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On the continuity of outcomes in a monopoly market

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  • Yang, Kai Hao

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.

Suggested Citation

  • Yang, Kai Hao, 2023. "On the continuity of outcomes in a monopoly market," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    • Handle: RePEc:eee:mateco:v:108:y:2023:i:c:s0304406823000800
    DOI: 10.1016/j.jmateco.2023.102887
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    References listed on IDEAS

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