SO 2 policy and input substitution under spatial monopoly

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1 SO 2 policy and input ubtitution under patial monopoly Shelby Gerking a, Stephen F. Hamilton b, * a Univerity of Central Florida, Orlando, FL 32816, United State b California Polytechnic State Univerity, San Lui Obipo, CA 93407, United State Following the U.S. Clean Air Act Amendment of 1990, electric utilitie dramatically increaed their utilization of low-ulfur coal from the Powder River Bain (PRB). Recent tudie indicate that railroad hauling PRB coal exercie a ubtantial degree of market power and that relative price change in the mining and tranportation ector were contributing factor to the oberved pattern of input ubtitution. Thi paper ak the related quetion: To what extent doe more tringent SO 2 policy timulate input ubtitution from high-ulfur coal to low-ulfur coal when railroad hauling low-ulfur coal exercie patial monopoly power? The quetion underpin the effectivene of incentive-baed environmental policie given the eential role of market performance in input, output, and abatement market in determining the ocial cot of regulation. Our analyi indicate that environmental regulation lead to negligible input ubtitution effect when clean and dirty input are highly ubtitutable and the clean input market i mediated by a patial monopolit. 1. Introduction Cap and trade ytem for pollution control are much heralded, and rightly o, for their ability to marhal market force to achieve pollution reduction at the lowet poible cot. An important apect governing the performance of market-baed approache to environmental problem i the ability of pollution market to align private incentive in the affiliated output, input and abatement market that interect with the policy. There i general conenu that the landmark ucce of the U.S. Clean Air Act Amendment of 1990, which achieved U.S. air quality objective at a fraction of the anticipated

2 cot (U.S. Department of Energy, 2000), wa driven largely by input ubtitution among U.S. electric utilitie from high-ulfur coal to low-ulfur coal (ee, e.g., Carlon et al., 2000). The ubtantial degree of input ubtitution that occurred between thee coal depoit contributed to low SO 2 allowance price, thereby defraying cotly ocial adjutment that would otherwie have taken place in electricity and pollution abatement market. Over the period , coal production from highulfur depoit in the Illinoi Bain (Illinoi, Indiana, and Wet Kentucky) declined by 42%, while lowulfur coal production from the Powder River Bain (PRB) of Wyoming and Montana doubled and the number of utilitie burning PRB coal more than tripled. Thi paper examine the potential role of the cap and trade ytem for SO 2 emiion allowance in driving the oberved pattern of input ubtitution in U.S. coal market. In principle, the creation of a pollution allowance market hould timulate a coordinated et of change in the market interecting with environmental policy. To upport a ocially optimal reource allocation, allowance price mut be derived from an optimal et of adjutment in output market (electricity), abatement market (e.g., crubber ), and input market (high-ulfur coal, low-ulfur coal, natural ga, oil) that erve to equalize the marginal return acro activitie. Becaue empirical tudie of energy market generally find houehold electricity demand to be highly price inelatic (Rei and White, 2005), the ability to achieve environmental objective with minimal diruption in conumer market i facilitated by elatic upply condition in abatement and input market. For example, if coal depoit with different ulfur content are perfectly ubtitutable in electricity production and available at equal factor price, SO 2 reduction could be met largely through input ubtitution, without the need for ubtantial invetment in abatement equipment or output adjutment. In the event that the upply of low-ulfur coal wa perfectly elatic, environmental objective could be obtained at zero cot. The main point of thi paper i that patial market power over low-ulfur coal deliverie to electric plant forecloe input ubtitution poibilitie that would otherwie occur in repone to SO 2 regulation. While it i evident that the effectivene of environmental policy depend on the preence of market power in the market for alternative input, our analyi highlight the perniciou effect of input market imperfection when deliverie are mediated by a patial monopolit. Indeed, in the cae of perfectly ubtitutable coal and perfectly elatic upply by mine, we how SO 2 policy to be completely ineffective in timulating input ubtitution between high- and low-ulfur coal. The direct implication of thi finding i that private incentive introduced by a market-baed policy for SO 2 emiion appear to be largely confined to electricity market, abatement market, and input market for alternative fuel beide low-ulfur coal. The indirect implication of thi finding i that much of the apparent ucce of the U.S. Clean Air Act Amendment in achieving environmental objective at lower-than-anticipated cot wa due to input ubtitution from high-ulfur coal to low-ulfur coal among electric utilitie that had little, if anything, to do with environmental policy. Intead, it appear that the timing of SO 2 policy wa imply erendipitou. A Ellerman and Montero (1998) oberve, the U.S. Clean Air Act Amendment of 1990 coincided with a period of ubtantial decline in the real price of mine mouth PRB coal and rail tranportation. Thee feature, unlike SO 2 policy, are capable of timulating the oberved, ubtantial increae in aggregate deliverie of low-ulfur coal by a railroad monopoly market. We frame our obervation around a model of patial monopoly power in the market for low-ulfur coal. The potential for railroad to exercie market power in the low-ulfur coal market i an important conideration, becaue virtually all low-ulfur coal in the U.S. i hauled eatward from Wyoming by a handful of railroad erving PRB mine. 1 Among railroad erving thee line, two firm Burlington Northern Santa Fe (BNSF) and Union Pacific (UP) currently initiate all tranportation of PRB coal. 2 The potential for railroad to exercie patial market power ha been recognized ince at leat the cae of Standard Oil (ee Granitz and Klein, 1996), and evidence exit that railroad hauling PRB coal out of 1 Alternative mode of coal tranportation out of the PRB either are not cot-effective (e.g., trucking) or ele do not exit (e.g., barge and coal lurry pipeline). 2 The Chicago and Northwetern Railroad, which entered the Wyoming coal tranportation market in the early 1980, no longer erve the PRB. Alo, the BNSF and UP do not alway complete deliverie to all power plant becaue coal i frequently tranhipped via other line.

3 Wyoming indeed exercie a coniderable degree of market power (Wolak and Koltad, 1988; Bue and Keohane, 2007). A large literature ha emerged to examine the potential for imperfection in permit market to erode the gain of market-baed environmental policie (ee, e.g., Hahn, 1984; Jokow et al., 1998; Montero, 1999, 2002). In light of thi fact, it i omewhat urpriing to note that little attention ha been focued on market performance in the market for abatement equipment and alternative input that interect with cap-and-trade policie. Our analyi bridge thi gap by examining the eential role of tranportation market for alternative input in mediating the performance of market-baed environmental policie. The remainder of the paper i organized a follow. In the next ection, we develop a imple model of patial intermediation by a monopoly railroad in the low-ulfur coal market. In Section 3, we calculate the effect of SO 2 policy on the aggregate quantity of PRB coal delivered to electric utilitie in the pecial cae of perfectly ubtitutable coal. In Section 4, we conclude with ome brief comment on the cae of differentiated coal depoit and outline direction for further reearch. 2. The model We conider a dominant firm-competitive fringe market tructure in which utilitie either buy lowulfur coal from a monopoly railroad or purchae high-ulfur coal from a competitive indutry. To focu the model on the implication of SO 2 policy for the low-ulfur coal market, we limit the fuel portfolio available to utilitie to two potential fuel input low-ulfur coal and high-ulfur coal and uppre the poibility of electric plant meeting the regulation through other compliance option. Implicitly, we are auming that coal-fired utilitie cannot burn natural ga or oil, and that witching from high-ulfur coal to low-ulfur coal i more cot-effective than avoiding fuel-witching altogether by intalling potcombution abatement equipment ( crubber ). 3 Although light difference exit in practice in the energy and ulfur content of each type of coal, depending on the particular mine from which the coal i ourced, we implify the analyi by treating depoit of each type of coal a uniform in compoition. In the Midwetern U.S., high-ulfur coal i generally procured from depoit in reaonably cloe proximity to individual utilitie. Relative to the market for low-ulfur coal, freight rate make up a maller percentage of delivered price for high-ulfur coal, reulting in delivered price that do not vary ubtantially acro location in practice. To focu the model on the low-ulfur coal market, we aume that high-ulfur coal i ubiquitouly available at a contant delivered price of p h. Monopoly price for low-ulfur coal, in contrat, vary over pace according to proximity of the utility demanding low-ulfur coal to the ource mine Utility demand for PRB coal Demand facing railroad for deliverie of low-ulfur coal i derived from the profit-maximization problem of electric utilitie who eek to produce energy from alternative fuel input. To clarify our obervation on the effect of a patially intermediated input market, we aume the electricity market i competitive and utilitie are homogeneou in all repect apart from their location in pace. 4 Utilitie are arrayed patially along the rail line and face different freight rate, and hence different delivered price, for PRB coal. The problem facing a utility at ditance x i to elect a quantity of PRB coal, q l (x), and a quantity of high-ulfur coal, q h (x), to maximize profit ubject to environmental policy on SO 2 emiion. Let denote the SO 2 emiion coefficient for high-ulfur coal, o that SO 2 emiion for a utility at ditance 3 A Carlon et al. (2000) oberve, input ubtitution at U.S. electric utilitie from high-ulfur coal to low-ulfur coal ha proven to be ubtantially more cot-effective a a method of emiion control than the ue of pot-combution abatement technology. 4 The implication of the model regarding incentive for fuel ubtitution among cot-minimizing electric utilitie are qualitatively imilar to thoe which would arie in a regulated monopoly electricity market. Under regulated monopoly, the ability of utilitie to pa-through cot change into electricity rate doe alter the output effect of SO 2 regulation in electricity market. Extending the analyi to the electricity ector, which would complicate the model by adding an independently regulated conumer pricing tructure, would provide a greater apparatu to ift through without fundamentally altering incentive for fuel ubtitution among utilitie eeking to minimize fuel cot.

4 x can be defined a e(x)=q h (x). Under cap-and-trade policy, each utility i given an initial endowment of SO 2 allowance (poibly zero) and mut purchae an SO 2 allowance for each unit of emiion above thi level at the permit price, denoted l. The market price of an SO 2 allowance i taken a given by each firm, but i determined endogenouly by the ize of the regulatory cap on emiion in the market. We repreent the patial market for coal input by arraying all electric utilitie on a unit line egment and denote total SO R R emiion a E ¼ 0 eðxþdx ¼ 0 q hðxþdx. The um of all SO 2 allowance held by utilitie mut meet the regulated level of E under the emiion cap, which we denote by E 0. Let p e denote the electricity price and p l (x) denote the delivered price of PRB coal at ditance x. A utility with an initial endowment of e 0 allowance maximize profit of p u ðxþ ¼ pe f ðq l ðxþ; q h ðxþþ p l ðxþq l ðxþ p h q h ðxþþlðe 0 eðxþþ; ubject to non-negativity contraint on the ue of low-ulfur coal, q l ðxþ0, and high-ulfur coal, q h ðxþ0, and the link between high-ulfur coal ue and SO 2 emiion, e(x)=q h (x). An electric utility that i a net eller of emiion allowance atifie e 0 eðxþ > 0, and a utility that i a net purchaer of emiion allowance atifie e 0 eðxþ < 0. The firt-order neceary condition for a maximum are G l p f l ð:þ p l ðxþ 0; G l q l ðxþ ¼0; (1) e G h p f h ð:þ p h l 0; G h q h ðxþ ¼0; (2) e where f l ð:þ and f h ð:þ denote the marginal product of each type of coal in electricity production. Let p =p h +l denote the effective price of high-ulfur fuel, which i the gro price of an input of highulfur coal incluive of it implicit SO 2 allowance requirement. Notice that the effective price of highulfur coal i independent of both ditance and the initial allocation of SO 2 allowance; hence the input mix at each utility between low-ulfur coal and high-ulfur coal depend only on the relative price, p l (x) and p. At an interior olution, the input mix for each utility equate it marginal rate of technical ubtitution with the ratio of price, p l (x)/p. In the event that delivered price for low-ulfur coal rie over ditance from the PRB, utilitie along the rail line faced with a contant effective price of highulfur coal moothly ubtitute away from low-ulfur coal and toward high-ulfur coal over pace to an extent that depend on the elaticity of ubtitution between thee fuel. Depending on the value of the elaticity of ubtitution, a corner olution i alo poible. Prevailing evidence ugget that low- and high-ulfur coal are highly ubtitutable input at electric plant (Gerking and Hamilton, 2008), implying a large elaticity of ubtitution. In the cae of perfect ubtitute, normalizing unit for the energy (BTU) content of each type of coal, we can define f l ð:þ ¼ f h ð:þ ¼ f 0 ð:þ and adjut unit accordingly. By inpection of expreion (1) and (2), the conditional (invere) demand for low-ulfur coal in the cae of perfectly ubtitutable fuel i given by pðq l ðxþþ for pðq l ðxþþ p and zero otherwie. Let D l ð p e; p l ðxþ; pþ and D h ð p e; p l ðxþ; pþ denote the demand function for low- and high-ulfur coal that olve condition (1) and (2) for the utility at location x. The demand for each type of coal at the electric plant depend on the electricity price, the delivered price of PRB coal and the effective price of high-ulfur coal The rail ector Our model extend the framework of Greenhut and Ohta (1972) to conider patial market power by a monopoly railroad over an endogenouly determined ervice region. The railroad purchae lowulfur coal at a contant price of w per unit from competitive mine located at the origin of a rail line and deliver it at a marginal cot of t per unit of ditance (x) to identical electric utilitie, which are aumed for analytic convenience to be uniformly ditributed along a rail line of unit length. 5 The total 5 Baed on proprietary railroad data in the market for PRB coal, Gerking and Hamilton (2007) conclude that the cot of hauling one ton of coal one unit of ditance i contant in the ervice region for PRB coal.

5 cot of delivering coal to a utility at ditance x i txd l ð p e ; p l ðxþ; p Þ, and the total cot of procuring and R delivering an aggregate quantity Q ¼ N D l 0 ð pe; p l ðxþ; pþdx of PRB coal in the market accordingly i cðqþ ¼ Z N 0 ðw þ txþd l ð p e; p l ðxþ; pþdx; where N1 i the extenive margin of ervice. Fixed cot, which are neceary to jutify the exitence of railroad market power, play no role in the analyi and are conequently omitted. The railroad problem i to elect the number of utilitie to erve, N *, and a delivered price p l ðxþ for each utility in the ervice region x 2½0; N Š. The railroad profit i Z N pðw; t; p Þ¼ ð p l ðxþ tx wþd l ð p ; p l ðxþ; p Þdx: (3) e 0 The firt-order neceary condition for a profit maximum are completely characterized by the Euler equation, D l ð p e ; p l ðxþ; p Þþðp l ðxþ tx wþd l l ð p e; p l ðxþ; p Þ¼0; forx 2½0; nš; (4) a boundary condition on interior pricing, D l ð p e ; p l ðxþ; p Þ¼q ð p Þ; for x 2½n; NŠ; (5) and the tranverality condition ð p l ðnþ tn wþd l ð p e ; p l ðnþ; p Þ¼0; (6) where 0 < q ð p Þ i a fixed quantity delivered to location nxn. Condition (4) (6) have traightforward interpretation. Condition (4) define the optimal monopoly price for delivery of PRB coal to a utility located at ditance x. It tate that the optimal monopoly price at ditance x be et o that the percent mark-up of delivered price over marginal cot, tx þ w, i equal to the reciprocal of the demand elaticity. Delivered price are higher for more ditant utilitie than for utilitie in cloer proximity to the ource of PRB coal becaue the marginal cot of delivery rie in x, wherea price-cot margin narrow for more ditant utilitie a demand become more elatic at higher delivered price. A delivered price rie over pace, utility demand for PRB coal decreae until one of two thing happen: (i) a minimum hipment ize i hit that atifie Eq. (5);or (ii) demand fall moothly to zero until the freight rate, p l ðnþ w, equate with unit tranportation cot, tn, at the ditance defined by Eq. (6). Eq. (6) define the location of the critical utility, x=n, beyond which hipment to more ditant utilitie no longer contribute poitively to railroad profit. Becaue a monopoly railroad can patially price dicriminate, railroad ervice continue until the delivered price i driven to marginal cot and profit fall to zero on the extenive margin of ervice. There are two reaon why a minimum hipment ize may bind on deliverie over pace in Eq. (5). Firt, a minimum hipment quantity may emerge due to integer contraint, for intance when it i not practical to deliver a fraction of a rail car of coal. 6 Second, the non-negativity contraint in utility demand Eq. (2) may bind, in which cae a monopoly railroad might maintain delivery price at the corner a deliverie continue over pace. For example, when low- and high-ulfur coal are perfect ubtitute, the delivered price for low-ulfur coal rie over ditance to p and then remain contant at that level until profit fall to zero on the extenive margin of ervice (ee below). In either cae, freight price et by a monopoly railroad would rie over pace in an interior pricing region over ditance 0<x<n, and then remain contant at a level neceary to maintain demand over the remaining ditance in the ervice region, nxn. Hereafter, we refer to the region of uncontrained monopoly pricing a region I and the region of contrained monopoly pricing a region II. Conider the cae of monopoly freight rate, f ðxþ ¼ p l ðxþ w, in the cae of perfectly ubtitutable fuel. A in a conventional dominant firm-competitive fringe model with perfectly elatic upply, demand for low-ulfur coal become horizontal at the effective price of high-ulfur coal, p, generating 6 Gerking and Hamilton (2008) claify hipment of le than 50 rail car of PRB coal a intermittent hipment ued for tet burn, which ugget deliverie do not moothly fall to zero along the rail line in practice.

6 a dicontinuity in the marginal revenue chedule for low-ulfur coal. Equilibrium freight rate in region I are determined by the interection of marginal revenue and marginal tranportation cot for PRB coal. Freight rate rie moothly over ditance in thi region until the delivered price of PRB coal rie to p. At thi point, the marginal revenue function facing the railroad i dicontinuou; the railroad can continue erving utilitie at further ditance, but only at a delivered price at or below p. Demand and marginal revenue are horizontal at price p in region II, becaue utilitie have perfectly elatic demand for low-ulfur coal at thi price. The ability to patially price dicriminate enure that the railroad continue erving utilitie in region II: At ditance x=n, a freight rate of p l ðnþ ¼ p more than compenate the railroad for the marginal cot of tranporting it, p l ðnþ tn w > 0, o that continuing ervice to utilitie at ditance beyond x=n contribute poitively to profit. Service continue to region II utilitie until tranportation cot rie at location x=n to meet the terminal condition (6). The econd-order neceary condition for a maximum are the Legendre condition, 2D l ð p ; p l ðxþ; p Þþðp l ðxþ tx wþd l ð p ; p l ðxþ; p Þ0; (7) l e ll e and the endpoint condition (ee Caputo and Wilen, 1995), F td l ð p e; pl ðnþ; pþ0: (8) Throughout the remainder of the paper, we aume thee condition are trictly met. Let p ðx; t; w; p ; p Þ; n ðt; w; p ; p Þ, and N l e e ðt; w; p e; pþ denote the olution to (4) (6). With exogenou p, the comparative tatic for the delivery chedule for region I and region II utilitie can then be derived from (4) and (5). Conider, firt, the delivered price chedule over ditance in region I. Dropping argument for notational convenience, ue of the implicit function theorem on (4) l td l ¼ > 0; (9) l 2D l þðp tx wþd l l l ll where the inequality hold by condition (7). A the marginal cot of delivering a unit of coal increae over ditance, the delivered price of PRB coal rie. The outcome for the patial pricing i a follow. The optimal freight chedule, f e e ðx; t; w; p ; p Þ¼ p l ðx; t; w; p ; p Þ w; (10) rie gradually over ditance by (9) until the region I boundary condition i met in Eq. (5), at which point deliverie continue at contant price until a ditance i reached where the freight rate equate with unit tranportation cot, f ðn ðt; w; p e; pþ; t; w; p e; pþ¼tn ðt; w; p e; pþ, on the extenive margin of ervice. At thi point, deliverie ceae. Fig. 1 compare the freight chedule under monopoly price dicrimination to that which would emerge in a competitive tranportation ector. Under competition, the freight rate, f c ðxþ ¼tx rie Fig. 1. Freight chedule over ditance under monopoly and competition.

7 moothly from zero at a rate of t over ditance until a price i reached where the delivered price meet the terminal condition (6). Under monopoly pricing, the freight rate i piecewie concave, beginning at a higher level, and ubequently riing more lowly over ditance. By Eq. (6), the terminal ditance, N *, mut coincide in each cae. How do change in SO 2 policy alter the aggregate utilization of PRB coal when input ubtitution i mediated by a monopoly railroad ector? The effect of a binding regulatory cap on SO 2 emiion i to raie the effective price of high-ulfur coal, which in turn caue utilitie to change the cotminimizing input mix in Eq. (1) and (2) and to decreae electricity upply. Much of the effectivene of environmental policy in achieving environmental objective with minimal conumer harm depend on the ability of utilitie to ubtitute away from high-ulfur coal and toward cleaner-burning input of low-ulfur coal to mitigate the decreae in energy upply a allowance price rie in repone to the policy. We denote the aggregate quantity of PRB coal delivered by Z Q ¼ D l ð p ; p ðxþ; p Þdx þðn n Þq ð p Þ: (11) n l e l 0 Differentiating Eq. (11) with repect to the allowance price and making the ubtitution ð p ; p ðnþ; p Þ¼q ð p Þ from Eq. (5) yield, D l e l Z n D ð p Þ ¼ ð p ; p ðxþ; p Þdx þ q ð p Þ þðn e l n ; l In general, the ability of SO 2 policy to timulate input ubtitution among utilitie toward lowulfur coal depend on three effect in Eq. (12). On the intenive margin of ervice, the rie in the effective price of high-ulfur coal increae input demand for low-ulfur coal among region I utilitie, which change the aggregate quantity of PRB coal delivered to region I utilitie by R n D l ð p ; p 0 e l ðxþ; pþdx unit. On the extenive margin of railroad ervice, the rie in the effective price of high-ulfur coal lead to two additional effect. Firt, there i a market expanion effect, which repreent the outward hift in the extenive margin of ervice to more ditant utilitie. The expanion effect i given by q ð pþ@n =@ p in (12). Becaue the extenive margin of railroad ervice i independent of market tructure (ee Eq. (6)), the expanion effect i identical under monopoly and competitive freight pricing. Second, under monopoly, there i a contraction effect, ðn n Þ@q ð pþ=@ p, which repreent a decreae in the equilibrium quantity of PRB coal delivered to region II utilitie. The contraction effect arie when the minimum hipment ize in Eq. (5) decreae in repone to an increae in the equilibrium price of low-ulfur coal charged to region II utilitie. The relative magnitude of the expanion and contraction effect depend on the manner in which the minimum hipment contraint enter Eq. (5). If the minimum hipment quantity i independent of the delivered price of low-ulfur coal, for intance if the minimum hipment quantity i 50 rail car irrepective of the delivered price, then there i no contraction effect. Alternatively, a we how below in the cae of perfectly ubtitutable input, if the minimum hipment quantity i elected to prevent utilitie from witching to high-ulfur coal in the PRB ervice territory, then the contraction effect operate againt the expanion effect to limit aggregate deliverie of low-ulfur coal to region II utilitie. Making ue of the implicit function theorem on Eq. (4), the effect of a marginal change in the price of SO 2 allowance on delivered price of low-ulfur coal in region I p p ðxþ ðd l þðp ðxþ tx wþd l l l p 2D l þðp ðxþ tx wþd l l l ll ¼ ¼ ; (13) which take the ign of D l þðp l ðxþ tx wþd l l by (7). Eq. (13) tate that the delivered price of PRB coal to each utility in region I rie in repone to a marginal increae in the SO 2 allowance price provided that the outward hift in PRB demand (D l > 0) i not coupled with a ufficiently trong

8 rotation effect that make PRB demand more price elatic. Making ue of (13), the effect of an allowance price increae on the quantity old to each utility in region I l ð p e ; p l ðxþ; p D l þ D l p l ðxþ Dl l Dl þðp l ðxþ tx wþðdl Dl ll Dl l Dl l ¼ Þ l p 2D l þðp ðxþ tx wþd l l e e l e e e l l ll In general, thi equation can take either ign; however, in the cae of linear demand and imperfect ubtitute, the delivered quantity increae for each utility in region I. To derive the effect of a change in SO 2 policy on the extenive margin erved by the railroad, ubtitute p ðx; t; w; p ; p Þ and N ðt; w; p ; p Þ into Eq. (6) to get p ðn ð:þ; t; w; p ; p Þ tn ð:þ w Dð p ; p ðn ð:þ; t; w; p ; p Þ; p Þ0 Implicitly differentiating thi equation and making ue of (4) ð p ðn Þ tn wþd l ð p ; p ðn Þ; p Þ ¼ > tdð p ; p Þ; p Þ l e l e ðn l An increae in the price of SO 2 allowance erve to expand the railroad ervice region. The foregoing analyi iolate the input ubtitution effect of SO 2 regulation in the patially intermediated market for low-ulfur coal by uppreing abatement market and electricity market effect. In repone to SO 2 policy, the equilibrium increae in the effective price of high-ulfur coal integrate each of thee repone. Following a rie in the input price of high-ulfur coal, utilitie burning thi fuel repond by upplying a lower quantity of electricity and engaging in greater abatement activitie. Conumer electricity price rie in repone, which in turn would timulate the ue of low-ulfur coal in Eq. (1) in addition to the direct input ubtitution motivation reulting from change in relative input price. 7 In the next ection, we characterize the input ubtitution effect of SO 2 regulation in the cae of perfectly ubtitutable fuel. Thi i an important cae, becaue the elaticity of ubtitution between high- and low-ulfur coal i likely to be quite high. The reaon i that generating unit at mot U.S. power plant are engineered to burn different depoit of coal more or le intenively a relative fuel price change. Coal obtained from different mine are commonly mixed with each other in an increaingly diverified fuel portfolio, and blending of low- and high-ulfur coal ha occurred at many power plant ince the early Perfect ubtitute To examine the role of patial market intermediation on the performance of the low-ulfur coal market, conider the cae in which low-ulfur coal and high-ulfur coal are perfect ubtitute. Normalizing unit to align the BTU content of each type of coal, we conider difference between coal depoit a ariing only from difference in ulfur content, o that f l ð:þ ¼ f h ð:þ ¼ f 0 ð:þ in expreion (1) and (2). For the cae of perfectly ubtitutable fuel, it i analytically convenient to recat the profitmaximization problem of a monopoly railroad a a quantity choice problem. From expreion (1) and (2), the conditional (invere) demand for low-ulfur coal facing the railroad i given by pðq l ðxþþ for pðq l ðxþþ p and zero otherwie. Railroad profit, accordingly, i Z n Z N pðw; t; p Þ¼ ð pðq l ðxþþ tx wþq l ðxþdx þ ð p tx wþq dx; 0 n where q olve pðq Þ¼ p in utility demand. 7 The magnitude of the energy price effect would differ according to whether the price adjutment in electricity market occurred through a decreae in electricity upply (a modeled here) or according to pa-through relationhip in a regulated monopoly electricity market. 8 Roughly 25% of coal-fired generating unit burn a blend of PRB and eatern coal and blending generally doe not occur at utilitie in cloe proximity to PRB mine (Gerking and Hamilton, 2008).

9 The firt-order neceary condition for a profit maximum are pðq l ðxþþ þ q l ðxþ p 0 ðq l ðxþþ tx w ¼ 0; forx 2½0; nš; (4 0 ) the region I boundary condition, pðq l ðxþþ ¼ pðq Þ¼ p ; forx 2½n; NŠ; (5 0 ) and the tranverality condition, ð p tn wþq ¼ 0: (6 0 ) Expreion (4 0 ) (6 0 ) are analogou to expreion (4) (6). The delivery chedule i et to equate marginal revenue with marginal cot for region I utilitie in (4 0 ). Delivered price rie moothly over thi initial portion of the ervice region until ome ditance, n *, i reached where pðq l ðn ÞÞ ¼ p in (5 0 ), whereupon price remain at thi level preempting utilitie from witching into high-ulfur coal until a ditance i reached on the extenive margin of ervice where profit i driven to zero. At the extenive margin in (6 0 ), railroad deliverie of PRB coal ceae, and utilitie at further ditance on the line egment burn high-ulfur coal. In equilibrium, the optimal freight chedule ha two ditinct patial region. In region I, utilitie purchae a ufficiently large quantity of PRB coal that interior monopoly price obtain, pðq l ðxþþ p. At ditance n *, the uncontrained monopoly price rie to p ; however, profit i till poitive at thi utility becaue of the dicontinuity in the marginal revenue chedule. 9 Becaue patial price dicrimination i poible, the monopoly railroad continue to erve more ditant region II utilitie, but doe o under the binding contraint that pðq Þ¼ p. Region II deliverie continue to the ditance N *, where p equate with marginal tranportation cot, tn þ w, and profit i fully diipated in (6 0 ). Next conider the effect of a change in the price of SO 2 allowance on railroad hipment of lowulfur coal. The aggregate quantity of PRB coal delivered by the railroad i Z Q ¼ q ðxþdx þðn n Þq ð p Þ: (11 0 ) n l l 0 Differentiating Eq. (11 0 ) with repect to the allowance price (l) and factoring term yield, @N l ð pþ ¼ ðxþdx þ q ðnþ þðn n Þ ; ( p 0 which i analogou to Eq. (12). Notice that the firt term on the right hand ide of Eq. (12 0 ) vanihe in the cae of perfect ubtitute, becaue demand for low-ulfur coal by utilitie in the uncontrained monopoly pricing region i independent of p. Nonethele, an increae in the effective price of high-ulfur coal create an expanion effect in the PRB coal market, which i the econd term in the quare bracket of (12 0 ). The expanion effect can be derived by ubtituting N ðt; w; pþ into Eq. (6 0 ) to get p tn ðt; w; p Þ w ¼ 0. Implicitly differentiating thi equation =@ p ¼ 1=t, o that the expanion effect i given q l ðnþ ql ðnþ ¼ p t The expanion effect of SO 2 policy in (14) repreent the ale of low-ulfur coal to utilitie entering the extenive margin of railroad ervice in repone to SO 2 policy. An increae in the allowance price of dl unit raie the price of high-ulfur coal by dl unit, which timulate an expanion on the extenive margin of railroad ervice of (/t)dl unit of ditance, raiing the total quantity of PRB coal deliverie by ql ðnþ=t dl unit. The expanion effect of SO 2 policy i identical under competition and monopoly freight pricing, becaue the terminal condition (6 0 ) i identical in each cae and q ðn l Þ¼ q ðn Þ¼q in equilibrium. l (14) 9 * Formally, pðq Þ tn w ¼ q p 0 ðq Þ > 0atx=n by Eq. (4 0 ), which implie ð pðq Þ tn wþq > 0.

10 The contraction effect can be found by ubtituting q ¼ q ðn Þ into boundary condition (5 0 ) to get pðq Þ¼ p. Dropping argument for notational convenience and implicitly differentiating thi equation =@ p ¼ 1= p 0, which yield a contraction effect q ðnþ N l n ¼ þ t p ð pþ ðn n Þ ðn n Þ ¼ : p p 0 An increae in the allowance price of dl unit raie the price of high-ulfur coal by dl unit, which bid up delivered price for low-ulfur coal along the utility demand curve, reducing the quantity delivered to each of the N * n * region II utilitie erved by the railroad by ð= p 0 ðq ÞÞdl unit. Thi contraction effect reult in a decreae in the total quantity of PRB coal deliverie of ððn n Þ= p 0 ðq ÞÞdl unit in the railroad ervice region. Summing term in (14) and (15) give Next, ubtitute N * from (6 0 ) into Eq. (15) to q l ðnþ p 0 þ p w n t ¼ ¼ tp 0 where the latter equality hold by inpection of (4 0 ). When patial market for low-ulfur coal are mediated by a monopoly railroad ector, environmental policie that raie the price of SO 2 allowance are incapable of timulating aggregate input ubtitution from high-ulfur coal to perfectly ubtitutable, low-ulfur coal. To better undertand thi outcome, conider the cae of linear demand among electric utilitie for coal, which i depicted in Fig. 2. Fig. 2 how the delivered quantity chedule over ditance in the ervice region for low-ulfur coal, x 2½0; N Š, and the remaining location of utilitie burning high-ulfur coal x 2ðN ; 1Š. Prior to environmental regulation, the delivered quantity chedule decline over ditance at rate t/2p 0 in region I(eeEq.(4 0 )), and then remain contant thereafter at q in region II. Region I extend outward from the ource mine to the ditance n and the length N n accordingly define the extent of region II. The total delivered quantity of PRB coal i the area under the quantity chedule q 0 (x * ). The total quantity of high-ulfur coal burned by electric utilitie um the quantity of coal demanded by utilitie located at ditance 1 N *. Becaue each plant outide the PRB ervice territory burn q0 unit of coal at price p,the total quantity of high-ulfur coal ued by all plant i ð1 N0 Þq 0, which i repreented in the figure by the area N 0 bc1. Prior to SO 2 regulation, total emiion are E 0 ¼ ð1 N 0 Þq 0. l (16) Fig. 2. Total quantity of PRB coal delivered under monopoly freight pricing.

11 After cap-and-trade regulation, total SO 2 emiion decreae to ome regulated level, E 1 < E 0. The decreae in indutry SO 2 emiion occur through a combination of input price effect that reduce the ue of high-ulfur coal by utilitie, q 1 < q 0, and fuel ubtitution effect from high-ulfur coal to PRB coal among utilitie on the extenive margin of ervice, N 1 > N0. For an arbitrary emiion cap of E 1 unit, the total amount of high-ulfur coal ued in the regulated indutry i repreented in Fig. 2 by the haded region, area N1 gh1. In equilibrium, total emiion atify E1 ¼ ð1 N1 Þq 1. Utilitie located at ditance between N0 and N1 comply with the regulation by ubtituting away from high-ulfur coal to PRB coal and elling their SO 2 allowance to utilitie located at greater ditance from the ource mine for PRB coal. The outward expanion of the ervice region for PRB coal drive up the delivered price of PRB coal, and the expanion of the PRB ervice territory continue to ditance N1 where the zero profit condition on the extenive margin of the railroad ervice region clear individual input demand for the remaining 1 N utilitie at the quantity (q ) Notice that the permit price that emerge in the SO 2 allowance market i independent of market tructure in the PRB tranportation ector. The reaon i that the permit price i driven by fuelwitching behavior at the extenive margin of railroad ervice (region II) and utility demand for PRB coal i perfectly elatic for thee utilitie. The quantity of high-ulfur coal purchaed by each utility located in the region 1 N1 mut clear the individual input demand at a level (q 1) that exactly allocate aggregate SO 2 emiion to meet the cap, and the effective price of high-ulfur coal, p, mut rie to clear demand at thi quantity. After cap-and-trade regulation on SO 2, the delivered quantity chedule for PRB coal i depicted in the figure by q 1 (x * ). The change in the total delivered quantity of PRB coal in repone to SO 2 regulation can be een in Fig. 2 a the um of the expanion effect, area N0 fgn1, and the contraction effect, area abfe. To ee why thee area mut be equal in the cae of perfectly ubtitutable coal, conider the linear (invere) demand function p(x)=a bq(x). In thi cae, the delivered quantity to a utility at ditance x=0iq(0)=a/2b by Eq. (4 0 ). The delivery quantity decline over ditance at rate t/2b in region I, and then remain contant thereafter at q in region II. Becaue the total ervice region expand by 1/t, the magnitude of the expanion effect i q 1 =t. The contraction effect can be decompoed a the area of the rectangle abfd le the triangle ade. The area of the rectangle i given by ðn0 n0þðq0 q1þ. The lope of the quantity chedule i t/2b, o that the quantity decreae along rail line of length n1 n0 ¼ 2=t i given by (q0 q 1)=1/b. The length of the region II ervice area, N0 n 0, can then be recovered in the linear cae from Eq. (4 0 ) (6 0 ). Evaluating (4 0 ) at n0 give a 2bq 0 ¼ tn0. Making ue of (5 0 ), thi implie p bq 0 ¼ tn 0. From (6 0 ), p ¼ tn0, and combining thee equation and canceling term give N0 n0 ¼ bq 0 =t. The area of rectangle abfd i thu q 0 =t. Now conider the triangle ade. Noting that the bae of the triangle i n1 n0 ¼ 2=t, it area i ðq0 q1þ=t. The magnitude of the contraction effect, therefore, i q 0 =t ðq0 q1þ=t ¼ q 1 =t, an amount that exactly offet the expanion effect in the market. Our analyi predict no direct input ubtitution from high-ulfur coal to low-ulfur coal arie in repone to SO 2 regulation in the cae of perfectly ubtitutable fuel and patial monopoly pricing. Neverthele, output effect in energy market that lead to increaed electricity price would provide incentive for increaed ue of low-ulfur coal (and impact SO 2 allowance price). With downwardloping electricity demand, SO 2 policy reduce the total amount of coal combuted by electric utilitie, which increae electricity price and hift the derived demand for coal outward at each utility. Thi effect would exit apart from the input ubtitution incentive we have iolated here. In Fig. 2, the rie in electricity price would create a level effect in coal input demand, and the magnitude of the level effect at the margin (i.e., at quantity level q 1 ) would be capitalized into SO 2 allowance price. 4. Evidence from PRB coal market Our analyi predict that SO 2 policy ha little effect on the oberved input ubtitution pattern from high-ulfur to low-ulfur coal when the tranportation market i mediated by a patial 10 Formally, under an emiion cap of E 1 unit the extenive margin of PRB ervice mut atify N 1 ¼ 1 E1 =q 1, which can be ued together with Eq. (5 0 ) and (6 0 ) to recover q1 and N1 ¼ 1 E1 =q 1. For a binding emiion cap, the equilibrium allowance price olve Eq. (6 0 ): l ¼ðtN1 þ w p h Þ=.

12 monopolit. Two empirical quetion emerge from thi obervation. Firt, what doe the available evidence ugget about patial market power in the low-ulfur coal market? And, econd, if the oberved input ubtitution from high-ulfur to low-ulfur coal wa not driven by SO 2 policy, then what feature of the PRB coal market were reponible for the hift? There i coniderable evidence that railroad hauling PRB exercie market power. In an earlier paper (Gerking and Hamilton, 2008) we examine data from the Carload Waybill Sample obtained from the U.S. Department of Tranportation, Surface Tranportation Board, for evidence of railroad market power in PRB deliverie. Along 353 oberved tranportation route for PRB coal, all deliverie over the period were initiated by one of two railroad (BNSF and UP), with market hare of 55.3% for BNSF and 44.7% for UP in Supplementing thee data with information taken from Form 423 of the Federal Energy Regulatory Commiion (FERC), we link the quantity of coal received by a power plant on each hipment to the delivered price and the ource mine for the PRB coal, reulting in comprehenive tranactional information on the patial pricing of PRB coal over 1229 obervation (mine-utility pair). We examine Lerner indice, controlling for route-pecific effect, and find that the average value of the Lerner indice fall with ditance in the ample, a finding that concur with the patial pricing profile depicted in Fig Another prediction of the model i that SO 2 policy would extend the length of region I and contract the length of region II for a patial monopoly railroad, increaing market power overall. Controlling for route-pecific effect, we indeed find that the annual average value of L * were 15% larger in 1999 than in 1988 (a difference that i ignificantly different from zero at the 1% level). We etimate that roughly 90% of the power plant in the data et are region II plant that are ubject to freight rate equal to p w. For thee plant, an exogenou hock in unit tranportation cot in the railroad ector (t) ha no affect on freight rate, and marginal change in tranportation cot alter freight rate only to electric utilitie le than 550 mile ditant from the ource mine (the hortet 10% of all ample route). Thi etimated relationhip between marginal tranportation cot and freight rate i inconitent with the operation of a competitive railroad ector, in which a one-unit decreae in marginal cot lead to a one-unit decreae in the freight rate throughout the ervice region, irrepective of ditance from the mine. The etimated ditinction between ervice region I and II for a railroad monopoly in Gerking and Hamilton (2008) provide eential inight into the market feature that upported the oberved fuel ubtitution from high-ulfur to low-ulfur coal. In the railroad ector, Ellerman and Montero (1998) and Ellerman et al. (2000) etimate that real per ton/mile freight rate from the PRB to the Midwet fell by 44% over the period , and argue that thee rate reduction occurred due to increaed competition following deregulation in the Stagger Rail Act in 1980 and to ignificant productivityenhancing improvement attained by railroad throughout the period. Controlling for ditance, we find real rail rate on PRB coal hipment decreaed by 22% over the period , with the remaining decline in freight rate explained by an expanion of the ervice territory on the extenive margin of railroad ervice to ditant utilitie that receive lower freight price per ton mile (Gerking and Hamilton, 2008). Depite the Stagger Rail Act, railroad behavior over the period appear to have become le competitive, a evidenced by the increae in the Lerner indice acro route of fixed length. Empirical evidence indicate that the real marginal cot of tranporting coal declined by 36% over the period in repone to efficiency gain that followed the hift from teel railcar to lighter weight aluminum railcar in the late 1980 and The decline in freight rate a tranportation cot decreaed in the rail ector. Another caual factor that contributed to the hift among electric utilitie to burning low-ulfur coal wa a dramatic reduction in extraction cot for PRB coal. Over the period , coal extraction cot declined by 57% from $12.84/ton to $5.55/ton and the average real mine mouth price of PRB correpondingly coal fell by 64% (from $13.97/ton v. $5.38/ton) (U.S. Department of Energy, 11 A tranportation route i defined a a railhead at or near a particular mine to a particular power plant. 12 The etimated value of the Lerner index over the entire ample (all date and route) in Gerking and Hamilton (2008) i 0.37, which accord well with the etimated value of 0.41 over the period in a recent tudy commiioned by the U.S. Department of Tranportation (Chritianen Aociate, Inc., 2008). Concern over railroad market power ha led to Companion Bill (S 146 and HR 233) preently before the U.S. Congre to amend the railroad antitrut exemption in the Clayton Act.

13 Energy Information Adminitration, variou year). The dramatic decreae in the mine mouth price of PRB coal, combined with lower freight rate in the rail ector that occurred through independent efficiency improvement attained by railroad at about thi ame time, appear to have been the predominant factor that facilitated the landmark hift in the utilization of PRB coal at electric utilitie in the period urrounding implementation of the U.S. Clean Air Act. 5. Concluion Several pertinent concluion may be drawn from our analyi of the effect of SO 2 policy on input ubtitution from high-ulfur coal to low-ulfur coal. Firt, SO 2 regulation lead to an increae in the average tranportation cot of delivered PRB coal. By increaing the (allowance-incluive) price of high-ulfur coal, SO 2 regulation expand the ervice territory for PRB coal and increae the average ditance each ton of coal i hipped. In the cae of a monopoly railroad and perfectly ubtitutable fuel, the rie in average delivery cot for PRB coal i coupled with no change in total deliverie of PRB coal, o that SO 2 policy erve only to reditribute low-ulfur coal hipment from nearby utilitie to thoe further away, reducing ocial return. Second, SO 2 regulation exacerbate railroad market power by increaing the wedge between the delivered low-ulfur coal price and marginal hipment cot to (incumbent) utilitie in region II. The reaon i that freight rate rie by the ame magnitude a the increae in the price of high-ulfur coal, wherea the cot chedule doe not change. Our obervation on the limited ability of SO 2 regulation to timulate increaed PRB coal hipment through input ubtitution are mot tark in the cae of: (i) a uniform patial ditribution of utilitie; (ii) perfect ubtitutability between low- and high-ulfur coal in electricity generation; and (iii) monopoly power by railroad hauling low-ulfur coal. While thi ituation provide a ueful benchmark to conider the effect of environmental policy in patially intermediated market, more general model that relax thee aumption how that SO 2 policy can either raie or lower the aggregate quantity of PRB coal hipped. Under a non-uniform patial ditribution of utilitie, SO 2 policy can potentially lead to negative input ubtitution that i, a decreae in PRB coal deliverie when the denity of region II utilitie decreae monotonically along the rail line toward the extenive margin of railroad ervice, a the contraction effect in thi cae would exceed the expanion effect of the policy. Overall, in the cae of U.S. SO 2 policy, the evidence ugget that harp decline in mining cot and railroad tranportation cot for PRB coal at around the time of the U.S. Clean Air Act Amendment are likely to have played a much larger role in facilitating the ubtitution from high-ulfur coal to lowulfur, PRB coal than the environmental regulation. Indeed, it i poible that environmental policy did not contribute to the oberved input ubtitution at all. Acknowledgement The author thank Spencer Banzhaf, Michael Caputo, John Horowitz, Charle Koltad, Wally Milon, and eminar participant at UC Berkeley, UC Santa Barbara, the Univerity of Maryland, the Univerity of Nebraka, the Univerity of Maachuett, and the NBER Summer Intitute Workhop on Environmental Economic for numerou contructive uggetion. Reference Bue, Meghan R., Keohane, Nathaniel O., Market effect of environmental regulation: coal, railroad, and the 1990 clean air act. RAND Journal of Economic 38 (4), Caputo, M.R., Wilen, J.E., Optimality condition and comparative tatic for horizon and endpoint choice in optimal control theory. Journal of Economic Dynamic and Control 19 (1 2), Carlon, Curti, Burtraw, Dalla, Cropper, Maureen, Palmer, Karen L., Sulfur dioxide control by electric utilitie: what are the gain from trade. Journal of Political Economy 108 (6), Chritianen Aociate, Inc., A Study of Competition in the U.S. Freight Railroad Indutry and Analyi of Propoal that might Enhance Competition. Madion, WI. Prepared for the Surface Tranportation Board, U.S. Department of Tranportation, Wahington, DC, Ellerman, A. Denny, Montero, Juan-Pablo, The declining trend in ulfur dioxide emiion: implication for allowance price. Journal of Environmental Economic and Management 36 (1),

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