
Ij,=r
P,cr,...,P,>r
4
0
0
+
+
+
0
x1+1
0
+
+
+
0
0
. . , &R)r
&lR=r P,=r
As we can see, 19xx denotes a time before the import constraint is imposed and 19~4’ denotes a time when the constraint is removed. This can be shown diagrammatically in Figure 1. We can see from Figure 1 that the difference between &fR and r or i>, - r fluctuates over the final exhaustion date of the resource. It turns down after the import constraint is imposed and then it goes through several cycles until it turns up before the constraint is removed.
Conclusion The oil price setting model developed here yields the pricing policies for oil in an oil-based economy which are related to total asset maximization in the non-oil rather than to the constrained profit sector, maximization principle discussed in the literature. The basic assumption of this model is that an essential percentage of oil revenue from oil exports is invested domestically in the non-oil sector. This non-oil investment will accumulate the stock of domestic nonoil capital which in turn will decrease the dependency of the economy on oil revenue in the long run.
ENERGY
ECONOMICS
October
1986
Oil pricing policies for an oil-based economy: M, Ahmadian
Appendix 1 This appendix attempts to find the M, from the macroeconomic model. Solving B, from Equation (13) and substituting respectively we have:
be >r
tiR < r
t
19xX
M,=C,+I,,+G,-G,-A,+E,-O,,
19YY Figure 1. &R-r,
(P=-r),
over the planning
horizon.
into Equation (lo), further substituting Equations (4), (5) and (11) for NNI,, 0, and E,,
+ NFI,-
NKO,
(24)
Setting I,, = aOe, and G, = G, + (1 -a)O=,, using Equations (6), (8), (12) and (14), rearranging the terms, M, becomes M,=-(l-c)ti(K,_,)+E(I,,)-A(F,_,)
With binding the required minimum-import constraint, this paper concludes that an oil exporter expects that the marginal revenue will first grow slower, then faster, than the rate of return on domestic investment. In the case of constant demand elasticity, a further conclusion is that the export price of oil first grows at a lower rate than the yield on internal investment, then switches to a position where it grows at a higher rate than that yield. Applications of these results for OPEC member countries are different. The countries with binding minimum-import requirement constraints may find it desirable not to follow Hotelling’s r-percent rule. On the other hand, the countries not imposing the minimum-import constraint may find it profitable not to deviate from the r-percent path. For example, Iran and Venezuela, as OPEC members, may not apply this rule as far as the import constraint is concerned.
(25)
+O,,+S, where S, includes
all exogenous
variables
as
S,=G,-O,,+NFI,-NKO,
G, includes the incomes from oil exports (1 - a)Oer and nonoil exports
G, used by the government.
Appendix 2 This appendix
derives & and f, from Equation
(17) as
follows:
f, = - (1 +d - c)O;aq,, - aq,,I? + (ba - 1her - Mq,, +%,~J then
References H. Hotelling, ‘The economics of exhaustible resources’, Journal ofPolitical Economy, Vol XXXIX, April 1931, pp 137-17.5. D. Levhari and R. S. Pindyck, ‘The pricing of durable exhaustible resources’, The Quurterly Journal of Economics, Vol XCVI, No 3, August 1981, pp 363-377. H. Motamen, Expenditure of Oil Revenue, St Martin’s Press, New York and Frances Pinter, London, 1980. M. Moussavian and L. Samuelson, ‘On the extractable of an exhaustible resource by a monopoly’, Journal of Environmental Economics and Management, Vol 11, No 2, January 1984, pp 139-146. H. Razavi, ‘Optimal rate of oil production for OPECmember countries’, Resources and Energy, Vol 4, No 3, September 1982. M. B. Stewart, ‘Monopoly and the intertemporal production of a durable extractable resource’, The Quarterly Journal of Economics, Vol XCIV, February 1980, pp 99-l 12.
ENERGY ECONOMICS
October
1986
where y=(l
+d-c)&‘+(l/a-b)+/?,!+A;(E,‘+
l/a)
0; is the incremental output-capital ratio at time I. E; is the ratio of non-oil exports to domestic investment at the margin, and A; is the marginal return on an additional portfolio of foreign assets at time t. Analogous to the ,/b, the partial derivative of Equation (17) with respect to q,,, ie ,& will be
f,= -aPerU: W, is strictly positive because each term in W, is strictly positive. The first term is strictly positive, ie (1 +d - c)& > 0, since by assuming O< d < 1 and 0 c or (1 +d-c)> 0. The second term is also positive, ie l/a-b>O, because by assuming O
255
Oil pricing policies for an oil-based economy: M. Ahmadian I/a> 1 by adding (-b) for both sides of l/a> 1 we have 1/a -b > 1-b > 0. The third term is also positive. Therefore
3. When x,>O and x,, t ~0, then 1
+x,H,)
in this case 1sLor
Appendix 3 This appendix derives all stages that were indicated in Table 1 from the numerator of Equation (23) when the minimumimport constraint becomes binding and when it is removed. These stages are summarized as follows:
MR ,+1 SMR,(I
+r)
The 5 is used here to indicate that there is no restriction: the left-hand side of the inequality may be greater or less than the right-hand side. 4. When x,> 0 and x,, , =O, then 1 = L( 1 + x,H,) which implies
When x,=0
and x,+r =O, then l>Lor
l=Lor
When x,=0 l
256
MR,+,>MR,(l+r)
MR,+,=MR,(l+r) and x,, , >O, then
MR,+,
5. Finally, when x, = 0 and x,, , = 0, we come back to stage 1, then l=Lor
MR,+,=MR,(l+r)
ENERGY
ECONOMICS
October 1986
This paper analyses the oil pricing policies for an oil-based economy within a national planning framework. It contains a total asset maximization problem in the non-oil sector and a macroeconomic model. The main conclusion is that Hotelling’s r-percent rule fails to apply for an oil-based nation if the minimum-import constraint becomes binding. Therefore, the diflerence between the marginal revenue growth rate and the yield on domestic investment turns down when the import constraint is binding and then it goes through several cycles before it turns up as the constraint is non-binding over the planning horizon. Keywords:
Oil; Pricing; Hotelling
rule
The theory of exhaustible resources was originated by Harold Hotelling [I], who first demonstrated that net marginal revenue grows at the rate of interest in the monopolistic market. This result is often called Hotelling’s r-percent rule in the exhaustible resources literature. Levhari and Pindyck [2] argued that this rpercent growth rule does not hold for a monopoly producer of durable extractable resources with rising extraction marginal cost.’ Moussavian and Samuelson [4] demonstrated that this r-percent path also fails to hold for a nondurable resource with a zero extraction cost.’ In these models, the traditional profit maximization principle is treated. The purpose of this paper is to analyse the pricing policies for oil in an oilbased economy by maximizing total assets over the life of the resource in the non-oil sector, rather than applying the profit maximization rule. It concludes that the r-percent growth rule breaks down for an oilbased nation as the required minimum-import constraint is imposed by the economy.
national planning framework. It is composed of a macroeconomic model and a total asset maximization problem in the non-oil sector. In the maximization problem, each oil-producing country chooses its oil pricing policy by maximizing its objective function subject to some constraints. An oilexporting country’s objective function is the sum oft he flows accumulated domestic investments in the non-oil sector over the life of the exhaustible resource. By assuming that a substantial percentage of revenue from oil exports is invested domestically by an oil producer in the non-oil sector. The constraints of the model are the required minimum-imports, resource exhaustion and export demand function for oil. This problem (P) is summarized as:
Model and notations
’ Indeed, they expand Stewart‘s [6] model by setting holding one unit of the resource stock in circulation marginal value of services from a unit of that stock. equalizing the resource price to the marpmal value. For
This section
presents
an oil pricing
model
within
a
The author may be contacted at 100 Edison Avenue, Buffalo, NY 14215, USA. The author is grateful to Professor Thomas Romans and Professor David Salant for their useful and helpful comments and suggestions. Final manuscript received 5 September 1985.
{qer3 and {p,,} maximize
C I,,( 1 + r)‘I -’ t=,
user cost of equal to the rather than more detail.
se-e Stewart [6]. ’ Their paperconcludes that with constant demand elasticity. a nondurable exhaustible resource monopolist expects the price to grow faster (slower) than the rate of interest as the initial stock ofcapital is large (small). In other words, the price of resource grows faster than (equal to) (slower than) the rate of interest as the saving rate is large (zero) (small).
0140-9883/86/040251-06 $03.00 0 1986 Butterworth & Co (Publishers) Ltd
251
pricing policies for an oil-based economy: M. Ahmadian
Oil
subject
to the required
M,,
demand
minimum-import
r=l,._.,
T
function
for oil
(1)
qel = qe(Pet), for t = 1, . . , T and the resource
depletion
constraint
(2)
constraint
Ro= 1 4et+ 1 qdt r-1
1=I
I,, is a proportion of revenue from oil exports and is assumed to be invested domestically in the non-oil sector. M, and M,, are actual imports and the required minimum-imports at time r. qer and qdr are the export and domestic production of oil. pet is the export price of oil at time t. r is the rate of return on domestic investment in the non-oil sector. T is the final exhaustion date of the resource. R, is the initial proven oil reserves. The macroeconomic model explains the basic of an oil-based structure and characteristics several definitional, includes economy.3 It behavioural, and structural relationships, such as: NNI, = 0, + 0, + At4
(4)
Or= Oe,+ Od,
(5)
o,=O(K,_ *)
(6)
K,=K,_,
(7)
+I,,
A,=A(F,-1)
(8)
Ft=Ft_l
(9)
+B,
t3, = E, - M, + NFI, - NKO,
(10)
E, = O,, + E,
(11)
3 For a comprehensive specification of a macroeconomic model related to an oil-based nation, see Motamen [3] and Razavi [S]. 4 The returns from the portfolio of assets held outside country A,, as a component of NNI,, are a recent characteristic of oil-based economies. Thischaracteristtc distinguishes them from the rest ofthe less developed countries. For example. the portfolios of foreign assets were generated for the Iranian and Saudi Arabian economies by the oil booms of November 1973 and January 1974. In these periods. these countries had balance-of-payments surpluses that enabled them to hold portfolios of foreign assets. Such portfolios were composed of deposits held by central banks and international financial institutions as well as funds paid for loans and investments abroad. A, in Equation (4) takes zero values for some OPEC nations like Algeria, Venezuela, Indonesia. etc. because they face serious balance-of-payments deficits.
252
(12)
NNP,=CI+I,,+G,+B,
(13)
ct=co*,
T
T
E,= &I,,)
o
1
(14)
Net national product Equation (4) consists of the incomes from the oil sector 0, and the non-oil sector 0, and also the returns from the portfolio of foreign assets A,. 0, in Equation (5) is equal to the net incomes from oil exports O,, and domestic oil consumption O,,. Equation (6) shows the net non-oil income as a positive function of the stock of domestic capital lagged one period K,_ 1, while K, is the sum of the previous period’s stock of domestic capital and the flow of internal investment Equation (7). The earnings from the portfolio of foreign assets are presented by a functional relationship in Equation (8) where F,_ 1 stands for the portfolio of foreign assets lagged one period. Equation (9) presents the sum of the previous period’s portfolio of foreign assets F,_ 1 and balanceof-payments surplus or deficit B,. B, in Equation (10) is defined as the sum of the net current balance E,- M,, net factor incomes from abroad NFI,, and net capital outflow NKO,. Equation (11) defines the value of total exports E, which is divided into the values of oil exports and non-oil exports E,. E, is assumed to be a positive function of domestic investment Equation (12). Finally, NNP is defined by Equation (13) where G, is total government expenditures and C, is private consumption expenditures. C, is related to the non-oil income by the average propensity to consume Equation (14). As explained before, the first constraint is concerned with the minimum-import requirement of the economy. To specify this constraint, M, is provided by Appendix 1 by utilizing the macroeconomic model as follows: M,=
-(l-c)ti(K,_,)+_&) (15)
-W’,-,)+O,,+S,
For the development needs in the non-oil sector, the economy needs the minimum imports. The required minimum-imports are defined as: M,, = bl,, + d6,,
O
and
O
(16)
It is assumed that a minimum percentage of the I,, should be imported from abroad bl,, and also a minimum percentage of the 0, should be spent for imports of raw materials do,. Substituting M, and M,, from Equations (15) and (16) into constraint (l), the
ENERGY
ECONOMICS
October
1986
Oil pricing policies for an oil-based economy: M. Ahmadiun
required
minimum-import
constraint
f(P,,,q,,;S,)=(~+d-c)~(~,-,)-~(~,,)
Here Q is the domestically.
+(ba-
l)O,,+A(F,-1)
-S,dO
fort=l,...,T
percentage
L,=R,-(17)
of 0,,
to
be
invested
Oil pricing policies The pricing policies for oil are determined problem (P). In doing this, the Lagrangean given by:
where Ly=qP,-qe(pe,),
L,=O,
is obtained:
by solving function is
i
t=1
get- i at=0
for all t
(21) (22)
1=1
q;, is the derivative
of qe, with respect to pet. f, and f, are the partial derivatives off‘@,,, qe,; S,) with respect to pet and qe, respectively (as shown in Appendix 2). Solving y, from Equation (19a) and substituting into Equation (18a), we can get per. Then, eliminating z between per and the lagged pe, + , , x, + 1 is given namely by: - 1 + L( 1 + x&z,) XI+1
=
H 1+1
(23)
where
L(p,,,
gel,
x,, Y,, z; 3
= 1 ~,,U+ dT-’
H,=
,=I
-,i1
and
X,f(P,,9 qe,; S,)
+
L=
c y,(q,,-q,(p,,)) R,-
:
get-
; r=l
r=1
qdt
where x,, y, and z are the multipliers associated with the minimum-import constraint, export demand function for oil and the resource depletion constraint, respectively. s includes all exogenous variables like S,, T, r, R, and a. The complementary slackness conditions are derived from the Lagrangean function as follows:5 q,, 2 0 but if qe, > 0, then Lq=ape,(l L,dO,
-x,f,+y,-z=O
+r)T-,
but if L&O,
then q,,=O
for all t
(18a) (18b)
pe, 2 0, but if per > 0, then
L,=aq,,(l L,
+r)‘-’
but if L,
-x,f,-~,4b,=O
M,, but if M,,<
U9a)
then per = 0 for all t (19b)
x, > 0, but if x, > 0, then M, = M,, M,,d
M,,
(2Oa)
then x, = 0, for all t (20b)
’
It
is important
ENERGY
to note that I,, = uO,, where 0,, = P,,q,,
ECONOMICS
October
MM1 + 4
for all t
MR,. I
r=1
+Z
&(l +r)‘-’
1986
Mb+ I denotes the marginal revenue from oil exports at time t + 1 and w is determined in Appendix 2. It follows from Equation (23) that the Lagrangean multipliers associated with minimum-import constraint x,s are interrelated over the exhaustion date of the resource. This interrelationship is useful for analysing the implications of Hotelling’s r-percent rule for an oil-based economy. This r-percent rule is investigated by parameter L in Equation (23) and by utilizing the values of the minimum-import multipliers determined due to the complementary slackness conditions (20). According to these conditions, x,s take positive or zero values. If x,>O, then the minimumimport constraint is binding; otherwise, the constraint is non-binding, ie x, = 0. This implies that the numerator of Equation (23) takes positive or zero values, while the denominator is strictly positive (see Appendix 2). Setting x,20 and x,+, 30, the numerator of Equation (23) is used to analyse the application of Hotelling’s r-percent rule in the different stages that the economy may follow. These stages are derived in Appendix 3 and represented in Table 1. Their economic implications are discussed as follows: 1. Consider the case in which the minimum-import constraint is non-binding in both the consecutive periods t and t + 1. This implies that the economy does not impose any limitation on its imports and purchases of any essential or non-essential foreign goods. In this
253
Oil pricing policies for an oil-based economy: M. Ahmadian
Table
I. Analysis and interrelationship
of the Lagrange
Stages
Characteristic of the Lagrange multiplier
I
x,=0 -Y +
2
multiplier of the minimum-import
Marginal revenue rate of oil export
growth
constraint in two consecutive periods.
Export price of oil growth rate with constant elasticity of demand ‘.-I
implication regarding the minimum-import constraint AI, > M ,,
ifR=r
-0
M,+,>lM,,+,
1 -
Y, = 0
M,’ M,, M t+,=JJfrt+,
iJ,
li4R
M, = M,,
.Y,> 0 x, + * > 0
4
M
x, > 0
P&.>r
tiR>r \‘, + , --0
5
M,+,>M,,+,
x, = 0 x, + , = 0
Note that &fR is the marginal
growth
tiR=r
rate of the export
M, ’ M,, Mr+~>M,t+,
Pe=r
revenue
case an optimal oil pricing policy for an economy will be a monopoly price path. Therefore, without binding the minimum-import constraint, equalizing the growth rate of the marginal revenue from oil exports to the rate of return on domestic investment yields Hotelling’s r-percent rule as far as our maximization problem is concerned. 2. Suppose the import constraint becomes binding in the period t + 1, ie the economy keeps its imports at the minimum level at that date. Then the optimal oil pricing policy will be determined when the marginal revenue from oil exports grows at a lower rate than the yield on domestic non-oil investment. 3. When the minimum-import constraint is binding in the two periods t and t + 1, ie .x,> 0 and x,, 1 > 0. it implies that Hotelling’s r-percent growth rule fails to apply for an oil-based economy, because the lower marginal revenue growth rate from stage two continues to be lower and then it switches to a growth rate higher than the rate of return on internal investment. 4. This stage is quite the reverse of stage two, when the minimum-import constraint is binding in period t but non-binding in period t + 1. The economy will follow the optimal oil pricing policy only if the growth rate of marginal revenue from oil exports is higher than the rate of return on domestic investment. 5. By this stage the economy is back to a position in which the constraint is non-binding in both periods r and r + 1. In this case, an optimal oil pricing policy for a country resulted from the r-percent path. In the case of constant export demand elasticity, the growth rate of the export price of oil is compared with the rate of return on domestic investment over the above-mentioned stages. In this case, without binding the import constraint, the r-percent rule applies for an
254
-M.,+,
If,--
M, = M,,
from oil and i’e is the rate of growth
of the export
price of oil.
oil producer in both monopolistic and competitive markets. These stages are summarized as follows: 19xx
194’4
kR=r
&lR(r,
or
Ij,=r
P,cr,...,P,>r
4
0
0
+
+
+
0
x1+1
0
+
+
+
0
0
. . , &R)r
&lR=r P,=r
As we can see, 19xx denotes a time before the import constraint is imposed and 19~4’ denotes a time when the constraint is removed. This can be shown diagrammatically in Figure 1. We can see from Figure 1 that the difference between &fR and r or i>, - r fluctuates over the final exhaustion date of the resource. It turns down after the import constraint is imposed and then it goes through several cycles until it turns up before the constraint is removed.
Conclusion The oil price setting model developed here yields the pricing policies for oil in an oil-based economy which are related to total asset maximization in the non-oil rather than to the constrained profit sector, maximization principle discussed in the literature. The basic assumption of this model is that an essential percentage of oil revenue from oil exports is invested domestically in the non-oil sector. This non-oil investment will accumulate the stock of domestic nonoil capital which in turn will decrease the dependency of the economy on oil revenue in the long run.
ENERGY
ECONOMICS
October
1986
Oil pricing policies for an oil-based economy: M, Ahmadian
Appendix 1 This appendix attempts to find the M, from the macroeconomic model. Solving B, from Equation (13) and substituting respectively we have:
be >r
tiR < r
t
19xX
M,=C,+I,,+G,-G,-A,+E,-O,,
19YY Figure 1. &R-r,
(P=-r),
over the planning
horizon.
into Equation (lo), further substituting Equations (4), (5) and (11) for NNI,, 0, and E,,
+ NFI,-
NKO,
(24)
Setting I,, = aOe, and G, = G, + (1 -a)O=,, using Equations (6), (8), (12) and (14), rearranging the terms, M, becomes M,=-(l-c)ti(K,_,)+E(I,,)-A(F,_,)
With binding the required minimum-import constraint, this paper concludes that an oil exporter expects that the marginal revenue will first grow slower, then faster, than the rate of return on domestic investment. In the case of constant demand elasticity, a further conclusion is that the export price of oil first grows at a lower rate than the yield on internal investment, then switches to a position where it grows at a higher rate than that yield. Applications of these results for OPEC member countries are different. The countries with binding minimum-import requirement constraints may find it desirable not to follow Hotelling’s r-percent rule. On the other hand, the countries not imposing the minimum-import constraint may find it profitable not to deviate from the r-percent path. For example, Iran and Venezuela, as OPEC members, may not apply this rule as far as the import constraint is concerned.
(25)
+O,,+S, where S, includes
all exogenous
variables
as
S,=G,-O,,+NFI,-NKO,
G, includes the incomes from oil exports (1 - a)Oer and nonoil exports
G, used by the government.
Appendix 2 This appendix
derives & and f, from Equation
(17) as
follows:
f, = - (1 +d - c)O;aq,, - aq,,I? + (ba - 1her - Mq,, +%,~J then
References H. Hotelling, ‘The economics of exhaustible resources’, Journal ofPolitical Economy, Vol XXXIX, April 1931, pp 137-17.5. D. Levhari and R. S. Pindyck, ‘The pricing of durable exhaustible resources’, The Quurterly Journal of Economics, Vol XCVI, No 3, August 1981, pp 363-377. H. Motamen, Expenditure of Oil Revenue, St Martin’s Press, New York and Frances Pinter, London, 1980. M. Moussavian and L. Samuelson, ‘On the extractable of an exhaustible resource by a monopoly’, Journal of Environmental Economics and Management, Vol 11, No 2, January 1984, pp 139-146. H. Razavi, ‘Optimal rate of oil production for OPECmember countries’, Resources and Energy, Vol 4, No 3, September 1982. M. B. Stewart, ‘Monopoly and the intertemporal production of a durable extractable resource’, The Quarterly Journal of Economics, Vol XCIV, February 1980, pp 99-l 12.
ENERGY ECONOMICS
October
1986
where y=(l
+d-c)&‘+(l/a-b)+/?,!+A;(E,‘+
l/a)
0; is the incremental output-capital ratio at time I. E; is the ratio of non-oil exports to domestic investment at the margin, and A; is the marginal return on an additional portfolio of foreign assets at time t. Analogous to the ,/b, the partial derivative of Equation (17) with respect to q,,, ie ,& will be
f,= -aPerU: W, is strictly positive because each term in W, is strictly positive. The first term is strictly positive, ie (1 +d - c)& > 0, since by assuming O< d < 1 and 0
255
Oil pricing policies for an oil-based economy: M. Ahmadian I/a> 1 by adding (-b) for both sides of l/a> 1 we have 1/a -b > 1-b > 0. The third term is also positive. Therefore
3. When x,>O and x,, t ~0, then 1
+x,H,)
in this case 1sLor
Appendix 3 This appendix derives all stages that were indicated in Table 1 from the numerator of Equation (23) when the minimumimport constraint becomes binding and when it is removed. These stages are summarized as follows:
MR ,+1 SMR,(I
+r)
The 5 is used here to indicate that there is no restriction: the left-hand side of the inequality may be greater or less than the right-hand side. 4. When x,> 0 and x,, , =O, then 1 = L( 1 + x,H,) which implies
When x,=0
and x,+r =O, then l>Lor
l=Lor
When x,=0 l
256
MR,+,>MR,(l+r)
MR,+,=MR,(l+r) and x,, , >O, then
MR,+,
5. Finally, when x, = 0 and x,, , = 0, we come back to stage 1, then l=Lor
MR,+,=MR,(l+r)
ENERGY
ECONOMICS
October 1986