Abstract
Profit-sharing licensing is quite a common business practice. In a Cournot duopoly model, we showed that if not subject to any restrictions this kind of technology for equity deal would lead to a decline in industry output and hurt consumers. To avoid the industry output contraction and protect the interests of consumers, the government can intervene in licensing by requiring that the profit-sharing rate specified by a licensing contract should not exceed the percentage difference of involved firms’ equilibrium outputs before licensing.
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Notes
Under quantity competition, if firm 1 increases output, the profit of firm 2 will decline. If there is no pecuniary correlation between the two firms, this negative externality will not be on the concern of firm 1. After equity transfer, however, this externality is partially internalized by firm 1, explaining why firm 1 has less incentives to increase production after licensing.
From a French data set consisting of 286 licensing contracts in 1990, Bousquet et al. (1998) found that \(78 \%\) of the contracts included royalties. Amongst the contracts with royalties, only nine specified a per-unit royalty while the remaining used an ad valorem scheme. Some real world examples of profit-sharing licensing are listed in the very beginning of this paper.
Note that, in the presence of costly technology transfer, Mukherjee and Tsai (2015) compared fixed-fee licensing with two-part tariff licensing and found that the equilibrium quality of the licensed technology and social welfare can be higher or lower under the two-part tariff contract as compared to the fixed-fee contract. This is in contrast to the general belief that firms are better off under the two-part tariff licensing contract, while social welfare is greater under the fixed fee contract.
A cost difference is said to be non-drastic if the monopoly price under the low cost exceeds the competitive price under the high cost.
Mathematically, this effect is reflected by the new positive item x appearing in firm 2’s first-order condition under licensing. This new positive item encourages firm 2 to raise output after licensing. Assumption 1 implies that the equilibrium is stable. A stable equilibrium indicates that a rise in firm 2’s output will reduce the output of its rival but will increase aggregate output.
Detailed calculations can be provided upon request.
Note that the percentage difference is measured from the perspective of firm 1’s (the licensor’s) output.
We would like to thank the referee for pointing out the necessity of this profitability check.
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Acknowledgements
I would like to thank the editor Prof. Giacomo Corneo and the two anonymous referees for helpful and insightful comments, which I believe have helped me substantially improve the paper. I am grateful also to the financial support from The Academic Prosperity Program by School of Economics, Shandong University and The Social Science Planning Fund Program by Shandong Province, China (16DJJJ05). I am responsible for all the remaining errors.
