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

  • Gilad Sorek EMAIL logo
Published/Copyright: November 23, 2020
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 21 Issue 1

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.

Keywords: industrial policy; Schumpeterian growth; two-sector-R&D; welfare
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 = 0 ∞ β t ln [ ( ∫ i = 1 M i ( q i , t x i , t ) 1 ε d i ) ε ] = ∑ t = 0 ∞ β t ln ( M t ε q t x t ) = ∑ t = 0 ∞ β t ln ( M t ε q t − 1 κ t [ L − M t + 1 f ( κ t + 1 ) M t ⏟ x ] )

Equation (A.1) implies that the present value of consumer’s life time utility function is additive separable in κ t and M t , and their effect on the consumer’s present value life time utility is summarized in the following expression:

(A.2) β t ln κ t 1 − β + β t − 1 ln [ L − M t f ( κ t ) ] + ( ε − 1 ) β t ln ( M t )

Maximizing the above expression with respect to M t and κ t yields to following first order conditions:

(A.3) f .o .c  1 for M t : f ( κ t ) L − M t ** f ( κ t ) = β ( ε − 1 ) M t **

f .o .c 2 for  κ t : M t f ′ ( κ t ** ) L − M t f ( κ t ** ) = β ( 1 − β ) κ t **

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 ∗ ∗ = s − 1 ϕ ( 1 − β ) ,   M ∗ ∗ = L f ( κ ∗ ∗ ) [ 1 ( ε − 1 ) β + 1 ]

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

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Contributions
  2. Quantifying the Effects of Patent Protection on Innovation, Imitation, Growth, and Aggregate Productivity
  3. Sectoral Productivity Gaps and Aggregate Productivity
  4. Optimal Industrial Policies in a Two-Sector-R&D Economy
  5. Entry Costs, Task Variety, and Skill Flexibility: A Simple Theory of (Top) Income Skewness
  6. Leaning-Against-the-Wind: Which Policy and When?
  7. Tax Policy and Toxic Housing Bubbles in China
  8. The Cyclicality of On-the-Job Search Effort
  9. A Test of Neo-Fisherism: 1964–2019
  10. Advances
  11. Evaluating Changes in the Transmission Mechanism of Government Spending Shocks
  12. Contributions
  13. On the Limits of Macroprudential Policy
  14. Robust Monetary Policy Under Uncertainty About the Lower Bound
  15. Monetary Policy and Cross-Border Interbank Market Fragmentation: Lessons from the Crisis
  16. International Welfare Spillovers of National Pension Schemes
https://doi.org/10.1515/bejm-2019-0197
Keywords for this article
industrial policy; Schumpeterian growth; two-sector-R&D; welfare

Articles in the same Issue

  1. Contributions
  2. Quantifying the Effects of Patent Protection on Innovation, Imitation, Growth, and Aggregate Productivity
  3. Sectoral Productivity Gaps and Aggregate Productivity
  4. Optimal Industrial Policies in a Two-Sector-R&D Economy
  5. Entry Costs, Task Variety, and Skill Flexibility: A Simple Theory of (Top) Income Skewness
  6. Leaning-Against-the-Wind: Which Policy and When?
  7. Tax Policy and Toxic Housing Bubbles in China
  8. The Cyclicality of On-the-Job Search Effort
  9. A Test of Neo-Fisherism: 1964–2019
  10. Advances
  11. Evaluating Changes in the Transmission Mechanism of Government Spending Shocks
  12. Contributions
  13. On the Limits of Macroprudential Policy
  14. Robust Monetary Policy Under Uncertainty About the Lower Bound
  15. Monetary Policy and Cross-Border Interbank Market Fragmentation: Lessons from the Crisis
  16. International Welfare Spillovers of National Pension Schemes
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