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Long-Run Equilibrium in the Market of Mobile Services in the USA

Author

Listed:
  • Anton Badev

    (Division of Supervision and Regulation, Federal Reserve Board of Governors, Washington, DC 20551, USA)

  • Stanimir Kabaivanov

    (Department of Finance and Accounting, Faculty of Economics and Social Sciences, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

  • Petar Kopanov

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

  • Vasil Zhelinski

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

  • Boyan Zlatanov

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

Abstract

We develop an empirical model of the market for mobile services in the USA based on providers’ response functions. Guided by a duopoly model, we obtain our empirical response functions from an approximation of quarterly response data on smartphone subscriptions by sigmoid functions of time. The robustness analysis suggests that our model fits the data well and outperforms the regression model. Further, we demonstrate that our empirical response functions satisfy the conditions for semi-cyclic contractions which guarantee the existence, uniqueness and stability of long-run equilibrium.

Suggested Citation

  • Anton Badev & Stanimir Kabaivanov & Petar Kopanov & Vasil Zhelinski & Boyan Zlatanov, 2024. "Long-Run Equilibrium in the Market of Mobile Services in the USA," Mathematics, MDPI, vol. 12(5), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:724-:d:1348624
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    References listed on IDEAS

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    4. Modis, Theodore, 1994. "Determination of the Uncertainties in S-Curve Logistic Fits," OSF Preprints n53pd, Center for Open Science.
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