Technology licensing, R&D and welfare

Accepted Manuscript Technology licensing, R&D and welfare Ray-Yun Chang, Hong Hwang, Cheng-Hau Peng PII: DOI: Reference:

S0165-1765(12)00606-4 10.1016/j.econlet.2012.11.016 ECOLET 5690

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Economics Letters

Received date: 13 July 2012 Revised date: 3 November 2012 Accepted date: 16 November 2012 Please cite this article as: Chang, R.-Y., Hwang, H., Peng, C.-H., Technology licensing, R&D and welfare. Economics Letters (2012), doi:10.1016/j.econlet.2012.11.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights (for review)

Highlights



We compare the R&D efforts of an insider innovator with and without



licensing. The availability of licensing does not necessarily foster the firm’s R&D



investment. It may suppress the R&D efforts of the innovator with high R&D efficiency.



Social welfare may go lower under licensing than no licensing.



A government has to be cautious when encouraging technology licensing among firms.

*Title Page

Technology Licensing, R&D and Welfare*

Ray-Yun Chang Department of Economics, Chinese Culture University, Taipei, Taiwan

Hong Hwang† Department of Economics, National Taiwan University, Taipei, Taiwan and RCHSS, Academia Sinica, Taiwan Cheng-Hau Peng Department of Economics, Fu Jen Catholic University, Taipei, Taiwan (Revised version for EL) Abstract This paper sets up a three-stage (R&D, technology licensing, and output) oligopoly game in which only one of the firms undertakes a cost-reducing R&D and may license the developed technology to the others by means of a two-part tariff (i.e., a per-unit royalty and an upfront fee) contract. It is found with surprise that if the licensor firm’s R&D efficiency is high, the availability of licensing subdues the firm’s R&D incentive, leading to a lower social welfare level. This result implies that a government has to be cautious when encouraging technology licensing among firms.

Keywords: Technology Licensing; R&D Investment; Social Welfare JEL Classification: D21, L13, L24, O31

*

We are indebted to an anonymous referee for helpful comments. Address for correspondence: Hong Hwang, Department of Economics, National Taiwan University, 21 Hsu Chow Road, Taipei 10055, Taiwan. Tel: +886-2-2351-9641 ext 446; Fax: +886-2-2358-4147; E-mail: [email protected]. 1 †

*Manuscript Click here to view linked References

Technology Licensing, R&D and Welfare 1 INTRODUCTION This paper examines how technology licensing affects a firm’s incentive for innovation. The benefits of cost-reducing R&D are two-fold. It gives the innovator a competitive edge over its rivals; it also provides the licensor with licensing revenue. It is generally believed that allowing a firm to license out its technology has a positive effect on its R&D (Salant, 1984, Gallini and Winter, 1985). In this paper however, we will show a counter example that licensing may cause an innovator to invest less. Firm’s R&D behavior and its effect on social welfare have drawn considerable attention and been debated extensively in the literature (see, for example, D’Aspremont and Jacquemin, 1988; Suzumura, 1992). But, they do not assume a firm’s R&D outcomes can be licensed out and fail to explain the burgeoning trend of technology licensing.1 Our paper is also related to the literature on insider licensing which mainly focuses on optimal forms of contracts (see, for example, Wang, 1998, and Kamien and Tauman, 2002). There are few papers along this strand addressing both R&D and licensing, including Salant, 1984, Gallini, 1984, and Gallini and Winter, 1985, but their focuses are quite different from ours. They all treat R&D as a binary variable and ignore that the intensity of R&D could be strategically affected by licensing. By treating R&D as exogenously given, they find that licensing is welfare-enhancing. In contrast, we treat R&D as an endogenous variable and show that the availability of licensing may subdue a firm’s R&D incentive, leading to a lower social welfare level.2 This kind of disincentive on R&D differs from those in the literature, such as technological spillover (D'Aspremont and Jacquemin, 1988), product differentiation (Lin and Saggi, 2002) and multi-product monopolist (Lin, 2007), and has never been documented in the literature. Furthermore, our result on welfare complements the welfare-reducing licensing literature which shows that licensing may reduce welfare if it facilitates a collusive outcome (Faulí-Oller and Sandonis, 2002), affects the R&D organization (Mukherjee, 2005), creates excessive entry (Mukherjee and Mukherjee, 2008); or changes the mode of operation of the foreign firm (Sinha, 2010).

2. THE MODEL Assume that there is a market with n + 1 firms-- one insider innovator, called Firm I, and the other n homogeneous firms, called Firm i, i  1,.., n , all producing a homogeneous good, 1

Nadiri (1993) shows that international payments for patents, licenses and technical know-how for Japan, U.K., France and U.S. were growing substantially between 1979 and 1988. 2 Mukherjee and Mukherjee (2002) also consider an endogenous decision on R&D. However, unlike our paper, the licensing effect on R&D in their paper is due to the effect on total profit and not due to the effect on marginal profit. 1

having the same marginal production cost c and competing in Cournot fashion. We assume that only Firm I undertakes a cost-reducing R&D, x , at the cost function V ( x ; v) with V x  0, V v  0,  2V xv  0 , where v is a parameter reflecting the R&D efficiency

and a higher v indicates lower R&D efficiency. 3 The R&D investment is assumed to be non-drastic throughout the paper.4 We further assume that Firm I (hereafter, the licensor firm) can license its technology to all the no-R&D firms (hereafter, the licensee firms) via a two-part tariff contract, i.e., a fixed fee ( F ) and a royalty rate ( r ). Thus, the licensor firm’s marginal production cost after licensing becomes c  x whereas those of the licensee firms are c  x  r . The inverse demand function for the good takes the following implicit form: p  p  Q  with n

p '(Q)  0 and Q  qI   qi where qI and qi are respectively the outputs of the licensor i 1

firm and the licensee firm. The game in question comprises three stages. In the first stage, the licensor firm determines its R&D investment. In the second stage, for a given R&D, the licensor firm licenses its technology to the licensee firms by means of a two-part tariff contract. In the third stage, all the firms compete in Cournot fashion in the final good market. The profit functions for the licensor firm and the licensee firms can be respectively expressed as follows: n

 IL  qI , qi ; F , r , x, v    p  Q   (c  x)  qI   rqi  nF  V ,

(1)

 iL  qI , qi ; F , r , x, v    p  Q   (c  x  r )  qi  F ,

(2)

i 1

i  1,..., n ,

where variables with a superscript “L” represent they are associated with the licensing regime. The first-order conditions for profit maximization are as follows:

 IL  p  (c  x )  pqI  0, qI

(3)

 iL  p  (c  x  r )  pqi  0 , qi

i  1,..., n .

(4)

The second-order conditions require that  2 IL qI2  0 and  2 iL qi2  0 , which are assumed to be satisfied. By symmetry, we have q1  q2  ....  qn  q in equilibrium. Utilizing this property, we can rewrite (4) as follows:

 iL  p  (c  x  r )  pq  0 , for all i . q

(5)

From (3) and (5), the comparative statics are derivable as follows:

3

This assumption is made to facilitate our analysis on licensing. If all the firms are capable of conducting R&D, there will be no cost difference among firms by symmetry and, as a result, licensing never occurs. 4 Wang (1998) shows that an innovator with a drastic innovation would never license the innovation to its rivals. 2

qIL  ii   Ii q L  iI   II q L  II qIL  Ii , ,     0,   0, x H x H r H r H where  II   2 IL qI2  2 p ' p '' qI  0 ,  ii   2 iL q2  (n  1) p ' np '' q  0 ,

(6)

 Ii   2 IL qI q  n( p ' p '' qI )  0 ,  iI   2 iL q qI  p ' p '' q  0 , and H   II ii   Ii iI  p  n  2  p  pQ   0 .

The profit function of the licensor firm in the second-stage game can be expressed as follows:

 





max  IL  p Q L (r )  (c  x) qIL (r )  nrq L (r )  nF (r )  V ,

(7)

subject to ( p  (c  x  r ))q L (r )  F  ( p  c)q N ( x) ,

(8)

x

where variables with a superscript “N” indicates they are associated with the no-licensing regime. By symmetry, the total fee revenue collected by the licensor firm is nF . Following the literature, we assume that the licensor firm is a dominant player in the licensing game and capable of extracting each licensee firm’s entire benefit from licensing. Thus, the fixed fee charged by the licensor firm is defined as F  [ p  (c  x  r )]q L (r )  ( p  c)q N . By differentiating (7) with respect to r and utilizing (3) and (5), we can derive the first-order condition for profit maximization as follows: L d IL  IL q L  IL  L F npq  n II   Ii  (np)2 q L  L  n I    0. dr q r r F r H H

(9)

This implies that the licensor firm’s optimal royalty rate is r  x . By substituting r  x into F , we can derive that the optimal fee equals to zero. The licensor firm uses only royalty to extract the rent of the licensee firm from licensing. Making use of these results, we can define the

profit

function

 

of

the



licensor

firm

for

the

first-stage

game

as

follows:



max  IL  p Q L (r ( x), x)  (c  x) qIL (r ( x), x)  nrq L (r ( x), x)  V  x ; v  . x

By differentiating this equation with respect to x , we can derive the first-order condition for profit maximization as follows:

 q L r q L  d IL  npqIL   qIL   dx  r  x  x   output effect





strategic effect

d (nrq L ) dx licensing revenue effect



dV dx

 0,

(10)

cost effect

where (q L r ) (r x) q L x   iI H  0 by (6). As shown in (10), there are four terms that jointly determine the licensor firm’s optimal R&D. The first term is called the strategic effect, which is positive. The second term is called the output effect, which is also positive. The third term is called the licensing revenue effect. The sign of this effect is ambiguous as nrq L is concave in x . The last term which is negative, represents the R&D cost effect.

3

3. R&D INVESTMENTS AND WELFARE COMPARISONS We now move to compare the R&D investments and the corresponding welfare levels between licensing and no-licensing regimes. With no licensing, the game degenerates to two stages. The last-stage game is similar to that in the licensing regime, i.e.,(1) and (2). The first-order condition for the licensor firm in the first stage of the no-licensing regime is derivable as follows:

d IN dq N  npqIN  dx dx





strategic effect

qIN output effect



dV dx

0,

(11)

cost effect

where dq N / dx   iI / H  0 . Moreover, given the second-order condition is satisfied and  2V xv  0 , it is straightforward to show that dx dv  0 . Before comparing the optimal R&D

levels under the two regimes, let us first compare their optimal outputs. Since r = x, each firm’s effective marginal cost remains unchanged after licensing. It implies that for any given x, each firm’s output remains unchanged after licensing, i.e., qIL  qIN , qiL  qiN , i  1,..., n . By utilizing these results and evaluating (10) at the R&D level derived from the no-licensing regime, i.e., (11), we obtain:

d IL dx

x  xN

     dq N   dr  N N d ( nr( x )q N ( x )) N   n  r( x (v ))      q ( x (v ))   0 , if v  v *. dx  dx   dx    x  xN 

(12)

It shows that the R&D investment of the licensor firm may increase or decrease after licensing, depending on the effect on licensing revenue which can be decomposed into two sub-effects. The first sub-effect ( r(dq N dx ) ), which is negative, shows that the licensor firm’s R&D lowers the output of each licensee firm which decreases the licensor firm’s licensing revenue. The second sub-effect ( (dr / dx )q N ) is positive, showing that an increase in R&D increases the royalty rate and therefore the licensor firm’s licensing revenue. By setting (12) equal to zero, we can derive the R&D efficiency level, v * , at which the R&D investments are the same under the licensing and no-licensing regimes. Furthermore, an increase in v dampens the negative sub-effect but enhances the positive sub-effect.5 Hence, we have: x N  x L ( x N  x L ) if the licensor firm’s R&D efficiency is high (low), i.e., v  v * ( v  v * ). From the above discussions, we can establish the following proposition.

Proposition 1. The R&D investment under the licensing regime is lower (higher) than that 5

The first sub-effect dampens as d ( r(dq N / dx)) dv  r  d (dq N / dx) / dv   ( dr dx)( dx dv)( dq N / dx)  0 , by

dr dx  1 , dx dv  0 , dq N / dx  0 and d (dq N / dx) / dv  d ( iI / H ) / dv  0 , whereas the second sub-effect increases with

v as dq N / dv  (dq N / dx)(dx / dv )  0 . 4

under the no-licensing regime if the R&D efficiency is high (low).

We now compare their social welfare levels. Social welfare is defined as the sum of consumer surplus and profits of the firms. The social welfare functions under the two regimes can be expressed as follows: SW j  CS  Q j ( x)    Ij  n ij , where j  L, N . Obviously, for any given R&D level, we have SW L  SW N  nrq  0 as licensing lowers the total production cost, producing a positive effect on social welfare. However, this result may not be true if R&D becomes endogenous. According to Proposition 1, if the R&D efficiency is high, the licensor firm tends to reduce its R&D investment after licensing. Hence, there is a tradeoff between lower cost under licensing and higher R&D under no licensing. If the R&D efficiency is high, the latter effect dominates the former effect and the social welfare with licensing is lower than that with no licensing. We can use Figure 1 to illustrate this outcome. As demonstrated before, for any given R&D level, such as x L or x N , social welfare is higher under licensing than no licensing. If the R&D efficiency is high such that the optimal R&D under the no-licensing regime is at B and that under the licensing regime is at A, social welfare is higher under the no-licensing regime. Thus, we can arrive at the following proposition.

Proposition 2. When R&D investment is endogenous, social welfare with licensing is lower (higher) than that with no licensing, if the R&D efficiency is high (low).

We can provide an example to illustrate our results. Assume there are one licensor firm and one licensee firm in the market. The inverse demand and the R&D cost functions are given as follows: p  a  (qI  q1 ) , and V ( x; v)  vx 2 . The optimal R&D investment and social welfare under the no-licensing and the licensing regimes and their differences are derivable as follows:

xN 

2(a  c) 2(a  c)2 (18v 2  14v  3) (a  c)2 (288v 2  34v  9) 7(a  c) L SW  , xL  , SW N  , . 9v  4 (9v  4)2 8(9v  1)2 2(9v  1)

xL  xN 

3(a  c)(9v  8)  0, if 2(9v  1)(9v  4)

SW L  SW N 

v  8/9 ;

3(a  c)2 (32  328v  1773v 2  1782v3 ) <0, if v  0.69 . 8(9v  1)2 (9v  4)2

It shows that the availability of licensing may reduce the licensor firm’s R&D, lowering social welfare. Specifically, the optimal R&D investment with licensing is lower than that with no licensing if v  8 / 9 and the social welfare under licensing is lower than that under no licensing if v  0.69 .

5

SW SW L

SW N

B A

0

xL

xN

x

Figure 1. Social welfare curves with and without licensing

4. CONCLUSIONS Over the past two decades, both R&D investment and technology licensing have received considerable attention and have been studied extensively. However, the literature on R&D and licensing has treated the R&D as a binary variable and ignored how the R&D intensity and welfare are affected by licensing. This paper has found that the licensor firm’s optimal R&D investment and the social welfare may both become lower after licensing if its R&D efficiency is high. This result is of interest as it goes against the conventional wisdom that licensing can encourage R&D and is beneficial to social welfare. This finding also bears a policy implication that a blanket encouragement of licensing may not be socially desirable.

REFERENCES D’Aspremont, C., Jacquemin, A., 1988. Cooperative and noncooperative R&D in duopoly with spillovers. American Economic Review 78, 1133-1137. Faulí-Oller, R., Sandonis, J., 2002. Welfare reducing licensing. Games and Economic Behavior 41, 192-205. Gallini, N., 1984. Deterrence by market sharing: a strategic incentive for licensing. American Economic Review 74, 931-941. Gallini, N., Winter, R., 1985. Licensing in the theory of innovation. Rand Journal of Economics 16, 237-52. Kamien, M., Tauman,Y., 2002. Patent licensing: the inside story. Manchester School 70, 7-15. Lin, P., 2007. Process R&D and product line deletion by a multiproduct monopolist. Journal of Economics 91, 245-262. 6

Lin, P., Saggi, K., 2002. Product differentiation, process R&D, and the nature of market competition. European Economic Review 46, 201-211. Mukherjee, A., 2005. Innovation, licensing and welfare. The Manchester School 73, 29-39. Mukherjee,A., Mukherjee,S.,2002. Licensing and the incentive for innovation. Keele Economics Research Papers 2002/17. Department of Economics, Keele University. Mukherjee, A., Mukherjee, S., 2008. Excess-entry theorem: the implications of licensing. Manchester School 76, 675-689. Nadiri, M., 1993. Innovations and technological spillovers. NBER Working Paper No. 4423. Salant, S.,1984. Preemptive patenting and the persistence of monopoly: comment. American Economic Review 74, 247 -250. Sinha, U., 2010. Strategic licensing, exports, FDI, and host country welfare. Oxford Economic Papers 62, 114-131. Suzumura, K., 1992. Cooperative and non-cooperative R&D in an oligopoly with spillovers. American Economic Review 82, 1307-1320. Wang, X.,1998. Fees versus royalty licensing in a Cournot duopoly model. Economics Letters 60, 55-62.

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