### Fee versus Royalty Licensing in an Endogenous R&D Model

1 2 ·2 3

1. Y. Lee, C.M. Lu , C.S. Tsm , C.S. Huang

1 Department of International Business, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan

### 2

Department of International Business, Kao Yuan University, Kaohsiung County, Taiwan3 Department of Economics, National Chung Cheng University, Chia-Yi County, Taiwan

(itjylee@cc.kuas.edu.tw, cm5757@cc.kyu.edu.tw, cstsai@cc.kyu.edu.tw, ecdah@ccu.edu.tw)

Abstract -The past researches study on the technology licensing considering a fixed-fee and a royalty by utilizing an exogenous research and development (R&D) model with the patentee has a cost-reducing innovation. In this paper, we discuss the patentee's R&D investment licensing under a fixed-fee licensing versus a royalty licensing with an outsider patentee. Two conclusions are: (1) the R&D investment with the fixed-fee licensing is always no less than with the royalty licensing, (2) the fixed-fee licensing is still the best strategy for the patentee himself and for the whole society.

Keywords - Technology licensing, research and

development, patent

I. INTRODUCTION

Since Solow (1957) finds that only a traction of per-capita growth is related to the increasing ratio of capital to labor. The role of technological progress in improving welfare is attracted by economists. Schumpeter (1943) points out that monopolies are natural breeding grounds for R&D and if one wants to induce firms to undertake R&D, one must accept the creation of monopolies as a "necessary evil". But Arrow (1962) finds that the patentee's licensing in a perfect competition market could earn more profit than in a monopoly market, and R&D activities would not decrease.

Taylor and Silberston (1973) fmd that there are 50% of patentees practice license through royalty, 10% utilize the fixed-fee, while 40% exploit a two-part pricing or a more complicated pricing policy. With respect to the technology licensing strategies, Rostoker's (1984) reveals that 39% of the patentees exploit the royalty, 13% of them employ it with the fixed-fee, and 46% of them select the mixed strategy--royalty plus fixed-fee.

Many literatures focus on the impacts on the patentee's profit and the social welfare under different licensing strategies assuming the patentee's innovation is exogenous. The theoretical studies on the technology licensing can be roughly classified into two categories: the patentee participates in production and not in

978-1-4244-3672-9/09/$25.00 ©2009 IEEE

production. Arrow (1962), Kamien and Schwartz (1982), Kamien and Tauman (1984, 1986), Gallini (1984), Gallini and Winter (1985), Gallini and Wrigh (1990), Muto (1993), Jin (1995), Sen (2005a, b), and Lee and Huang (2006a, b) discuss the technology licensing when the patentee participates without production. And they only focus on the issue of licensing revenue. Besides, in the studies of Wang (1998, 2002), Kamien and Tauman (2002), Wang and Yang (2004), and Sen and Tauman (2007), they all assume that the patentee is both a market participant and licensor. These researches not only focus on the revenue of licensing but the strategic effect of licensing.

Some other literatures also study on the R&D investment on strategic effect, spillover effect, research joint ventures and the network externalities considering an endogenous innovation. And Tirole (1988) has a perfect review and discussion about these. Meanwhile, those researches less discuss the effects of the licensing strategies on the R&D investment.

Katz and Shapiro (1985) utilize duopoly model to discuss the patentee's R&D investment, licensing strategy, and the licensee's production quantity based on the dynamic game. But they neither discuss the patentee's profit and the R&D investment under different licensing strategies nor overlook the cost of R&D investment. Tn this paper, we assume the patentee is an outsider and discuss the choices of R&D investment and licensing strategy considering the linear demand function. Besides, the related social welfare is discussed.

Our model combines the endogenous R&D model established by D'Aspremont and Jacquemin (1988) and the technology licensing model in Kamien and Tauman's (1986) research. The decision sequence of the patentee is as followed: firstly, to choose an optimum R&D investment; secondly, to choose the optimum licensing strategy (non-licensing, royalty licensing or fixed-fee licensing); thirdly, the licensee decides to accept the licensing or reject it; finally, to decide the production quantity when entering the market. This licensing strategy structure could be defmed as a dynamic game with perfect information. We use a backward induction to get the sub-game perfect Nash equilibrium.

c, when p and a are relatively small, we infer that

r* <t:

### ;

;otherwise, r*=I:### ;

.When the royalty licensing is adopted and marginal cost is given, if R&D efficiency is relatively high and the market scale is relatively small, the royalty rate is smaller than the cost of R&D can save. This is a reasonable result since it is the same as other studies that the drastic technology superior can make by R&D activities under a higher R&D efficiency and a smaller market scale, then E: > a - c Otherwise, when the efficiency of R&D is relatively low and the scale of market is relatively large, then E:::; a - c .

On the other hand, the cost saving innovation will reach the maximum technically when market scale is relatively large or market scale is small with a high R&D efficiency. Otherwise, there is an interior solution in R&D. And this is similar to the results with fixed-fee licensing.

Ill. DlSSCUSSION

A. R&D investment and profit of the patentee

According to the foregoing discussion, we infer the following proposition by comparing the patentee's profit and R&D investment between these two different licensing : .

Proposition 3:

(1) The R& D investment under the fixed-fee is always not less than that under the royalty, and the patentee s

optimal licensing strategy is the fixed-fee authorization.

(2) The profit of the licensee under the royalty is always no less than that under the fixed-fee.

The economic intuition of proposition 3 is that the licensee can make the most efficient production expansion with the fixed-fee licensing since the reducing cost is larger than the royalty. The patentee will face a higher induced demand of innovation under a fixed-fee licensing. When the other conditions remains constant, the patentee will invest more R&D and the margin of innovation will be higher than the royalty. Therefore, the R&D investment under the fixed-fee is always no less than that under the royalty. Similarly, the patentee can earn more profit under fixed-fee is always not less than that under the royalty.

With respect to the profit of the licensee, it is no difference between the fixed-fee licensing and the non-licensing. With the royalty licensing, if r < t: , the patentee's profit will be increased by the effect of cost economizing ; if r = t: , there is no cost economizing effect then the profit is the same as with non-licensing.

1986

B. Consumer s surplus and social welfare

Assume the consumer's surplus is cs = x2

## /2,

and let sw = Jr + CS + n as the social welfare.Proposition 4:

The consumer surplus and social welfare under a fixed-fee licensing is always no less than under a royalty licensing.

With a fixed-fee licensing, since the margin of cost saving is the biggest then the consumer surplus is at most. This result is the licensing game which is Pareto improvement and the cost saving effect is shared both by the patentee and the licensee. Because the effect of cost saving is the highest under fixed-fee licensing, the profits of the patentee and the licensee are both at most. We can conclude that the fixed-fee licensing is the optimal choice for the patentee and from the view of the social welfare.

TV. CONCLUSION

The past studies indicated that the fixed-fee licensing would be the best choice both to the patentee himself and to the whole society considering an

exogenous technology innovation and the patentee was not in production. This research fmds that even with the endogenous R&D investment, the fixed-fee is still the best licensing to the patentee himself and to the whole society. The reason is that the R&D investment under the fixed-fee is always no less than that under the royalty, and the extent of the marginal cost saved is at most for a higher induced demand of innovation.

ACKNOWLEDGMENT

We gratefully acknowledges financial support from the Taiwan National Science Council through the contract No. NSC-95-

_{2}

415-H-_{2}

44-001.
REFERENCES

[I] Arrow, K., "Economic Welfare and the Allocation of Resources for Invention", in R.R. Nelson (Ed.), The Rate and Direction of Incentive Activity, Princeton University Press. 1962.

[2] D'Aspremont, C. and A. Jacquemin, "Cooperative and Noncooperative R&D in Duopoly with Spillovers", American Economic Review, vo1.78, pp. 1l33-1137, 1988. [3] Gallini, N., "Deterrence by Market Sharing: A Strategic

Incentive for Licensing", American Economic Review, vo1.74, pp.93 1-941 , 1984.

[4] Gallini, N. and R. Winter, "Licensing in the Theory of Innovation", Rand Journal of Economics, vo1.16, pp.237-252, 1985.

[5] Gallini, N. and B. Wright, "Technology Transfer under Asymmetric Information", Rand Journal of Economics,

vol.21, pp. 147-160, 1990.

[6] Jin, J.y', "Innovation Announcement with Vertical Differentiation", Journal of Economic Behavior & Organization, vo1.28, pp.399-408, 1995.

[7] Kamien, M.T. and N. Schwartz, Market Structure and Innovation, Cambridge University Press, 1982.

[8] Kamien, M.T. and Y. Tauman, "The Private Value of Patent A Game Theoretic Analysis", Journal of Economics (Supplement), vol.4, pp.93-118, 1984.

[9] Kamien, M.l., and Y. Tauman, "Fees versus Royalties and the Private Value of a Patent", Quarterly Journal of Economics, voLlOl, pp.471-491, 1986.

[10] Kamien, M.l., and Y. Tauman, "Patent Licensing: The Inside Story," Manchester School, vol.70, pp.7-15, 2002. [II] Katz, M. and C. Shapiro, "On the Licensing of

Innovations", The RAND Journal of Economics, vol.16, pp.504-520, 1985.

[12] Lee, J. Y. and C. S. Huang, "Vertical Differentiation and Licensing Strategies", Industrial Economics Research, (in Chinese), vol.4, pp.I-1 0, 2006a.

[13] Lee, J.Y. and C.S. Huang, "Fees versus Royalties Licensing under Asymmetric Information", Economics Research Journal, (in Chinese), vol.41, pp.44-51, 2006b. [14] Muto, S., "On Licensing Policy in Bertrand Competition",

Game and Economic Behavior, vol.5, pp.257-267, 1993. [15] Rostoker, M., A Survey of Corporate Licensing. IDEA,

vo1.24, pp.59-92, 1984.

[16] Schumpeter, J., Capitalism, Socialism and Democracy. London: Unwin University Books, 1943.

[17] Sen, D., "Fee versus Royalty Reconsidered," Games and Economic Behavior, vo1.59, pp.163-186, 2005a.

[18] Sen, D., "On the Coexistence of Different Licensing Schemes," International Review of Economics and Finance, vo1.l4, pp.393-413, 2005b.

[19] Sen, D. and Y. Tauman, "General Licensing Schemes for a Cost-reducing Innovation," Games and Economic Behavior, vol.59, pp. 163-186, 2007.

[20] Solow, R., "Technical Change and the Aggregate Production Function", Review of Economics and Statistics, vo1.39, pp.312-3120, 1957.

[21] Taylor, c.T. and Silberston, Z.A., The Economic Impact of the Patent System: a Study of the British Experience, Cambridge University Press, Cambridge, 1973.

[22] Tiro1e, 1., The Theory of Industrial Organization, The MIT Press. 1988.

[23] Wang, X.H., "Fee versus Royalty Licensing in a Coumot Duopoly Model", Economics Letters, vol.60, pp.55-62, 1998.

[24] Wang, X.H., "Fee versus Royalty Licensing in a Differentiated Coumot Duopoly", Journal of Economics and Business, vo1.54, pp.253-266, 2002.

[25] Wang, X.H. and B.Z. Yang, "On Technology Licensing in a Stackelberg Duopoly", Australian Economic Papers, vo1.43, pp.448-458, 2004.

[26] Young, A., "Lessons from the East Asia NICs: A Contrarian View". European Economic Review, vol.38, pp.964-973, 1994.