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## MARGINAL COST AND SECOND-BEST PRICING FOR WATER SERVICES

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**MARGINAL COST AND SECOND-BEST PRICING FOR WATER SERVICES**H. Youn Kim Presented by Adekunle Dada**INTRODUCTION**• Regulatory commissions faced with maintaining ideal pricing structure. • Average cost pricing, AC = P. Profit maximizing • Marginal cost pricing, MC = P. Welfare maximizing. • Devise second best pricing rules .**PURPOSE OF STUDY**• Estimate marginal cost and apply the second best pricing for water services. • Water Utility viewed as multiproduct firm Residential and Nonresidential services. • Translog multiproduct cost funstion.**Marginal cost equation and Second best pricing rules**• lnC = Where C = Using Shephard’s Lemma to get cost share equations: Where This is the total cost accruing to input j.**Equations (contd)**• Cost elasticity of output used in deriving marginal cost : • and i = R, N Thus = • Degree of overall scale economies for the multiproduct firm SL is defined as the reciprocal of the sum of cost elasticities of individual outputs (Baumol, Panzar and Willig 1982) • Ratio of total production cost is equal to total revenue.**Inadequacy of MC pricing**• If SL > 1, economies of scale If SL = 1, constant returns to scale If SL < 1, diseconomies of scale • Economies of scale exist only if revenue yielded from MC pricing falls short of TC • Diseconomies exist if TR exceeds TC • CRTS exist if TR equals TC MC pricing cannot be used for a firm operating under conditions of economies of scale as it pertains to financial viability. Example: Water Utilities with large FC but small MC.**Subsidy**• So if D = subsidy D(YR, YN) = C(YR, YN) – R(YR, YN) Recall SL = C/R, then R = C/SL Thus D(YR, YN) = C(YR, YN) – C(YR, YN)/S = C(YR, YN)(1 – 1/SL) • If SL is large then subsidy must be large • If SL is close to 1 (CRTS) subsidy and MC pricing may be a viable policy alternative • If SL < 1 then unsubsidized marginal cost pricing is feasible.**Maximizing Social Welfare**• Suppose water supply firm faces budget or profit constraint: Max V( PR, PN, I) IUF St PRYR + PNYN – C(YR, YN) = B Soln: (PR – MCR)/PR= ηNN – ηRN (PR – MCR)/PNηRR - ηNR ηNN & ηRR – own price elasticities of demand for nonresidential and residential water. ηNR &ηRN – cross price elasticity is zero since residential is independent of nonresidential output. Thus: PR – MCR = PN – MCN PR *ηNN PN *ηRR**Welfare loss**• The amount by which price diverges from MC for each output is inversely proportional to the elasticity of demand. • If ηRR <1, PR – MCR is large This is reduction in welfare loss • Overhead expenses for services produced with economies of scale are best covered with revenues from the more inelastic part of service.**DATA AND ESTIMATION**Cross section of 60 water utilities collected during the survey of water utilities by US environmental protection agency in 1973 • Cost shares are calculated by dividing cost attributable to each input by TC • Output is measured in terms of amount of water treated in millions of gallons per day. • Price of labor is obtained by dividing gross payroll by number of yearly man-hours. • Price of energy measured by dividing total power expenditures by yearly kilowatt hour usage. • Price is capital computed by considering interest rate on long term debt and depreciation rate. • Capacity utilization measured by load factor for water system. • Service distance measured by miles of distribution pipelines.**RESULTS AND DISCUSSION**• The parameter estimates of the translog multiproduct cost function from table one are used to derive estimates of cost elasticities of outputs and marginal costs of outputs.**Overall Economies of Scope and Scale**• Economies of scope (Baumol, Panzar and Willig, 1982) measures % cost increase due to joint production of residential and nonresidential services. • Cost elasticity of residential output is estimated by ɛCR = 0.53037 - 0.42487lnYR + 0.10086lnYN + 0.08885lnWL - 0.11238lnWK + 0.02353lnWE- 0.59305lnZU +0.44056lnZM • Cost elasticity of nonresidential output is given by ɛCN =0.25741 + 0.10086lnYR + 0.14868lnYN - 0.02182lnWL + 0.01496lnWK + 0.00686lnWE + 0.13495lnZU – 0.32537lnZM • Overall cost elasticity obtained by summing both cost elasticities is ɛCY =0.78778 – 0.32401lnYR + 0.24954lnYN + 0.06703lnWL – 0.09742lnWK + 0.03039lnWE – 0.45810lnZU + 0.11519lnZM**Degree of scale economics is the inverse of overall cost**elasticity. • Effects of relative price movement of labor, capital and energy are generally small relative to effects of outputs, capacity utilization and service distance. • Economies of scale are largely determined by levels of output, capacity utilization and service distance.**Small utilities exhibit marked economies of scale while**large utilities exhibit moderate diseconomies of scale. Small utilities cannot adopt MC pricing as it would lead to financial insolvency.**Marginal cost elasticities of output, input prices and**operating variables.% change in MC of residential and nonresidential output due to change in variables.Substantial effect of operating variables on MCs of water supply.**Price-marginal cost margins for residential and**nonresidential are greater than zero. Residential water service priced 158% above MC.Nonresidential priced 40% above MC.Price discrimination seems to be favor nonresidential users.**Second best prices are only slightly higher than prices**actually charged.% change from residential water price to second best is 0.10. For nonresidential, it is 0.09.Thus, the move to the calculated optimal rates requires a 10% increase for residential customers and a 9% increase for nonresidential customers.**SUMMARY AND CONCLUSION**• Discussed implication of MC pricing. • Examined second best pricing scheme. • While existing price structure is different from MC, it does not appear to deviate substantially from second best optimum. • This study is significant to regulators, policy makers and water supply managers.**THANK YOU FOR LISTENING**No questions please.