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Journal of Quantitative Economics

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08.11.2017 | Original Article

Fee vs. Royalty Licensing and Consumers’ Welfare

verfasst von: Tarun Kabiraj

Erschienen in: Journal of Quantitative Economics | Ausgabe 3/2018

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Abstract

In a duopolistic trade model we have shown that a tariff can influence the optimal licensing strategy of the foreign firm. A high tariff will induce fee licensing and a low tariff will result in a royalty licensing. From the viewpoint of the consumers both high tariff and high royalty are distortionary; hence there is a trade-off between a tariff and a royalty. Assuming consumers’ welfare maximization as an objective of the government, we show that royalty licensing is induced if the cost saving under foreign technology is small; otherwise fee licensing is induced by an appropriate choice of tariffs.

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See the World Tariff Profiles 2015 (http://www.wto.org/statistics).

There are in fact a host of articles which have shown that in a duopoly, with patentee as a producing firm, the optimal licensing contract is the royalty contract where an appropriate royalty is charged per unit of output of the transferee. See, for instance, Wang (1998, 2002), Mukherjee and Balasubramanian (2001) and Fauli-Oller and Sandonis (2002), etc. In all these papers royalty licensing is generally preferred from the viewpoint of the patentee, but the fee licensing generates a larger consumer surplus.

There are some papers which have shown the possibility that tariffs can benefit the consumers, but that is completely in a different situation. See, for instance, Jones and Takemori (1989), and Helpman and Krugman (1989).

In the present paper we restrict our analysis to the cases of fee licensing and royalty licensing only. In the setup of our paper when tariffs are in the intermediate range, ‘fee plus royalty licensing’ can be shown to be optimal from the perspective of the patentee. But since in our model the government likes to maximize consumers’ welfare, which occurs only when fee licensing is induced by an appropriate choice of the tariff rate, in (subgame perfect) equilibrium, therefore, fee plus royalty will never occur.

Under Cournot equilibrium, with zero tariff, the local firm’s output is \(q{ }_2=(a-c-\varepsilon )/3\). Therefore the local firm survives if and only if \(\varepsilon <a-c\).

Actually, if the foreign firm prefers no licensing equilibrium, it will give an unacceptable offer.

If the innovation is drastic, i.e., \(\varepsilon \ge a-c\), without tariffs it is monopoly of the foreign firm, but a tariff protection may yield a duopoly market. Then the assumption of initial duopoly requires the restriction that \(\varepsilon -(a-c)\le \tau <\frac{a-c+2\varepsilon }{2}\).

Formally, \(\Delta _2 =\{(\varepsilon ,\tau )|\varepsilon \in (0,a-c)~\hbox {and}~\tau \in [\max \{0,\frac{3\varepsilon -2(a-c)}{8}\}, \min \{\frac{(\hbox {a}-\hbox {c})}{5}, 5(\hbox {a}-\hbox {c})-5\varepsilon \}]\}\) and \(\Delta _3 =\{(\varepsilon ,\tau )|\varepsilon \in (\frac{2(a-c)}{3},a-c)~\hbox {and}~\tau \in [0, 5(\hbox {a}-\hbox {c})-5\varepsilon ]\}\).

Note that for all \((\varepsilon ,\tau )\) in QRSQ, only royalty licensing is profitable (fee licensing is not), therefore royalty contract with \(r^{*}=\bar{\hbox {r}}\) will occur.

If fee licensing could be enforced, consumers’ surplus would be the highest with \(\tau =0\). But the problem is that if \(\tau =0\), the technology will be transferred under the royalty contract with royalty rate \(\varepsilon \). Then in this case there will be no increase in consumers’ surplus under licensing, and a royalty contract with \(\tau >0\) will reduce consumers’ surplus.

To see this more formally, let \(\hbox {CS}_{1}\) be the maximum consumer surplus under the objective of maximizing consumer surplus only, and the corresponding tariff revenue of the government is \(\hbox {TR}_{1}\). Now, if the government wants to maximize consumer surplus plus tariff revenue, let those values be \(\hbox {CS}_{2}\) and \(\hbox {TR}_{2}\) respectively such that \(\hbox {CS}_{2} + \hbox {TR}_{2}\) is the maximum amount under this objective. Then clearly, \(\hbox {CS}_{2} + \hbox {TR}_{2} \ge \hbox {CS}_{1 }+ \hbox {TR}_{1}\). Now suppose \(\hbox {CS}_{2 }< \hbox {CS}_{1}\), then it must be the case that \(\hbox {TR}_{2}>\hbox {TR}_{1}\). This means, if the government can redistribute tariff revenue freely, it is always possible to have the situation that \(\hbox {CS}_{2} + \hbox {TR}_{2} -\hbox {TR}_{1} \ge \hbox {CS}_{1}\) where the left hand side is the consumer’s benefit under the objective of consumers’ welfare maximization.

This possibility suggested by one referee of this journal, is important and insightful; In the present paper, however, we have not attempted to model this so as to keep the other results undisturbed.

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Titel: Fee vs. Royalty Licensing and Consumers’ Welfare
verfasst von: Tarun Kabiraj
Publikationsdatum: 08.11.2017
Verlag: Springer India
Erschienen in: Journal of Quantitative Economics / Ausgabe 3/2018
Print ISSN: 0971-1554
Elektronische ISSN: 2364-1045
DOI: https://doi.org/10.1007/s40953-017-0111-6

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