A Pedagogical Note on Multi-tier Pricing Scheme
Forthcoming in The American Economist
23 Pages Posted: 15 Apr 2016 Last revised: 15 Nov 2017
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: Suggested Citation