Optimal knowhow transfers in licensing contracts

Authors: Pedro Mendi Rafael MonerColonques José J SempereMonerris

Publish Date: 2015/12/12

Volume: 118, Issue: 2, Pages: 121-139

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Abstract

This paper studies optimal licensing contracts in the presence of moral hazard associated with costly provision of knowhow by the licensor In our setting the target market is defined as the fraction of consumers that have a positive valuation for the product that is licensed It is shown that no matter how thin the target market is knowhow transfer always takes place Consistent with actual practice the optimal licensing contract includes a royalty on sales to attenuate the moral hazard problem However full knowhow transfer will not occur for low enough maximum willingness to pay and high enough convexity of knowhow cost Finally it is also shown that the effective inclusive of the royalty marginal cost exceeds the one when knowhow transfer does not occur thus showing a potential malfunction of knowhow transfer specially if the recipient is a developing countryWe thank the editor and two anonymous referees for their helpful comments and suggestions We also thank comments from seminar participants at Universidad de Navarra and Strathmore University as well as to conference participants in the 11th International Industrial Organization Conference at Boston and XXVIII Jornadas de Economía Industrial at Segovia Financial support from Fundación Ramón Areces Mendi as well as from the Spanish Ministry of Economy and Competitiveness under the Project ECO201345045R and from Generalitat Valenciana under the Project PROMETEOII/2014/054 MonerColonques and SempereMonerris is gratefully acknowledged All errors are our ownIn order to prove the propositions it is first important to present first the three different cases that arise when there is partial transfer of knowhow As presented in the text there are two different intervals in the royalty rate that induce partial knowhow transfers The first one for a12mc r le a12mcbig frac2alpha a2alpha ac2big corresponds to kr = k which implies en effective marginal cost of hatc= a12m and therefore all consumers in the relevant market buy the good qhatc=m Thus the licensor maximizes the following function rm+ am2fracalpha 1+ fracra12mc22 The interior equilibrium royalty rate is r=fracmc2alpha + a12mc it is decreasing in m and leads to kr = k =frac mcalpha and f=am2 Thus for this region the licensor profits are equal to Pi L p= fracmc22alpha + ma1mcConsider now a12mcfrac2alpha a2alpha ac2 r le frac 2 alpha ac Noticing that kr = k in this interval and that hatcr= c1 fracr c2 alpha a+ r so that not all consumers in the highend market buy the good The licensor maximizes the following function r frac a hatcr2a + frac ahatcr24a fracalpha 2fracr c2 alpha a2 Yielding an interior solution which equals r= frac2 alpha a c2ac4 alpha 2 a2+2 alpha a c2c4 Given r the equilibrium knowhow the fixed fee licensor’s payoffs and technology payments are as follows kr=fracc3ac4 alpha 2 a2+2 alpha a c2c4 f= frac4 alpha 4 a3 ac24 alpha 2 a2+2 alpha a c2c42 Pi L p= fracalpha 2 alpha a + c2ac2 24 alpha 2 a2+2 alpha a c2c4Next it must be checked whether the above interior solutions r and r are consistent with the intervals at which they apply That is whether r in a12mc a12mc frac2alpha a2alpha ac2 and r in a12mcfrac 2alpha a2alpha ac2frac2alpha ac Considering first r it is easy to show that it is always greater than the lower bound in the interval but to satisfy the upper bound it is required that m fracalpha ac4 alpha ac2=m Then we conclude that the equilibrium royalty is r if m m while it is overliner if m m where overliner is precisely the upper bound in the interval ie overline r = a12mcfrac2alpha a2alpha ac2=frac4alpha a22alpha ac2overlinemm Next consider r it is easy to check that it is greater than the lower bound in the interval as long as m frac2 alpha 2 aa c4 alpha 2 a2+2 alpha a c2c4= m Thus if m m then the equilibrium royalty rate is r being overliner otherwise Finally r is smaller than the upper bound in the interval if and only if alpha fracc sqrt4ac+c2c4 a When the equilibrium royalty is overliner then koverliner=frac2 a c2alpha ac2mm hatcoverliner=a12m also qhatcoverliner=m the fixed fee equals am2 and the licensor’s profits are frac8 alpha 2 a2 m a1mcc2alpha ac2+2am22 alpha ac2 22alpha ac22

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