The road not taken: competition and the R&D portfolio

• Author: Igor Letina
• Date: 01 May 2016
• Published date: 01 May 2016
• DOI: http://doi.org/10.1111/1756-2171.12133

RAND Journal of Economics

Vol.47, No. 2, Summer 2016

pp. 433–460

The road not taken: competition

and the R&D portfolio

Igor Letina∗

This article examines the effects of marketstructure on the variety of research projects undertaken

and the amount of duplication of research. A characterization of the equilibrium market portfolio

of R&D projects and the socially optimal portfoliois provided. It is shown that a merger decreases

the variety of developed projects and decreasesthe amount of duplication of research. An increase

in the intensity of competition among firms leads to an increase in the variety of developed projects

and a decrease in the amount of duplication of research.

1. Introduction

In 1998, the US Department of Justice blocked the proposed merger of Lockheed Martin

and Northrop Grumman, the largest blocked merger in the US history at the time. The merger

would have reduced the number of firms supplying aircraft and electronic systems to the

Department of Defense from three (including Boeing) to only two. According to Robinson

(1999) and Rubinfeld and Hoven (2001), one of the main reasons why the Department of

Justice, supported by the Department of Defense, opposed the merger was the concern that the

merger would have had negative effects on innovation. However, the issue was not so much with

the amount of funds invested in innovation, the bulk of which comes from the Department of

Defense anyway (Rubinfeld and Hoven, 2001). Rather, the principal concern was that reducing

the number of firms in the industry would reduce the diversity of approaches to innovation.

This article develops a model where the effects of such a mergeron the variety of approaches

to innovation and the amount of duplicative research can be studied explicitly. From society’s

point of view,higher variety of research projects being developed is desirable because it increases

the probability that the innovation will be discovered. On the other hand, more duplication of

research projects is also desirable because it implies stronger product market competition ex post

and lower dead-weight loss. The market R&D portfolio is a function which captures how many

firms are investing in each of the possible projects, and the variety of approaches is the fraction of

projects which are developed by at least one firm. Of course, more variety and more duplication

∗University of Zurich; igor.letina@econ.uzh.ch.

I am grateful to Ufuk Akcigit, Paul Heidhues, Arnd Heinrich Klein, Nick Netzer, Georg N¨

oldeke, Daniel L. Rubinfeld,

Sabrina Studer, Xavier Vives,David Wettstein, E. Glen Weyl, Fabrizio Zilibotti, and to seminar participants for helpful

discussions and suggestions. Special thanks are due to Armin Schmutzler for numerous suggestions and comments.

Financial support of the Swiss National Science Foundation (projects P1ZHP1 155283 and 100014 131854) is gratefully

acknowledged.

C2016, The RAND Corporation. 433

434 / THE RAND JOURNAL OF ECONOMICS

are costly. The main object of analysis will be the market R&D portfolio. The model will allow

us to study how a change in the market structure will change the equilibrium R&D portfolio.

The main model assumes that there are Nsymmetric firms competing in a market. In the

first stage, the firms can invest in innovation. There is a set of heterogeneous research projects,

and firms simultaneously choose the subset they wish to develop. The innovation is assumed to

be drastic1and the discovery procedure is stochastic. All approaches are ex ante equally likely

to be successful, but ex post only one approach will be successful. The approaches differ only

in the cost needed to pursue them. There are no spillovers or patents. Each firm which invested

in the successful approach receives the innovation, whereas each firm that did not invest in the

successful project receives nothing from its research. In the second stage, the firms compete on

the product market either with or without the innovation.

As all approaches are ex ante equally likely to be successful, the firms have an incentive to

develop only the cheapest projects. However, the number of firms developing any given project

also determines the number of firms which will compete on the product market with the new

technology. Thus, when choosing which projects to develop, the firms face a trade-off—cheaper

approaches cost less to develop but will in equilibrium attract more competitors. I show that an

equilibrium of the investment game always exists and that the equilibrium market R&D portfolio

is uniquely determined. I provide a simple characterization of the equilibrium R&D portfolio

and show that it follows a step function—with more expensive approaches being developed by

fewer firms.

The characterization of the R&D portfolio is then used to derive comparative statics. I show

that a decrease in the number of firms weakly decreases the variety of approaches to innovation

and also weakly decreases the amount of duplication. Hence, a merger leads to a weaklydecreas-

ing variety of approaches to innovation. A policy implication drawn from this analysis is that the

competition authorities should take into account the negative effects of a merger on the variety

of approaches to innovation, in part giving theoretical foundation to the concern expressed in the

Lockheed-Northrop case. However, if a merger leads to efficiency gains, this result need not hold.

Next, I consider the effects of a change in the intensity of competition between firms. I

define an increase in the intensity of competition as any exogenous change which decreases firm

profits.2An increase in the intensity of competition is shown to increase the variety of approaches

to innovation and to decrease the amount of duplication in equilibrium. Thus, an increase in

the intensity of product market competition leads to more specialized R&D portfolios. This

illustrates why an increase in the intensity of competition can increase and decrease the amount

of resources invested in R&D—if the reduction in duplication of research efforts is greater than

the increase in variety of research efforts, the total amount invested in R&D will decrease. If the

opposite is true, the total amount invested in R&D will increase.

I provide a characterization of the socially optimal R&D portfolio and compare it with the

market R&D portfolio. I derive the condition under which the market investmentin the variety of

research approaches is optimal, too low, or too high. Similarly,I derive the condition under which

the market duplication of research approaches is optimal, too low, or too high. I show that in a

large class of homogeneous goods models, the market will always underinvest in the variety of

approaches to process innovation. This result implies that there is a role for government subsidies

of R&D. Furthermore, it implies that the subsidies should be targeted at research projects with

high development costs and high potential payoffs.

The main body of the article assumes that the innovation is drastic, firms are symmetric,

have unlimited budgets, and use only pure strategies. I consider the effects of relaxing these

assumptions in turn and show that the equilibrium structure is, in general, robust. In particular,

1Innovation is drastic if whenever at least one firm innovates, firms without the innovation cannot compete. This

assumptionwas introduced by Arrow (1962); see also Gilbert (2006). This assumption is not needed for the characterization

of the equilibrium and is relaxed in Section 7.

2A similar approach is taken in Schmidt (1997) and Schmutzler (2013).

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