Abstract
We analyze the interplay of privatization and technology licensing under a public budget constraint, where a cost-disadvantaged public firm has to generate profits to pay for the license. In a mixed duopoly, we consider the licensing of a cost-reducing technology by an outsider innovator. The innovator chooses to license smaller sizes of innovation to both firms, whereas larger innovation is licensed exclusively to the private firm. The public firm alone never gets the license. Thus, the public firm can never “catch up” with its more efficient private rival. We find the possibility of both partial and full privatization in our model. Additionally, from a social planner’s perspective, licensing to both firms is always preferred.
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We do not analyze or generate any datasets.
Notes
The optimal degree of privatization depends critically on the production technology, where marginal costs can be increasing or constant. In the increasing marginal cost case, partial privatization can improve welfare even if the private and public firms are equally efficient (De Fraja and Delbono,1989; Matsumura 1998). However, in the constant marginal cost case, a public monopoly emerges in equilibrium if there is no cost asymmetry (Matsumura 2003a; Pal 1998; Fujiwara 2007).
There exists a vast literature on optimal licensing in a purely private oligopoly, which studies both the outsider and insider innovator context. For instance, in case of an outsider innovator, fixed fee licensing is found to be better than per-unit royalty licensing (see Kamien and Tauman 1986; Katz and Shapiro 1986; Kamien et al. 1992), but in case of an insider (i.e., a competitor), per-unit royalty licensing is preferred over fixed-fee (Wang 1998, 2002; Kamien and Tauman 2002). Poddar and Sinha (2010), on the other hand, show the optimality of fixed fee, royalty and two-part tariff in an asymmetric Cournot duopoly model with an insider innovator.
See Sinha (2016) for the definition of common innovation as opposed to a new technology innovation.
Non-drastic in our model requires that the output of firm \(i\) is positive when firm \(j\) is the only recipient of the new technology, \(i\ne j\).
Note that in order to keep the analysis simple, we allow for discriminatory licensing fees for the two firms. An alternative approach would be to charge a uniform fee to the firms such that both of them find it acceptable. In that case, the innovator can charge the minimum of the two firms’ willingness to pay as the licensing fee. This alternative licensing scheme would reduce the attractiveness of offering two licenses for the innovator. But, such a pricing structure will complicate the algebra without adding much value to the paper.
We assume no breach of contract of payments or renegotiation of the licensing contract.
Note that \({q}_{0}^{{\text{NL}}}>0\) by Assumption 1.
Note that by Assumption 1, \({q}_{0}^{L0}\) and \({q}_{0}^{L1}\) are positive and by Assumption 2, \({q}_{1}^{L0}>0\).
The second order conditions for partial privatization in all regimes are satisfied under Assumptions 1 and 2.
Suppose under some parameter values, the innovator foresees a rejection by the public firm in game \(G0\) due to its welfare consideration (i.e., if \({W}^{L0} < {W}^{L1}\)) then the innovator will not choose \(G0\), but will instead choose one of the other two games depending on its payoff.
Given the complicated expressions, we use Mathematica software for our analysis.
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Acknowledgements
We are immensely thankful to the Editor, Vivek Ghosal and an anonymous referee of this journal for their insightful comments and suggestions that significantly improve this paper’s presentation. We are also grateful to the seminar participants at the Delhi School of Economics and the 16th Annual Conference of Forum for Global Knowledge Sharing at the Indian Institute of Technology, Bombay. In particular, we would like to thank Sourabh Bikas Paul and Neelanjan Sen for very useful feedback on an earlier version of the paper. The usual disclaimer applies.
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Shastry, M.H., Sinha, U.B. Privatization and Licensing Under Public Budget Constraint. J Ind Compet Trade 24, 9 (2024). https://doi.org/10.1007/s10842-024-00411-y
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DOI: https://doi.org/10.1007/s10842-024-00411-y