A Pedagogical Note on Multi-tier Pricing Scheme

Forthcoming in The American Economist

23 Pages Posted: 15 Apr 2016 Last revised: 15 Nov 2017

See all articles by Winston W. Chang

Winston W. Chang

University at Buffalo - Department of Economics

Tai-Liang Chen

Zhongnan University of Economics and Law

Date Written: October 25, 2017


This note derives a new formula for determining a monopolist's optimal multi-tier pricing scheme for any given number of tiers. It further characterizes Gabor's (1955, Review of Economic Studies) two-tier pari passu marginal revenue function to the n-tier case. By introducing the individual tier's marginal revenue and the pari passu marginal revenue in a linear demand case, this note provides a perceptive graphical representation of the optimal pricing scheme, revealing that all tiers' outputs are equal, the last tier's price is always higher than the marginal cost, and an increase in the number of tiers increases social welfare. In a class of non-linear demand functions, it shows that starting from the first tier, the tiers' outputs are monotonically increasing (decreasing) if the demand function is strictly convex (concave). It also shows that the equal-tier-output property preserves in the linear demand case with the total output fixed as a constraint.

Keywords: Monopoly, second-degree price discrimination, multi-tier pricing, public utility pricing, social welfare

JEL Classification: D01, D21, D42, L12, L21

Suggested Citation

Chang, Winston W. and Chen, Tai-Liang, A Pedagogical Note on Multi-tier Pricing Scheme (October 25, 2017). Forthcoming in The American Economist, Available at SSRN: https://ssrn.com/abstract=2761904 or http://dx.doi.org/10.2139/ssrn.2761904

Winston W. Chang (Contact Author)

University at Buffalo - Department of Economics ( email )

453 Fronczak Hall
Department of Economics, SUNY at Buffalo
Buffalo, NY 14260
United States
716-645-8671 (Phone)
716-645-2127 (Fax)

HOME PAGE: http://arts-sciences.buffalo.edu/economics/faculty/faculty-directory/chang.html

Tai-Liang Chen

Zhongnan University of Economics and Law ( email )

182 Nanhu Avenue, East Lake High-tech Development
Wuhan, 430073

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