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Uniqueness of market equilibrium on a network: A peak-load pricing approach

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  • Grimm, Veronika
  • Schewe, Lars
  • Schmidt, Martin
  • Zöttl, Gregor

Abstract

In this paper we establish conditions under which uniqueness of market equilibrium is obtained in a setup where prior to trading of electricity, transmission capacities between different market regions are fixed. In our setup, firms facing fluctuating demand decide on the size and location of production facilities. They make production decisions constrained by the invested capacities, taking into account that market prices (partially) reflect scarce transmission capacities between the different market zones. For this type of peak-load pricing model on a network we state general conditions for existence and uniqueness of the market equilibrium and provide a characterization of equilibrium investment and production. The presented analysis covers the cases of perfect competition and monopoly—the case of strategic firms is approximated by a conjectural variations approach. Our result is a prerequisite for analyzing regulatory policy options with computational multilevel equilibrium models, since uniqueness of the equilibrium at lower levels is of key importance when solving these models. Thus, our paper contributes to an evolving strand of literature that analyzes regulatory policy based on computational multilevel equilibrium models and aims at taking into account individual objectives of various agents, among them not only generators and customers but also, e.g., the regulator deciding on network expansion.

Suggested Citation

  • Grimm, Veronika & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2017. "Uniqueness of market equilibrium on a network: A peak-load pricing approach," European Journal of Operational Research, Elsevier, vol. 261(3), pages 971-983.
  • Handle: RePEc:eee:ejores:v:261:y:2017:i:3:p:971-983
    DOI: 10.1016/j.ejor.2017.03.036
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    References listed on IDEAS

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    Cited by:

    1. Ambrosius, M. & Egerer, J. & Grimm, V. & Weijde, A.H. van der, 2020. "Uncertain bidding zone configurations: The role of expectations for transmission and generation capacity expansion," European Journal of Operational Research, Elsevier, vol. 285(1), pages 343-359.
    2. Yang, Dong & Zhang, Lingge & Luo, Meifeng & Li, Feng, 2020. "Does shipping market affect international iron ore trade?– An equilibrium analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    3. Lars Schewe & Martin Schmidt, 2020. "The impact of potential-based physics models on pricing in energy networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 1003-1029, September.
    4. Krebs, Vanessa & Schmidt, Martin, 2018. "Uniqueness of market equilibria on networks with transport costs," Operations Research Perspectives, Elsevier, vol. 5(C), pages 169-173.
    5. Grimm, Veronika & Grübel, Julia & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2019. "Nonconvex equilibrium models for gas market analysis: Failure of standard techniques and alternative modeling approaches," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1097-1108.
    6. Veronika Grimm & Lars Schewe & Martin Schmidt & Gregor Zöttl, 2019. "A multilevel model of the European entry-exit gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 223-255, April.
    7. de Frutos Cachorro, Julia & Willeghems, Gwen & Buysse, Jeroen, 2020. "Exploring investment potential in a context of nuclear phase-out uncertainty: Perfect vs. imperfect electricity markets," Energy Policy, Elsevier, vol. 144(C).
    8. Grimm, Veronika & Rückel, Bastian & Sölch, Christian & Zöttl, Gregor, 2019. "Regionally differentiated network fees to affect incentives for generation investment," Energy, Elsevier, vol. 177(C), pages 487-502.
    9. Ambrosius, Mirjam & Grimm, Veronika & Kleinert, Thomas & Liers, Frauke & Schmidt, Martin & Zöttl, Gregor, 2020. "Endogenous price zones and investment incentives in electricity markets: An application of multilevel optimization with graph partitioning," Energy Economics, Elsevier, vol. 92(C).
    10. Runge, Philipp & Sölch, Christian & Albert, Jakob & Wasserscheid, Peter & Zöttl, Gregor & Grimm, Veronika, 2019. "Economic comparison of different electric fuels for energy scenarios in 2035," Applied Energy, Elsevier, vol. 233, pages 1078-1093.
    11. Ambrosius, Mirjam & Grimm, Veronika & Sölch, Christian & Zöttl, Gregor, 2018. "Investment incentives for flexible demand options under different market designs," Energy Policy, Elsevier, vol. 118(C), pages 372-389.
    12. Ruderer, Dominik & Zöttl, Gregor, 2018. "Transmission pricing and investment incentives," Utilities Policy, Elsevier, vol. 55(C), pages 14-30.
    13. Krebs, Vanessa & Schewe, Lars & Schmidt, Martin, 2018. "Uniqueness and multiplicity of market equilibria on DC power flow networks," European Journal of Operational Research, Elsevier, vol. 271(1), pages 165-178.

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