On the Mean Residual Life of Cantor-Type Distributions: Properties and Economic Applications

Abstract

In this paper, we consider the mean residual life (MRL) function of the Cantor distribution and study its properties. We show that the MRL function is continuous at all points, locally decreasing at all points outside the Cantor set and has a unique fixed point which we explicitly determine. These properties readily extend to the parametric family of p-singular, Cantor type distributions introduced by Mandelbrot (1983). The findings offer evidence that, contrary to common perceptions, Cantor-type distributions are tractable enough to be considered for practical applications. We provide such an example from the field of economics in which Cantor-type distributions can be used to model markets with recurrent bandwagon effects and show that earlier anticipated bandwagon effects lead to higher monopolistic prices. We conclude with a simple implementation of the algorithm by Chalice (1991) to plot Cantor-type distributions.

References in corpus (5)

• Measuring Market Performance with Stochastic Demand: Price of Anarchy and Price of Uncertainty
• Monopoly Pricing in Vertical Markets with Demand Uncertainty
• Comparative Statics via Stochastic Orderings in a Two-Echelon Market with Upstream Demand Uncertainty
• On the Equilibrium Uniqueness in Cournot Competition with Demand Uncertainty
• A Class of Distributions for Linear Demand Markets

Cited by in corpus (1)

• Measuring Market Performance with Stochastic Demand: Price of Anarchy and Price of Uncertainty