Does the Cost Paradox Preclude Technological Progress under Imperfect Competition?

• Author: CHRISTINE HALMENSCHLAGER,MALGORZATA KNAUFF,RABAH AMIR
• DOI: http://doi.org/10.1111/jpet.12199
• Date: 01 February 2017
• Published date: 01 February 2017

DOES THE COST PARADOX PRECLUDE TECHNOLOGICAL PROGRESS

UNDER IMPERFECT COMPETITION?

RABAH AMIR

University of Iowa

CHRISTINE HALMENSCHLAGER

Universit´

e Paris II Panth´

eon-Assas

MALGORZATA KNAUFF

Warsaw School of Economics

Abstract

We consider a two-stage model of R&D/Cournot competition with isoe-

lastic demand satisfying the cost paradox (i.e., that equilibrium profits

increase with unit cost). The R&D process has a binary structure, with

spillover effects. We provide a negative answer to the question in the

title: Under noncooperative R&D, firms will conduct R&D for a broad

parameter range, despite the presence of the cost paradox, as a result

of being caught in a prisoner’s dilemma. A second-best social planner

is shown to have a higher propensity for R&D than the noncooperative

scenario. However, if firms engaged in any of the known R&D cooper-

ation scenarios, the answer to the question in the title would become

affirmative. It follows that R&D cooperation leads to lower producer

and consumer surpluses. This constitutes a major departure from the

conclusions of the standard R&D model. Therefore, R&D cooperation

in such environments should not receive favorable antitrust treatment.

1. Introduction

This paper brings together two separate strands of literature on oligopoly theory. The

first deals with the interplay between market structure and research and development

(or R&D) and is concerned with the effects of market competition on firms’ endoge-

nous technological progress (Brander and Spencer 1983; Spence 1984, among others),

and with the private and social incentives for R&D cooperation (see, e.g., Katz 1986;

d’Aspremont and Jacquemin 1988). The second strand of literature deals with the com-

parative statics effects of an exogenous common change in firms’ production costs on

Rabah Amir, Department of Economics, University of Iowa, Iowa City, IA 52242 (rabah-amir@

uiowa.edu). Christine Halmenschlager, CRED, Universit´

e Paris II Panth´

eon-Assas, 75005 Paris, France

(Christine.Halmenschlager@u-paris2.fr). Malgorzata Knauff, Warsaw School of Economics, Warsaw,

Poland (mknauff@sgh.waw.pl).

This paper has benefited from comments and suggestions by Claude d’Aspremont, Charlene

Cosandier, David Encaoua, Yassine Lefouili, and Isabelle Maret.

Received December 15, 2014; Accepted November 19, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 19 (1), 2017, pp. 81–96.

81

82 Journal of Public Economic Theory

firms’ equilibrium output levels and profits. A key, counter intuitive, result is the “cost

paradox”: That a common increase in firms’ unit costs leads to an increase in their

equilibrium profits whenever market inverse demand is sufficiently convex in a Cournot

framework (see, e.g., Seade 1985; Anderson, de Palma, and Kreider 2001; Fevrier and

Linnemer 2004).

Taking off from these strands of literature, the present paper has two main inter-

related goals. The first is to address the natural question as to whether anything of

interest might be said concerning firms’ R&D behavior in Cournot markets character-

ized by the cost paradox. A spontaneous intuitive argument might lead one to conclude

that, when confronted with the cost paradox, firms will simply refrain from conducting

any R&D. Indeed, why would firms wish to expend resources for process R&D when the

resulting lower production costs will lead to lower profits? This seemingly self-evident

view probably explains why this natural question has not been investigated in the theo-

retical literature on R&D so far, despite the recent drastic expansion of this literature.1

It turns out that this intuition is actually flawed, as it fails to incorporate some simple

strategic considerations inherent to the R&D game. The main insight of the present pa-

per is to identify a robust set of circumstances under which identical firms will engage in

R&D in (a simplified version of) the standard two-stage duopoly game of R&D/Cournot

competition in the presence of the cost paradox. In addition, the paper also explores

the implications of this a priori surprising finding, in terms of social welfare and of the

incentives of firms to engage in R&D cooperation.

The standard two-stage game of R&D with spillovers is amended by considering an

isoelastic demand function that gives rise to the cost paradox in a global sense, and by

restricting R&D to a binary process. Each firm decides whether or not to undertake a

fixed R&D investment level, which leads with certainty to a given level of cost reduction.

This simple way of modeling R&D lends itself to an insightful interpretation of process

R&D in terms of technology adoption, i.e., as a choice between two possible affine tech-

nologies. Indeed, identifying R&D investment with a fixed cost of production, the firm

faces a choice between the status quo technology with high marginal cost and no fixed

cost, and the new technology with low marginal cost and some fixed cost. The binary

nature of the R&D process is also appropriate for the issues analyzed in the present

paper for other reasons that will become apparent later.

The main result of the paper characterizes the firms’ equilibrium R&D behavior. In

spite of the presence of the cost paradox, at equilibrium, the firms will actually engage

in R&D for a broad parameter configuration. More precisely, provided the demand

elasticity is sufficiently greater than 1/2, and the scope of cost reduction is not too high

relative to the demand elasticity, the decision to engage in R&D (or equivalently to

adopt the new technology) will be taken by both firms, just one firm, or none of the

firms, according as the (fixed) cost of R&D is low, intermediate, or high.

Absent the cost paradox, this finding would be fully intuitive. Nevertheless, we now

argue that a proper intuitive understanding of this result can be arrived at even in the

presence of the cost paradox. Tobegin with, obser ve that the cost paradox deals with the

effect on each firm’s profit of a common cost decrease, but does not address the effects

of a unilateral cost decrease on own profit. It turns out that, under the two conditions

1While much of the literature considers linear demand for analytical convenience, studies with a gen-

eral focus also rule out the cost paradox with an explicit assumption to this effect: See Assumption

A2(iii) in Amir and Wooders (2000) and Assumption A2 in Amir, Encaoua, and Lefouili (2014). Two

exceptions are Kline (2000), who considers cartels in industries with the cost paradox, and Katz (1986),

who alluded to the paradox.