Quasilinear Utility and Two Market Monopoly

Stephen K Layson

doi:10.5539/ibr.v10n3p164

Abstract

The use of quasilinear utility functions in economic analyses is widespread. This paper presents an overdue clarification on the implications of quasilinear utility for two market monopoly. The paper begins by deriving the demands facing a two market monopoly from a representative consumer with quasilinear utility. Expressions are derived for the profit margins expressed solely in terms of the own and cross-price elasticities of demand. The paper also analyzes the implications of quasilinear utility for other issues in two market monopoly: pricing below marginal cost in a market, third-degree price discrimination when the monopoly products are substitutes and pricing in the inelastic region of demands.

Highlights

Thanks in large part to Varian (1985, 1992) the assumption of quasilinear utility is ubiquitous in economic policy analyses because it allows one to measure social welfare as profit plus consumer surplus
This paper presents an overdue clarification of the implications of quasilinear utility for the behavior of two market monopoly and in the process corrects some errors in Varian (1989, 1992)
3.1 Pricing below Marginal Cost under Two Market Monopoly. It has been well known for some time that if the two products are complements it’s possible that price may be below marginal cost in one market

Summary

Introduction

Thanks in large part to Varian (1985, 1992) the assumption of quasilinear utility is ubiquitous in economic policy analyses because it allows one to measure social welfare as profit plus consumer surplus. This paper presents an overdue clarification of the implications of quasilinear utility for the behavior of two market monopoly and in the process corrects some errors in Varian (1989, 1992). After deriving the demands facing a two market monopoly from a representative consumer, the paper derives simple expressions for the monopoly profit margins expressed solely in terms of own and cross-price elasticities of demand. The paper discusses three other implications of quasilinear utility for two market monopoly: (1) the possibility of pricing below marginal cost (2) the theory of third-degree price discrimination when the monopoly products are substitutes and (3) pricing in the inelastic region of demands

Method

Profit maximization for a two product firm

Pricing below Marginal Cost under Two Market Monopoly

Third-degree Price Discrimination When Demands Are Interdependent

Pricing in the Inelastic Regions of Demands

Discussion