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A Mathematical Formulation of the Peak-Load Pricing Problem

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  • Israel Pressman

Abstract

This paper formulates peak-load pricing problems using mathematical micromodels. The optimal strategy chosen for the public utility is that of maximizing the social satisfaction derived from services provided. The notion of consumers' surplus is used, and period demands are assumed to be both independent and dependent. The case of dependent demands, a heretofore unsolved problem, is handled using the line-integral calculus. Several specific models are analyzed, with both capacity constraints and profit constraints being considered. In some models it is shown that prices should depend on marginal operating costs but not on marginal capacity costs. Trade-offs between these marginal costs are explored in the peak-load pricing context. In other models the relationships of price with both demand elasticities and marginal costs are developed. Several of the existing peak-load pricing models of the literature can be shown to be subcases of models developed herein.

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  • Israel Pressman, 1970. "A Mathematical Formulation of the Peak-Load Pricing Problem," Bell Journal of Economics, The RAND Corporation, vol. 1(2), pages 304-326, Autumn.
    • Handle: RePEc:rje:bellje:v:1:y:1970:i:autumn:p:304-326
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    Cited by:

    1. Kraus, Marvin, 2003. "A new look at the two-mode problem," Journal of Urban Economics, Elsevier, vol. 54(3), pages 511-530, November.
    2. Kraus, Marvin, 2012. "Road pricing with optimal mass transit," Journal of Urban Economics, Elsevier, vol. 72(2), pages 81-86.
    3. Ramos, Raúl & Silva, Hugo E., 2023. "Fare evasion in public transport: How does it affect the optimal design and pricing?," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    4. A. Gürhan Kök & Kevin Shang & Şafak Yücel, 2018. "Impact of Electricity Pricing Policies on Renewable Energy Investments and Carbon Emissions," Management Science, INFORMS, vol. 64(1), pages 131-148, January.
    5. Chen, Daqiang & Ignatius, Joshua & Sun, Danzhi & Goh, Mark & Zhan, Shalei, 2018. "Impact of congestion pricing schemes on emissions and temporal shift of freight transport," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 77-105.
    6. Catherine C. Eckel & William T. Smith, 2014. "The Discriminating Beta: Prices and Capacity with Correlated Demands," Southern Economic Journal, John Wiley & Sons, vol. 81(1), pages 56-67, July.
    7. Basso, Leonardo & Zhang, Anming, 2006. "Peak-Load Pricing In A Vertical Setting: The Case Of Airports And Airlines," 47th Annual Transportation Research Forum, New York, New York, March 23-25, 2006 208029, Transportation Research Forum.
    8. N. Vijayamohanan Pillai, 2003. "A contribution to peak load pricing theory and application," Centre for Development Studies, Trivendrum Working Papers 346, Centre for Development Studies, Trivendrum, India.
    9. Christoph Böhringer & Knut Einar Rosendahl, 2009. "Green Serves the Dirtiest: On the Interaction between Black and Green Quotas," CESifo Working Paper Series 2837, CESifo.
    10. J. Salerian, 1992. "The Application of a Temporal Price Allocation Model to Time-of-Use Electricity Pricing," Economics Discussion / Working Papers 92-11, The University of Western Australia, Department of Economics.
    11. Skiera, Bernd & Spann, Martin, 1999. "The ability to compensate for suboptimal capacity decisions by optimal pricing decisions," European Journal of Operational Research, Elsevier, vol. 118(3), pages 450-463, November.
    12. Long Gao & Liang Guo & Adem Orsdemir, 2021. "Dual‐Channel Distribution: The Case for Cost Information Asymmetry," Production and Operations Management, Production and Operations Management Society, vol. 30(2), pages 494-521, February.
    13. Liu, Louie Nan & McDonald, John F., 1998. "Efficient Congestion Tolls in the Presence of Unpriced Congestion: A Peak and Off-Peak Simulation Model," Journal of Urban Economics, Elsevier, vol. 44(3), pages 352-366, November.
    14. Peter Hartley & Chris Trengove, 1984. "The Marginal Costs of Electricity Supply in Victoria," The Economic Record, The Economic Society of Australia, vol. 60(4), pages 340-355, December.
    15. Liu, Louie Nan & McDonald, John F., 1999. "Economic efficiency of second-best congestion pricing schemes in urban highway systems," Transportation Research Part B: Methodological, Elsevier, vol. 33(3), pages 157-188, April.
    16. Aliaga Lordemann, Javier, 2009. "Energy Technology Assessment," Documentos de trabajo 8/2009, Instituto de Investigaciones Socio-Económicas (IISEC), Universidad Católica Boliviana.
    17. Gulli, Francesco, 2006. "Small distributed generation versus centralised supply: a social cost-benefit analysis in the residential and service sectors," Energy Policy, Elsevier, vol. 34(7), pages 804-832, May.
    18. Karthik Murali & Michael K. Lim & Nicholas C. Petruzzi, 2019. "The Effects of Ecolabels and Environmental Regulation on Green Product Development," Manufacturing & Service Operations Management, INFORMS, vol. 21(3), pages 519-535, July.
    19. Gullì, F., 2003. "Distributed Generation versus Centralised Supply: a Social Cost-Benefit Analysis," Cambridge Working Papers in Economics 0336, Faculty of Economics, University of Cambridge.
    20. Böckers, Veit & Haucap, Justus & Jovanovic, Dragan, 2013. "Diskriminierende Gebotsbeschränkungen im deutschen Großhandelsmarkt für Strom: Eine wettbewerbsökonomische Analyse," DICE Ordnungspolitische Perspektiven 52, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).

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