Abstract
Several features may separately or in combination influence conduct and performance of an industry, e.g., the numbers of sellers or buyers, the degree of economies of scale in production and distribution, the temporal and spatial dimensions, uncertainty about long run development of demand in particular combined with large investments in production capacity and infrastructure, etc. Our focus is modeling in order to obtain insight into market mechanisms and price formation. In particular, we demonstrate the rather different solutions obtained from the price-taking behavior versus the oligopolistic Cournot behavior when the spatial dimension is observed.
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- 1.
Smeers (1997) reviews models and issues in the European gas market.
- 2.
Mathiesen et al. (1987) argue that shadow prices of the vast gas resources of the larger suppliers are close to zero whereby a static approach is appropriate from a resource perspective. The large profits in gas production are oligopolistic rents that stem from uneven distribution of the resources and not scarcity.
- 3.
In order to reduce the risks caused by long lead times and large uncertainties, parties involved write long term contracts for deliveries. The terms of such contracts may not match price formation in an equilibrium model. But it seems that contracting clauses rather than being written in stone are modified when market conditions change, thereby adapting to the logic of the market mechanism.
- 4.
Algeria, Russia, and The Netherlands each have only one (large) producer, while in Norway a central board coordinated sales for years.
- 5.
For the analysis of investment in pipe capacities, modeling of flow as dependent on pressure at nodes may be important (see De Wolf and Smeers 1993).
- 6.
The Statoil model is expanded, its database is updated, and the interactive program improved. It is helpful to analysts (see Fuglseth and Grønhaug 2003), but it may also be too complicated for most non-academics.
- 7.
For a homogeneous product \(\partial p/\partial {x}_{1} = \partial p/\partial {x}_{2} = \ldots = \partial p/\partial {x}_{n} = p^{\prime}\).
- 8.
Bowley (1924) introduced the idea. Game theorists dislike the concept – only the Nash solution θi = 0 is consistent. Others point out that θi≠0 in particular markets and that should be taken as a datum along with costs and demand. Bresnahan (1989) reviews several studies where such terms have been estimated.
- 9.
A leader assumes that his followers adjust their volumes to satisfy their individual first order conditions. Their aggregate response follows from totally differentiating these conditions. The difference between the models stems from the different behavior of the followers – Cournot-players versus price-takers.
- 10.
It is assumed that the cartel behaves as one Nash–Cournot player against non-members. Thus, θi = 0.
- 11.
The acronym stands for A Sequence of Linear Complementarity Problems, describing a Newton-like iterative process where the linear conditions in each step are solved by Lemke’s method.
- 12.
GAMS is a software package for a variety of optimization and equilibrium problems. It has become an industrial standard. See www.gams.com for details on content and how to obtain this package.
- 13.
- 14.
Cf., integrability of demand in economic theory (see, e.g., Varian 1992).
- 15.
With (p, Z) = (10, 40), price elasticity is − 1. When elasticities differ between regions ( − 0. 6 to − 1. 4), price differences in the Cournot equilibrium are still smaller.
- 16.
- 17.
The Cournot equilibrium may have all nm flows positive, while the competitive equilibrium has at most (\(n + m - 1\)) positive flows. The latter fact is well known within operations research as a feature of a basicsolution to the transportation model and within trade theory through the notion of no cross-hauling.
- 18.
It is interesting to note that a collusive outcome – where all producers coordinate their sales (see 2.3) – has the same efficient trade pattern as the competitive solution, although volumes are about 40% lower.
- 19.
Of course, even though contracts involve sales from North to South and vice versa, transmission companies may avoid actual cross-hauling.
- 20.
In reality, fixed costs of deliveries block small flows. In modeling terms, this feature implies non-convexities that are hard, but not impossible, to implement in an optimization or equilibrium model.
- 21.
In line with the regional disaggregation of this example, the European natural gas market has at present about 20 positive flows. When asked why Statoil would sell to Italy rather than Germany, a sales representative commented: “We already sell much in Germany and selling larger volumes would depress our prices there.”
- 22.
Of course, deliveries from any supplier could be constrained in the competitive model in order to prevent such dominance.
- 23.
Traded volumes in the competitive equilibrium depend on transportation cost in a step-like manner, that is, a volume stays fixed for cost variations over some range and then jumps. The difference in net-back prices between a market that is served and one that is not served may be arbitrarily small. In our example, N does not serve market 3 until transportation cost is below 1.99. But at a unit cost of 1.98 A shifts his entire volume (17) from market 1 to market 3 and B shifts a similar volume oppositely. Who sells where in a competitive equilibrium is therefore very sensitive to relative transportation costs. Individual flows in the Cournot equilibrium are much more stable to such parameter changes. (Aggregate flows of production and consumption, however, are very stable in both models.)
- 24.
When establishing a gas model for the European market in the mid-1980s it seemed that actual gas-prices were reduced going east to west in Europe. The reason could be that USSR met no competition in eastern markets, while there were alternative suppliers and hence competition in the West.
- 25.
The MCP-solver of GAMS replicated the Nash equilibrium when the mark-up was computed immediately following the computation of the (true) Nash, but it generated a trade pattern with 9 flows when the mark-up equilibrium was computed immediately following the competitive one (or when the matrix of λij’s was input to a new run). Although both these trade patterns had 9 positive flows only two flows were positive in both equilibria. The reason for these seemingly arbitrary trade patterns in the mark-up equilibrium stems from the definition of λij whereby reduced costs \(\{{p}_{\mathrm{j}} - ({c}_{\mathrm{i}} + {t}_{\mathrm{ij}})(1 + {\lambda }_{\mathrm{ij}})\} = 0\), all i, j, at the equilibrium admitting any trade pattern that adds up to equilibrium production and consumption volumes.
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Acknowledgements
This paper summarizes my experience of gas market modeling. Very helpful comments from two referees are acknowledged.
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Mathiesen, L. (2010). On Modeling the European Market for Natural Gas. In: Bjørndal, E., Bjørndal, M., Pardalos, P., Rönnqvist, M. (eds) Energy, Natural Resources and Environmental Economics. Energy Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12067-1_6
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