Mathematics (Feb 2024)

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

  • Anton Badev,
  • Stanimir Kabaivanov,
  • Petar Kopanov,
  • Vasil Zhelinski,
  • Boyan Zlatanov

DOI
https://doi.org/10.3390/math12050724
Journal volume & issue
Vol. 12, no. 5
p. 724

Abstract

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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.

Keywords