Asian Journal of Business and Management (ISSN: 2321 - 2802) Volume 03 – Issue 01, February 2015 Asian Online Journals (www.ajouronline.com ) 77 Optimal Two-Part Tariff Licensing under Returns to Scale A. Karakitsiou 1* , A. Mavrommati 2 1 Industrial Logistics, ETS, Luleå University of Technology 97187 Luleå, Sweden 2 Department of Economics, University of Ioannina, Greece * Corresponding author’s email: athkar [AT] ltu.se _________________________________________________________________________________ ABSTRACT---- In this study we investigate a two-part tariff licensing contract that enables an incumbent innovator to license a cost reducing innovation in a Cournot duopoly characterized by non-constant returns to scale. We identify the optimal two-part tariff licensing contract based on the cost reduction imposed by the use of the new technology and the market parameter. Keywords—Patent Licensing; Royalty; Ad-valorem; two tarrif, Cournot Duopoly; Game Theory _________________________________________________________________________________ 1. INTRODUCTION A patent is defined as the exclusive right provided by the law to inventors in order to make use of, and to exploit, their inventions for a limited period of time. Therefore, the aim of a patent is twofold, firstly, acts as incentive of innovation and secondly, provides the inventors with diffusion control of their inventions. Patent licensing is the main tool used for disseminating the effects of innovation. The owner of a patent charges some payments for using the new technology to the authorized firms obtaining in this way a return on his investment in research and development. The profits of the patentee will depend on the structure adopted by the licensing agreement. In the literature the licensing policies are categorized into the following main categories, (a) up frond fee, which is usually a fixed fee that entitles the licensee to use the new technology to produce as many units as he wishes; (b) per unit royalty, that requires the licensee to pay a certain amount per unit of production; (c) value based (ad valorem) royalty, which in its simplest form consists of a uniform percentage (the rate) of the value of the products sold by the licensee; and (d) a two-part tariff, that is, a hybrid license consisting of a fixed fee and either a per-unit or an ad valorem royalty. The technology transfer by means of one of these type of contracts can be done in different oligopoly models, as Cournot, Bertrand or Stackelberg model. After its initialization by Arrow (1962), the patent licensing analysis has developed along three main research directions. The research work belonging to the first direction seeks to find the optimal licensing scheme under the assumption that there exists an external patentee whose sole objective is to sell the patent to other firms. Following this line, Kamien and Tauman (1986), in their seminal work, considered an external patentee and a homogeneous Cournot oligopoly and shown that licensing by means of up frond fees dominates licensing by a per unit royalty. Similar results can be found in Katz and Shapiro (1986) and Kamien et al., (1992). Bousquet et al., (1998) consider an external innovator trying to identify the optimal licensing policy (ad valorem or per unit) under uncertainty. See also Kamien (1992) for a survey. The second direction on the other hand, investigates the optimal licensing scheme by assuming that the patentee is an internal inventor. Considering the case of an internal innovator, Wang (1998) found that in a Cournot duopoly a per- unit royalty licensing can be superior to an up frond fee licensing if the innovation is non-drastic. Kamien and Tauman (2002) consider the Wang's model in the case of any number of competitors, their findings shows that when the number of firms in the industry exceeds a certain threshold number, the patentee's profit is optimized when licensing by means of a royalty rather than by auctioning fixed fee licenses. Filippini (2005) modeled the competition as a Stackelberg duopoly with the innovator as the Stackelbergleader, he proved that the optimal policy has only royalty and no upfront fee. The works of Wang (2002) and Wang and Yang (1999) are concerned with the superiority of up frond fee under Bertrand and Cournot competition in the presence of product differentiation. While San Martin and Saracho (2010) have shown that in the classic homogenous good Cournot duopoly an internal patentee will always prefer the ad valorem royalty to a per unit royalty.