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Licensed Unlicensed Requires Authentication Published by De Gruyter November 23, 2020

Optimal Industrial Policies in a Two-Sector-R&D Economy

Gilad Sorek

Abstract

This study characterizes welfare-enhancing industrial policies in a two-sector-R&D economy that incorporates both vertical and horizontal innovation. It elaborates on current welfare analyses of two-sector-R&D economies along two lines. First, it explores the welfare properties of non-drastic innovations whereas current analyses are confined to drastic innovations. It is shown that while the endogenously chosen size of drastic innovations is insufficient compared to social optimum, the size of non-drastic innovations may be excessive compared with the welfare maximizing one. Second, it explores welfare-enhancing policies designed to restrict innovators’ market power, whereas current policy analyses focus on R&D and market-entry subsidies. The welfare-maximizing policies presented here combine proper limitations on innovators’ market power along with a corresponding production tax (or subsidy). The limitations over innovators’ market power are aimed to support the optimal innovation size, and the corresponding production tax is set to support the optimal product variety span.

JEL Classification: O-30; O-40

Corresponding author: Gilad Sorek, Department of Economics, Auburn University, Auburn, Alabama, USA, E-mail:
I thank two referees of this journal for numerous thoughtful and constructive comments which helped improving this paper significantly. I have also benefitted from comments by seminar participants at the 2017 Spring Midwest Macroeconomic Meeting at Louisiana State University, 2018 Fall Midwest Macroeconomics Meeting at Vanderbilt University, and the 2019 DEGIT Conference at the University of Southern Denmark. This work modifies, corrects, and extends an earlier circulated working paper titled “Market power, welfare, and growth through horizontal and vertical competition”.
Appendix

The allocation of labor over R&D and production activity that maximizes the lifetime utility (1), defines the socially-optimal innovation size and product variety span, where the optimal growth path is subject to the aggregate resources uses constraint (8). Substituting (8) into (1) we write the welfare maximization objective function:[38]

(A.1)U=t=0βtln[(i=1Mi(qi,txi,t)1εdi)ε]=t=0βtln(Mtεqtxt)=t=0βtln(Mtεqt1κt[LMt+1f(κt+1)Mtx])

Equation (A.1) implies that the present value of consumer’s life time utility function is additive separable in κt and Mt, and their effect on the consumer’s present value life time utility is summarized in the following expression:

(A.2)βtlnκt1β+βt1ln[LMtf(κt)]+(ε1)βtln(Mt)

Maximizing the above expression with respect to Mt and κt yields to following first order conditions:

(A.3)f.o.c 1forMt:f(κt)LMt**f(κt)=β(ε1)Mt**
f.o.c2for κt:Mtf(κt**)LMtf(κt**)=β(1β)κt**

Then, substituting the above first order conditions into each other, and using the explicit form of the innovation cost function (4), yields the welfare maximizing innovation size and variety span presented on Eq. (15), which are stationary:

κ=s1ϕ(1β),M=Lf(κ)[1(ε1)β+1]

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Received: 2019-09-25
Accepted: 2020-10-28
Published Online: 2020-11-23

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