On the continuity of outcomes in a monopoly market

Kai Hao Yang

Journal of Mathematical Economics, 2023, vol. 108, issue C

Abstract: A monopolist with a constant marginal cost faces an arbitrary nondecreasing and upper-semicontinuous demand function on R+ that takes a value in {0,1} outside of a fixed compact interval. This paper derives topological properties of outcomes induced by this monopolist’s optimal pricing problem. Specifically, the monopolist’s optimal profit is continuous in the marginal cost and the demand (under the weak-* topology); the optimal price and output correspondences are upper-hemicontinuous in the marginal cost and the demand; and the consumer surplus is upper (lower)-semicontinuous when the monopolist charges the lowest (highest) optimal price. These results further imply similar topological properties of outcomes in settings that feature either second-degree price discrimination or third-degree price discrimination.

Keywords: Monopoly pricing; Continuity; Second-degree price discrimination; Third-degree price discrimination (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:108:y:2023:i:c:s0304406823000800

DOI: 10.1016/j.jmateco.2023.102887

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