Spillovers, subsidies, and second‐best socially optimal R&D

• DOI: http://doi.org/10.1111/jpet.12411
• Author: Rabah Amir,Joana Resende,Dominika Machowska,Huizhong Liu
• Date: 01 December 2019
• Published date: 01 December 2019

J Public Econ Theory. 2019;21:1200–1220.wileyonlinelibrary.com/journal/jpet1200

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© 2019 Wiley Periodicals, Inc.

Received: 16 July 2019

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Accepted: 22 October 2019

DOI: 10.1111/jpet.12411

ORIGINAL ARTICLE

Spillovers, subsidies, and second‐best socially

optimal R&D

Rabah Amir

1,2

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Huizhong Liu

3

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Dominika Machowska

4

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Joana Resende

5

1

Department of Economics, University of

Iowa, Iowa City, Iowa

2

Max Planck Institute for Tax Law and

Public Finance, Munich, Germany

3

Wenlan School of Business, Zhongnan

University of Economics and Law,

Wuhan, China

4

Department of Econometrics, University

of Lodz, Poland

5

Cef.up, Economics Department,

University of Porto, Porto, Portugal

Correspondence

Huizhong Liu, Wenlan School of

Business, Zhongnan University of

Economics and Law, Wuhan 430073,

China.

Email: huizhong-liu@hotmail.com

Abstract

This paper provides a thorough second‐best welfare

analysis of the standard two‐stage model of R&D/

product market competition with R&D spillovers. The

planner’s solution is compared to the standard non‐

cooperative scenario, the R&D cartel, and the cartelized

research joint venture (or joint lab). We introduce the

notion of a social joint lab, as a way for the planner to

avoid wasteful R&D duplication. With no spillovers, the

non‐cooperative scenario, the joint lab, and the second‐

best planner’s solutions coincide. However, with spil-

lovers, all three scenarios yield R&D investments that

fall short of the socially optimal level. To shed light on

the role of the spillover level on these comparisons, we

observe that the gaps between the market outcomes and

the planners solutions widen as the spillover parameter

increases. Finally, we establish that a social planner and

a social joint lab solutions may be achieved starting from

any of the three scenarios by offering firms respective

suitably weighted quadratic R&D subsidization sche-

dules.

KEYWORDS

cooperative R&D, second‐best R&D, social joint lab, socially efficient

R&D subsidization

JEL CLASSIFICATION

D60; L13; O35

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INTRODUCTION

Starting from Schumpeter (1942), the interplay between market structure and firms’propensity

for innovation has been a continuously active major research issue. In recent years, the fact that

this debate has integrated cooperation in research and development (henceforth R&D) may be

seen as an extension of the set of possible market structures that one might instructively

compare in terms of the resulting incentives firms have for conducting R&D. Another

important feature that this literature has brought to the fore is the imperfect appropriability of

R&D. The importance of this feature on multiple counts is amply reflected in the recent

literature on R&D in industrial organization, both in its empirical and its theoretical strands.

The main purpose of this paper is to conduct a second‐best welfare analysis of the standard

two‐stage duopoly of R&D/product market competition, in settings where know‐how is

imperfectly appropriable by firms. The main emphasis is on the role of R&D spillovers

in a detailed comparison of the second‐best outcome with the well‐known market‐based

scenarios for conducting R&D. A second objective of the paper is to investigate the scope for

respective efficiency‐restoring subsidies, starting from non‐cooperative R&D and an R&D cartel

as initial (unregulated) situations.

Spence’s (1984) pioneering work on R&D, market performance and public policy introduced the

idea of a constant spillover parameter as a practical and tractable way of modeling the imperfect

appropriability of research and development. In his model, a constant proportion of each firm’sR&D

expenditure flows freely to all the rival firms. This constant proportion is itself defined as the

spillover parameter, postulated to lie in the unit interval, with the end values of 0 and 1

corresponding, respectively to R&D being a purely private good and a purely public good. Much of

the follow‐up literature adopted this convenient modeling trick in investigating further the role of

spillovers in imperfectly competitive markets with R&D as a strategic variable. See Katz (1986),

d’Aspremont and Jacquemin (1988, 1990), Kamien, Muller, and Zang (1992), Amir (2000), and Amir,

Evstigneev, and Wooders (2003), among many others (also see the very early study by Ruff (1969).

In much of the follow‐up literature on R&D and market structure, the underlying non‐

cooperative benchmark scenario for strategic R&D is a standard two‐stage game where firms

choose process R&D levels in the first stage, and then Cournot outputs in the second stage.

Starting with Ruff (1969) and Spence (1984), most of the extant literature on imperfectly

appropriable R&D focuses on understanding the distortions implicit in the underlying strategic

interaction, and on providing corrective measures to alleviate these distortions. A recent highly

active strand of literature focuses in particular on R&D cooperation, and on its overall market

performance relative to the usual, default non‐cooperative scenario.

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Perhaps surprisingly, the extant literature has so far devoted little attention to the usual

benchmarks of first and second‐best social planner’s solution as part of the aforementioned

comparisons. In this regard, two important exceptions to this broad observation must

be explicitly mentioned. First, d’Aspremont and Jacquemin’s influential study had considered

the first‐best planner’s solution as a theoretical benchmark for comparative purposes

when evaluating the merits of R&D cooperation relative to non‐cooperation. In addition,

Suzumura (1992) showed that the planner’s solution leads to less R&D than the non‐cooperative

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A brief list of related studies includes Brander and Spencer (1983), Amir and Wooders (2000), Jin and Troege (2006), Tesoriere (2008), Cosandier, De Feo, and

Knauff (2017), Martin (2002), Stepanova and Tesoriere (2011), Burr, Knauff, and Stepanova (2013), Vives (2008), and Poyago‐Theotoky (1999), among many

others. The literature on R&D cooperation has more recently been extended to other areas of economics, including environmental innovation (Mantovani &

Ruiz‐Aliseda, 2015; McDonald & Poyago‐Theotoky, 2017; Dijkstra and Gil‐Moltó, 2018), licensing (Fan, Jun, & Wolfstetter, 2018), and the organization of the

firm (Chalioti, 2015; Chalioti & Serfes, 2017; Niu, 2018).

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