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A Model of the Operation and Development of a National Oil Company*
Peter Hartley, Department of Economics, Rice University
Kenneth B. Medlock III, James A Baker III Institute for Public Policy, Rice University
Abstract
We present a model of the exploration and development activities of a National Oil
Company (NOC), which uses similar technology to a private firm to extract a depletable
resource. However, unlike the private firm, the NOC may have a wider range of
objectives than maximizing the present value of profits. Specifically, we assume an
objective function that balances firm profitability against a political desire to favor
domestic consumer surplus and domestic employment. We find that the non-commercial
objectives faced by a NOC tend to reinforce each other in their effects on profitability,
the timing of cash flows and employment.
I. Introduction
National oil companies (NOCs) now dominate the international petroleum market.
According to the U.S. Energy Information Agency (EIA, reporting data from Oil & Gas
Journal), in every year since 1991 countries with a NOC have held nearly 90% of all
worldwide crude oil reserves, excluding Alberta tar sands or other unconventional
sources. In addition, the proportion of crude oil produced in countries with a NOC
increased from 50% in the mid-1980s to 66% from the mid-1990s. As private,
international oil companies (IOCs) find it increasingly difficult to gain access to large oil
and gas prospects, the control of resources by NOCs is likely to increase. It is therefore
important to understand whether NOCs are likely to behave differently from IOCs when
responding to different types of shocks affecting the world oil market.
In order to characterize systematic differences between the behavior of a NOC
and a shareholder-owned IOC, we develop a model of NOC operation and development
* The authors thank Stacy Eller for valuable research assistance.
in which the NOC seeks to maximize the flow of revenue from the production of a
depletable resource but is also influenced by the alternative objectives of politicians. At
any period in time, the behavior of any one NOC will reflect many factors peculiar to the
history and circumstances of that organization. However, the longer-term average
behavior of a NOC is likely to reflect systematic influences of the institutional
arrangement of being owned and controlled by a government rather than shareholders.
The model reflects two fundamental features of a NOC. First, the NOC must
examine intertemporal trade-offs of extracting a depletable resource today versus
tomorrow. Second, the key distinguishing feature of a NOC as opposed to an IOC is that
the two firms have a different set of owners, or principals, who will have different
objectives. Thus, the principal-agent paradigm introduced by Jensen and Meckling
(1976) and Harris and Raviv (1978)1 is critical to motivating the expanded set of
objectives faced by a NOC relative to a comparable IOC.
II. Principals and agents in a National Oil Company
When contrasting the decisions of a NOC and an IOC, we assume that the IOC
maximizes the present value of expected profits at the market-determined required rate of
return.2 While maximizing firm value is commonly assumed as an objective for
corporations with publicly traded ownership shares, it has been recognized as a
simplification. In particular, it ignores potential inconsistencies between the goals of
shareholders and managers. Nevertheless, a wide range of evidence is consistent with the
1 Jensen and Meckling, however, credit Adam Smith for the observation that managers in a common-stock
company cannot be expected to watch over the shareholders’ money “with the same anxious vigilance with
which the partners in a private copartnery frequently watch over their own.”
2 It should be clear that maximizing the present value of profits is not equivalent to ensuring an efficient
outcome. For example, a privately owned monopoly is likely to produce an inefficient outcome precisely
because it has a strong incentive to maximize profits.
2
hypothesis that managers of corporations maximize firm value most of the time, while
many of the institutional features of shareholder-owned firms can be interpreted as
mechanisms to allow owners to effectively control managers. Examples include
Holmström (1979), Holmström (1999), and Harris and Raviv (1991).
More specifically, Holmström (1979) demonstrates that the principals benefit
from being able to observe an additional signal (other than the payoff) that reflects the
actions of the agent. This can motivate, for example, stringent accounting and financial
reporting practices. In addition, Holmström (1999) shows that competition in the
managerial labor market gives managers an incentive to perform, an outcome that can be
strengthened by explicit performance-related compensation such as shares or share
options. Harris and Raviv (1991) observe that firm leverage can also encourage
managers to maximize profits.3 Holding constant a manager’s absolute investment in the
firm, an increase in leverage increases the manager’s share of equity and aligns his
interests more closely with those of the remaining shareholders.4 Furthermore, managers
may lose substantially from bankruptcy, for example, because their firm-specific skills
and knowledge are devalued. Larger debt service payments can then force managers to
maintain firm cash flow to reduce the chance of bankruptcy. This may, in turn, limit the
extent to which managers can use firm cash flow for their own ends.
In government-controlled business enterprises, politicians take the place of the
shareholders. Although politicians usually do not receive any residual cash flow directly
from the firm, the politicians’ objectives include political benefits from having additional
revenue flow into the Treasury. Moreover, politicians can influence the production,
3 Jensen and Meckling (1976) also discussed corporate capital structure at some length.
4 Granting the manager share options rather than actual shares can raise the sensitivity of his personal
wealth to changes in the underlying value of shares and also help align his interests with the shareholders.
3
employment, and pricing decisions of the NOC to gain support from special interests.
Two critical features of a government-owned firm are: (i) residual ownership
claims cannot be transferred to another party without the firm ceasing to be government-
owned, and (ii) the government guarantees debt issued by the firm. These differences
have important effects on the principal-agent conflict and hence on the objectives and
decisions of the firm. In particular, the commitment to government ownership means that
the firm can always count on being “bailed out” if it gets into financial difficulties.
Laffont and Tirole (1991) observe that managers of government-owned firms, like
their counterparts in private firms, can be fired for making bad decisions. They also can
be required to produce audited accounts or use formal control systems analogous to those
used in private firms. However, while the market value of the private firm’s shares is
readily observable to shareholder-owners of a private corporation, no such metric is
available to politicians to gauge the performance of a government-owned firm.
Furthermore, as we elaborate in more detail below, politicians are likely to be interested
in a more diffuse set of performance criteria than firm market value, which can make the
reporting requirements of the NOC much more complex and less effective.
Laffont and Tirole (1991) also note that while shareholders can lose wealth if
managers do not perform, a politician can lose office. However, the time horizons of
politicians and investors in a private firm are likely to differ.5 Politicians, as a result of
more myopic goals, may opt to use the NOC return to capital for purposes other than
reinvestment in resources, even though it would damage the NOC’s future profitability.
By contrast, an investor in a private corporation cares about the resale value of shares,
which will in turn depend on the future profitability of the firm. Shareholders therefore
5 Jensen and Meckling (1979) identify a similar time horizon problem in a labor-managed firm.
4
have an incentive to encourage management to make an efficient trade-off between
current income and future profitability.
In summary, many institutional features have evolved to control the principal-
agent problem within corporations. Government-owned firms often lack many of these
features. The information available to politicians is also inferior to the information
revealed by stock prices. As a result, managers of government owned firms are likely to
be monitored less well than their corporate counterparts. Thus, we would expect the
objectives of a government-owned firm to reflect managerial prerogatives to a greater
extent than is the case for a private corporation.6
Despite the potential compromise of managerial efficiency, a greater ability to
control other inefficiencies may make the NOC a preferred vehicle for exploiting oil and
gas deposits, particularly in developing countries.7 For one, a large privately owned
mining firm could monopolize the domestic market. Second, the development of
transportation infrastructure and training of local workers may have a public goods
element because roads, railroads or ports also serve other users while training for workers
may raise their skills at many tasks. Whereas a private firm may under-invest in these
activities, a government-owned firm could be directed to expand investments to
internalize the additional social benefits. Finally, production royalties or taxes used to
redistribute mineral resource “rents” to citizens may also impose substantial efficiency
6 Shleifer and Vishny (1994) consider the operation of government-owned firms when contracts between
politicians and managers are incomplete. They distinguish ownership of residual cash flow from control of
production decisions. They model production decisions as the outcome of a Nash bargaining game between
the manager and politician. Different allocations of control rights or ownership of cash flow influence the
outcome by altering the threat points in the Nash bargaining game. The equilibrium outcome also depends
on whether “bribes” (direct transfers between the politician and manager) are allowed.
7 Sappington and Stiglitz (1987), Pint (1991), Laffont and Tirole (1991) and Roemer and Silvestre (1992)
were among the first to provide arguments along these lines from within the principal-agent paradigm.
5
losses that might reduced by using a NOC.8
Another explanation for government ownership of firms, however, is that the
politicians are concerned about objectives other than operational efficiency. In fact,
politicians may give favor to certain people or powerful domestic interest groups when
determining new investment projects or assigning high profile positions, even if such
decisions compromise economic efficiency.9 The groups that are favored will vary from
one country to the next depending on factors such as the nature of the political system,
social and ethnic diversity, and the geographical concentration of the hydrocarbon
resources within the country.
In general, two groups that politicians often favor are: (1) domestic consumers of
oil products and (2) employees or other suppliers of variable inputs to the NOC. As for
domestic consumers, they may see a low domestic oil price as one way to share in
resource rents. Regarding employees (or domestic suppliers of other inputs) of the NOC,
they may be a cohesive group (for example, they may be unionized) able to exert political
pressure on matters of vital importance to their own welfare.10 Politicians then could
increase their political support by acquiescing, for example, in excessive employment in
8 As Grossman and Hart (1986) observe, opportunistic and inefficient behavior is quite likely “in situations
where there are large amounts of surplus to be divided ex-post and in which, because of the impossibility of
writing a complete, contingent contract, the ex-ante contract does not specify a clear division of the
surplus.” Disputes over distributing the rents associated with mining projects is one element of the so-
called “resource curse” (see, for example, Gelb et. al. (1988)) or “paradox of plenty” (Karl(1999)) wherein
the discovery of significant mineral resources ends up making the country worse off rather than better off.
9 The notion that politicians aim to maximize efficiency may be especially deficient for explaining why
developing countries often establish a NOC to exploit domestic hydrocarbon resources. As argued
forcefully by Karl (1999), for example, redistribution of petroleum rents to favored political groups
dominates political institutions within such countries. The “weak administrative structures, insecure
property rights [and] nonexistent judicial constraints” in developing countries exacerbate the tendencies to
promote redistribution at the expense of economic efficiency. Yet as Karl remarks, “such economically
inefficient decision-making is not a miscalculation when viewed politically. Instead, it is an integral part of
the calculation of rulers to retain their support.”
10 As Shleifer (1998) observes, “trade unions around the world are typically the strongest opponents of
privatization, precisely because they obtain significant benefits for their members from the government-
owned firms in exchange for political support.”
6
the NOC. In addition, managers of the NOC may favor higher employment because a
larger firm may give the managers more prestige, and, by raising the production costs,
higher employment may increase funds under managerial control.
Another difference between an IOC and an NOC is that the NOC is likely to have
a higher discount rate. Politicians overseeing the NOC, like shareholders in a private
firm, prefer the NOC to generate higher revenue. NOC profits accrue to the Treasury and
allow politicians to gain support by increasing spending or reducing other taxes. In
addition, politicians, like investors in a corporation, will be concerned about future as
well as immediate profits. However, we might expect politicians to discount future
profits more heavily. In addition, managers of the NOC may desire a higher rate of
return than their private sector counterparts. Although managers in the private sector
have relatively symmetric incentives to take actions that raise share values or stop share
values from declining, the lack of an agreed and readily measured objective for the NOC
makes rewards and punishments in the public sector more asymmetric. When mistakes
are made, resources are expended to discover and discipline those deemed to be
responsible, but successes can more difficult to accurately attribute to any one individual.
The result is that managers of NOCs may be more risk averse than their private sector
counterparts.
In the following section, we propose a general objective for the NOC that can
reflect a mixture of the objectives of managers and politicians. In particular, the NOC
must weigh profitability (providing funds to the Treasury) against benefits to consumers
and suppliers of variable inputs, such as labor. Since we also need to model the
intertemporal aspects of decision-making, however, we keep the objective simple.
7
III. A model of a National Oil Company
We contrast the operation and investment decisions of the NOC with the decisions
of a private corporation. We assume that the latter maximizes the present value of profits
subject to a set of physical and financial constraints, such as the technically recoverable
resource, the fixed and operating costs of exploitation, transportation and marketing
costs, and the price (or marginal revenues) in end-use markets.
To focus on the effect of differing objectives, we assume the NOC and private
firm use the same technology. This may be an over-simplification, especially where
proprietary techniques or equipment are needed to profitably exploit the resources. The
profit motives for a private firm may lead to more rapid adoption of new technology,
particularly since managers in private firms may be more highly motivated to improve
productivity. Thus, while managerial inefficiency in the NOC may also result in
technical inefficiency, we focus on allocative inefficiency. If technical inefficiency does
exist, our analysis will understate the loss in output from the NOC.
Denoting oil exports by
0X≥
, we assume that the export price is
( )p X
with
0p′>
so that higher exports depress the international oil price.11 We also allow for oil
imports,
0M≥
. Some NOC’s with little domestic production are primarily oil
importers, but even a NOC with domestic production may eventually exhaust domestic
resources and import oil to satisfy domestic demand. For simplicity, we ignore
transportation costs and assume that the NOC is not a large purchaser in the international
oil market, and hence cannot exercise monopsony power. These assumptions imply that
11 Bernard and Weiner (1996) emphasize that the relative prices of various crude oil grades can fluctuate
substantially with changes in final product demands, effective refinery capacity and so forth. They do not,
however, find strong evidence of a difference in prices obtained or paid by NOCs and privately owned
firms. We therefore assume that the NOC and a privately owned firm face the same price functions.
8
the price of oil imports
(0) ( ) ( )
M
p p p X Xp X
′
= > +
for all
0X>
.12
Let the domestic derived demand for crude oil be
( )
d
d p
where the domestic price
d
p
need not equal the export price. Total domestic output, Q, plus imports will be sold
either on the domestic market or exported, so that
( )
d
Q M X d p+ = +
.
Oil is produced using labor (or, more generally, variable inputs), L, and proved
reserves, R. For several reasons, we would expect the productivity of L to fall as
cumulative past exploitation, E, rises.13 For example, more water injections may be
required to keep older reservoirs producing. In addition, reservoirs that are easier to
exploit are likely to be mined first. We also assume that the maximum annual output Q
obtainable from a given level of proved reserves is bounded above by
1
γ
<
, which will
depend on geological factors such as reservoir pressure and the porosity of the rocks
containing the hydrocarbons. Thus, we assume that current production is given by
( ) ( )
Q RF L G E=
where
0G
γ
< ≤
,
0G′<
,
0G′′<
,
0 1F< <
,
0F′>
,
0F′′<
and
1F→
as
L→∞
. We
assume there is a physical upper limit
0
S
to the amount of resource that can be found and
12 As a model of the OPEC cartel facing a competitive fringe, X becomes the joint supply from the cartel,
allocated across producers to minimize costs, p(X) is world demand less supply from the competitive
fringe, and
M
p
is the price of supplying energy through a backstop technology that has constant real costs.
13 Solow and Wan (1976) and Heal (1976) investigate resource extraction in general equilibrium growth
models where extraction costs depend on cumulative past exploitation. They motivate the assumption with
the observation that the real prices of natural resource commodities show a long-term decline, while the
simplest Hotelling model predicts exponential increases. In their models, output is produced using
reproducible capital, an exhaustible resource and, in the Solow and Wan case, exogenously supplied labor.
Solow and Wan assume that the number of units of the composite output good needed to extract one unit of
the exhaustible resource increases with cumulative extraction. Heal assumes that the cost of extracting a
unit of the exhaustible resource is increasing in cumulative past production until costs rise to equal the
constant cost of producing the resource using a backstop technology. Slade and Thille (1997) observe that
factors such as large unanticipated discoveries, technical change that lowers mining costs, and the
development of substitute materials that reduce demand could also explain declining resource prices.
9
0G→
as
0
E S→
. By definition, implies that E will satisfy a differential equation
( ) ( )
E RF L G E=
&
with initial
0E=
.
Since
0F′′ <
, the marginal productivity of L declines as output increases, which
leads to rising marginal costs of production in the short run (taking E and R as given at a
moment in time). Since
0G′<
and
0G′′<
, maintaining a given production level becomes
increasingly difficult as past exploitation rises. Hence, it is unlikely that the resource will
be physically exhausted. Rather the firm experiences “economic resource exhaustion”,
ultimately switching to imports that are available at a constant price.
Figure 1 illustrates the short run marginal costs of production (varying L holding
R and E fixed). If the wages paid to employees (or more generally the marginal
payments to variable inputs) are w, then the short run marginal costs can be written:
( ) ( ) ( )
( )
wF L
w w
Q L RG E F L QF L
= =
′ ′
∂ ∂
Then as
L→∞
,
( ) 1F L →
and
( ) 0F L
′→
so that marginal costs become unbounded as
( )Q RG E→
. Also, since
0G′<
, as cumulative exploitation E rises, the short run
marginal cost curve will shift up, while the maximum level of output (the asymptote in
Figure 1) shifts to the left.
We also assume that the firm can invest
0I≥
to prove up additional reserves.
Allowing S to denote the cumulative demonstrated resource, the change in S will equal I:
S I=
&
Current proved reserves, R, then equal cumulative investment less cumulative production:
R S E= −
10
Using and , output can be written in terms of the state variables E and S as
( ) ( ) ( )
Q S E F L G E= −
We assume that exploration and development becomes more expensive as the
firm exploits more marginal prospects.14 Thus, the cost of investment needed to replace
R increases with S. We also assume that short run constraints on capital availability, for
example the rising cost of rigs as exploration increases, lead to rising marginal
investment costs in the short term. These adjustment costs will constrain the rate at
which resources can be proved and readied for exploitation. More formally, we assume
that the costs of investment required to replace reserves can be written as
( ) ( ) ( )
,C I S I H Sψ=
where
(0) 0
ψ
=
,
0
ψ
′>
,
0
ψ
′′>
,
(0) 1H=
,
0H′>
,
0H′′>
and
( )H S → ∞
as
0
S S→
.
Since
( )
0, 0C S =
, the cost of investment is zero if
0I=
regardless of the value of S. The
assumption that
0H′′>
implies that investment costs will increase as S increases. In
particular, the assumption that
( )H S → ∞
as
0
S S→
implies that as demonstrated
resources approach the technically feasible limit the total and marginal cost of developing
additional reserves becomes prohibitive. Thus, rising investment costs, like rising
production costs, will cause oil production to cease prior to physical exhaustion of the
field. Figure 2 illustrates the investment cost function for several values of S.
The above description of the geologic, technological and market environments
leads to an expression for instantaneous profits:
( ) ( ) ( ) ( )
m d d
Xp X p M p d p wL I H Sπ ψ= − + − −
.
14 We ignore uncertainty regarding the size or composition of the resource base since it is not particularly
salient for the issues under discussion.
11
We assume that capital market competition constrains the private corporation to
maximize its market value. If the risk-adjusted continuously compounded return required
for investments is r, the market value of the firm would be:
( ) ( ) ( ) ( )
rt
m d d
e Xp X p M p d p wL I H S dtψ
−− + − −
⎡ ⎤
⎣ ⎦
∫
.
The NOC faces the same geologic, technological and market environments as the
private firm, but the discount rate for the NOC is
r
r r
ρ ν
= + ≥
. As a result, the NOC is
likely to forgo investments that would be considered profitable if the firm were a private
corporation. The funds that otherwise would have been invested are available for other
purposes, including increasing the amount currently flowing to the Treasury.
Following from the previous section, the NOC will also trade off current profits to
further other goals. We assume that the politicians (perhaps through a regulatory
mechanism) directly set the domestic price of oil. The interests of domestic consumers
can be represented by their consumer surplus:
( )
d
p
p
d x dx
∫
where
p
is the “choke price” at which domestic demand falls to zero. Also following
from the previous section, the influence of employees of the NOC, either as a result of
their direct political influence or the indirect effect of weak monitoring of managers, can
be represented by an implicit subsidy to the use of the variable input L. Specifically, we
assume that the NOC chooses the input L as if its cost is below w.
Using and , and recalling that the discount rate for the NOC is
ρ
, the overall
objective function for the NOC is given as:
12
( ) ( ) ( ) ( ) ( ) ( )
d
p
t
m d d L c
p
e Xp X p M p d p w L I H S d x dx dt
ρν ψ ν
−⎧ ⎫
⎪ ⎪
− + − − − +
⎨ ⎬
⎪ ⎪
⎩ ⎭
⌠
⎮
⎮
⌡∫
.
We assume that the weight of consumers in the political support function, relative to
NOC profitability, is given as
c
ν
. Thus, when domestic oil consumers are neither taxed
nor subsidized relative to other constituents,
1
c
ν
=
. In addition, the labor cost
adjustment that reflects the importance of labor is given as
L
ν
. Notice that when
r
ν
,
c
ν
and
L
ν
are zero, the NOC objective becomes that of the private firm.15
Letting the co-state variables for the differential constraints and be q and
µ
respectively, the current value Hamiltonian for the unconstrained problem becomes:
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) d
p
m d d L c
p
H Xp X p M p d p w L I H S d x dx
q S E F L G E I
ν ψ ν
μ
= − + − − − +
+ − +
∫
Incorporating constraint and the non-negativity constraints on X, M, L and I yields the
Lagrangian:
( ) ( ) ( ) ( )
d X M L I
H S E F L G E M X d p X M L Iϕλ λ λ λ= + − + − − + + + +
⎡ ⎤
⎣ ⎦
L
.
The control variables for maximizing are X, M, pd, L and I, and the corresponding first
order conditions are, in the same order:
( ) ( ) 0, 0, 0, 0
X X X
p X Xp X X Xϕλ λ λ
′
+ − + = = ≥ ≥
0, 0, 0, 0
m M M M
p M M
ϕ λ λ λ
− + + = = ≥ ≥
( ) ( ) ( ) ( ) 0
d d d c d d
d p p d p d p d pν ϕ
′ ′
+ − − =
15 In particular, with
ν
c = 0, the private firm would not take any loss of domestic consumer surplus into
account when setting pd and would act as a monopolist when selling to domestic consumers.
13
( )( ) ( ) ( ) L
0, 0, 0, 0
L L L
w q S E G E F L L Lν λ ϕλ λ
′
− + + + + − = = ≥ ≥
( ) ( ) 0, 0, 0, 0
I I I
I H S I Iψ μ λ λ λ
′
− + + = = ≥ ≥
.
The co-state equations are:
( ) ( ) ( ) ( ) ( )
q q q F L G E S E G Eρ ϕ′
= + + − −
⎡ ⎤
⎣ ⎦
&
( ) ( ) ( ) ( ) ( )
I H S q F L G Eμ ρ μ ψ ϕ
′
= + − +
&
We also recover the constraint and the differential equations and (5).
IV. Some qualitative implications of the model
We can describe the life history of the NOC as follows. In regime 1, domestic
production will be insufficient to satisfy domestic demand and the NOC will be an
importer. If the costs of production and investment costs are low enough relative to the
cost of imported oil, and total resources are sufficiently large, the NOC will soon become
an exporter (regime 2). Investment eventually ceases when its cost becomes prohibitive
(regime 3). With reserves falling and cumulative extraction increasing, production costs
rise, leading to a decline in domestic output. When domestic oil resources become
insufficient to satisfy domestic demand, the NOC will again become an importer (regime
4). Cumulative production will cease when production costs rise above the import price.
Thus, the resource is “exhausted” economically, but not physically, as increasing
production costs render continued extraction unattractive even though known untapped
resource remains.
Before elaborating on the different regimes in which the NOC will operate, we
establish some basic principles implied by the model. To begin, we note that, since
domestic and foreign produced oil are perfect substitutes, the NOC will not
14
simultaneously import and export oil. If imports are positive,
0M>
, then
0
M
λ
=
and,
from ,
m
p
ϕ
=
. In addition, from ,
( ) ( ) 0
X m
p p X Xp Xλ ′
= − + >
⎡ ⎤
⎣ ⎦
and hence exports
must be zero. Conversely, if exports are positive, implies
( ) ( )
'p X Xp Xϕ= +
, which
by assumption is less than
m
p
. Along with , this implies
0
M
λ
>
and hence that imports
are zero.
Next, the co-state variable
µ
is the shadow value of the cumulative resource
proved to date. The first order condition implies that if
( )
0μ ψ ′
≤
we must also have
0I=
. In particular, if there is to be any investment in reserves, and hence any
production at all, it must be that
0
µ
>
at
0t=
.
In addition, since
0F>
,
G
γ
≤
,
' 0G<
and
0S E− >
, differential equation
implies that
0q>
&
if
0q>
. Once production ceases, however, a marginal change in E
would not affect the value of the objective function and q must be zero. Therefore, it
must be that the shadow value of cumulative production, q, is less than zero for periods
prior to the cessation of production.
When employment L > 0,
0
L
λ
=
and equation (18) can be rearranged to yield
( ) ( ) ( )
L
wq
S E G E F L
ν
ϕ−
= −
′
−
The first term on the right-hand side of can be interpreted as the marginal cost of
production using the “shadow wage”,
L
w
ν
−
, rather than the actual wage, w.16 Because
ϕ
16 Formally, if we define the cost function that is dual to the production function :
C w −
νΛ
,
Θ
,
Ρ
,
Ε
( )≡ µιν
Λω
−
νΛ
( )
Λ
+
λ Θ
−
Σ
−
Ε
( )
Φ Λ
( )
Γ Ε
( )
[ ]
then marginal cost ∂C/∂Q =
λ
= (w–
ν
L)/[(S–E)G(E)F
′
(L) from the first order condition for L.
15
is equal to either the import price,
m
p
, or the marginal export revenue of oil,
( ) ( )
'p X Xp X+
, implies that the implicit marginal value of oil should exceed the
marginal cost of production by the shadow value of reserves,
0q− >
. The term
q−
is
therefore also a measure of the rents, or “marginal user cost”, associated with mining the
resource.17 Therefore, equation reveals that total marginal cost (the sum of marginal
production cost and marginal user cost) must equal marginal revenue, or
( ) ( ) ( ) ( ) ( ) ,when importing
,when exporting
M
Lp
wqp X Xp X
S E G E F L
ν⎧
−− = ⎨′
+
′
−⎩
.
Using (22), differential equation implies rents in this model evolve as follows:18
1q C
q q E
ρ
∂
= + ∂
&
The marginal effect of cumulative production on costs is again measured using the
“shadow wage”,
L
w
ν
−
, rather than the actual wage w. Since an increase in E raises
costs,
0
C
E
∂>
∂
, equation (23) implies that rents rise at a slower rate than the discount rate,
ρ
(recall
0q<
). Mining today not only reduces the supply of resource available to be
mined in the future, it also raises future production costs. The Hotelling-type
implications for the evolution of rents in this model are therefore similar to the
implications of other dynamic optimization models of resource depletion where
extraction costs depend on cumulative past exploitation.19
17 Equation (22) is the analog in our model of the well-known result graphed as Figure 1b in Oren and
Powell (1985). The user cost in their analysis is –q, while their price pt corresponds to
ϕ
in our model.
While pt rises to equal the backstop price in their model,
ϕ
rises to equal the import price pm.
18 From the expression for the cost function,
( ) ( ) ( ) ( )[ ]
C E F L G E S E G Eλ ′
∂ ∂ = − −
.
19 The empirical evidence on the validity of such modified Hotelling models at the individual firm level is
16
Regime 1
In regime 1, the NOC imports until investments in domestic reserves allow for
domestic production. When the NOC is an importer,
m
p
ϕ
=
and becomes:
( ) ( )
( )
1d
m d c
d
d p
p p d p
ν− = − ′
This reveals that if the consumer surplus of domestic consumers of oil is weighted
equally to NOC revenue, so that
1
c
ν
=
, then the domestic price of oil is set equal to the
import price,
m d
p p=
. Such would be the case, for example, if the government cared
only about efficiency, so the lost consumer surplus from taxing, or the marginal cost of
subsidizing, domestic oil consumption would match the marginal benefit of an increase in
NOC net income. By contrast, a private firm with a monopoly on the domestic market
would care only about firm profits and would set
0
c
ν
=
. The outcome would of course
be inefficient, as is usually the case with a monopoly.
If the political importance of consumers is low (
1
c
ν
<
), (24) implies
m d
p p<
. Oil
mixed. Early tests by Farrow (1985) and Young (1992), for example, were quite negative. Using the same
copper mine data as Young (1992), Slade and Thille (1997) found somewhat more positive results by
incorporating a return to risk bearing into the model via the CAPM. They assume that technological
progress and the exogenous mineral price follow geometric Brownian motions, but otherwise assume
mining costs depend on both current output and cumulative past exploitation. In their model, the analog to
equation (23) has the riskless rate r plus the appropriate risk premium implied by the CAPM in place of
ρ
.
The empirical results suggest that the implied user cost has a negative overall correlation with the market
return, so the risk adjusted return on mineral reserves should be below the riskless rate of interest. They
cannot reject the hypotheses implied by the joint Hotelling-CAPM model. However, although the Hotelling
model coefficients (on r and ∂C/∂E) have the expected signs, only the depletion effect is marginally
statistically significant. Furthermore, Slade and Thille conclude that the implied extent to which copper
reserves are a hedge against general movements in stock prices is unbelievable. In a more recent analysis,
Chermak and Patrick (2001) examined data from 29 natural gas wells owned by 5 firms. They modify the
model to allow for decreasing marginal production costs, physical bounds on production in each period,
and interactions between the stock of the resource, the periodic production bounds and the production path.
Their formulation is a much better representation of the underlying geologic engineering theory than was
the case in the other studies mentioned above. They also incorporate the need to process the output to
produce a final product. They find estimates that are consistent with the modified Hotelling model.
17
imported at the world price is sold to domestic consumers at a mark-up that declines as
the elasticity of demand increases. Domestic oil sales are taxed and the revenue returned
to the Treasury. Conversely, if consumer surplus from oil sales carries greater political
weight,
1
c
ν
>
and (24) implies
d m
p p<
. Thus, domestic prices are discounted relative to
world price by an amount that declines as the elasticity of demand increases. Domestic
oil consumption is subsidized at the expense of general revenue.20
Equation (24) and its implications hold regardless of whether domestic production
is positive, as long as imports are positive. If there is no domestic production, setting
d
p
is the only decision the politicians can make.21 When the NOC has domestic production,
its employment and investment decisions also can be used to influence political support.
The first order condition for employment implies that, if
0L>
,
( )( ) ( ) ( ) L
q S E G E F L wϕν
′
+ − = −
From the right-hand side of (25), the firm reduces the price of labor to reflect the political
value of employment. As a result, the firm will use more labor than would a comparable
private sector firm facing a cost of labor equal to the wage rate w.
Formally, one can obtain the solution to the model in regime 1 as follows. Since
the NOC is an importer,
ϕ
is constant at
m
p
, and, if production is positive, (25) can be
solved for L as a function of the state and co-state variables
( )
, , ; , m
L E S q w p
. In
addition, is solved for investment as a function of
µ
and S,
( )
,I Sμ
. Differential
equations (3) (with R = S – E) and (5) then determine the evolution of E and S while the
20 In accounting terms, the expenditure on the subsidy could be funded from the profits of the NOC so that
the NOC returns less money to the Treasury than it would if the subsidy requirement were absent.
21 In this model, there is no domestic employment associated with refining, transporting or marketing oil
products. More generally, there could also be over-employment in these other types of activities.
18
co-state equations (20) and (21) determine the evolution of q and
µ
.
Regime 2
In regime 2, the NOC’s domestic production is sufficient to allow oil exports.
The marginal revenue from exports,
( ) ( )
'p X Xp X+
, then plays the role of
m
p
in (24).
Thus, the NOC operates like a monopolist on the export market, but the relationship
between domestic prices and the marginal revenue from foreign sales depends on the
political importance of consumers relative to general revenue. Even if domestic
consumer surplus is treated identically to marginal public funds (so
1
c
ν
=
), the foreign
price will in general exceed the domestic price since the domestic price would be equated
to the marginal revenue from exports. More specifically, the domestic price
d
p
(and
hence domestic demand) and exports will be jointly determined by
( ) ( ) ( ) ( )
( )
1d
d c
d
d p
p X Xp X p d p
ν
′
+ − = − ′
and
( ) ( ) ( ) ( ) ( )
( )
, , , ;
d
d p X S E G E F L E S p X Xp X q w
⎡ ⎤
′
+ = − +
⎣ ⎦
for given values for E, S and q. Note that we have utilized the result that the demand for
L can also be written as an implicit function of E, S, the marginal revenue from exports
and q. This follows from the fact that, when the NOC exports oil,
ϕ
becomes the
marginal revenue from oil exports and equation (25) can be solved for L as a function of
E, S, q, and the marginal revenue from exports, or
( ) ( )
, , , ;L E S p X Xp X q w
′
+
.
Investment, as in regime 1, is found by solving and can be expressed as a function of
µ
19
and S,
( )
,I S
µ
. The differential equations again determine the evolution of the state and
co-state variables.
Regime 3
In regime 3, as in regime 2, the NOC exports oil, but the NOC no longer invests
in developing reserves as rising investment costs make further resource development cost
prohibitive. Note that if the NOC ceases to invest in new reserves, it will not resume
investment at a later date. This follows from the assumption that the backstop is
available at any quantity for a given price,
m
p
. Thus, once investment costs rise to make
proving reserves unattractive, nothing can change to later make it attractive once again.22
Since there is no investment in proving additional reserves, S remains constant at its final
maximum value,
S
. However, E,
µ
and q will continue to change until production
becomes too costly relative to
m
p
and domestic production ceases. Thus, the NOC
economically exhausts its domestic resource base.
Regime 4
In regime 4, as in regime 1, the NOC is an importer of oil. In regime 1, however,
the NOC has investment and no domestic production, while in regime 4 it has domestic
production but no investment.
V. Numerical analysis
Allowing
ϕ
to represent either
m
p
or the marginal revenue from exports,
differential equations , , and can be written as a simultaneous system of four equations
involving four endogenous functions of time:
22 In a more general model, shocks to the international market could lead to discontinuous production.
20
( ) ( ) ( )
, , , ;E S E G E F L E S q wϕ= − ⎡ ⎤
⎣ ⎦
&
( )
,S I Sμ=
&
( ) ( ) ( ) ( ) ( )
, , , ;q q q F L E S q w G E S E G Eρ ϕ ϕ ′
= + + − −
⎡ ⎤⎡ ⎤
⎣ ⎦⎣ ⎦
&
( ) ( ) ( ) ( ) ( )
, , , , ;I S H S q F L E S q w G Eμ ρ μ ψ μ ϕ ϕ
′
= + − +
⎡ ⎤ ⎡ ⎤
⎣ ⎦ ⎣ ⎦
&
To find a unique solution to this set of simultaneous equations we need to specify four
initial or terminal conditions for the state and co-state variables. We assume that initially
0R S= =
. The remaining two conditions follow from the requirement that when
production ceases at time T it must be that
( ) ( ) 0T q Tμ = =
.
We numerically solve the model using the particular functional forms given in
Table 1. These functions were chosen to give a realistic general shape with a minimum
number of parameters to be specified. The parameter
α
in the production function
determines how rapidly short run operating costs increase as output expands. An increase
in
α
makes
( )F L
closer to a right angle curve with the implication that a small increase
in variable input L will greatly increase output toward its upper limit. The latter is
determined by the geologic characteristics of the field.
The geologic characteristics of the field are encoded into three parameters
determining
( )G E
. An increase in
γ
raises the rate of deliverability for a given quantity
of proved reserves, R, and field maturity level as determined by cumulative past
production, E. The parameter
β
determines how rapidly productivity declines with
cumulative past production, and
0
S
represents a physical limit to the amount of
hydrocarbon resource available to be identified.
21
In the function describing exploration and development investment,
1
ψ
measures
the marginal cost of exploration investment when
0I S= =
, while
2
ψ
determines how
costs increase as the NOC raises investment at any time. The parameter
30
ψ
>
measures
how investment costs increase as the NOC moves to more marginal opportunities.
The function explaining foreign demand for NOC exports allows an increase in X
to reduce the export price. However, as
0X→
, the elasticity of demand becomes
infinite and the NOC takes the export price as given and equal to the import price,
m
p
.
The function for domestic demand is determined by three parameters. The
maximum price where domestic demand falls to zero, or choke price, is
p
. We shall
assume that
p
is substantially above
m
p
, so that the NOC must become an importer
when domestic production is zero. The exponent
ε
determines the elasticity of demand,
while A determines the maximum domestic demand if
d
p
falls to zero.
Scenario Analysis
Table 2 presents numerical values for the parameters used to model a NOC and a
corresponding efficient case assuming the same geology, production function and other
underlying fundamentals. The efficient outcome may not be achievable in practice, but is
used as a benchmark for NOC performance. In the efficient case, the firm maximizes the
sum of producer and domestic consumer surplus, but otherwise is not subject to any
political influence, that is,
0, 0, and 1
r L c
ν ν ν
= = =
.23
The parameter values in Table 2 are chosen to illustrate the implications of the
23 This is not efficient from a world perspective because the firm is a monopolist to foreign consumers.
22
model and do not necessarily correspond to any observed firm. With
0.6
α
=
, output will
be around 75% of its feasible level (given R and E) when
2.3L=
. Over most of the
production horizon, reserves are between 0.5 and 1.0 (or 12–25% of the physical resource
stock) and production between 0.1 and 0.35, as measured in the same units. With
w = 0.01, annual profits ignoring investment costs are on the order of 0.12 to 0.25 (using
pm as numeraire). For
1.75
β
=
, the potential output/reserve ratio is around 97% of its
original value (given by
γ
) when the known resource is half depleted (
2.0E=
) and
slightly over 82% of its original value when only 25% of the resource is left (
3.0E=
).
Setting
0.2
Lw
ν
=
implies that the NOC will perceive L to be 20% less expensive
to employ than is actually the case. Hence, L will be higher than would be the case were
its cost perceived to be w. However, the profits of the firm will be lowered as a result,
since the firm still has to pay w to the domestic variable input suppliers.
The marginal cost of investment in the absence of adjustment costs equals the cost
(
w
) of the variable input (although the units are different). When investment is positive,
it takes values up to around 0.5. The adjustment cost parameter (
20.5
ψ
=
) then yields
peak marginal investment costs (ignoring the effect of S) that are around 10 times the
peak cost of L, reflecting an assumption that the oil production industry is capital-
intensive. The parameter
3
ψ
controls how rapidly investment costs escalate as more of
the resource base is developed. For
30.1
ψ
=
, costs are increased by about 10% when
half the resource has been developed, and slightly less than 30% when three fourths of
the resource has been developed. Costs do not increase by 50% until more than 83% of
the original resource base has been developed. Hence, costs escalate quite gradually,
23
reflecting an assumption that the geologic characteristics of the resource endowment are
relatively homogeneous.
The assumed (real) commercial discount rate of 10% is within the range of rates
typically used in commercial evaluations of oil exploration and production projects. The
10% political premium for the NOC (
0.1
r
ν
=
) would produce an overall discount rate for
the NOC that is at the high end of the range of rates typically used by the oil majors.
With
ξ
= 0.2, the elasticity of the export demand curve remains greater than 1 for
a level of exports almost equal to one-fourth of the NOC’s total resource endowment.
This elasticity is much higher than the elasticity of domestic demand, but it reflects both
the elasticity of foreign demand for oil and the elasticity of supply from competing
suppliers. Even for a NOC of an OPEC member, the alternative sources of supply are not
simply the “competitive fringe” of non-OPEC producers. The cartel’s production quotas
can be difficult to enforce, and a supply decrease by any one OPEC member is likely to
produce some offsetting supply increase from other OPEC members.
Although the assumption
1.05
c
ν
=
implies that domestic oil consumption will be
heavily subsidized, we would still expect the domestic price to be close to the
(normalized) import price of 1.0.24 For the parameters in Table 2, domestic demand
around these prices will be quite inelastic (with an elasticity of slightly more than 0.01),
reflecting an assumption that there are few good substitutes for oil in many of its
domestic uses. If the domestic price rises above the world price, however, domestic
demand declines and ultimately is eliminated at a choke price ten times the world price.
24 Recall that we are assuming the NOC will be a price taker in the oil import market. This reflects the fact
that most NOC’s from oil-exporting nations are in nations with relatively small populations and economies
even though their endowment of hydrocarbon resources is high.
24
Efficient and NOC solutions
The appendix provides algebraic expressions for the equations characterizing the
optimal solution (equations , , and –) for the functional forms in Table 1. After
specifying numerical values for the various parameters, we used a numerical differential
equation solver (in MATLAB) to obtain approximate solutions to the resulting system of
simultaneous differential equations.
As can be seen in Table 2, the parameters in the functions describing production,
investment and demand are the same in each case. However, this does not mean that
those functions will take the same values because
, , and
r L c
ν ν ν
will affect the values of
the endogenous variables L, S, E, I, X and pd.
For the NOC parameter values in Table 2, the critical terminal years for the
different regimes are T1 = 0.16797, T2 = 0.22667, T3 = 21.916, T4 = 23.563 and
T5 = 79.1579. Thus, the NOC produces output for more than 79 years, although
production is very small for the last 40 or so years. In fact, domestic production is
insufficient to meet domestic demand for the final 50 years (from T4 to T5). Investment in
developing new reserves ends slightly less than 24 years after the first investment occurs.
The initial period of zero production lasts only about 2 months after investment starts,
and soon after production commences the NOC begins to export oil.
In contrast to the NOC, the critical terminal years for the different regimes in the
efficient case are T1 = 0.30693, T2 = 0.36614, T3 = 23.4939, T4 = 25.3131 and
T5 = 112.7434. Thus, the NOC begins but also ceases production earlier than is efficient.
Figures 3 through 7 illustrate the differences in outcomes between the NOC and
efficient firm. The figures graph the paths of output, reserves, employment, domestic
25
demand and cash flow25 over the first 30 years. We see in Figure 3 that the NOC output
exceeds the efficient output, but this reverses itself after about nine and half years.
Figure 4 illustrates that the NOC invests less in reserves than would the efficient
firm. In the efficient case, resources are not diverted away from investment activities.
Figure 5 illustrates the effect of the increased political weight on domestic
employment. We see that the NOC level of employment increases by roughly 35% over
the efficient case. This explains the increased NOC output over the efficient case in the
near term. Reduced output in the longer term occurs regardless of higher employment in
the NOC due to the lower investment in reserves by the NOC.
Figure 6 shows how subsidized domestic prices increase domestic demand and
thus reduce the NOC’s exports. While increased employment in the NOC results in
higher output in the near term, higher domestic demand prevents exports from rising by
the amount that they do in the efficient case.
The effects of government objectives on employment and demand, which are
illustrated in Figures 5 and 6, manifest themselves in the cash flows of the NOC relative
to the efficient firm, which are illustrated in Figure 7. In particular, cash flows to the
NOC are lower than for the efficient firm because the NOC over-employs and sells a
portion of its output at below world market prices.
Figures 8 and 9 illustrate the evolution of marginal costs and resource rents. Total
marginal cost is equal to the vertical sum of the marginal extraction cost (the blue area,
equal to
( ) ( ) ( ) ( )
( )
L
w S E G E F Lν ′
− −
) and the resource rents (the red area, equal to
q−
). Resource rents accrue until time period
5
T
when production ceases. The NOC is an
25 The appendix provides algebraic expressions for the cash flow of the NOC in the different regimes.
26
exporter during the time period when the total marginal cost is below 1. We see this by
examination of equation (22). Equation (22) requires
ϕ
to be equal the sum of the
apparent marginal cost of L (the blue area in Figures 8 and 9) and
q−
(the red area in
Figures 8 and 9). We also know that
ϕ
equals the price of imports when the NOC is
importing and the marginal revenue from exports when it is exporting. Thus, the vertical
sum of the two areas in each of Figures 8 and 9 is 1.0 when the NOC is importing, but
dips below this value when the NOC is exporting.
The blue area in Figure 9 is labeled as an “apparent” marginal cost because the
true marginal extraction cost is given as
( ) ( ) ( )
w
S E G E F L
′
−
whereas the NOC behaves as if marginal extraction cost is
( ) ( ) ( )
L
w
S E G E F L
ν−
′
−
An implication of this behavior is that the true marginal cost curve would lie above the
boundary of the blue region in Figure 9, and some of the resource rents are dissipated by
the subsidy to the employment of L.
Comparative statics – Increasing the political discount rate
While the above discussion illustrates the effect of changing all of the political
influence parameters simultaneously, it does not give us a good indication of the marginal
effects arising from each type of distortion. In this section, we examine the effects of
changing each political influence parameter one at a time, again using the efficient case
as a benchmark.
Higher discount rates reduce the relative weight of future cash flows, which
27
encourages the firm to shift cash flows to the present. Conversely, a decrease in the
political discount premium should favor later increases in cash flows. Hence, it is not
surprising that Figure 10 shows that an increase in the political discount premium raises
cash flows in the early years at the expense of later years. As we increase the political
discount premium to 5% and then 10%, cash flows are higher than when
0
r
ν
=
in the
beginning of the time horizon but are lower later in the time horizon.
Figure 10 also shows the effects of higher discount rates on production,
employment and reserves. The results are consistent with the cash flow picture.
Increasing the discount rate causes output and employment to rise in the initial time
periods relative to the efficient case. Reserves, however, are only slightly higher in the
initial periods, with the increase almost disappearing as
r
ν
rises to 0.1. Production is
higher despite reserves being lower (from year 5 through 9 in the case
0.05
r
ν
=
) as the
firm substitutes labor for capital. Beyond year 9, cash flows, reserves and output are all
below the efficient case, although employment remains above the efficient case until year
20. At this point, employment dips below the efficient case because the marginal benefit
of more variable input is diminished with fewer proved reserves and lower cash flows.
Comparative Statics – Increasing the weight of domestic employment
In the second set of sensitivity cases, we increased the political imperative to
employ more variable input L by setting
0.1
Lw
ν
=
and
0.2
Lw
ν
=
. The results are
graphed in Figure 11. As might be expected, a firm that must meet the objective of
employing a larger workforce has a higher level of employment in all time periods than
in the efficient case. Thus, over-employment by a NOC does not necessarily mean that it
28
is technically inefficient. Rather it is just meeting a different objective. The effects on
cash flows, output and reserves, however, are also of interest. Cash flows are initially
higher in these cases as the increased labor input results in more output. However, the
additional cost of labor relative to the efficient case means that investment in proving
new reserves is sacrificed. As a result, cash flows ultimately fall relative to the efficient
case as it becomes impossible to keep production higher.26
Comparative Statics Case – Increasing the weight of the domestic consumer
In the third set of sensitivity cases, we increased the political weight of domestic
consumers to
1.025
c
ν
=
and
1.05
c
ν
=
. In both cases, the effects on output and reserves
are virtually zero. Cash flows are negatively affected, but are simply decreased in every
year by the amount of the subsidy (not pictured). Figure 12 shows, however, that the
domestic subsidy increases employment in the short run as in the previous two cases.27
The larger domestic consumption of oil, and forgone revenues from domestic sales,
requires the firm to raise its employment while it is an exporter in order to generate
additional output for export. When the firm later moves toward becoming an importer, it
must sell all of its output at subsidized prices. The resulting reduction in cash flows
reduces employment below that of the efficient case.
VI. Concluding remarks
The effects of varying the political influence parameters showed that many of the
political influences that may be exerted on a NOC tend to push it in the same direction.
An increase in the political discount premium encourages greater employment, increased
26 The discontinuity in cash flows around year 26 is the result of the firm ceasing to invest in new reserves.
This leads to n abrupt change in expenditures.
27 The lines in Figure 12 wiggle because the effects are so small that we are getting very close to the
accuracy of the spline approximation needed to calculate differences in time paths.
29
output and a higher cash flow in the short run, but ultimately results in lower
employment, output and cash flows in the long run. Reserves are generally lower
throughout the time horizon, with the possible exception of the first few years.
Similarly, any political or bureaucratic imperative to raise employment will lead
to higher employment throughout the time horizon. Nevertheless, output, cash flow and
reserves, while higher in the initial time periods, are all lower relative to the efficient case
in the longer term.
Finally, forcing the NOC to subsidize domestic consumers also shifts production
from the future toward the present. This results in greater employment in the initial time
periods. While the firm is an exporter, increased employment and output provide
additional revenue that can be used to offset the losses associated with domestic sales.
While the scenarios examined in this paper are by no means exhaustive, they are
informative. In particular, the predictions of the model in response to the imposition of
various political objectives are consistent with NOC’s being more focused on current
output and cash flow and less focused on forward looking strategies in developing
resources than private firms.
30
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Journal of Public Economics (1992), 48:67–81.
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Journal of Policy Analysis and Management (1987), 6(4): 567–582.
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Shleifer, A. “State versus Private Ownership.” Journal of Economic Perspectives (1998),
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33
Figures and Tables
Output
Q
Marginal cost
( ) ( )
0
w
RG E F ′
RG(E)
Figure 1: Short run marginal costs of production
S(t2)
S(t3)
S(t1)
S(t0)
Investment cost
I
Figure 2: Investment costs
34
Figure 3: NOC and efficient production
Figure 4: NOC and efficient reserves
35
Figure 5: NOC and efficient employment
Figure 6: NOC and efficient domestic demand
36
Figure 7: NOC and efficient cash flow
Figure 8: Graphical representation of equation (22): Efficient case
37
Figure 9: Graphical representation of equation (22): NOC case
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
0 5 10 15 20 25 30
Years
v
r
= 0.05
v
r
= 0.1
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0 5 10 15 20 25 30
Years
v
r
= 0.05
v
r
= 0.1
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 5 10 15 20 25 30
Years
v
r
= 0.05
v
r
= 0.1
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
0 5 10 15 20 25 30
Years
v
r
= 0.05
v
r
= 0.1
Change in output
Change in reserves
Change in employment Change in cash flow
Figure 10: Effects of increasing the political discount premium
38
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0 5 10 15 20 25 30
Years
v
L
= 0.1w
v
L
= 0.2w
-0.035
-0.030
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0 5 10 15 20 25 30
Years
v
L
= 0.1w
v
L
= 0.2w
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 5 10 15 20 25 30
Years
v
L
= 0.1w
v
L
= 0.2w
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0 5 10 15 20 25 30
Years
v
L
= 0.1w
v
L
= 0.2w
Change in output Change in reserves
Change in employment Change in cash flow
Figure 11: Effects of increasing the employment incentive
-0.0008
-0.0006
-0.0004
-0.0002
0.0000
0.0002
0.0004
0.0006
0 5 10 15 20 25 30
Years
v
c
= 1.025
v
c
= 1.05
Figure 12: Employment effects of increasing the subsidy to domestic consumption
39
Table 1: Functional forms used in the numerical analysis
Part of model Functional Form Graph
Production
( )F L
1L
e
α
−
−
1
L
( )G E
( )
0
0
1
1
S E
S
e
e
β
β
γ− −
−
⎡ ⎤
−
⎣ ⎦
−
S0
E
Investment
( ) ( )I H S
ψ
( )
23
1 2
0
1S
I I S S
ψ
ψ ψ ⎛ ⎞
+ +
⎜ ⎟
−
⎝ ⎠
I
Demand
( )p X
2
m
p X
ξ
−
for X ≥ 0, pm otherwise
pm
X
( )
d
d p
( ) for , 0 otherwise
d d
A p p p p
ε
− ≤
p
pd
d
40
Table 2: Parameter values under efficiency and for the NOC
Parameter
Efficien
t NOC
Production
α
0.6 0.6
β
1.75 1.75
γ
0.4 0.4
S04.0 4.0
w0.01 0.01
Investment
ψ
10.01 0.01
ψ
20.5 0.5
ψ
30.1 0.1
r0.1 0.1
Demand
pM1.0 1.0
ξ
0.2 0.2
A0.0018 0.0018
p
10.0 10.0
ε
0.8 0.8
Political variables
ν
L0.0 0.2w
ν
c1.0 1.05
ν
r0.0 0.1
41
Appendix: Algebraic solution for the specific functional forms in Table 1
It is useful to begin with the equations determining investment. When investment
is positive, the first order condition implies
( )( )
( )
1 0 1 3
2 0 3
2 1
S S S
IS S
μ ψ ψ ψ
ψ ψ
− − −
=+ −⎡ ⎤
⎣ ⎦
and an increase in S or decrease in
µ
will reduce I. In particular, since S = 0 initially,
investment will only begin if the initial value of
µ
>
ψ
1. Investment will cease when
µ
and S solve
3
1
0
1S
S S
ψ
µ ψ
= +
−
that is, when
µ
equals the marginal cost of investment at I = 0. Equation will have a
solution since the right side increases as S increases, while
µ
must start above
ψ
1 and
ultimately decrease to zero. Using the solution for I, becomes
( ) ( )
( )
1 0 1 3
2 0 3
2 1
S S S
SS S
µ ψ ψ ψ
ψ ψ
− − −
=+ −
&
while I remains positive. Once investment ceases, S will retain the value, say
S
, that it
has at that time.
Now consider the short run production problem. For the production function in
Table 1, the solution for employment L is given by
( ) ( )
( )
( )
( )
( )
( )
( )
( )
00
00
11
1ln for
11
0 otherwise
S E S
L
SS E
L
q S E e w e
S E
Lw e q e
ββ
ββ
α ϕ γ ν
αναγ ϕ
− − −
−− −
+ − − − −
− ≥
=
− −
+ −
In particular, the NOC begins with cumulative production E = 0. Investment in reserves
42
will raise S, but will not lead to positive output until S (and thus proved reserves) attains a
minimum value:28
( )
L
w
Sq
ν
αγ ϕ
−
=+
When proved reserves are above the minimum required level, output will be
( )
( )
( )
0
0
1
1
S E
L
S
S E e w
Qe q
β
β
γν
α ϕ
− −
−
− − −
= −
− +
until E increases to solve
( )
( )
( )
( )
0
0
1
1
S
L
S E
w e
E S
q e
β
β
ν
αγ ϕ
−
− −
− −
+ =
+ −
where
S
represents the maximum level of S attained by the time investment I ceases.29
Thus, for
S S≥
and
E E≤
cumulative output will evolve according to
( )
( )
( )
0
0
1
1
S E
L
S
S E e w
Ee q
β
β
γν
α ϕ
− −
−
− − −
= −
− +
&
with
0E=
&
otherwise. For this production function, differential equation becomes
( )
( )
( )
0
0
1
1
S E
S E
e
q q q Q S E e
β
β
β
ρ ϕ
− −
− −
= + + +
−−
&
for
S S≥
and
E E≤
and
q q
ρ
=
&
otherwise. Output Q in will be given by .
Similarly, differential equation becomes
( )
( )
2
3 0 1 2
2
0
SI I
S S
ψ
µ ρµ ψ ψ
= + +
−
&
28 The required minimum level of reserves to begin production will be larger the higher the effective cost of
variable input and smaller the higher the productivity of the variable input
α
, the flow rate
γ
or the price of
oil (represented by
ϕ
).
29 Note that the left side of is an increasing function of
E
.
43
when I > 0 but output is zero,
( )
q Q
S E
ϕ
µ ρµ
+
= − −
&
when output is positive but investment is zero, and
( ) ( )
( )
2
3 0 1 2
2
0
q Q SI I
S E S S
ϕψ
µ ρµ ψ ψ
+
= − + +
−−
&
when both investment and output are positive. In equations – ,
ϕ
is either the marginal
revenue of exports (in the exporting regime) or the price of oil imports (in the importing
regimes).
The domestic price (and hence domestic demand) in the importing regimes can be
found from with
ϕ
= pm. For the specific form of the domestic demand function in Table
1, this can be written
( )
1
1
m c
d
c
p p
p
ε ν
ε ν
+ −
=+ −
As we noted in the qualitative discussion, pd > pm if the political importance of consumers
is very low (νc < 1). In addition, if
ε
→ 0, domestic consumption becomes a good tax
vehicle and the domestic price increases toward the choke price
p
. If the weight on the
loss of consumer surplus equals the marginal cost of public funds,
ν
c = 1 and the
domestic price is set equal to the import price. Finally, if domestic consumers of oil
products are a favored special interest group,
ν
c > 1 and pd < pm. In the latter case, the
difference between pm and pd is given by
( ) ( )
1
1
c m
c
p p
νε ν
− −
+ −
which is decreasing in
ε
. A small value of
ε
implies that the subsidy can be increased
44
without a great efficiency cost. We cannot have
ε
so small and
ν
c so large that
ν
c –
ε
≥ 1.
The level of imports will be given by the difference between domestic demand
and domestic production . At the transitions between importing and exporting regimes
domestic production has to equal domestic consumption of oil.
When the NOC also is exporting oil,
ϕ
equals marginal export revenue and is also
time varying. Furthermore, proved reserves have to be sufficient to support domestic
production. Thus, X and pd are determined (as functions of E, S and q) by the solutions to
the following two equations:
( )
( )
2
3 1
1
m c
d
c
p X p
p
ε ξ ν
ε ν
− + −
=+ −
( ) ( )
( )
( )
0
0
2
1
13
S E
L
dS
m
S E e w
X A p p eq p X
β
εβ
γν
α ξ
− −
−
− − −
+ − = −
−+ −
Substituting into we obtain a non-linear equation to solve for X:
( )
( )
( )
( )
0
0
2
2
1
3
1 1 3
S E
mL
S
cm
S E e
p p X w
X A eq p X
εβ
β
γ
ε ξ ν
ε ν α ξ
− −
−
− −
− + −
+ = −
+ − − + −
In addition, since
2
3
m
p X
ϕ ξ
= −
, the differential equations , , and now also
involve X. In practice, since we cannot solve analytically for X as a function of E, S, q
and the parameters, we differentiate with respect to time, substitute for
, and E S q
&
&&
and
include the resulting equation as a fifth differential equation to be solved simultaneously
with the remaining four.
Finally, we also need expressions for the cash flow of the firm. For the functional
forms in Table 1, the cash flow of the NOC can be written as
45
( ) ( )
( )
( )
( )
2 2
2
23
1 2
0
3 1 3
1 1
1
m c m
m
c c
p X p p p X
X p X A
S
wL I I S S
ε
ε ξ ν ε ξ
ξε ν ε ν
ψ
ψ ψ
− + − − +
− + + − + −
− − + +
÷
−
when the firm is exporting and
( ) ( )
( )
23
1 2
0
11
1 1
m c m
m
c c
p p p p S
A p M wL I I S S
ε
ε ν ε ψ
ψ ψ
ε ν ε ν
+ − −
− − − + +
÷
+ − + − −
when the firm is importing.
46
