Chapter 4 Regulating Natural Gas Transportation as an Exhaustible Resource The thrust of infrastructure reform in recent decades has been to separate competitive elements and to regulate remaining natural monopolies. In the natural gas industry ‘open access’ regimes have been operative since the 1990s. Natural monopoly transporters are separated from other elements of the industry (producers, traders, retailers) and are compelled to provide their services at regulated prices. The objective is to promote competition outside the transportation sector, and to ensure that the benefits of this competition are passed to consumers. Where there was once a single market for delivered gas, access regulation creates separate markets for gas and for transportation services. Pioneers of access regulation have included Argentina,1 Australia,2

1

In 1992 the state-owned monopoly Gas del Estado was divided into two transmission and eight distribution companies. An independent regulator, Enargas was established to regulate transmission and distribution. Energas uses price cap regulation. The cap is reset each five years to cover operating costs, maintenance, expansion and a reasonable return on invested capital. (Gomez-Lobo & Foster 1999). 2 In 1997 the national and state governments adopted the ‘National Third Party Access Code for Natural Gas Pipeline Systems.’ If a transporter and access seeker do not agree on terms of access either party may seek binding arbitration under terms consistent with the Code. The construction of major new pipelines in recent years has simultaneously increased the possibilities for competition between producers. Regulated prices under the Code are based on the cost of service, including a reasonable return on invested capital.

97

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Canada,3 New Zealand,4 the United Kingdom5 and the United States.6 The European Union’s 1998 gas directive marks a step towards liberalization although implementation across all countries will take time. Academic analysis of access regulation in the gas industry is a relatively new field, developing largely in response to these observed new policies. There are obvious similarities with access regulation in other infrastructure industries, but a significant difference is exhaustibility of gas reserves. Since Hotelling’s (1931) classic paper, it has been well known that exhaustible resources have special properties. In particular, maximizing profits or welfare requires that fixed stocks be rationed across time such that marginal rents rise over time at the rate of interest. This implies different pricing strategies from intra-period profit or welfare maximization. Despite the long pedigree of literature on exhaustible resources, it seems not to have been incorporated into the literature on access regulation of gas transportation. For example, Cremer & Laffont (2002), Cremer, Gasmi & Laffont (2003) and Oviedo Arango (2000) do not discuss exhaustibility. It may be that analysts have considered that taking account of exhaustibility imposes excessive informational requirements on the regulator. We return to this argument in the conclusion. Alternatively, it might be thought that the issue of exhaustibility has minimal consequences for analysis of access regulation. There is some strength to this argument. As we shall see, when gas production is workably competitive, setting transportation prices close 3

The 1985 Agreement on Natural Gas Prices between the Federal government, Alberta, British Columbia and Saskatchewan deregulated natural gas commodity prices. Pipeline prices are generally determined by the National Energy Board, and distribution prices are determined by provincial authorities. Regulated prices are based on the cost of providing service. 4 Open access to one of the major pipeline systems and the distribution networks is provided by asset owners pursuant to the Pipeline Access Code. The Code was developed voluntarily by a group of industry participants as a means of ensuring compliance with New Zealand competition laws prohibiting misuse of a dominant position. The Code has been operating since 1998. It provides that access must be provided on a non-discriminatory basis, but does not provide any principles for pricing of pipeline services. No access arrangements apply to the major Maui pipeline system, but the government is encouraging industry-wide access arrangements and has indicated that it may regulate if necessary. See www.med.gov.nz/ers/gas/review. 5 In 1986 British Gas was privatized as a vertically integrated producer, transporter and retailer. At the same time large consumers or independent shippers and traders were permitted to contract directly with producers. New competition was slow to emerge, however, until the 1997 structural separation of British Gas’s transportation and storage business from its production and retail business. Natural gas markets are now substantially deregulated, while gas transportation remains heavily regulated. 6 The 1992 FERC Order 636 separated gas sales from transportation services and created open access to pipeline capacity for both producers and consumers.

99 to marginal cost results in approximately optimal prices for delivered gas. Nevertheless, there are important reasons for bringing exhaustibility into the analysis of access regulation. One reason is that practical regulation almost never uses marginal cost pricing. Using terminology such as ‘long-run incremental cost’ or ‘reasonable rate of return on capital’, regulators allow fixed costs to be incorporated into the regulated price, to provide incentives for ongoing investment and maintenance. Once price is above marginal cost, there are positive rents. The Hotelling logic suggests that these rents should rise over time. In fact, we will see that the existence of these rents even in competitive markets provides a means for regulators to cover fixed costs that may be superior to standard regulatory strategies. The second reason is that there are many countries where gas production is monopolized. From Hotelling we know that the behavior of a monopolist of an exhaustible resource cannot be analyzed in the same way as that of a conventional monopolist. To understand the consequences of access regulation in the presence of a production monopoly, we need to take account of exhaustibility. It might be thought that if production is monopolized there is little point in introducing access regulation. But countries may introduce access regulation in the hope that it will stimulate the entrance of new producers. In at least some markets in Australia and Britain, access regulation was introduced before there were possibilities for strong competition between producers. Moreover, there are several examples of countries that receive gas from a foreign producer with market power. These countries cannot hope to influence the market structure of production. Relevant examples include the Argentina-Chile pipeline, the Bolivia-Brazil pipeline, Europe’s increasing dependence on Russia and North Africa, or the proposed pipeline using gas from Nigeria to supply countries as distant as Côte d’Ivoire. In these cases it seems important to understand the effects and limitations of pipeline regulation. This paper is concerned only with access regulation. We do not consider regulation of the final consumer price, or of producers’ well-head prices. In section 4.1 we set out assumptions and notation that are common across subsequent sections. We use a simple model, with constant marginal costs of transportation. In section 4.2 we briefly review Hotelling’s rule. In section 4.3 we present the regulator’s strategy for maximizing welfare, under the assumption that firms and the regulator use only linear prices.7 When 7

Following standard terminology, linear pricing is any price structure p(x) = j with j constant. Nonlinear pricing is any price structure where the price of a marginal x-th unit is a function of x. Affine functions of the form p(x) = r + sx with r and s constant thus belong to the class of nonlinear prices. See Wilson (1997).

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production is competitive, a simple rule for the regulated transport price allows the transporter’s fixed costs to be covered, and yields optimal depletion of the resource stock over time. When production is monopolized, a similar rule yields optimal depletion of the resource stock, but the limited (possibly negative) rents earned by the transporter limit the practical usefulness of this rule. In section 4.4 the analysis is extended to the case where firms and the regulator may use non-linear prices. In section 4.5 we briefly consider the case when transportation consists of separate transmission and distribution monopolies. We conclude in section 4.6.

4.1

Assumptions and Notation

We consider a stylized natural gas industry in which gas flows from a single gas field (perhaps having multiple competing producers) to a single transmission pipeline to a single city’s distribution network and then to consumers. The transportation infrastructure, like the gas field itself, is an exhaustible resource: the more gas that is transported the earlier the infrastructure will be rendered valueless. For simplicity we suppose that pipelines have no scrap value, and rights of way have no resale value. The premise of access regulation is that transmission pipelines and distribution networks constitute bottleneck facilities, with the potential to extract monopoly rents from consumers. In the absence of regulation we suppose that gas transporters purchase gas from producers and sell delivered gas to consumers. We focus on consumer access, which permits consumers to purchase gas directly from gas producers and to purchase delivery through the transportation system separately and at regulated prices. We take industry structure as fixed, and consider the optimal regulatory response. The model can be considered part of a larger game between investors and the regulator. In the larger game, investors develop gas fields and build transportation facilities depending on the rents they expect to gain. Once the infrastructure is built, the regulator can treat the industry structure as fixed. In our model, we do not consider the dynamic effects on investment of anticipated regulation. We make several assumptions about industry technology. We generally treat transmission pipelines and distribution networks as a single business, called transportation. Transportation is characterized by large fixed costs, K, associated with establishment of the infrastructure, and low marginal costs for delivering gas, assumed constant and equal to c. We do not consider fixed costs of transportation incurred each period. Because the focus is on regulation of transportation, we assume there are no fixed costs in production.

4.1. ASSUMPTIONS AND NOTATION

101

Production has constant marginal costs equal to d. Under both profit and welfare maximizing strategies price is above social marginal cost. We assume that the present value of the fixed costs are ‘not too large’ in the sense that the present value of rents under the welfaremaximizing strategy is greater than the value of fixed costs, so that gas extraction increases total welfare. We assume that transportation facilities are not subject to capacity constraints. Whereas transportation is a natural monopoly, production (i.e. extraction) may be competitive or monopolized. In our stylized market, where a single pipeline connects a single gas field with a single distribution network, the development of each element of the infrastructure is dependent on the other. It is thus natural to suppose that construction of the infrastructure will be subject to bargaining, with long-term contracts sharing the rents before any construction begins. Given this background, we assume that situations of bilateral monopoly can be analyzed using Nash bargaining and the maximization of joint profits. To keep the analysis simple we focus on linear consumer demands and we suppose that demand does not change over time. Competition between gas and other energy sources is reflected in the slope and intercept of demand for gas. At a sufficiently high price, consumers abandon gas and move to other energy sources. Linear demand curves reflect quasi-linear utility, with no income effects arising from price changes. When we consider inter-period allocations we can measure time forward from the present (t = 0), or backward from the date that reserves are exhausted, E. When necessary to refer to time-periods we express variables as a function of t to indicate that time is measured from the present (e.g. Q(t) is the quantity of gas t time periods from the present) or with subscript E − τ to indicate time measured relative to the exhaustion date (e.g. QE−τ is the quantity of gas τ periods before the exhaustion date). We assume a one-to-one correspondence between units of gas produced, transported and delivered, implying no wastage of gas in transportation. The production price of gas (well-head price) is denoted PG , the price of transportation services is PT , and the price of delivered gas is the sum of the well-head and the transportation prices: PD = PG + PT . We define ‘marginal welfare’ as the sum of consumer and producer surplus W W obtained on sale of a marginal unit of gas. We denote by λW D , λT and λG marginal welfare in the markets for delivered gas, transportation services and well-head gas respectively. We define ‘marginal profit’ as the producer surplus obtained on sale of a marginal unit of gas, and denote by λπD , λπT and λπG marginal profit in the markets for delivered gas, transport services and well-head gas respectively. The social optimum maximizes total welfare in

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the market for delivered gas. We denote the social optimum with an asterisk superscript. Thus, λ∗D (t) is the optimal value of λW D at time t. At points in the analysis we contrast our proposed regulatory strategy with a crude caricature of a ‘standard’ regulatory strategy. The standard strategy is to set a fixed price of transportation equal to marginal cost plus a fixed markup to cover fixed costs, PT = c + g. The method of calculating g is left deliberately vague. It can be thought of as cost-plus pricing, or price cap regulation for a single product. The important point is that g is constant over time. In reality regulated prices rise with inflation and fall with technological progress, but in our model both of these effects are assumed to be zero.

4.2

Hotelling’s Rule

The characterization of problems of exhaustible resources has been wellknown since Hotelling (1931). The problem can be expressed as finding RE the extraction path Q(t) so as to maximize V = 0 R(Q)e−rt dt subject to RE Qdt = Z where R is the optimizer’s intra-period reward function, Q(t) is 0 the quantity of gas extracted in period t, E is the (unfixed) time of exhaustion, r is the interest rate, and Z is the known total stock of gas reserves. R(Q) can be interpreted as either firm profit or social welfare, depending on the maximizer’s objective. Provided R is concave in Q, the absolute maximum of V can be identified using the first order condition, R0 (Q) = φert where φ is the multiplier on the gas stocks constraint. Define λ ≡ R0 (Q) and let a hat over a variable denote the inter-temporal rate of change of the variable. The first order condition implies Hotelling’s Rule, that intra-period marginal rewards increase over time at the rate of interest: b ≡ ∂λ/∂t = r λ λ

4.3

(4.1)

Regulation with Linear Prices

In this section we assume that firms and the regulator can only use linear prices. We contrast access regulation when production is competitive and when it is monopolized. In each period aggregate demand for delivered gas is given, in inverse form, by PD = a − bQ, with a > c + d and b > 0. The marginal welfare obtained on sales of delivered gas is λW D = PD − (c + d). The marginal welfare obtained on sales of transportation services is λW T = PT − c. The W marginal welfare obtained on well-head gas sales is λG = PG − d.

4.3. REGULATION WITH LINEAR PRICES

4.3.1

103

Welfare Maximization versus Monopoly

To provide benchmarks for comparison with regulated outcomes we first contrast welfare maximization with monopolistic profit maximization in a vertically integrated industry. Under our assumptions monopolistic profit maximization results in excessive conservation of gas reserves, a result that has been familiar since Hotelling’s (1931) paper. Along the optimal time path λ∗D = λW D = PD − (c + d). Applying Hotelling’s Rule, along the optimal path the price of delivered gas rises at the rate (PD∗ (t) − c − d)r ∗ Pc = D PD∗ (t)

(4.2)

In contrast, in a monopolized industry, marginal profits are given by: λπD = PD +

∂PD Q − (c + d) ∂Q

(4.3)

which for any given Q > 0 is less than marginal social welfare. Using the assumed demand curve and Hotelling’s Rule, the implied monopoly price path for delivered gas rises at a slower rate than optimal: (2PDπ − a − c − d)r ∗ π < Pc Pc = D D 2PDπ

(4.4)

Since marginal rewards increase monotonically at the rate of interest, they reach a maximum value when reserves are exhausted at time E. Under both welfare maximization and monopoly the maximum marginal rewards are identical: a − (c + d) when Q = 0. Consequently, the marginal rewards are the same under profit and welfare maximization at all periods E − τ , i.e. λπ (QπE−τ ) = λW (QW E−τ ). But within any period, for any given Q > 0, λπ (Q) < λW (Q). So in each period the monopolist sells less than is socially optimal: QπE−τ < Q∗E−τ . With fixed total stocks, the monopolist’s exhaustion date is further from the present than optimal, E π > E ∗ .

4.3.2

Competing Producers

An unregulated transporter has complete market power when dealing with perfectly competitive producers. By making a take-it-or-leave-it offer to purchase a desired quantity from competing gas producers, the transporter can reduce the demand curve facing producers to a single point in each period. The transporter exerts monopsony power to set PG = d in each period. Producers earn zero rents (λπG = 0) in all periods. The problem

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then facing the unregulated transporter is to choose the quantity in each period which ensures that marginal profits rise at the rate of interest. The transporter has marginal costs of c plus the well-head price of gas PG = d and sells delivered gas at price PD , as defined by the consumers’ aggregate demand curve. The transporter’s intra-period marginal profit is given by: D (Q) Q − (c + d). Comparison with (4.3) reveals that the λπT (Q) = PD (Q) + ∂P∂Q unregulated transporter chooses the same quantities as a vertically integrated monopolist, selling less gas in each period than is socially optimal. Access regulation of transportation changes the bargaining relationships in the industry. Consumers purchase gas from producers and transportation services from the transporter, rather than buying delivered gas from the transporter. Since the transport price is regulated, producers are no longer constrained by the transporter’s monopoly power. By (4.1), competitive producers set prices such that their marginal profit rises at the rate of interest: π λc G = r. Competitive producers are price takers so their marginal profits are equal to marginal welfare in the production sector: λπG = λW G. Marginal welfare in the market for delivered gas is the sum of marginal welfare in the markets for transportation services and well-head gas: λW T = W . Knowing that marginal welfare in the well-head market rises at − λ λW G D the rate of interest, the regulator should ensure that marginal welfare in the transportation services market rises at the rate of interest, to ensure that marginal welfare in the market for delivered gas rises at the rate of interest. W ∗ c That is, to achieve λc D = λD = r the regulator should set transport prices W such that λc T = r. This implies the price of transport should rise at the rate cT = (PT − c)r (4.5) P PT The regulator may choose any final period price for transportation that lies on the interval [c, a − d]. Which price path the regulator chooses determines the division of rents between producers and the transporter. Under marginal cost pricing, PT = c in all periods and the well-head price of gas rises to a maximum of PG = a − c, at which time demand for delivered gas is driven to zero. This achieves the socially optimal depletion of gas reserves, with all rents flowing to gas producers rather than the transporter. An alternative means of achieving the socially optimal price path for delivered gas is to have the price of transportation rise over time at the rate specified by (4.5) to achieve a price of PT = a − d at time E ∗ , the optimal depletion time. The maximum price producers can achieve at time E ∗ is d, implying that producers’ marginal profits are zero in the final period. Thus, by (4.1) producers’ marginal profits are zero in all periods, PG = d. All rents flow to the transporter.

4.3. REGULATION WITH LINEAR PRICES

105

There is a unique price path that satisfies (4.5) and that exactly covers the transporter’s fixed costs. In the initial period the regulator provides a markup over marginal cost equal to the fixed establishment costs divided by the optimal number of periods: PT (0) = c + EK∗ . The regulator increases price over time at the rate (4.5), or equivalently increases the transporter’s marginal profit at the rate of interest. The present value at time t = 0 of the markup (marginal profit) in each period t ≥ 0 is thus equal to EK∗ . Summed across all periods fixed costs are exactly reimbursed. Within limits, this strategy forgives regulatory error. If the regulator overestimates E ∗ the transporter’s fixed costs are not fully covered, but the price-path of delivered gas remains optimal. If the regulator underestimates E ∗ , but increases price at the rate (4.5), the transporter’s share of rents is higher, but the price-path of delivered gas is optimal. An important limit on the ‘forgiveness’ of the strategy is that if the regulator underestimates E ∗ by too much the starting price of transportation is too high, and reaches PT > a − d before time E ∗ . If this occurs there are unconsumed gas reserves at E ∗ , a sub-optimal result. We may contrast these regulatory strategies with ‘standard’ regulatory practice, under which PT = c + g. The residual inverse demand curve facing producers is PG = PD − PT = a − bQ − c − g so that marginal welfare in the well-head market is λW G = a − bQ − c − d − g. Competitive production ensures that marginal welfare in the market for well-head gas rises at the rate of interest. The resulting price path for delivered gas rises at the rate (PD −c−d−g)r ∗ < Pc Pc D = D . Standard practice results in excessive conservation PD of gas relative to the social optimum. The smaller is g the closer standard practice approximates the optimal regulatory strategy. If g < a−c−d then 2 π c Pc D > PD , and standard practice is an improvement on the unregulated outcome.

4.3.3

Production Monopoly

Figure 4.1 sets out the price paths for delivered gas with a production monopoly under different regulatory regimes. In the absence of regulation, a bilateral monopoly arises. The joint profit maximization problem involves demand for delivered gas, PD = a − bQ, and joint marginal cost, c + d. The resulting price path for delivered gas is thus the same as the monopoly price path used by the unregulated transporter when faced with competing producers: the price for delivered gas rises at the rate (4.3). In this instance, however, profits are shared between the producer and the transporter.

CHAPTER 4. REGULATING GAS TRANSPORTATION

Price for Delivered Gas

106

Standard regulation Unregulated monopoly Constrained regulation Optimal regulation

Time to exhaustion

Figure 4.1: Transport Regulation with a Production Monopoly

With regulated consumer access, the producer is freed from the bilateral monopoly relationship and may exercise unrestrained monopoly power subject to the well-head demand for gas. Inverse well-head demand, however, is the residual of inverse demand for delivered gas less the regulated price of transportation: PG (Q) = PD (Q) − PT . The regulator’s problem is to manipulate the transportation price to constrain the producer’s market power. It might seem that the regulator could use the transporter’s market power to reduce the well-head demand to a single price and quantity in each period. Thus, the regulator might set PT = PD∗ − d at all times. If the producer responded by setting PG = d in all periods, marginal profits would be zero in all periods and condition (4.1) would be satisfied. The price for delivered gas would then be optimal in all periods and reserves would be exactly exhausted at time E ∗ . But if the producer sets price PG > d the producer makes a positive profit in each period, less gas is consumed in each period than optimal, and reserves are not exhausted at time E ∗ . Given the regulator’s strategy, the producer does not wish to extract gas after time E ∗ , so the producer is freed from the resource constraint and may set prices to maximize profits in each period. Prices for delivered gas are higher than optimal in all periods and there are unconsumed reserves at time E ∗ . Thus, the regulator must take the bilateral monopoly into account when

4.3. REGULATION WITH LINEAR PRICES

107

setting transport prices. For the producer, the transport price is fixed in any period, so the producer’s intra-period marginal profit is λπG (Q) = PD + ∂λπ ∂PD G T Q − P − d = 2P − P − a − d. This implies that = 2 ∂P∂tD − ∂P . If T D T ∂Q ∂t ∂t the price of delivered gas is optimal in each period, then by (4.2) we have ∂λπ G T = 2(PD∗ −c−d)r − ∂P . Applying (4.1), the monopolist’s pricing strategy ∂t ∂t ∂λπ π ∗ G sets ∂t = rλG = r(2PD − PT − a − d). Equating expressions we obtain the rate of change of the regulated price of transport that achieves the optimal price path for delivered gas: cT = (PT + a − 2c − d)r P PT

(4.6)

To compensate for the monopolist’s tendency to increase prices too slowly over time, the regulator sets transport prices that rise faster than the rate used when production is competitive: equation (4.6) implies a faster rate of price change than equation (4.5). Any transportation price path that satisfies (4.6) with PD (E ∗ ) ≤ a − d results in the optimal price path for delivered gas. The price path giving the highest possible stream of rents to the transporter has a final period price of PT (E ∗ ) = a − d. Under this regulatory strategy, the marginal profit earned by the producer in the final period is zero. By (4.1) the producer’s marginal profit is zero in every period. That is, the producer sets the intraperiod profit-maximizing price in each period, as if there were no resource constraint. If reserves are sufficiently great, the transportation price in periods far from exhaustion is less than marginal cost, or even negative. For example, with an annual interest rate of 5%, and values a = 5, c = 1, and d = 1, the implied regulated transport price equals zero 22 years before exhaustion and reaches the marginal cost of transportation 14 years before exhaustion.8 Although the regulatory strategy gives high rents to the transporter in the final periods before exhaustion, these may not be sufficient to cover losses incurred in early periods and/or fixed costs. Even if the regulatory strategy generates an overall profit for the transporter after fixed costs are included, it is possible that a regulatory strategy that sets price below marginal cost in some periods is not politically feasible. We may wish to introduce an additional constraint that PT ≥ k, where k is some positive number, greater than or equal to marginal cost. Introducing this constraint results in a regulatory policy of PT = k for early periods, prior k+a−2c−d ∗ . Knowing that λW PT = 2PD − a − d = k implies λW D = D increases at the 2 k+a−2c−d rτ rate of interest to a final value of a − c − d we have ( )e = a − c − d. This implies 2 2(a−c−d) 1 PT = k when τ = r ln k+a−2c−d . 8

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to some time t˜, and the unconstrained regulatory policy PT = 2PD∗ − a − d for final periods after time t˜.9 After time t˜, the regulatory policy achieves the first-best price-path for delivered gas. Prior to time t˜, if k = c the price path for delivered gas rises at the vertically integrated monopolist’s π rate, Pc D defined by (4.4), albeit at a lower price level. If k > c, prior to π 10 time t˜ the price path for delivered gas rises at a slower rate than Pc D. The constrained regulatory policy unambiguously improves welfare if the price path for delivered gas under regulation never exceeds the unregulated vertically integrated monopolist’s price path. We can again examine ‘standard’ regulatory practice, in which the regulator fixes the transportation price at PT = c + g in all periods. Standard regulatory practice causes the price of delivered gas to rise more slowly than the price of an unregulated monopolist, over-conserving gas relative to the monopoly position. Standard regulation actually diminishes welfare when there is a production monopoly.

4.4

Regulation with Non-Linear Prices

The model of gas markets with linear prices is useful for understanding relationships between various agents in the gas markets, but actual pricing practices are clearly richer. In this section monopoly firms in gas markets and the regulator are able to set different marginal prices for different quantities. As previously, a profit-maximizer wishes intra-period marginal profit to increase at the rate of interest, and the regulator wishes intra-period marginal welfare to increase at the rate of interest. The inter-period problem is thus essentially the same as before: quantities of gas are allocated across time so as to satisfy (4.1). The difference arises in the nature of the intra-period pricing structure: how given quantities should be allocated across consumers within each period. 9

If the unconstrained problem has a Hamiltonian equation H(PT , PG ), addition of the constraint gives a Lagrangean equation L = H(PT , PG )+φ(PT −k). If φ > 0 the constraint is binding, and we immediately know that PT = k. If PT > k then φ = 0 and the problem reduces to the original Hamiltonian, giving the same first order condition concerning the rate of change of PT as in the unconstrained problem. 10 The monopoly producer faces inverse demand PG = a − bQ − PT . The producer’s ∂λπ G marginal profit can be expressed as λπG = 2PG − a − d + PT , from which ∂tG = 2 ∂P ∂t . ∂λπ ∂PG π G From (4.1) ∂t = rλG . Equating these expressions we find ∂t = (2PG + PT − a − d) 2r . r Using PD = PG + PT we find that Pc D = (2PD − PT − a − d) 2PD .

4.4. REGULATION WITH NON-LINEAR PRICES

4.4.1

109

Welfare Maximization versus Monopoly

To contrast access regulation of an industry with competitive production versus an industry with a production monopoly it is useful first to characterize the within period non-linear pricing structures under welfare maximization and monopoly. Within each period, the firm or the regulator’s problem is to find a pricing structure that sells the period’s allocation of gas for the maximum reward. We suppose that in each period heterogeneous consumers of type θ are willing to pay m(x, θ) = θ − bx for an x-th marginal unit of delivered gas, where b > 0 is a parameter. We suppose that consumer types, θ, are dis¯ Only consumers know their own types.11 All tributed continuously on [0, θ]. parameters are assumed time-invariant. The non-linear pricing structures adopted for a vertically integrated industry under welfare maximization and under profit maximization are examined in Chapter 5. Under our assumptions, the welfare-maximizing intraperiod pricing structure is linear: PD (x) = j with j constant. This is true more generally, as can be seen with a little reflection. If the prices at the m-th and n-th increments are different, say PD (m) > PD (n), total welfare can be increased by lowering PD (m) sufficiently to induce one more unit to be sold at the m-th increment, and by correspondingly increasing PD (n) sufficiently to reduce sales at the n-th increment by one unit. This process of transferring individual units of the fixed Q from consumers with lower marginal valuations to consumers with higher marginal valuations can be continued until the price schedule is linear, i.e. constant for all x. Although non-linear prices are feasible, the welfare-maximizing pricing structure for delivered gas is, in fact, linear in each period. In contrast, a vertically-integrated profit maximizer chooses a non-linear price structure in each period. Hotelling’s Rule implies that the monopolist chooses to have marginal profit rising at the rate of interest. Once the maximum marginal rent is known, the interest rate fixes the marginal rent at any time. The marginal rent is a function of quantity, so the monopolist’s desired quantity is fixed at any time. Chapter 5 shows that to maximize intra-period profit subject to the constraint of selling a specific quantity, Q, q 2 k(b−1) ¯ − b k + bθQ, the monopolist’s pricing structure is P (x) = θ¯ − bx + 2

2

2

4

where k is the vertically-integrated monopolist’s marginal cost. The fact that 11

These conditions are sufficient to give a well-structured problem in the standard literature on non-linear pricing (see Goldman, Leland & Sibley (1984)). We present a variation on this literature by considering optimal non-linear pricing in the presence of a quantity constraint. The constraint does not, however, alter the concavity of the problem, so the maximization problem remains well structured.

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this pricing structure is downward sloping in x is sufficient to show that it is not welfare-maximizing.

4.4.2

Competing Producers

In a market with competitive producers, competition ensures linear pricing. The welfare maximizing price schedule for delivered gas is linear in each period. Thus in a market with competitive production, the regulator’s problem and the optimal regulatory strategy are the same as in section 4.3. The price of transport should rise at the rate specified by (4.5), and to cover fixed costs exactly, the price in the initial period should be PT = c + EK∗ . To ensure a linear price for delivered gas, the regulated transport price should be linear in each period. This contrasts with many observed regulatory policies where the price for transportation is non-linear: a fixed ‘capacity’ fee and a price per unit of gas transported.

4.4.3

Production Monopoly

Analysis of a production monopoly using non-linear prices proceeds in the same fashion as the analysis when only linear prices are used. In the absence of regulation there is a bilateral monopoly that behaves like a vertically integrated monopolist. Introducing regulation of the transport price breaks the bilateral monopoly. As with the analysis where only linear prices were used, marginal cost pricing in the transport market does not induce the producer to behave optimally. Setting the price of transport at PT = c in all periods shifts the demand curves facing the producer down by the constant c (i.e. the producer faces derived inverse demand PG = PD − c. Since the producer is interested in marginal profit this is analytically equivalent to increasing the producer’s marginal cost to k = c + d. The producer’s intra-period non-linear pricing problem is then the same as the vertically integrated profit maximizer’s problem analyzed above. The producer uses non-linear pricing for well-head gas that results in the same inter-temporal prices as an unregulated vertically integrated monopolist. Following the same logic as in section 4.3.3 the regulator can target the optimal price of delivered gas in each period, supposing that the producer maximizes intra-period profits in each period. A difference arises from section 4.3.3, however, because the intra-period profit maximizing price schedule used by the producer is non-linear. If the regulator sets a non-linear price for transport, PT (x), the residual demand facing a monopoly producer for each consumer of type θ is m(x, θ) =

4.5. TRANSMISSION AND DISTRIBUTION

111

θ − bx − PT (x). As seen by the producer, the marginal consumer at each x-th unit is defined by θˆ = PG (x) + bx + PT (x). The number of consumers who purchase an x-th unit of gas when the producer price is PG (x) is given R θ¯ ¯ θ¯ − PG (x) − bx − PT (x)}. by n(x, PG (x)) = θˆ f (θ)dθ = (1/θ){ If the producer maximizes intra-period profit R x¯ without regard to resource constraints, the problem is Max Π(PG (x)) = 0 (PG (x)−d)n(x, PG (x))dx−K subject to PG (¯ x) = θ¯ − b¯ x − PT (¯ x). The producer’s first order condition provides the profit maximizing price schedule: PG (x) = 12 (θ¯+d−bx−PT (x)). To achieve a target linear price for delivered gas, the regulator must set the transportation schedule PT (x) such that PT (x) + PG (x) = PD . Setting PT (x) = (2PD − θ¯ − d + bx) causes the producer to choose the price schedule: PG = (θ¯ + d − bx − PD ), and results in the target price for delivered gas, PD constant for all x. The price for transport increases with x, just sufficiently to offset the downward slope of the monopoly producer’s price schedule. Again, as in section 4.3.3, if reserves are sufficiently large, regulated transport prices in early periods may be less than marginal cost or even negative. We may again be concerned to add an additional constraint concerning politically feasible pricing structures for transportation. For example, we could introduce constraints such as PT (x) ≥ c for all x, or a requirement that the transporter not make an intra-period loss. In early periods the constraint will bind the regulator, and only in periods closer to exhaustion can the regulator achieve the optimal price for delivered gas. Whether standard regulatory practice, (i.e. setting PT = c + g) improves or worsens welfare (relative to no regulation) is ambiguous in this setting. As the markup allowed for fixed costs (i.e. g) diminishes, interand intra-temporal prices tend toward the prices of the vertically integrated monopolist.

4.5

Transmission and Distribution

We have so far assumed a single gas transportation firm. In practice, the transmission pipeline and the distribution network are often separately owned monopolies. In the absence of regulation, the distributor and the pipeline form a bilateral monopoly, and under Nash bargaining pursue a joint profit maximization strategy. In the case of competitive producers, the distributor and the pipeline will exercise monopsony power to hold the well-head price of gas down to marginal cost. In the case of a monopoly producer, a trilateral monopoly exists in which all three firms may pursue the joint profit maximization strategy, dividing profits according to Nash bargaining.

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If just one of the distributor or pipeline is regulated, the remaining sector, acting with the production sector, takes the place in the earlier analysis of a monopolized production sector. If all firms and the regulator are constrained to use linear prices, the analysis of section 4.3.3 can be applied. When non-linear pricing is used, it is important that the regulator is able to influence the price structure for delivered gas. This is the case, for example when (i) only distribution is regulated; or (ii) only transmission is regulated and consumers purchase the transmission service separately from distribution and well-head gas. In these cases the analysis of section 4.4.3 can be applied, treating the unregulated sectors as a single profit maximizing monopolist. But the regulator is unable to influence the price structure of delivered gas if the only regulated sector is the pipeline, and the distributor purchases transmission services and sells delivered gas to consumers. In this setting the regulator can determines the total amount that the distributor pays for transmission services. The regulator cannot alter the form of consumer demand faced by the distributor for different ‘x’-th increments. The regulator can cause marginal welfare to rise at the rate of interest, but cannot induce the optimal rationing between consumers within each period. This is a case where regulation should be extended to either the price of distribution services, or the price of delivered gas. We can apply the same logic when comparing consumer access and producer access. Throughout we have assumed that it is consumers who purchase regulated transportation services, and purchase gas directly from producers. It is also possible that producers purchase regulated transportation services and sell delivered gas directly to consumers. If production is competitive, the regulator can achieve the optimal inter-temporal and intra-temporal rationing. If production is monopolized, the regulator can achieve the optimal inter-temporal rationing, but cannot offset the nonlinearity of the producer’s intra-temporal prices for delivered gas. Either consumer access or regulation of the price of delivered gas would be preferable to producer access when production is monopolized.

4.6

Conclusion

When production is competitive, ‘standard’ regulation is likely to be better than no regulation. As fixed costs diminish, standard regulation approaches the social optimum. We have suggested, however, an alternative regulatory strategy that will actually achieve the social optimum and exactly cover the transporter’s fixed costs. When production is monopolized we have also

4.6. CONCLUSION

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found a regulatory strategy that will deliver optimal prices for delivered gas. This strategy will be of little comfort, however, to countries that are dependent on foreign monopoly suppliers, since it depends on large rent transfers to the monopoly producer. Independently of the implications for access regulation, the analysis of the monopoly situation carries important implications concerning non-linear pricing by gas utilities. Gas regulators have typically drawn upon experience from electricity or telecommunications pricing when reviewing non-linear pricing. Our analysis suggests that exhaustibility of gas reserves implies quite different pricing strategies. In particular, exhaustibility implies that to maximize social welfare the price of delivered gas should be linear in each period: a linear price is the most efficient means of rationing a fixed quantity. This contrasts with most observed regulatory policies that permit non-linear pricing as a supposedly efficient (or least inefficient) means of covering fixed costs. The information required to implement optimal regulatory strategies is information that would be required for standard regulation. For the case of competitive production, the transporter’s marginal cost and the interest rate are the only information needed to ensure that the transport price rises at the rate given by (4.5). The value of fixed costs and the estimated date of exhaustion are additionally required if fixed costs are to be covered exactly. All of these data are commonly used in standard regulation, where a markup over marginal cost is given to amortize fixed costs over the life of the gas reserves. Moreover, the proposed regulatory strategy is forgiving, in the sense that if the regulator is mistaken about the optimal exhaustion date, the socially optimal prices of delivered gas may still be achieved. When production is monopolized, achieving optimal prices for delivered gas is more information-intensive for the transportation regulator. In addition to information required for the competitive case, the regulator needs information concerning the producer’s cost structure in order to calculate the optimal price path for delivered gas. Further, the regulator needs as much information about demand conditions as the firm itself in order to offset the producer’s intra-period non-linear pricing. If these informational requirements seem prohibitive, the alternative of standard regulation is even less attractive. Standard regulation may actually diminish welfare relative to an unregulated industry. If fixed costs are relatively small standard regulation merely approximates the outcome of an unregulated industry. Our analysis can be extended in many directions. The literature on exhaustible resources incorporates many features such as marginal cost or demand that evolves over time, uncertainty over the extent of reserves, the effect of discovery of new reserves and more thorough analyses of market

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power than the two extremes (monopoly and perfect competition) considered here. Incorporating such features can have substantial consequences for the optimal path of delivered gas – for example, repeated discoveries of additional reserves may result in a downward price path. The literature on access regulation incorporates features such as more complicated pipeline networks, capacity constraints on pipelines, private information concerning costs and more complicated regulatory games in which the market structure responds to the regulatory strategy. Clearly more work is required to integrate these branches of the literature.

Bibliography Cremer, H., Gasmi, F. & Laffont, J.-J. (2003), ‘Access to pipelines in competitive gas markets’, Journal of Regulatory Economics 24(1), 5–33. Cremer, H. & Laffont, J.-J. (2002), ‘Competition in gas markets’, European Economic Review 46(4–5), 928–935. Goldman, M., Leland, H. E. & Sibley, D. S. (1984), ‘Optimal nonuniform prices’, Review of Economic Studies 51(2), 305–319. Gomez-Lobo, A. & Foster, V. (1999), The 1996-97 gas price review in Argentina, Public Policy for the Private Sector, Note 181, World Bank. Oviedo Arango, J. D. (2000), ‘Analysis of optimal tariff schedules in gas transportation under open access’, Revista de Economia de la Universidad del Rosario III, 93–138. Wilson, R. B. (1997), Nonlinear Pricing, Oxford University Press.

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