The amazing geometry of price competition with quality dependent production costs

Pires, Cesaltina Pacheco; Pinho, Joana; Jorge, Sílvia Ferreira; Catalão-Lopes, Margarida

http://hdl.handle.net/10400.14/55557

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Authors

Pires, Cesaltina Pacheco

Pinho, Joana

Jorge, Sílvia Ferreira

Catalão-Lopes, Margarida

Abstract(s)

This paper provides a full characterization of price competition in a vertical differentiation model with quality dependent marginal production costs. For each vector of qualities, we determine the Nash equilibrium and show graphically the different market regions for different values of the lowest quality valuation parameter, which reveals an amazing geometry. Besides the classical cases of high-quality monopoly or duopoly with partial or full coverage, we show that, when the high-quality firm has a too high quality, the equilibrium is a low-quality monopoly. Moreover, for positive lowest quality valuation, there always exist interior and corner full coverage duopoly equilibria. On the contrary, partial coverage duopoly do not exist when the lowest consumers’ valuation of quality is high whereas high-quality monopoly are not possible for low values of lowest quality valuation. Our findings are the backbone of future analysis of quality choices and may be relevant for firms and policy makers.

Keywords

Market coverage configurations Quality dependent marginal costs Quality valuation dispersion Vertical differentiation

URI

http://hdl.handle.net/10400.14/55557

Citation

Pires, C. P., Pinho, J., Jorge, S. F., & Catalão-Lopes, M. (2022). The amazing geometry of price competition with quality dependent production costs. SSRN. https://doi.org/10.2139/ssrn.4232585