The Informational Role of Prices*

• DOI: http://doi.org/10.1111/sjoe.12272
• Author: Marc Santugini,Leonard J. Mirman
• Published date: 01 April 2019
• Date: 01 April 2019

Scand. J. of Economics 121(2), 606–629, 2019

DOI: 10.1111/sjoe.12272

The Informational Role of Prices*

Leonard J. Mirman

University of Virginia, Charlottesville VA22904-4182, USA

lm8h@virginia.edu

Marc Santugini

University of Virginia, Charlottesville VA22904-4182, USA

ms3ae@virginia.edu

Abstract

We consider a dominant firm with a competitivefringe in order to investigate the informational

role of prices. The fringe is necessary for the existence of a unique, fully revealing equilibrium,

in which the price reveals the quality of the good to uninformed buyers. A higher price triggers

more sales on the part of the competitive fringe, reducing both residual demand and profits. We

find that a larger share of uninformed buyers increases the price and reduces the quantity sold by

the dominant firm, but increases the quantity sold by the competitive fringe.This, in turn, reduces

consumer surplus and welfare.

Keywords: Asymmetric information; dominant firm with fringe competition; informational

externality; learning; monopoly; quality; signaling

JEL classification:D21; D42; D82; D83; D84; L12; L15

I. Introduction

Information is at the heart of decision-making, and the interaction of agents

in markets requires each agent to use both public and private information

to form expectations about relevant economic variables. The mechanism

for information and learning (i.e., the acquisition of information) is thus

an essential element in economic analysis. Consistent with the existing

economic literature, we take rational expectations as the foundation for our

analysis. The notion of rational expectations is at the root of all economic

studies, as it provides a powerful way to embed asymmetric information

and learning in an economic environment. In particular, it is assumed that

*This version replaces a previous version of this paper entitled “Monopoly Signaling: Non-

Existence and Existence”. We are very grateful to two anonymous referees for their invaluable

comments. We also thank Lu´ıs Cabral, Joseph Harrington, Nicolas Sahuguet, Bernard Salani´e,

and Larry Samuelson, as well as seminar participants at Kobe University, Michigan State

University, the 2009 Latin American Meetings of the Econometric Society, and the 2010

International Industrial Organization Conference. M. Santugini gratefully acknowledges support

from the FQRSC and Direction de la recherche at HEC Montr´eal.

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The editors of The Scandinavian Journal of Economics 2017.

L. J. Mirman and M. Santugini 607

each agent uses all available information in order to form expectations,

which must be consistent with the economic environment.1

One important source of information is market prices. Several

studies have provided conditions under which privately held information

by firms becomes public through prices, beginning with perfectly

competitive markets (Kihlstrom and Mirman, 1975; Grossman, 1976,

1978; Grossman and Stiglitz, 1980; Mirman et al., 2014a, 2015)

and continuing with imperfectly competitive markets (Wolinsky, 1983;

Riordan, 1986; Bagwell and Riordan, 1991; Judd and Riordan, 1994;

Daughety and Reinganum, 1995, 2005, 2007, 2008a,b; Fluet and Garella,

2002; Hertzendorf and Overgaard, 2004; Yehezkel, 2008; Janssen and Roy,

2010; Daher et al., 2012). In the case of perfectly competitive markets, firms

have no control over prices and thus have no ability to directly influence

the amount of information conveyed by them.

Although situations in which all firms have market power (e.g., a

monopoly) have been considered in the literature on the informational role

of prices, these rarely occur. In many sectors, one firm has a greater market

share relative to the remaining firms. In other words, one of the firms is

dominant, e.g., Kodak for photographic film or IBM for the mainframe

computer industry. In this paper, we study the infor mational role of prices

when not all firms have market power. To that end, we embed asymmetric

information and learning in a model of a dominant firm facing a competitive

fringe. The dominant firm sets the price and the competitive fringe is a

price-taker. Moreover, the dominant firm has a cost advantage compared

to the competitive fringe. Finally, all firms produce the same good, for

example, the dominant firm is an innovator and the competitive fringe

firms are imitators.2The size of the competitive fringe is fixed, which

means that imitation is possible but is not available to ever ybody so there

is no unlimited entry. The quality of the good is known to all firms, b ut

unknown to uninformed buyers who extract the information from prices.

For comparability with the existing literature, we retain the linear demand in

which the quality is related to the reservation or choke price (Bagwell and

Riordan, 1991; Daughety and Reinganum, 1995, 2005, 2008a). Moreover,

as in Bagwell and Riordan (1991), demand is assumed to be composed of

informed and uninformed buyers. Unlike these previous studies, we assume

1This means neither that the agents have complete information, nor that they have the same

information. Rather,whatever information they have they use to conjecture the valuesof economic

variable s.

2Weconsider the standard framework of a dominant firm facing a competitive fringe with a cost

disadvantage.The fringe fir m knowsthe quality of the good. In our paper, the quality is the same

across firms. In Section V, we discuss the case of the dominant firm and the competitive fringe

selling different and unknown qualities.

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The editors of The Scandinavian Journal of Economics 2017.