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Journal of Economics and Finance

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30-10-2015

Output subsidies in mixed oligopoly with research spillovers

Authors: Shoji Haruna, Rajeev K. Goel

Published in: Journal of Economics and Finance | Issue 2/2017

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Abstract

Output subsidies have been proposed as a policy to rectify inefficiencies in mixed markets with public and private firms. This paper adds to the literature on mixed oligopolies by examining the behavior of firms, with research spillovers, and the government subsidizes output. A key finding is that output subsidies, unlike R&D subsidies, do not necessarily attain efficient resource allocation. Output subsidies are justified only at relatively low R&D spillovers. The rankings of optimal output subsidies, output and profits under alternate scenarios are significantly affected by spillovers. Social welfare ranking, on the other hand, is independent of spillovers, and welfare is largest under R&D competition.

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The role of the public firm has been examined by De Fraja and Delbono (1989); Delbono and Denicolo (1993) and Harris and Wiens (1980).

For significant papers on mixed oligopolies, see De Fraja and Delbono (1990); Pal and White (1998) and White (1996).

Output subsidy in mixed oligopolies is considered in Fjell and Heywood (2004); Pal and White (1998); Tomaru and Saito (2010), and White (1996). However, this body of research does not consider R&D spending and related spillovers.

See World Trade Organization, “The Economics of Subsidies”, http://www.wto.org/english/res_e/booksp_e/anrep_e/wtr06-2c_e.pdf for background on output subsidies; and A. Rangachari, “Check Fiscal Recklessness”, The Hindu, http://www.thehindubusinessline.com/opinion/check-fiscal-recklessness/article5530663.ece; and D. Schellberg, “Drilling, Mining Boom does not Spell Environmental Doom”, Central Daily, http://www.centredaily.com/2013/12/31/3965648/drilling-mining-boom-does-not.html for examples of related debate in the media.

An interesting extension is modeled by Matsumura and Kanda (2005) where they allow entry of private firms in mixed oligopolies.

Mixed oligopolies emerging from privatization might involve multiple private firms competing with a public firm (see White (1996)). Analytically, one could extend our analysis to include more than one private firm, especially when private firms are identical. However, intuitively, this might decrease the need for an output subsidy due to reduced output distortion between public and private firms. This aspect has been noted elsewhere (see Kesavayuth and Zikos (2013, p. 95)).

Gil-Molto et al. (2011) examine privatization in a mixed oligopoly with an R&D subsidy, while Zikos (2007) introduces two kinds of subsidies, e.g., R&D and output subsidies, albeit without research spillovers, and White (1996) considers privatization in a mixed oligopoly with an output subsidy. More recently, Kesavayuth and Zikos (2013) compare welfare under research and output subsidies in the presence of research spillovers.

We do not allow for a tax instead of a subsidy when the optimal solutions of subsidies are negative. For example, even if the government could use a subsidy or a tax as a policy, it is not likely or practical for the government to smoothly change its policy, e.g., from a subsidy to a tax, every time R&D spillovers change.

It is shown by Myles (2002) and Poyago-Theotoky (2001) that the irrelevance result also holds in more general models.

It can also be verified easily that the marginal production costs of the public and private firms are equal in equilibrium: the efficient resource allocation is achieved.

Tomaru (2007) considers a mixed duopoly with a domestic public firm only performing R&D, but without spillovers.

When R&D is conducted only by a public firm, there is no room for the government to introduce output subsidy - the policy loses its intended function.

For examples on research spillovers, see Bernstein and Yan (1997); Caminati and Stabile (2010), and Jaffe (1986). Research spillovers can change when there is easier imitation and increased technology transfer via more patent citations (e.g., Maurseth and Verspagen (2002)). Of course, the ability to benefit from others' research is dependent upon a firm’s absorptive capacity (see Kamien and Zang (2000)).

As stated above, Zikos (2007) assumes no spillovers, while Heywood and Ye (2009) assume β = 1.

As the R&D decision of firms is more flexible than that of subsidies set by the government, we assume that subsidies and R&D are determined in the first stage and the second stage, respectively. In contrast, a model where R&D and subsidies are determined in the reverse order might theoretically be built.

Details about the first-order conditions are not reported but are available upon request.

Both firms' output reaction curves are downward sloping. The slope of the public firm’s reaction curve is steeper than that of the private firm’s. Thus, quantity equilibrium is locally stable.

The second-order condition with respect to R&D is satisfied for any β.

The second-order condition, d ² W/ds ² < 0, is satisfied as −16 − 16β + 48β ² − 18β ³ < 0.

We use Mathematica to investigate properties of W ⁺. In the following analyses, it is used to investigate functional properties.

R&D competition in mixed oligopolies has been studied by Gil-Molto et al. (2011); Heywood and Ye (2009); Ishibashi and Matsumura (2006); Nett (1994), and Zikos (2007).

The second-order conditions of both firms with respect to their R&D are also satisfied for any β. In addition, we have\( \left({\partial}^2W/\partial {x}_0^2\right)\left({\partial}^2{\pi}_1/\partial {x}_1^2\right)-\left({\partial}^2W/\partial {x}_1\partial {x}_0\right)\left({\partial}^2{\pi}_1/\partial {x}_0\partial {x}_1\right)=75+575\beta -575{\beta}^2+75{\beta}^3>0 \). In contrast, R&D equilibrium in a pure duopoly is not always stable (Henriques (1990)).

The effects of output subsidies on outputs are also dependent on spillovers, so the effects are different from those in the absence of R&D (see Pal and White (1998) and White (1996)).

We compare the coefficients of (a − c) to rank output subsidies and outputs.

We compare the coefficients of (a − c)² to rank profits and welfare.

This finding can be seen in line with findings of Kesavayuth and Zikos (2013), where (under simultaneous R&D choice) they find R&D subsidies to be more desirable to output subsidies at high spillover rates. We show that even without research subsidies, output subsidies might not be desirable.

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Title: Output subsidies in mixed oligopoly with research spillovers
Authors: Shoji Haruna
Rajeev K. Goel
Publication date: 30-10-2015
Publisher: Springer US
Published in: Journal of Economics and Finance / Issue 2/2017
Print ISSN: 1055-0925
Electronic ISSN: 1938-9744
DOI: https://doi.org/10.1007/s12197-015-9346-2

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