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Models of cartel behaviour in an industry extracting a nonrenewable resource
Models of cartel behaviour in an industry extracting a nonrenewable resource Michael Folie Department
of Economics,
University of New South Wales, Sydney, Australia
Alistair Ulph Department
of Economics,
University of Southampton,
Southampton
SO9 5NH, UK
(Received June 19 79; revised January 1980)
Introduction
Industry with a cartel and competitive
This paper discusses various attempts to model the dynamic behaviour of an industry depleting an exhaustible resource, where some of the firms in the industry are cartelized; one such attempt is a model we have developed, and we will present some of the results of our work. An obvious motivation for such work is the interest in energy policy, particularly following OPEC’s action in raising the world price of oil. The long-term energy problem can be characterized by the transition from cheap, convenient but exhaustible forms of energy such as oil and gas to more expensive but abundant forms of energy. A key factor controlling this transition is the price path for oil, currently determined by OPEC. It is of some interest, therefore, to understand the behaviour of industries with a structure similar to the oil industry. Questions one could consider include : what are the likely price and production paths for such an industry; how stable is the cartel; what are the relative gains to the cartel and other firms in the industry? Until recently, the analysis of such questions was confined to static models, i.e. for markets where the product is infinitely reproducible. It is important to know the extent to which the conclusions of such static models are valid for the case of an exhaustible resource. Our earlier work’ suggests that exhaustibility of a resource introduces novel features to a model of cartels. Specifically, unlike the static model, the act of cartelization can reduce the value of the reserves of the fringe firms in an industry. This result was derived for a fairly special case, and part of our interest in building simulation models is to test the robustness of this conclusion. The structure of this paper is as follows. The general structure of a model of a partially cartelized industry depleting an exhaustible resource is outlined. The models that have been developed to analyse the oil industry are reviewed, noting particularly the variety of assumptions made. The work we have done to analyse some theoretical issues in studying cartels and exhaustible resources is discussed and finally some results from a more general model we have developed and applied to the oil industry are presented.
Consider an industry with an arbitrary number of firms producing a finite resource. There is a global demand for this commodity and each firm faces convex marginal costs of extraction, which may depend on the cumulative level of the resource already removed. Each firm can face different costs (which include transport costs to the market) and may have different stocks of reserves. Demand is bounded from above, since it is assumed that there is a price at which some suitable backstop technology will become widely abundant:
0307-904X/80/030199-06/$02.00 0 1980 IFT Business Ress
fringe
P = f@; t) Demand may vary over time and at some future time t*, when the demand Q(t*) = 0, then P(t*) = F, where F is the price at which a substitute technology will be competitively supplied. (In order to simplify notation, functions .of timevarying variables will not explicitly show such time dependence). There are two groups of firms, a cartel and a competitive fringe. The identity of the firms in the cartel will be designated by the index set J, and the fringe of competitive firms by the index set I. At time t, each firm, i, in the cartel has used Xi(t), of its total reserves Xi, and faces convex extraction costs Kj((zi, Xi; t). Similar notation applies to firms in the fringe. It is assumed that all reserves are economic and therefore will be exhausted before the backstop technology becomes economic at price F. There are two possible forms of market behaviour after cartelization. In a Nash-Cournot model, the fringe takes prices as given and depletes its reserves so as to maximize the present value of profits, while the cartel takes the fringe output as given, and sets prices (and its own output) to maximize the present value of its profits. In a Dominant Firm model, the cartel plays a less passive role, and takes account of the fact that as it changes price so the fringe’s production path will change. The cartel thus takes account of the reaction function of the fringe in setting its policy. The equilibria of these two models will differ, but the analysis presented here will be done explicitly for the Nash-Cournot model.
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Competitive behaviour The competitive firms take the market price, P(t) as given and choose a production pattern &i(t) to maximize the discounted present value of profits. Thus the problem can be expressed as:
of the cartel completely exhaust their finite stock of reserves. In this case, the cartel can affect the price by restricting the total output from the cartel. A more formal statement of the problem is:
I;: ;:;,S i
Ti [P(t) Qdt)
-
Ki(Qi,
xi;
t)I eAt
dt
Lf(Q;
xjj
t) Qj(t)
-Kj(QjT
Xi;
t)] e-6tdt
i
0
iEJ
subject to:
0
subject to:
*i(t) = Qi(t>
*j(t)
WE1
20
Q,(t)
Xi(O)= 0
Xj(Ti) =
Ri
Ti is the unknown terminal time, when firm i exhausts its reserves, which may be before the price reaches F. It can be shown that the production pattern Qi(t) which maximizes the above system must satisfy the set of differential equations that are derived from the application of Pontryagin’s pointwise maximum principle. After some algebraic operations it can be shown that the optimal production pattern for each firm must satisfy the following conditions: P(t)
~7~
-
MKi
AT(~) =
hi
G AT(t)
Ti
I
e6f +
&i(t)
2
0
aK.
2
e-s(7-f)d7
aXi
where MKi is the mariinal extraction cost = Xi/aQi. The first of these conditions requires that at any moment of time firms will produce up to the point where price equals marginal cost of production plus a ‘user cost’. This user cost, h:(t) consists of two parts. The first, hi es*, measures the profit foregone by extracting at time t rather than some other time. This term is often referred to as ‘exhaustion rent’. The second term measures the increased cost imposed on later extraction by lowering the stock of remaining reserves. Figure 1 illustrates the solution at time t. MK is firm i’s marginal cost curve. With price P(t) = OA, and output Qi(t), user cost is AT(t) = OA - OD = AD, that is price less marginal cost of production at of(t). Total profit is ABCE, of which ABCD is user cost. With no stock effect on production costs, ABCD would represent just exhaustion rents earned at time t. Cartel behaviour The cartel takes as given the production plans of the competitive fringe of firms (Qi(t), Vi E I) and chooses a production plan, Qi(t), Vj EJ, that maximizes the present value of profits subject to the constraint that the members
I
0
0, b+)
Figure
1
200
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=
VjEJ
Qj(t)
Xi(O) = 0
VjEJ
X,(Ti) = xi
VjEJ
Q(t)
= c
Qi(t‘i + c
jGJ
a(t)
iEI
Again, the optimal production plan for the cartel must satisfy the differential equations derived from applying Pontryagin’s pointwise maximum principle: P(t) +
5 [Q&t)] -MKi
h?(t) = hi es* +
G AT(t)
Q/(t)
2
0
TJaK.
s
_-! e--6(‘--*) aXj
d7
VjEJ
t
Market equilibrium An equilibrium price path will have the characteristic that the competitive production pattern assumed by the cartel in setting its production levels will be the one actually chosen by the competitive firms, while the price path assumed by the competitive firms in setting their production levels will be the one actually selected by the cartel. At each point in time, the equilibrium price path will result in production levels for both the cartel members and the competitive fringe that are market clearing, while over time all reserves must be exhausted by the time the market price reaches the backstop price, F. Solution Clearly, if the price path P(t) was known, then for each of the competitive firms, i E I, production plans could be determined by solving an optimal control problem for each firm, where the control variable is Qi(t) and there is a single state variable Xi(t). However, it is more difficult to see how control theory could be invoked to solve the cartel’s intertemporal optimization problem. If the production levels of the competitive fringe firms was known by the cartel, then its problem is merely a control problem (this is the approach used by Pindyck and his workers which will be discussed later). However, the underlying economics of this particular class of problems suggests an alternative approach. Essentially, the only difference between the dynamic equilibrium and the well known static equilibrium market behaviour is that in the dynamic case each firm, irrespective of the market structure, is producing a resource which is finite. It turns out that provided each firm imputes the correct user cost to its particular stock of the resource, then the myopic single period profit maximizing strategy will be compatible with the dynamic profit maximizing decision. These ‘user costs’ are the XT(t) and h:(t) values that appear in the first order conditions. These user costs are complex
Models of cartel behaviour: M. Folie and A. Ulph functions of all the given parameters that characterize the industry which are not known implicitly. Hence the solution to the problem consists of assigning a user cost to each firm, and computing a market clearing price and corresponding quantities supplied by each firm for each time period until the price reaches F. The total quantity produced over time by each firm is compared with its reserves, and if it exceeds its reserves, the user cost assigned must be raised, while if total production falls short of reserves, user cost is lowered. There is a single market demand for this particular resource and the only intrinsic difference between each firm’s output lies in the difference in the extraction costs. Hence each firm’s output can be considered to be grossly substitutable for any other firm’s output. The aggregate demand for each firm’s stock of the resource is given by: VkEIUJ
Dk = Dk(&) a& ah,
>o
lfk
Vk,lElU/
l=k
This follows from the property of the other firms’ reserves being gross substitutes. Aggregate excess demand for each firm’s resource stock is simply:
xD,=Dk-_&
VkEIUJ
and the Jacobian of XDk is equal to the Jacobian of D,. The problem is to find a set of 4, such that:
xD,(?$ = 0 Given the property of gross substitutability between the excess demand for firms’ reserves it is possible to invoke the well known theorem that the application of Walrasian tatonnement will ensure that the equilibrium values of h will be reached. Unfortunately, the step size must be very small to ensure convergence, and this usually requires an inordinately large number of iterations. Thus a variant of Newton’s method for solving simultaneous nonlinear equations was used here, since for guesses ‘reasonably’ near to the solution, the procedure is quadratically convergent. This requires computing the Jacobian matrix numerically at each guess and then updating. The procedure is conceptually a more sophisticated tatonnement, since this approach implies that each firm recognizes that an increase in its value of h will not only reduce the demand for its reserves, but will increase the demand for all other firms’ reserves. By using this extra information, the equilibrium set of user costs will be found more rapidly. Finally, it should be noted that this technique for solving the Nash-Cournot problem can also be used to solve for a perfectly competitive equilibrium. It also has the obvious advantage that there is no restriction on the number of firms in the industry, although the computational burden increases with the number of firms. The number of iterations required to compute the Jacobian rises linearly with the number of different firms in the industry.
A survey of studies of cartels Most of the studies into cartel behaviour have been computationally oriented, and frequently concerned only with the problem of forecasting the future price path for oil. A good survey of the modelling attempts up to mid-1975 is given by Fisher et al.2 The two basic approaches used are simulation studies and optimization models.
Essentially, for a simulation study, a basic model is specified and then by assuming plausible values for the parameters describing the economic system, such as demand elasticities and demand growth rates, supply conditions for cartel and noncartel firms, a series of price paths can be generated and ranked according to some criterion or a price path is arbitrarily selected as being the ‘most likely’ scenario. Good examples of this fairly conventional approach of dynamic simulations are the studies reported by Blitzer et al. 3 and the medium run model (up to 1995) in Kalymon.4 In contrast to simulation models, which examine a finite number of arbitrarily prespecified price paths, optimization models use a plausible and quantifiable objective function, usually the present value of cartel profits to select the best price path. Since the level of complexity that can be solved for in optimal control problems is fairly restrictive, the specification of dynamic cartel models has been relatively simple, which limits the generality of the conclusions regarding the realism of the optimal price paths. Another, related, question which some models examine is a comparison between the price trajectory that would prevail under competitive conditions and under a partial cartelization of the market. From a resource allocation standpoint, it is desirable to have some indication of the magnitude and duration of the deviation of cartelized prices from the competitive norm, since this provides some indication of the extent of the misallocation of the world’s resources. Since a strategy directed towards breaking up a cartel entails real costs, it is important to know whether the misallocation warrants incurring such costs. Kalymon4 has the simplest model, which essentially considers that OPEC is the residual supplier of oil, and thus faces the rest of the world’s excess demand for oil. A slight twist introduced by Kalymon is that he includes OPEC’s domestic demand for oil, which may be priced below the world price. He assumes marginal costs of extraction constant with respect to current output, but rising with cumulative output. Demand is linear and grows over time. He computes a price path that maximizes the present value of oil revenues less extraction costs, plus the present value of the consumer surplus stemming from the domestic OPEC consumption of oil. The solution technique is not alluded to by Kalymon, but his specification leads to a large, potentially decomposable, quadratic programming problem; it could also be solved by optimal control methods. Any solution method will lead to a single, globally optimal price trajectory since the objective function is strictly concave in the prices. A more complex model is used by Marshalla, who is interested in determining a plausible price path for the world oil industry if OPEC did not act as a cartel, but was a price taker. Marshalla’s model includes a number of interesting features. Although the model considers only the oil market, and hence is a partial view of the energy market, the demand for oil is calibrated against a ‘reference’ path for oil prices and quantities derived from the models developed by FEA and the Stanford Research Institute of global energy markets. The demand function also includes lags to capture sluggish response to price changes. Instead of assuming a simple ‘backstop technology’ price, as was done in the previous section, Marshalla derives a time path of ‘zero oil demand’ prices, allowing for the influence of technical progress in developing substitutes. He also allows these prices to be influenced by the path of actual prices, reflecting the fact that the pace of technical progress may
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be affected by the speed at which current prices rise. Marshalla solves for the competitive price path, and shows, unsurprisingly, that, even allowing for the exhaustibility of oil and the rising cost of obtaining it, oil is substantially overpriced. Although Marshalla introduces a number of features which make his model more realistic than others, he can do this because his model is relatively simple in other respects. Thus he ignores the fact that other sources of oil are also exhaustible, and he models competitive rather than cartel behaviour. The first of the true cartel models is the study done by Cremer and Weitzman.6 They developed a simple model with both a price setting cartel and a price following competitive fringe, which was subject to an exogeneously imposed capacity constraint. This is the first model which approaches the theory outlined in the previous section. Expressed in continuous time, with i denoting the fringe and j the cartel, their model is:
long run this short-term gain can be eliminated through free entry. Pindyck formulates his model as a nonlinear optimal control problem with an implicit resource constraint on the cartel’s reserves to overcome the free terminal time problem. A continuous time specification of his problem is:
max p(t)
s[
m
P(t) -~ R(O) - Xi(f)
ewrt dt 1D(t)
0
subject to: kj
=
D(t)
I??(t) = S(t) S(t)
= f(P(t), S(t - 1)) e-cu’FS(t)
TD(t) = g@‘(t),Y(t), TD(f - 1)) D(r)t S(t) = TD(f)
Problem C:
{p(t) @i(t) - Ci(Xi)} eVrif dt
max f
Pi(r)
0
subject to YF?~(~) = &(t); 0 S L?(t) < 0 e” ‘; X(0) = 0 given price sequence P(t) . Problem M:
IIM;
s
{P(t)[D(P, t) - Qi(t)] - C&X,>>e-
‘jr dt
0
subject to A?j(t) = D(P, t) - Qi(t); Qj(t) Z 0; Xi(O) = 0 given the competitive fringe’s output (Jr(t) . This can be solved by assuming initially zero production for the fringe and solving problems M and C iteratively until the price and competitive production paths converge. Note that the resource constraint is treated implicitly in the cost function, which rises rapidly as remaining reserves dwindle; this supposes that the oil will be priced out of the market before it is fully exhausted. Although unstated, this is a device to overcome the computational difficulties surrounding the numerical solution of optimal control problems with free terminal time. This is particularly true when either the cartel or the fringe could exhaust its reserves before the other. This disadvantage is not present in the method suggested here. Although ignored by Cremer and Weitzman, their method cannot compare their computed price path for the partially cartelized market to the case where the industry is competitively organized. In fact the major outcome of their study is to conclude that for short-run problems up to 1995, the static model of cartel behaviour provides a good approximation to reality. A more recent approach to examining cartel behaviour, which is the best of the current models, is the work done by Pindyck,7 Hnyilicza and Pindyck.8 The main weakness of Pindyck’s approach is that the fringe is assumed to behave myopically and completely ignores the fact that current production will raise future costs of production. However, Pindyck explicitly introduces lags into his model. This is particularly interesting since it is commonly accepted that the cartel can make substantial short-term gains from raising the price if there are significant delays in introducing substitutes or building new capacity, even if in the
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Essentially, the cartel selects a profit maximizing price sequence, subject to the excess demand for the commodity in question, since the fringe firms are assumed to supply all they wish at the current market price. Another difficulty with Pindyck’s model lies in the selection of the parameters to describe the supply and demand conditions. The coefficients of the lagged terms, in both the market demand function and the fringe supply function, results in a set of constraints that leaves little room for optimization. Essentially, the price path obtained from dynamic simulation is not far removed from the optimal price trajectory. It is not surprising, given the passive role of the fringe suppliers with unlimited reserves, that Pindyck finds that the major source of profit gains from cartelization stem from the lags in the fringe suppliers adjusting to production cots imposed by the cartel. However, Pindyck has a crude model to generate competitive price paths so that he can compute the gains from cartelization, which greatly enhances the value of his work. In terms of the generic model introduced in the previous section of this paper, it can be seen that all of the studies surveyed above introduce significant simplification. The Pindyck and Cremer-Weitzman models ignore physical exhaustion constraints and assume that rising costs will price the resource out of the market; Pindyck even ignores the effect this has on the fringe’s decisions. On the other hand, Pindyck and Cremer-Weitzman explicitly consider the joint optimization problem facing the cartel and the fringe, although again this is greatly simplified; in Pindyck’s case this is done by replacing the fringe’s dynamic optimization problem by a series of one-period optimization problems; in the Cremer-Weitzman case it is done by introducing an exogenous capacity constraint in the fringe. Of course, the complexity of the problem requires that some simplifications be made, and in the next section we present some of our own work, where the joint optimization problem is considered explicitly, initially at the expense of considerable simplification elsewhere in the model, but later at a more general level of analysis.
Theoretical results of the effects of cartelization The models surveyed in the previous section were all concerned with forecasting the future price path for a particular
Models
commodity, oil. However, as we noted in the introduction, there are interesting theoretical issues in the study of cartels for exhaustible resources and simulation can be used to illuminate some of these issues. Salant first showed that if one assumed that an industry depleting an exhaustible resource was composed of a number of identical firms, some of whom joined together to form a cartel, then in a Nash-Cournot equilibrium, the fringe firms would benefit from cartelization. In the case of constant marginal costs, the profits of the fringe would rise proportionately more than the profits of the cartel. However, Salant’s results depend strongly on the assumption of identical units in the industry, and we reworked his analysis using more general assumptions about the costs and reserves of the fringe and cartel. Under fairly strong assumptions - a constant linear demand curve, constant linear cost curves for the fringe and cartel - it can be shown that in a Nash-Cournot equilibrium there are three possible price paths and five possible production patterns.’ The necessary conditions for a particular price path, and the corresponding production pattern, can be derived from the first order equilibrium conditions presented earlier in this paper for the general model applied to the special assumptions of our model. The most interesting case is when one group of firms has a ‘sufficient’ cost advantage over the rest of the industry. Then, with a perfectly competitive market structure, the low cost firms will produce till their reserves are exhausted, at which point the high cost firms will start to deplete their reserves. Now, when the low cost producers form a cartel, there are two possible price paths although for a given set of parameters the price path will be unique. The first possibility is where the cartel initially produces alone, then after some time, the competitive fringe commences production with both the cartel and competitive fringe firms producing together until the cartel exhausts its resources; finally, there will usually be a period during which the competitive firms produce alone until they exhaust their reserves. The alternative price path is where the effect of the price rise due to cartelization is to accelerate the development of the fringe firm’s reserves, so that initially both the cartel and the fringe are producing at the same time; this continues until the cartel firms exhaust their reserves and this leaves the competitive firms alone in the market and they continue to produce until their reserves are depleted, by which time the price rises to the level of the substitute technology. For both these cases by comparing the price paths before and after cartelization, it can be proved’ that cartelization reduces the profitability of the higher cost fringe firm’s reserves. Thus cartelization is at the expense not only of consumers but of other members of the industry as well. With the assumptions of the model, the degree of cost advantage required for the fringe is to lose is not very great. Since the result derived from the simple model outlined above is not what one would expect from static models of cartels, it is clearly important to examine the robustness of the conclusions. This can be done by use of the numerical simulation model described earlier.
A general model of cartel behaviour In order to test the theoretical results discussed in the previous section, and to simulate the behaviour of real-
of cartel behaviour:
M. Folie and A. Ulph
world cartels we have developed a general model of an industry depleting an exhaustible resource in which some firms are cartelized, while others form a competitive fringe. The model is the one outlined earlier in this paper, and allows for any pattern of demand, for cost curves which have cumulative output as well as current output as arguments and which can shift over time, and for arbitrary numbers of firms in the fringe and cartel. Unlike the simple model described in the previous section of this paper, which is solved analytically, the general model has to be solved by the method outlined in the section on an industry with a cartel and competitive fringe that is by a kind of tatonnement procedure to find the equilibrium set of exhaustion rents. The model can compute either perfectly competitive or Nash-Cournot equilibria. As an illustration of the kind of problem we can handle with the general model, we present some preliminary results from an attempt to study the oil industry. Following Cremer and Weitzman ,6 we assume that the demand for oil at the consuming centres is characterized by the following dynamic demand relationship: P(t) = 35 - 1.66670
e-“*03t
where Q is the total market demand at time f. The demand for oil falls to zero when the price reaches $35 per bl. The long-run demand elasticity is -0.4 when the price is $10 per bl and the demand is 15 bbl/yr, and the demand is considered to grow at 3% pa. On the supply side, it was assumed that OPEC consisted only of the Persian Gulf and north African nations. The fringe producers were the existing USA and western European producers (North Sea oil) and the remainder of the world. Details of supply conditions and reserve levels are given in Table I, with a more detailed breakdown of the marginal cost at zero production given in Table 2. The bre;lkdown of marginal costs at zero production derives from Cremer and Weitzman,6 although the capital costs used here correspond to their ‘steady-state’ capital costs. We have added an arbitrary nonlinear term to reflect problems most nations would face in expanding output, where these problems may arise as bottlenecks in various parts of the nation’s infrastructure (and so be social rather than private costs), as well as bottlenecks in expanding production capacity. The required real rate of return on all assets was assumed to be 8%.
Table 1 Supply functions
Reserves (bbl)
OPEC
1 .15 + 0.0019;
USA and W. Europe
4.22
+ 0.0019;
100
Rest of world
2.21 + 0.0019;
180
500
Table 2 Capital costs
Transport costs
Current costs
OPEC
0.18
0.85
0.12
USA and W. Europe
3.12
0.40
0.70
Rest of world
0.66
0.85
0.70
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Models of cartel behaviour: M. Folie and A. Ulph Tab/e 3
Profits and rents for different
market
structures
OPEC
USA and W. Europe
Rest of world
Profits Rents
1147 2.17
175 1.71
364 1.90
OPEC as price setter
Profits Rents
1316 0.95
278 2.76
683 3.29
Saudi Arabia as price setter
Profits Rents
181 1.78
385 2.03
Competitive
market
b 4a40 1.48
784 2.50
a, Saudi Arabia; b, Rest of OPEC.
Comparing the perfectly competitive equilibrium with that of a Nash-Cournot equilibria, we obtain a doubling of the price of oil, following cartelization, in 1972, to a price of $7 per bl. The reason for the divergence between this price and the observed price of $13 per bl is accounted for by the fact that our model captures long-run behaviour and it is well known that the short-run demand elasticity for oil is very low. This point was made by Pindyck’s analysis, which showed that much of OPEC’s initial monopoly power arose from their ability to exploit the long lags in adjusting to the new price. Pindyck predicted a fall in the real world oil price once major countries had eventually adjusted to the initial price rise, which did in fact occur. Some further analysis, again of a preliminary nature, was undertaken. Some commentators have claimed that OPEC itself is not the monopolist, but rather Saudi Arabia, and that the rest of the OPEC countries are as much part of the fringe as USA, western Europe and the rest of the world.9 We reran the model using Saudi Arabia as the cartel, but found that the equilibrium price was not much different from the perfectly competitive price. This suggests that Saudi Arabia by itself could not exert very significant monopoly power, so this analysis implies that OPEC is the monopolist rather than Saudi Arabia. However, we stress the preliminary nature of these results; in particular it would be more plausible to examine dominant firm equilibria rather than Nash-Cournot. Table 3 illustrates the profits and exhaustion rents earned by the three groups under the three different market structures.
References
Conclusions In this paper, we have discussed two main uses of simulation models to study exhaustible resource cartels - to examine theoretical properties of such models, and to predict the future behaviour of key variables, such as prices, in real world industries, especially oil. On the theoretical side the need for simulation models arises from the complexity of the possible price and production paths over time, even for relatively simple models, so that analytical comparison of the outcomes under different market structures becomes impossible. In our own work, our interest has centred on the possibility of fringe firms losing following cartelization, and we have shown
204
Appl.
that this is a possibility in quite a wide range of models. With the general programme described in the previous section, we can examine a wide range of questions, such as the benefits to different firms from being in the cartel or the fringe. More work has been done on analysing the likely future behaviour of real-world cartels, particularly OPEC, and we noted the variety of assumptions made in different studies. In many cases, the choice of assumption is designed to turn the very complex problem of the simultaneous determination of time paths of outputs and prices by the cartel and fringe into a much simpler problem, essentially a control problem with a single control variable. Most studies agree that the real price of oil will continue to rise, although more slowly during the eighties than the dramatic increase witnessed in the early seventies. The behaviour of oil prices during the seventies reflects the pattern predicted by Pindyck - a sharp increase to exploit short-term lags inherent in adjusting behaviour to a regime of substantially higher world oil prices, followed by a small decline in real terms as the adjustment processes work themselves through the economic systems, and then further, small, increases in real terms during the eighties. In comparing the predictions from such models with actual behaviour, three points need to be borne in mind. First, the models predict real prices for oil, while the actual price reflects adjustments for monetary phenomena such as inflation and shifting exchange rates. How to adjust for these phenomena is a matter of considerable dispute. Second, the models abstract from numerous short-term disturbances to the oil market caused by political crises, adverse weather conditions, strikes, etc., and should be viewed as underlying trends for oil prices, rather than forecasts. Finally, the initial reaction of some countries, like USA and Australia, of holding domestic crude oil prices below world parity, in effect makes oil demand even less elastic. Most studies assume, implicitly, that rising prices will be allowed to have their full effect in reducing demand. It should be emphasized that the work reported in this paper is very recent, and many interesting issues in the analysis of cartels and exhaustible resources remain to be explored.
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I 8 9 10
Ulph, A. and Folie, M. Disc. Pap. 3 1, School of Economics, University of New South Wales, 1978 Fischer, D. et al. J. Development Econ. 1975,2,363 Blitzer. C. et al. J. Development Econ. 1975,2,319 Kalymbn, B. J. Developmtwt Econ. 1975,2,337 Marshalla. R. A. Ann. Econ. Social Measurement, 1977,6,203 Cremer, J: and Weitzman, M. L. European Econ. Rev. 1976,8, 155 Pindyck, R. S. M.I.T. Energy Lab. Working Pap. MITEL76-012 WP, 1975 Hnyilicza, E. and Pindyck, R. S. European Econ. Rev. 1976,8, 139 Salant, S. W. J. Polit. Econ. 1976,84, 1079 Erickson, E. and Winokur, H. In ‘Oil in the Seventies’ (ed. C. Watkins and M. Walker), The Fraser Institute, Vancouver
of Economics,
University of New South Wales, Sydney, Australia
Alistair Ulph Department
of Economics,
University of Southampton,
Southampton
SO9 5NH, UK
(Received June 19 79; revised January 1980)
Introduction
Industry with a cartel and competitive
This paper discusses various attempts to model the dynamic behaviour of an industry depleting an exhaustible resource, where some of the firms in the industry are cartelized; one such attempt is a model we have developed, and we will present some of the results of our work. An obvious motivation for such work is the interest in energy policy, particularly following OPEC’s action in raising the world price of oil. The long-term energy problem can be characterized by the transition from cheap, convenient but exhaustible forms of energy such as oil and gas to more expensive but abundant forms of energy. A key factor controlling this transition is the price path for oil, currently determined by OPEC. It is of some interest, therefore, to understand the behaviour of industries with a structure similar to the oil industry. Questions one could consider include : what are the likely price and production paths for such an industry; how stable is the cartel; what are the relative gains to the cartel and other firms in the industry? Until recently, the analysis of such questions was confined to static models, i.e. for markets where the product is infinitely reproducible. It is important to know the extent to which the conclusions of such static models are valid for the case of an exhaustible resource. Our earlier work’ suggests that exhaustibility of a resource introduces novel features to a model of cartels. Specifically, unlike the static model, the act of cartelization can reduce the value of the reserves of the fringe firms in an industry. This result was derived for a fairly special case, and part of our interest in building simulation models is to test the robustness of this conclusion. The structure of this paper is as follows. The general structure of a model of a partially cartelized industry depleting an exhaustible resource is outlined. The models that have been developed to analyse the oil industry are reviewed, noting particularly the variety of assumptions made. The work we have done to analyse some theoretical issues in studying cartels and exhaustible resources is discussed and finally some results from a more general model we have developed and applied to the oil industry are presented.
Consider an industry with an arbitrary number of firms producing a finite resource. There is a global demand for this commodity and each firm faces convex marginal costs of extraction, which may depend on the cumulative level of the resource already removed. Each firm can face different costs (which include transport costs to the market) and may have different stocks of reserves. Demand is bounded from above, since it is assumed that there is a price at which some suitable backstop technology will become widely abundant:
0307-904X/80/030199-06/$02.00 0 1980 IFT Business Ress
fringe
P = f@; t) Demand may vary over time and at some future time t*, when the demand Q(t*) = 0, then P(t*) = F, where F is the price at which a substitute technology will be competitively supplied. (In order to simplify notation, functions .of timevarying variables will not explicitly show such time dependence). There are two groups of firms, a cartel and a competitive fringe. The identity of the firms in the cartel will be designated by the index set J, and the fringe of competitive firms by the index set I. At time t, each firm, i, in the cartel has used Xi(t), of its total reserves Xi, and faces convex extraction costs Kj((zi, Xi; t). Similar notation applies to firms in the fringe. It is assumed that all reserves are economic and therefore will be exhausted before the backstop technology becomes economic at price F. There are two possible forms of market behaviour after cartelization. In a Nash-Cournot model, the fringe takes prices as given and depletes its reserves so as to maximize the present value of profits, while the cartel takes the fringe output as given, and sets prices (and its own output) to maximize the present value of its profits. In a Dominant Firm model, the cartel plays a less passive role, and takes account of the fact that as it changes price so the fringe’s production path will change. The cartel thus takes account of the reaction function of the fringe in setting its policy. The equilibria of these two models will differ, but the analysis presented here will be done explicitly for the Nash-Cournot model.
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Models of cartel behaviour: M. Folie and A. Ulph
Competitive behaviour The competitive firms take the market price, P(t) as given and choose a production pattern &i(t) to maximize the discounted present value of profits. Thus the problem can be expressed as:
of the cartel completely exhaust their finite stock of reserves. In this case, the cartel can affect the price by restricting the total output from the cartel. A more formal statement of the problem is:
I;: ;:;,S i
Ti [P(t) Qdt)
-
Ki(Qi,
xi;
t)I eAt
dt
Lf(Q;
xjj
t) Qj(t)
-Kj(QjT
Xi;
t)] e-6tdt
i
0
iEJ
subject to:
0
subject to:
*i(t) = Qi(t>
*j(t)
WE1
20
Q,(t)
Xi(O)= 0
Xj(Ti) =
Ri
Ti is the unknown terminal time, when firm i exhausts its reserves, which may be before the price reaches F. It can be shown that the production pattern Qi(t) which maximizes the above system must satisfy the set of differential equations that are derived from the application of Pontryagin’s pointwise maximum principle. After some algebraic operations it can be shown that the optimal production pattern for each firm must satisfy the following conditions: P(t)
~7~
-
MKi
AT(~) =
hi
G AT(t)
Ti
I
e6f +
&i(t)
2
0
aK.
2
e-s(7-f)d7
aXi
where MKi is the mariinal extraction cost = Xi/aQi. The first of these conditions requires that at any moment of time firms will produce up to the point where price equals marginal cost of production plus a ‘user cost’. This user cost, h:(t) consists of two parts. The first, hi es*, measures the profit foregone by extracting at time t rather than some other time. This term is often referred to as ‘exhaustion rent’. The second term measures the increased cost imposed on later extraction by lowering the stock of remaining reserves. Figure 1 illustrates the solution at time t. MK is firm i’s marginal cost curve. With price P(t) = OA, and output Qi(t), user cost is AT(t) = OA - OD = AD, that is price less marginal cost of production at of(t). Total profit is ABCE, of which ABCD is user cost. With no stock effect on production costs, ABCD would represent just exhaustion rents earned at time t. Cartel behaviour The cartel takes as given the production plans of the competitive fringe of firms (Qi(t), Vi E I) and chooses a production plan, Qi(t), Vj EJ, that maximizes the present value of profits subject to the constraint that the members
I
0
0, b+)
Figure
1
200
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=
VjEJ
Qj(t)
Xi(O) = 0
VjEJ
X,(Ti) = xi
VjEJ
Q(t)
= c
Qi(t‘i + c
jGJ
a(t)
iEI
Again, the optimal production plan for the cartel must satisfy the differential equations derived from applying Pontryagin’s pointwise maximum principle: P(t) +
5 [Q&t)] -MKi
h?(t) = hi es* +
G AT(t)
Q/(t)
2
0
TJaK.
s
_-! e--6(‘--*) aXj
d7
VjEJ
t
Market equilibrium An equilibrium price path will have the characteristic that the competitive production pattern assumed by the cartel in setting its production levels will be the one actually chosen by the competitive firms, while the price path assumed by the competitive firms in setting their production levels will be the one actually selected by the cartel. At each point in time, the equilibrium price path will result in production levels for both the cartel members and the competitive fringe that are market clearing, while over time all reserves must be exhausted by the time the market price reaches the backstop price, F. Solution Clearly, if the price path P(t) was known, then for each of the competitive firms, i E I, production plans could be determined by solving an optimal control problem for each firm, where the control variable is Qi(t) and there is a single state variable Xi(t). However, it is more difficult to see how control theory could be invoked to solve the cartel’s intertemporal optimization problem. If the production levels of the competitive fringe firms was known by the cartel, then its problem is merely a control problem (this is the approach used by Pindyck and his workers which will be discussed later). However, the underlying economics of this particular class of problems suggests an alternative approach. Essentially, the only difference between the dynamic equilibrium and the well known static equilibrium market behaviour is that in the dynamic case each firm, irrespective of the market structure, is producing a resource which is finite. It turns out that provided each firm imputes the correct user cost to its particular stock of the resource, then the myopic single period profit maximizing strategy will be compatible with the dynamic profit maximizing decision. These ‘user costs’ are the XT(t) and h:(t) values that appear in the first order conditions. These user costs are complex
Models of cartel behaviour: M. Folie and A. Ulph functions of all the given parameters that characterize the industry which are not known implicitly. Hence the solution to the problem consists of assigning a user cost to each firm, and computing a market clearing price and corresponding quantities supplied by each firm for each time period until the price reaches F. The total quantity produced over time by each firm is compared with its reserves, and if it exceeds its reserves, the user cost assigned must be raised, while if total production falls short of reserves, user cost is lowered. There is a single market demand for this particular resource and the only intrinsic difference between each firm’s output lies in the difference in the extraction costs. Hence each firm’s output can be considered to be grossly substitutable for any other firm’s output. The aggregate demand for each firm’s stock of the resource is given by: VkEIUJ
Dk = Dk(&) a& ah,
>o
lfk
Vk,lElU/
l=k
This follows from the property of the other firms’ reserves being gross substitutes. Aggregate excess demand for each firm’s resource stock is simply:
xD,=Dk-_&
VkEIUJ
and the Jacobian of XDk is equal to the Jacobian of D,. The problem is to find a set of 4, such that:
xD,(?$ = 0 Given the property of gross substitutability between the excess demand for firms’ reserves it is possible to invoke the well known theorem that the application of Walrasian tatonnement will ensure that the equilibrium values of h will be reached. Unfortunately, the step size must be very small to ensure convergence, and this usually requires an inordinately large number of iterations. Thus a variant of Newton’s method for solving simultaneous nonlinear equations was used here, since for guesses ‘reasonably’ near to the solution, the procedure is quadratically convergent. This requires computing the Jacobian matrix numerically at each guess and then updating. The procedure is conceptually a more sophisticated tatonnement, since this approach implies that each firm recognizes that an increase in its value of h will not only reduce the demand for its reserves, but will increase the demand for all other firms’ reserves. By using this extra information, the equilibrium set of user costs will be found more rapidly. Finally, it should be noted that this technique for solving the Nash-Cournot problem can also be used to solve for a perfectly competitive equilibrium. It also has the obvious advantage that there is no restriction on the number of firms in the industry, although the computational burden increases with the number of firms. The number of iterations required to compute the Jacobian rises linearly with the number of different firms in the industry.
A survey of studies of cartels Most of the studies into cartel behaviour have been computationally oriented, and frequently concerned only with the problem of forecasting the future price path for oil. A good survey of the modelling attempts up to mid-1975 is given by Fisher et al.2 The two basic approaches used are simulation studies and optimization models.
Essentially, for a simulation study, a basic model is specified and then by assuming plausible values for the parameters describing the economic system, such as demand elasticities and demand growth rates, supply conditions for cartel and noncartel firms, a series of price paths can be generated and ranked according to some criterion or a price path is arbitrarily selected as being the ‘most likely’ scenario. Good examples of this fairly conventional approach of dynamic simulations are the studies reported by Blitzer et al. 3 and the medium run model (up to 1995) in Kalymon.4 In contrast to simulation models, which examine a finite number of arbitrarily prespecified price paths, optimization models use a plausible and quantifiable objective function, usually the present value of cartel profits to select the best price path. Since the level of complexity that can be solved for in optimal control problems is fairly restrictive, the specification of dynamic cartel models has been relatively simple, which limits the generality of the conclusions regarding the realism of the optimal price paths. Another, related, question which some models examine is a comparison between the price trajectory that would prevail under competitive conditions and under a partial cartelization of the market. From a resource allocation standpoint, it is desirable to have some indication of the magnitude and duration of the deviation of cartelized prices from the competitive norm, since this provides some indication of the extent of the misallocation of the world’s resources. Since a strategy directed towards breaking up a cartel entails real costs, it is important to know whether the misallocation warrants incurring such costs. Kalymon4 has the simplest model, which essentially considers that OPEC is the residual supplier of oil, and thus faces the rest of the world’s excess demand for oil. A slight twist introduced by Kalymon is that he includes OPEC’s domestic demand for oil, which may be priced below the world price. He assumes marginal costs of extraction constant with respect to current output, but rising with cumulative output. Demand is linear and grows over time. He computes a price path that maximizes the present value of oil revenues less extraction costs, plus the present value of the consumer surplus stemming from the domestic OPEC consumption of oil. The solution technique is not alluded to by Kalymon, but his specification leads to a large, potentially decomposable, quadratic programming problem; it could also be solved by optimal control methods. Any solution method will lead to a single, globally optimal price trajectory since the objective function is strictly concave in the prices. A more complex model is used by Marshalla, who is interested in determining a plausible price path for the world oil industry if OPEC did not act as a cartel, but was a price taker. Marshalla’s model includes a number of interesting features. Although the model considers only the oil market, and hence is a partial view of the energy market, the demand for oil is calibrated against a ‘reference’ path for oil prices and quantities derived from the models developed by FEA and the Stanford Research Institute of global energy markets. The demand function also includes lags to capture sluggish response to price changes. Instead of assuming a simple ‘backstop technology’ price, as was done in the previous section, Marshalla derives a time path of ‘zero oil demand’ prices, allowing for the influence of technical progress in developing substitutes. He also allows these prices to be influenced by the path of actual prices, reflecting the fact that the pace of technical progress may
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be affected by the speed at which current prices rise. Marshalla solves for the competitive price path, and shows, unsurprisingly, that, even allowing for the exhaustibility of oil and the rising cost of obtaining it, oil is substantially overpriced. Although Marshalla introduces a number of features which make his model more realistic than others, he can do this because his model is relatively simple in other respects. Thus he ignores the fact that other sources of oil are also exhaustible, and he models competitive rather than cartel behaviour. The first of the true cartel models is the study done by Cremer and Weitzman.6 They developed a simple model with both a price setting cartel and a price following competitive fringe, which was subject to an exogeneously imposed capacity constraint. This is the first model which approaches the theory outlined in the previous section. Expressed in continuous time, with i denoting the fringe and j the cartel, their model is:
long run this short-term gain can be eliminated through free entry. Pindyck formulates his model as a nonlinear optimal control problem with an implicit resource constraint on the cartel’s reserves to overcome the free terminal time problem. A continuous time specification of his problem is:
max p(t)
s[
m
P(t) -~ R(O) - Xi(f)
ewrt dt 1D(t)
0
subject to: kj
=
D(t)
I??(t) = S(t) S(t)
= f(P(t), S(t - 1)) e-cu’FS(t)
TD(t) = g@‘(t),Y(t), TD(f - 1)) D(r)t S(t) = TD(f)
Problem C:
{p(t) @i(t) - Ci(Xi)} eVrif dt
max f
Pi(r)
0
subject to YF?~(~) = &(t); 0 S L?(t) < 0 e” ‘; X(0) = 0 given price sequence P(t) . Problem M:
IIM;
s
{P(t)[D(P, t) - Qi(t)] - C&X,>>e-
‘jr dt
0
subject to A?j(t) = D(P, t) - Qi(t); Qj(t) Z 0; Xi(O) = 0 given the competitive fringe’s output (Jr(t) . This can be solved by assuming initially zero production for the fringe and solving problems M and C iteratively until the price and competitive production paths converge. Note that the resource constraint is treated implicitly in the cost function, which rises rapidly as remaining reserves dwindle; this supposes that the oil will be priced out of the market before it is fully exhausted. Although unstated, this is a device to overcome the computational difficulties surrounding the numerical solution of optimal control problems with free terminal time. This is particularly true when either the cartel or the fringe could exhaust its reserves before the other. This disadvantage is not present in the method suggested here. Although ignored by Cremer and Weitzman, their method cannot compare their computed price path for the partially cartelized market to the case where the industry is competitively organized. In fact the major outcome of their study is to conclude that for short-run problems up to 1995, the static model of cartel behaviour provides a good approximation to reality. A more recent approach to examining cartel behaviour, which is the best of the current models, is the work done by Pindyck,7 Hnyilicza and Pindyck.8 The main weakness of Pindyck’s approach is that the fringe is assumed to behave myopically and completely ignores the fact that current production will raise future costs of production. However, Pindyck explicitly introduces lags into his model. This is particularly interesting since it is commonly accepted that the cartel can make substantial short-term gains from raising the price if there are significant delays in introducing substitutes or building new capacity, even if in the
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Essentially, the cartel selects a profit maximizing price sequence, subject to the excess demand for the commodity in question, since the fringe firms are assumed to supply all they wish at the current market price. Another difficulty with Pindyck’s model lies in the selection of the parameters to describe the supply and demand conditions. The coefficients of the lagged terms, in both the market demand function and the fringe supply function, results in a set of constraints that leaves little room for optimization. Essentially, the price path obtained from dynamic simulation is not far removed from the optimal price trajectory. It is not surprising, given the passive role of the fringe suppliers with unlimited reserves, that Pindyck finds that the major source of profit gains from cartelization stem from the lags in the fringe suppliers adjusting to production cots imposed by the cartel. However, Pindyck has a crude model to generate competitive price paths so that he can compute the gains from cartelization, which greatly enhances the value of his work. In terms of the generic model introduced in the previous section of this paper, it can be seen that all of the studies surveyed above introduce significant simplification. The Pindyck and Cremer-Weitzman models ignore physical exhaustion constraints and assume that rising costs will price the resource out of the market; Pindyck even ignores the effect this has on the fringe’s decisions. On the other hand, Pindyck and Cremer-Weitzman explicitly consider the joint optimization problem facing the cartel and the fringe, although again this is greatly simplified; in Pindyck’s case this is done by replacing the fringe’s dynamic optimization problem by a series of one-period optimization problems; in the Cremer-Weitzman case it is done by introducing an exogenous capacity constraint in the fringe. Of course, the complexity of the problem requires that some simplifications be made, and in the next section we present some of our own work, where the joint optimization problem is considered explicitly, initially at the expense of considerable simplification elsewhere in the model, but later at a more general level of analysis.
Theoretical results of the effects of cartelization The models surveyed in the previous section were all concerned with forecasting the future price path for a particular
Models
commodity, oil. However, as we noted in the introduction, there are interesting theoretical issues in the study of cartels for exhaustible resources and simulation can be used to illuminate some of these issues. Salant first showed that if one assumed that an industry depleting an exhaustible resource was composed of a number of identical firms, some of whom joined together to form a cartel, then in a Nash-Cournot equilibrium, the fringe firms would benefit from cartelization. In the case of constant marginal costs, the profits of the fringe would rise proportionately more than the profits of the cartel. However, Salant’s results depend strongly on the assumption of identical units in the industry, and we reworked his analysis using more general assumptions about the costs and reserves of the fringe and cartel. Under fairly strong assumptions - a constant linear demand curve, constant linear cost curves for the fringe and cartel - it can be shown that in a Nash-Cournot equilibrium there are three possible price paths and five possible production patterns.’ The necessary conditions for a particular price path, and the corresponding production pattern, can be derived from the first order equilibrium conditions presented earlier in this paper for the general model applied to the special assumptions of our model. The most interesting case is when one group of firms has a ‘sufficient’ cost advantage over the rest of the industry. Then, with a perfectly competitive market structure, the low cost firms will produce till their reserves are exhausted, at which point the high cost firms will start to deplete their reserves. Now, when the low cost producers form a cartel, there are two possible price paths although for a given set of parameters the price path will be unique. The first possibility is where the cartel initially produces alone, then after some time, the competitive fringe commences production with both the cartel and competitive fringe firms producing together until the cartel exhausts its resources; finally, there will usually be a period during which the competitive firms produce alone until they exhaust their reserves. The alternative price path is where the effect of the price rise due to cartelization is to accelerate the development of the fringe firm’s reserves, so that initially both the cartel and the fringe are producing at the same time; this continues until the cartel firms exhaust their reserves and this leaves the competitive firms alone in the market and they continue to produce until their reserves are depleted, by which time the price rises to the level of the substitute technology. For both these cases by comparing the price paths before and after cartelization, it can be proved’ that cartelization reduces the profitability of the higher cost fringe firm’s reserves. Thus cartelization is at the expense not only of consumers but of other members of the industry as well. With the assumptions of the model, the degree of cost advantage required for the fringe is to lose is not very great. Since the result derived from the simple model outlined above is not what one would expect from static models of cartels, it is clearly important to examine the robustness of the conclusions. This can be done by use of the numerical simulation model described earlier.
A general model of cartel behaviour In order to test the theoretical results discussed in the previous section, and to simulate the behaviour of real-
of cartel behaviour:
M. Folie and A. Ulph
world cartels we have developed a general model of an industry depleting an exhaustible resource in which some firms are cartelized, while others form a competitive fringe. The model is the one outlined earlier in this paper, and allows for any pattern of demand, for cost curves which have cumulative output as well as current output as arguments and which can shift over time, and for arbitrary numbers of firms in the fringe and cartel. Unlike the simple model described in the previous section of this paper, which is solved analytically, the general model has to be solved by the method outlined in the section on an industry with a cartel and competitive fringe that is by a kind of tatonnement procedure to find the equilibrium set of exhaustion rents. The model can compute either perfectly competitive or Nash-Cournot equilibria. As an illustration of the kind of problem we can handle with the general model, we present some preliminary results from an attempt to study the oil industry. Following Cremer and Weitzman ,6 we assume that the demand for oil at the consuming centres is characterized by the following dynamic demand relationship: P(t) = 35 - 1.66670
e-“*03t
where Q is the total market demand at time f. The demand for oil falls to zero when the price reaches $35 per bl. The long-run demand elasticity is -0.4 when the price is $10 per bl and the demand is 15 bbl/yr, and the demand is considered to grow at 3% pa. On the supply side, it was assumed that OPEC consisted only of the Persian Gulf and north African nations. The fringe producers were the existing USA and western European producers (North Sea oil) and the remainder of the world. Details of supply conditions and reserve levels are given in Table I, with a more detailed breakdown of the marginal cost at zero production given in Table 2. The bre;lkdown of marginal costs at zero production derives from Cremer and Weitzman,6 although the capital costs used here correspond to their ‘steady-state’ capital costs. We have added an arbitrary nonlinear term to reflect problems most nations would face in expanding output, where these problems may arise as bottlenecks in various parts of the nation’s infrastructure (and so be social rather than private costs), as well as bottlenecks in expanding production capacity. The required real rate of return on all assets was assumed to be 8%.
Table 1 Supply functions
Reserves (bbl)
OPEC
1 .15 + 0.0019;
USA and W. Europe
4.22
+ 0.0019;
100
Rest of world
2.21 + 0.0019;
180
500
Table 2 Capital costs
Transport costs
Current costs
OPEC
0.18
0.85
0.12
USA and W. Europe
3.12
0.40
0.70
Rest of world
0.66
0.85
0.70
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Models of cartel behaviour: M. Folie and A. Ulph Tab/e 3
Profits and rents for different
market
structures
OPEC
USA and W. Europe
Rest of world
Profits Rents
1147 2.17
175 1.71
364 1.90
OPEC as price setter
Profits Rents
1316 0.95
278 2.76
683 3.29
Saudi Arabia as price setter
Profits Rents
181 1.78
385 2.03
Competitive
market
b 4a40 1.48
784 2.50
a, Saudi Arabia; b, Rest of OPEC.
Comparing the perfectly competitive equilibrium with that of a Nash-Cournot equilibria, we obtain a doubling of the price of oil, following cartelization, in 1972, to a price of $7 per bl. The reason for the divergence between this price and the observed price of $13 per bl is accounted for by the fact that our model captures long-run behaviour and it is well known that the short-run demand elasticity for oil is very low. This point was made by Pindyck’s analysis, which showed that much of OPEC’s initial monopoly power arose from their ability to exploit the long lags in adjusting to the new price. Pindyck predicted a fall in the real world oil price once major countries had eventually adjusted to the initial price rise, which did in fact occur. Some further analysis, again of a preliminary nature, was undertaken. Some commentators have claimed that OPEC itself is not the monopolist, but rather Saudi Arabia, and that the rest of the OPEC countries are as much part of the fringe as USA, western Europe and the rest of the world.9 We reran the model using Saudi Arabia as the cartel, but found that the equilibrium price was not much different from the perfectly competitive price. This suggests that Saudi Arabia by itself could not exert very significant monopoly power, so this analysis implies that OPEC is the monopolist rather than Saudi Arabia. However, we stress the preliminary nature of these results; in particular it would be more plausible to examine dominant firm equilibria rather than Nash-Cournot. Table 3 illustrates the profits and exhaustion rents earned by the three groups under the three different market structures.
References
Conclusions In this paper, we have discussed two main uses of simulation models to study exhaustible resource cartels - to examine theoretical properties of such models, and to predict the future behaviour of key variables, such as prices, in real world industries, especially oil. On the theoretical side the need for simulation models arises from the complexity of the possible price and production paths over time, even for relatively simple models, so that analytical comparison of the outcomes under different market structures becomes impossible. In our own work, our interest has centred on the possibility of fringe firms losing following cartelization, and we have shown
204
Appl.
that this is a possibility in quite a wide range of models. With the general programme described in the previous section, we can examine a wide range of questions, such as the benefits to different firms from being in the cartel or the fringe. More work has been done on analysing the likely future behaviour of real-world cartels, particularly OPEC, and we noted the variety of assumptions made in different studies. In many cases, the choice of assumption is designed to turn the very complex problem of the simultaneous determination of time paths of outputs and prices by the cartel and fringe into a much simpler problem, essentially a control problem with a single control variable. Most studies agree that the real price of oil will continue to rise, although more slowly during the eighties than the dramatic increase witnessed in the early seventies. The behaviour of oil prices during the seventies reflects the pattern predicted by Pindyck - a sharp increase to exploit short-term lags inherent in adjusting behaviour to a regime of substantially higher world oil prices, followed by a small decline in real terms as the adjustment processes work themselves through the economic systems, and then further, small, increases in real terms during the eighties. In comparing the predictions from such models with actual behaviour, three points need to be borne in mind. First, the models predict real prices for oil, while the actual price reflects adjustments for monetary phenomena such as inflation and shifting exchange rates. How to adjust for these phenomena is a matter of considerable dispute. Second, the models abstract from numerous short-term disturbances to the oil market caused by political crises, adverse weather conditions, strikes, etc., and should be viewed as underlying trends for oil prices, rather than forecasts. Finally, the initial reaction of some countries, like USA and Australia, of holding domestic crude oil prices below world parity, in effect makes oil demand even less elastic. Most studies assume, implicitly, that rising prices will be allowed to have their full effect in reducing demand. It should be emphasized that the work reported in this paper is very recent, and many interesting issues in the analysis of cartels and exhaustible resources remain to be explored.
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Ulph, A. and Folie, M. Disc. Pap. 3 1, School of Economics, University of New South Wales, 1978 Fischer, D. et al. J. Development Econ. 1975,2,363 Blitzer. C. et al. J. Development Econ. 1975,2,319 Kalymbn, B. J. Developmtwt Econ. 1975,2,337 Marshalla. R. A. Ann. Econ. Social Measurement, 1977,6,203 Cremer, J: and Weitzman, M. L. European Econ. Rev. 1976,8, 155 Pindyck, R. S. M.I.T. Energy Lab. Working Pap. MITEL76-012 WP, 1975 Hnyilicza, E. and Pindyck, R. S. European Econ. Rev. 1976,8, 139 Salant, S. W. J. Polit. Econ. 1976,84, 1079 Erickson, E. and Winokur, H. In ‘Oil in the Seventies’ (ed. C. Watkins and M. Walker), The Fraser Institute, Vancouver