Trading in the downstream European gas market: a successive oligopoly approach.

This depicts the individual trader's gas demand [y.sub.rng] given the border price b[p.sub.ng]. Thus:

b[p.sub.ng] [greater than or equal to] [p.sub.ng] - d[c.sub.ng] + [p'.sub.ng] * [y.sub.rng] (3)

If [y.sub.rng] > 0, then (3) holds as an equality. If we instead assume perfectly competitive traders, the inframarginal revenue effect [p'.sub.ng] * [y.sub.rng] in (2) would be dropped. The border price would then be no less than the difference between end-user price and transmission costs:

b[p.sub.ng] [greater than or equal to] [p.sub.ng] - d[c.sub.ng] (4)

Again, this holds as an equality if [y.sub.rng] > 0.

Following Golombek et al. (1995), we assume an affine demand curve for consumers:

[p.sub.ng] = [D.sub.ng.sup.-1]([x.sub.ng] - exo[g.sub.ng]) [equivalent to] [[alpha].sub.ng] + [[beta].sub.ng] * ([x.sub.ng] - exo[g.sub.ng]) (5)

where [[alpha].sub.ng] > 0 and [[beta].sub.ng] < 0 are the parameters to be calibrated at assumed prices, consumption and elasticities for the base year (1995). (4) This procedure ensures that all demand functions go through the actual market outcomes in that year (Mathiesen et al., 1987). Moreover, we assume that each market segments' quantity demanded is at least equal to the exogenous amount, i.e., that retail price is less than the price intercept of the demand function:

[p.sub.ng] < [[alpha].sub.ng] (6)

Relationship (6) held in all the simulations of this paper. Where traders are competitive, (6) is equivalent to the border price condition b[p.sub.ng] < [[alpha].sub.ng] - d[c.sub.ng]. In the case of Cournot traders, it can be shown that the bound is tighter: b[p.sub.ng] < [[alpha].sub.ng] - d[c.sub.ng] + [[beta].sub.ng] [y.sub.rng] for any r, where [[beta].sub.ng][y.sub.rng] < 0. (These results are obtained by recognizing that [p'.sub.ng] < 0 in (3), and that (3) and (4) hold as an equality if [y.sub.rng] > 0; then (3) or (4) is substituted into (6).) An implication of these assumptions, along with the assumption that the cost of serving a particular market segment is identical for all traders, is that throughput quantities [y.sub.rng] > 0, and (3) and (4) hold as equalities.

Since symmetry of traders implies that producers will not price discriminate among them, there is no need to divide the sales variable for producer i into sales to individual traders. Therefore, [q.sub.ing] can denote the total gas delivered to all traders in market ng by producer i. We assume that total sales to ng by producers [[SIGMA].sub.i][q.sub.ing] equal total sales to that segment by traders [[SIGMA].sub.r][y.sub.rng]. Therefore, if traders are perfectly competitive, and (6) holds, then the effective demand curve that faces producers for market segment ng is:

b[p.sub.ng] = [[alpha].sub.ng] + [[beta].sub.ng] * ([x.sub.ng] - exo[g.sub.ng]) - d[c.sub.ng] = [[alpha]'.sub.ng] + [[beta]'.sub.ng] * [summation over (i)] [q.sub.ing] (7)

where [[alpha]'.sub.ng] [equivalent to] [[alpha].sub.ng] - d[c.sub.ng] and [[beta]'.sub.ng] [equivalent to] [[beta].sub.ng]. Equation (7) shows that in the competitive trader case, the traders' willingness to pay for gas (i.e., the effective demand facing producers) is the consumer demand that traders see, but shifted downward by amount d[c.sub.ng]. Else, if traders are Cournot players, the slope of the willingness-to-pay curve changes to [[beta]'.sub.ng] [equivalent to] [[beta].sub.ng]([[R.sub.ng] + 1]/[R.sub.ng]), where [R.sub.ng] is the number of traders serving market segment ng. (The intercept [[alpha]'.sub.ng] is the same as in the competitive trader case.) Thus, within-country transmission costs shift the original demand curve downwards, as [[alpha]'.sub.ng] < [[alpha].sub.ng], while trader market power steepens the demand curve, as |[[beta]'.sub.ng]| > |[[beta].sub.ng]|. With zero transmission costs and a large number of traders, it can be shown that the traders' willingness to pay converges to the consumers' demand curve.

Some further relationships can also be defined. In each market ng, (5) and (7) imply that when traders are competitive, the border price is related to the retail price thus: b[p.sub.ng] = [p.sub.ng] - d[c.sub.ng]. But in the Cournot case, we instead have b[p.sub.ng] = [p.sub.ng] - d[c.sub.ng] + [[beta].sub.ng][[SIGMA].sub.i][q.sub.ing]/[R.sub.ng]. Because [[beta].sub.ng] < 0, this shows that for a given border price b[p.sub.ng], Cournot traders increase the retail price (and thus increase their margin) by amount |[[beta].sub.ng][[SIGMA].sub.i][q.sub.ing]/[R.sub.ng]|. Finally, in either the competitive or Cournot trader case, each trader r in market ng sells the same amount [y.sub.rng] = ([x.sub.ng] - exo[g.sub.ng])/[R.sub.ng], under our assumption that traders and producers included in the model do not supply the exogenous portion of consumer demand.

Upstream

Assume that the production of gas is oligopolistic and that producers choose their sales quantities simultaneously (one-stage game), maximizing profit given the quantities chosen by other firms. The resulting equilibrium, if it exists, is therefore Nash-Cournot.

The objective function for a profit-maximising gas producer i is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

As we explain below, the border price b[p.sub.ng] is an endogenous function of the quantity variables in the producer's model (8), unlike the trader's model (1). Thus, producers anticipate the reaction of traders; i.e., producers are Stackelberg leaders with respect to traders. The cost of producing quantity [summation over (n,g)][q.sub.ing] is given by [c.sub.i] (*), [c'.sub.i] > 0 and [c".sub.i] [greater than or equal to] 0. The cost of long-distance transport from producer i to country n equals [t.sub.in] per unit of gas delivered [q.sub.ing]. Again, we neglect gas losses during transmission; we also do not explicitly consider pipeline capacity limitations, but assume that they, along with losses, are reflected in [t.sub.in]. (5)

In order to link the upstream and downstream profit maximisation problems, the expression for the border price in (7) is substituted for b[p.sub.ng], making price endogenous:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

The first-order condition for maximising producer i's profits is then:

[[partial derivative][[pi].sub.i]]/[[partial derivative][q.sub.ing]] = [[alpha]'.sub.ng] + [[beta]'.sub.ng]([summation over (j)][q.sub.jng]) + [[beta]'.sub.ng] * [q.sub.ing] - ([t.sub.in] + [c'.sub.i]) [less than or equal to] 0; [q.sub.ing] [greater than or equal to] 0; [[[partial derivative][[pi].sub.i]]/[[partial derivative][q.sub.ing]]][q.sub.ing] = 0 (10)

If [q.sub.ing] > 0, the first-order condition for [q.sub.ing] yields:

[q.sub.ing] = -[b[p.sub.ng] - ([t.sub.in] + [c'.sub.i])]/[[beta]'.sub.ng] (11)

An implication of (11) is that a Cournot equilibrium does not equate the marginal delivered costs of producers, unlike perfect competition. Too little is produced and the industry's cost of production is not minimised. Since we assume that traders also compete on quantities, their throughput quantities are also too little given b[p.sub.ng] and, in general, transmission costs are not minimised (although under our simple assumptions, transmission does occur at minimum cost). As our results below show, market distortions decrease when trade companies are price takers, i.e., when the border price in (7) is defined using [[beta]'.sub.ng] = [[beta].sub.ng]. In contrast, in the Cournot trader case, |[[beta]'.sub.ng]| > |[[beta].sub.ng]|, and the [q.sub.ing] found in (11) will be smaller than for competitive traders.

3. EMPIRICAL SPECIFICATIONS

Demand and Price Elasticities

Consumption of natural gas in the European Union (EU-15) totalled 346 bcm in 1995 (IEA, 1997). However, the majority (97%) of total EU consumption occurs in just eight mature markets. Thus, n = {Austria, Belgium, France, Germany, Italy, Netherlands, Spain, UK}. Within a country, gas is consumed in three segments: g = {households, industry, power generation}. With eight countries and three segments, we distinguish 24 gas markets and prices.

The price elasticity of demand for the case of linear demand (5) equals:

[[epsilon].sub.ng] = [[[partial derivative]([x.sub.ng] - exo[g.sub.ng])]/[[partial derivative][p.sub.ng]] * [[p.sub.ng]/([x.sub.ng] - exo[g.sub.ng])] = [[beta].sub.ng.sup.-1] * [[p.sub.ng]/([x.sub.ng] - exo[g.sub.ng])], (12)

i.e., [[beta].sub.ng] = [[p.sub.ng]/[[epsilon].sub.ng] * ([x.sub.ng] - exo[g.sub.ng])]] and [[alpha].sub.ng] = [p.sub.ng](1 - [1/[[epsilon].sub.ng]])

We specify the price elasticity of the demand curve for each country and sector at the 1995 price/quantity pairs (Table 1). Elasticities are taken from Pindyck (1979). However, he did not define a separate power sector, so in the base case we take the elasticities for industry as a proxy. Moreover, he did not distinguish Austria and Spain as consuming countries, so we set their elasticities equal to those of Germany and France, respectively.