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Formalization of Cost and Utility in Microeconomics

Author

Listed:
  • Asad Ahmed

    (School of Electrical Engineering and Computer Science, National University of Sciences and Technology (NUST), Islamabad H-12, Pakistan)

  • Osman Hasan

    (School of Electrical Engineering and Computer Science, National University of Sciences and Technology (NUST), Islamabad H-12, Pakistan)

  • Falah Awwad

    (College of Engineering, United Arab Emirates University, Al-Ain 15551, UAE)

  • Nabil Bastaki

    (College of Engineering, United Arab Emirates University, Al-Ain 15551, UAE)

Abstract

Cost and utility modeling of economics agents based on the differential theory is fundamental to the analysis of the microeconomics models. In particular, the first and second-order derivative tests are used to specify the desired properties of the cost and utility models. Traditionally, paper-and-pencil proof methods and computer-based tools are used to investigate the mathematical properties of these models. However, these techniques do not provide an accurate analysis due to their inability to exhaustively specify and verify the mathematical properties of the cost and utility models. Additionally, these techniques cannot accurately model and analyze pure continuous behaviors of the economic agents due to the utilization of computer arithmetic. On the other hand, an accurate analysis is direly needed in many safety and cost-critical microeconomics applications, such as agriculture and smart grids. To overcome the issues pertaining to the above-mentioned techniques, in this paper, we propose a theorem proving based methodology to formally analyze and specify the mathematical properties of functions used in microeconomics modeling. The proposed methodology is primarily based on a formalization of the derivative tests and root analysis of the polynomial functions, within the sound core of the HOL-Light theorem prover. We also provide a formalization of the first-order condition, which is used to analyze the maximum of the profit function in a higher-order-logic theorem prover. We then present the formal analysis of the utility, cost and first-order condition based on the polynomial functions. To illustrate the usefulness of proposed formalization, the proposed formalization is used to formally analyze and verify the quadratic cost and utility functions, which have been used in an optimal power flow problem and demand response (DR) program, respectively.

Suggested Citation

  • Asad Ahmed & Osman Hasan & Falah Awwad & Nabil Bastaki, 2020. "Formalization of Cost and Utility in Microeconomics," Energies, MDPI, vol. 13(3), pages 1-19, February.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:3:p:712-:d:317418
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    References listed on IDEAS

    as
    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    2. Ketter, W. & Collins, J. & Block, C., 2010. "Smart Grid Economics: Policy Guidance through Competitive Simulation," ERIM Report Series Research in Management ERS-2010-043-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Hendrik Bessembinder & Michael L. Lemmon, 2002. "Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets," Journal of Finance, American Finance Association, vol. 57(3), pages 1347-1382, June.
    4. Debertin, David L., 2012. "Applied Microeconomics: Consumption, Production and Markets," Monographs: Applied Economics, AgEcon Search, number 158321, November.
    5. Frank A. Wolak, 2001. "Identification and Estimation of Cost Functions Using Observed Bid Data: An Application to Electricity Markets," NBER Working Papers 8191, National Bureau of Economic Research, Inc.
    6. Poria Astero & Bong Jun Choi, 2016. "Electrical Market Management Considering Power System Constraints in Smart Distribution Grids," Energies, MDPI, vol. 9(6), pages 1-30, May.
    7. Marcel Boumans & Matthias Klaes, 2013. "Introduction," Chapters, in: Marcel Boumans & Matthias Klaes (ed.), Mark Blaug: Rebel with Many Causes, chapter 1, pages 1-8, Edward Elgar Publishing.
    8. Moretti, M. & Djomo, S. Njakou & Azadi, H. & May, K. & De Vos, K. & Van Passel, S. & Witters, N., 2017. "A systematic review of environmental and economic impacts of smart grids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 68(P2), pages 888-898.
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