Modelling pricing behaviour for access charges under partial price-caps

C. Riechmann r Energy Economics 22 2000 187]207 193 Ž of customers from some reference level Q; in practice: units distributed and . customer numbers of the previous year . We might state this regulatory constraint as n Ž . a Q y r Q y Q y R F 2 Ž . Ž . Ý i i i i i is 1 where r represents the per unit revenue adjustment for deviations of units i Ž . Ž distributed Q from the reference level i.e. for simplicity we ignore the impact of i . Ž . changes in customer numbers . For base revenue set close to estimated cost at 15 Ž Ž .. reference quantities i.e. R s C Q and the revenue adjustment factor set close Ž Ž . . 16 to marginal cost of distribution i.e. r s ­C Q r­Q the price control formula i i collapses to cost based regulation: 17 n Ž . Ž . a Q F C Q . 3 Ý i i is 1 To avoid algebraic complications we continue with the simplified regulatory re- Ž . straint as characterised by inequality 3 . For our analysis it is important that Ž . Ž restraint Eq. 3 captures regulatees’ discretion to develop charge structures i.e. . Ž . the vector a . As is shown in Riechmann 1999, p. 191 main findings of the following analysis extend to alternative regulatory rules, e.g. one where the revenue Ž . adjustment factor r does not equate with marginal cost of distribution i Ž Ž . . ­ C Q r­Q and to the regulatory rule that was developed by Vogelsang and i Ž . 18 Finsinger 1979 under normative considerations.

5. Modelling pricing behaviour for access charges under partial price-caps

5.1. Analytical analysis of access pricing beha ¨ iour Proposition 1: The level of a particular access charge a is not relevant for the i Ž . extent of market entry productive efficiency and thus for the intensity of observ- able competition. 19 15 In a dynamic environment the regulatory constant R might be determined by the regulator as the Ž Ž . level of network cost observed in the previous period i.e. R s R s C Q . t ty 1 16 In UK practice r has been set at 50 of average cost. i n n n U Ž . ­ C Q Q 17 i Ž . Ž . This is since a Q y dQ y C Q s a Q y C Q F 0. H Ý Ý Ý i i i i i ­ Q Q i i is 1 is 1 is 1 n 18 Ž . In our terminology the Vogelsang and Finsinger 1979 rule would be written as a Q F R . This Ý i i is 1 rule is intended to induce improvements in the allocative efficiency of the charge structure in a Ž . multi-period framework where managers are only interested in the next period’s profits . 19 We note that the level of access charges is, however, relevant for the degree of allocative efficiency as by the ‘imputation rule’ the access charge a feeds through into the final price p . i i C. Riechmann r Energy Economics 22 2000 187]207 194 Proof: A floor price of the incumbent’s retail business is determined by the Ž Ž . . incumbent’s cost of energy procurement ­G q r­q and the opportunity cost of i Ž earning revenue from providing grid access to the entrant and leaving a retail deal . Ž floor Ž . . to the entrant of a i.e. p s ­G q r­q q a . The incumbent leaves sales to i i i i Ž entrants, whenever the market price is lower than his floor price i.e. whenever Ž . . ­ G q r­q g , while he will sell in the retail market, whenever the market price i E i Ž Ž . exceeds his floor price ­G q r­q - g ; the incumbent is indifferent with respect i E i Ž . . Ž . to retail sales if ­G q r­q s g . Altering the level of the access charge a has i E i i no impact on this result as the difference between market price and floor price is unaffected. B This proposition is useful in determining profit maximising access charges from the incumbent’s perspective. The grid owners total profit consists of the profits Ž Ž . Ž .. earned in the retail business Ý p y a q y G q and in the grid business i i i i Ž Ž .. Ý a Q y C Q . Should M’s supply business have better procurement conditions i i i Ž . than the competitive fringe ­Gr­q - g , M will still ask p s g q a in order i E i i E i i to realise a marginal profit of g y ­Gr­q 0. We can, therefore, rewrite retail E i i Ž Ž .. profit as Ý g q y G q . The grid operator will maximise his profits by optimising i E i i Ž . w Ž .x 20 grid access charges a subject to a regulatory constraint 3 . In the following formal analysis we must also take account of non-negativity constraints for retail Ž . Ž . sales q G 0 ; i s 1, . . . ,n . Writing l and g as Lagrange multipliers l, g G 0 i i i of the regulatory constraint and non-negativity constraints, respectively, the La- grangean expression can be written as n Ž Ž .. Ž Ž Ž ... L s g q p a y G q p a Ý E i i i i is 1 n Ž Ž .. Ž Ž Ž ... q a Q p a y C Q p a Ý i i i i ž is 1 n n Ž Ž .. Ž Ž Ž ... Ž Ž .. Ž . y l a Q p a y C Q p a q g q p a 4 Ý Ý i i i i i i i i ž is 1 is 1 From the FOCs with respect to access charges a we can derive equilibrium access m Ž U prices charged by the incumbent denoting an equilibrium; see Appendix A for . details : Ž Ž Ž U ... Ž Ž .. ­ C Q p a Q p a m m m U a s q m Ž Ž .. ­ Q y­Q p a r­ p m m m m m Ž Ž Ž ... ­ G q p a g y q g E m m ž ­ q m Ž . y ; m s 1, . . . ,n. 5 U Ž Ž .. 1 y l a , . . . 20 Ž . Ž . Quantities q effectively sold by his retail supply business will be determined by the fringe market Ž . prices p s g q a and his competitive position relative to fringe companies. i E i i C. Riechmann r Energy Economics 22 2000 187]207 195 Ž . Ž U . We note that the RHS of Eq. 5 includes endogenous terms in a which, m however, does not preclude meaningful interpretation of results. From complemen- tary slackness conditions we can infer that whenever M’s retail business is competi- tive in supplying any relevant quantity of final product m that y s 0. If M’s m supply business is at a competitive disadvantage in supplying m at some relevant w Ž Ž Ž .. positive quantity i.e. if the incumbent’s cost procurement cost G q p a is increasing in a way that prevents it from serving any positive quantity or the entire x demand in one segment , then g s ­Gr­q y g as g is simply the shadow m m E m m cost of supplying a good for which M has a competitive disadvantage at the margin Ž . i.e. g is the marginal loss of selling good m at market price p . m m Ž . For Eq. 5 we, therefore, have to distinguish two cases: 1. If M’s supply, business is not competitive in supplying the entire demand in segment m, then Ž . Ž . ­ C Q Q p m m U U Ž Ž . . Ž . a s q ; m such that g - ­ G q r­q . 6 m E m m ­ Q y­Q r­ p m m m Ž This implies that the access charge in segments where M is uncompetitive or . becomes uncompetitive at the margin will be made up of two elements. The Ž . first term on the RHS of Eq. 6 represents the marginal cost of grid access. Ž . The last term on the RHS of Eq. 6 is a monopoly-rent term. Note that while under a Ramsey pricing rule this last term would be pre-multiplied by a Ramsey term 21 which is smaller than 1, here it is pre-multiplied by 1. Rear- ranging would give the familiar inverse elasticity rule for monopolistic pricing. 22 The intuition behind this phenomenon will be outlined below. 2. If M’s supply business is competitive in supplying any relevant quantity of m, Ž Ž . . then note that for g ­ G q r­q : E m m Ž . Ž . Ž Ž . . ­ C Q Q p g y ­G q r­q m m E m m U a s q y m Ž . ­ Q y­Q r­ p 1 y l m m m Ž . Ž . ; m for which q , so that g ­ G q r­q . 7 m E m m Ž . Ž . The formal expression in Eq. 7 is identical in structure to Eq. 6 except for Ž . an additional term on the RHS of Eq. 7 . Note that this additional price component is negative. 23 This implies that access charges are reduced by the Ž . grid owner M in segments m where M’s retail business is at a competitive Ž Ž . . advantage g ­ G q r­q in the entire relevant range. E m m 21 Ž . Ž . Ž . Ž . See e.g. Laffont and Tirole 1994 , Eq. 18 or Armstrong et al. 1996 , Eq. 23 . 22 Ž X Ž .. X Ž . Ž . Ž . Ž . I.e. a y C Q ra s 1rh with C Q s ­C Q r­Q , h s y ­Q r­a r Q ra and m m m m m m m Ž . ­ Q r­a s ­Q r­ p . See also Tirole 1988, p. 66 . m m m m 23 Ž Ž . Ž . From l G 0 and l - 1 see also Riechmann 1999 we can infer that 1 y l 0. Since we consider Ž . the case where g ­ G q r­q the last term is positive, but has a negative sign. E m m C. Riechmann r Energy Economics 22 2000 187]207 196 5.2. Graphical illustration of access pricing beha ¨ iour To illustrate our results so far, we intuitively derive equilibrium network access Ž charges in a model reduced to two market segments i.e. n s i, j; it is straightfor- . ward to extend the analysis to any number of market segments . In segment i the Ž . incumbents retail business has a competitive advantage in energy procurement Ž Ž . X . over the fringe g ­G q r­q s G . In segment j the fringe has a competitive E i i i Ž Ž . X . advantage over the incumbent g - ­ G q r­q s G . We refer to this set-up as C j j j Ž . the ‘two sector scenario’ in the following. For the graphical analysis Fig. 1 we further assume that the network operator has constant marginal cost of network Ž Ž . X 24 Ž . access ­C Q r­Q s C . Assume, e.g. that access charges a had initially m m m Ž X . been set at the level of marginal cost C and that this would imply a binding m regulatory constraint. 25 Ž . By charging at the fringe price p s a q g in segment i the incumbent is i i E i Ž X X . able to exploit a rent in the retail business characterised by E F at the margin . If Ž X . access charges had initially been set at efficient levels a s C , the incumbent i i Ž X . could increase the retail rent by reducing the access charge below cost a - C . i i Ž This reduces the market price and lets the incumbent sell additional units with . Ž positive rent in segment i. The marginal loss in the distribution business by pricing grid access below marginal cost in segment i; and thus cross-subsidising in Ž .. the terminology of Faulhaber 1975 can be financed by increasing network access charges in segment j in which the incumbents retail business has no stake Ž X . a C . The limit of raising funds in segment j in order to balance a reduction of j j access charges in segment i is given by monopoly prices for network access in segment j. In equilibrium, the incumbent will raise an amount represented by the area ABCD in Fig. 1 in segment j and will reduce access charges in segment i Ž X X X X . correspondingly so that ABCD s A B C D . This enables the incumbent to earn an additional retail rent characterised by the area C X D X E X F X . 5.3. Methodological remarks With respect to the characterisation of possible equilibrium situations we note that: 1. Our specific modelling of the regulatory constraint is not critical to our main findings. 26 24 Constant marginal cost is an untypical characterisation for a natural monopoly business such as electricity distribution. We have shown main results for a more general specification of the cost function of distribution in the above formal analysis. The simplifying assumption of linear distribution cost is purely used for didactical purposes. This simplification allows us to isolate the regulatory problem of full Ž . Ž cost recovery with potentially decreasing marginal cost and fixed cost of network provision without . loss of generality . 25 In the absence of fixed network cost this would be considered as efficient pricing. The absence of fixed cost is untypical of a network business but is a permissible simplifying assumption for our purpose Ž . see footnote 24 . 26 Ž . Similar results hold for practicable regulatory rules as is shown in Riechmann 1999 . C. Riechmann r Energy Economics 22 2000 187 ] 207 197 Ž . Fig. 1. Strategic pricing for network access under partial Price-caps } graphical illustration Source: Own illustration . C. Riechmann r Energy Economics 22 2000 187]207 198 2. The above modelling allows for ranges of indeterminate solutions. 27 3. The above modelling only explains a downward manipulation of grid access charges for segments which are fully supplied by the grid owner’s retail Ž business i.e. segments where M’s retail business is able to earn non-negative . retail profits . Results obtained above may extend to a framework where rivals also gain some market shares upon simple modifications to the model. 28 Ž Within the above framework we could model this by setting ­q r­p s 1 y m m . Ž . Ž . a ­ Q r­ p in Eq. 7 , where a 0 - a - 1 is the fraction of demand which m m m m m can be supplied by the incumbent retailer at least cost, but which is contracted to Ž . rival retailers note that for simplicity a is determined exogenously . In this case m Ž . Eq. 7 can be rewritten: Ž . Ž . Ž . Ž Ž . . ­ C Q Q p 1 y a g y ­G q r­q m m m E m m Ž . a s q y . 8 m Ž . ­ Q y­Q r­ p 1 y l m m m w The primary effect of some share of sales always going to rival retailers i.e. when Ž . Ž .x moving from Eqs. 7 and 8 is that the extent of charge manipulation to favour 29 Ž . the own retail supply business tends to be lower. Eq. 8 can explain a downward w Ž .x trend in grid access charges represented by the third term on the RHS of Eq. 8 in market segments, where the grid owner’s retail business loses some market share to competitors while still being the dominant supplier. For conceptual clarity we Ž . Ž . focus on the model as characterised by access pricing rules Eq. 6 and Eq. 7 for the following discussion.

6. Main propositions on incumbents’ access pricing behaviour