Licensing a new product: Fee vs. royalty licensing with unionized labor market

Labour Economics 17 (2010) 735–742

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Labour Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / l a b e c o

Licensing a new product: Fee vs. royalty licensing with unionized labor market Arijit Mukherjee ⁎ School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, UK The Leverhulme Centre for Research in Globalisation and Economic Policy, UK

a r t i c l e

i n f o

Article history: Received 2 November 2007 Received in revised form 17 May 2009 Accepted 5 September 2009 Available online 15 September 2009 JEL classification: D43 L13 J51

a b s t r a c t In an economy with unionized labor market, we show that the payoff of an outside innovator may be higher under royalty licensing than under fixed-fee licensing and auction, if bargaining power of the labor union is sufficiently high. This result holds for both decentralized and centralized bargaining. It follows from our analysis that a combination of fixed-fee and output royalty can be preferable to the innovator compared to both royalty only licensing and auction (or fixed-fee licensing). We discuss the implications of positive opportunity costs of the licensees. © 2009 Elsevier B.V. All rights reserved.

Keywords: Auction Fixed-fee Labor union Licensing Royalty

⁎ School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. Fax: +44 115 951 4159. E-mail address: [email protected].

Choi, 2001), risk aversion (Bousquet et al., 1998), incumbent innovator (Shapiro, 1985; Kamien and Tauman, 2002; Sen and Tauman, 2007), leadership structure (Kabiraj, 2004), strategic delegation (Saracho, 2002) and integer constraint on the number of licenses (Sen, 2005a). There is a related literature which shows the superiority of royalty licensing and licensing with a combination of fixed-fee and royalty when the licenser and the licensees compete in the product market (see, e.g., Rockett, 1990; Wang, 1998, 2002; Wang and Yang, 1999; Filippini, 2001; Mukherjee and Balasubramanian, 2001; Faulí-Oller and Sandonis, 2002; Fosfuri, 2004; Kabiraj, 2005; Poddar and Sinha, 2005; Mukherjee, 2007). The competition softening effect of output royalty makes the royalty licensing preferable than fixed-fee licensing if the licenser and the licensees compete in the product market. A common feature of the above-mentioned works is to assume that technology licensing does not affect the input price. In other words, they implicitly assume that the input markets are perfectly competitive, thus ignoring the role of the input markets in determining optimal licensing contract. However, the situation in real world is often different. Many industries are characterized by vertical relationships, and the input prices are not always independent of firms' actions. For example, the labor markets are often unionized in many countries and firms bargain with the labor unions for wage rates,4 which affect the costs of production and firms' performance.

1 Licensing by the Universities or independent research labs to the producers may be the examples of this scenario. 2 See Kamien (1992) for a nice survey of this literature. 3 Outside innovator refers to the situation where the innovator (who is the licenser) and the licensees do not compete in the product market.

4 Unionization structure differs significantly between countries. While decentralized wage setting may be relevant, e.g., in Japan and North America, centralized wage setting is relevant, e.g., in Germany and Scandinavia. See Iversen (1998) for the index of centralization of wage bargaining in different countries.

1. Introduction Technology licensing is an important element of conduct in many industries and has attracted a fair amount of attention in recent years. The seminal works by Kamien and Tauman (1984, 1986) show that, if an innovator, who is not a producer,1 licenses the technology to final goods producers and the product market is characterized by Cournot competition, licensing with output royalty generates lower profit to the innovator compared to fixed-fee licensing and auction, regardless of the industry size and/or magnitude of the innovation.2 In view of this theoretical result, the wide prevalence of output royalty in the licensing contracts (see, e.g., Taylor and Silberstone, 1973; Rostoker, 1984) has remained a puzzle, and has generated significant amount of theoretical research to explain the superiority of royalty licensing over other types of licensing contracts. The factors attributed to the presence of output royalty in a licensing contract offered by an “outside innovator”3 are asymmetric information (Gallini and Wright, 1990; Beggs, 1992; Poddar and Sinha, 2002; Sen, 2005b), product differentiation (Muto, 1993; Poddar and Sinha, 2004), moral hazard (Macho-Stadler et al., 1996;

0927-5371/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.labeco.2009.09.003

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It is well known that labor unions may have significant effect on firms' actions and performance (see, Flanagan, 1999), which has generated a vast literature in analyzing the effects of the unionized labor markets. However, the literature so far did not pay much attention to uncover the relationship between labor union and technology licensing, which is an important element of conduct in many industries and has attracted significant amount of attention from the researchers working on industrial organization. Given the prevalence of unionized labor markets across countries, the purpose of this paper is to emphasize the role of labor union in determining the licensing contract, thus creating a bridge between the literatures on technology licensing and on labor market institution.5 We develop a simple model of technology licensing by an outside innovator to the Cournot oligopolists in the presence of labor unions, where the wage rates are determined through a generalized Nash bargaining between the firms and the unions. Considering zero opportunity costs of the licensees, which correspond to the case of drastic innovation in the sense of Arrow (1962), we show that royalty licensing may generate higher payoff to the innovator compared to fixed-fee licensing and auction, if the bargaining power of the unions is sufficiently high. It follows from our analysis that a combination of fixedfee and output royalty can be preferable to the innovator compared to a royalty only licensing and auction (or fixed-fee licensing). Our results hold for both decentralized bargaining and centralized bargaining. While comparing the effects of different bargaining structures, we find that the wage rates (profits of the innovator) are higher (lower) under centralized bargaining than under decentralized bargaining for all types of licensing contracts. The innovator's incentive for royalty licensing over auction (or fixed-fee licensing) is higher under decentralized bargaining than under centralized bargaining, if there is at least three potential licensees. We also discuss the implications of positive opportunity costs on our results. Though royalty licensing (compared to fixed-fee licensing and auction) creates distortion in the product market by imposing positive output royalty, it helps to reduce the wage rate charged by the labor unions. If bargaining power of the labor union is very high, the benefit from lower wage rate can outweigh the distortion due to output royalty, thus generating higher payoff to the innovator under royalty licensing than under both fixed-fee licensing and auction. Royalty licensing leaves positive surplus to the producers, and therefore, a combination of fixedfee and output royalty is preferable to the innovator compared to a royalty only licensing. Since royalty helps to reduce the wage rates and fixed-fee helps to extract surpluses from the licensees, the innovator may prefer a combination of fixed-fee and royalty compared to both royalty only licensing and auction (or fixed-fee licensing). The next section describes the model with decentralized and centralized bargaining and derives the results. Section 3 shows the implications of positive opportunity costs of the producers. Section 4 concludes. 2. The model and the results Assume that there is an innovator, called I, who has invented a new product. However, I cannot produce the good. There are n ≥ 1 symmetric potential producers of the product, and I can license its technology to the potential producers. To avoid analytical complexity, we ignore integer constraint and consider the number of producers (i.e., n) as a continuous variable. To show the implications of labor union on technology licensing in the simplest way, we assume that each producer's opportunity cost of having a license is 0, which corresponds to the case of drastic innovation in the sense of Arrow (1962).6 As an alternative 5 Recently, Mukherjee et al. (2008) showed the effect of labor union on the incentive for technology licensing by a monopolist producer to a potential product market competitor. Hence, in contrast to this paper, they consider licensing by an inside innovator, where the innovator is a producer. See Tauman and Weiss (1987) for the effects of labor union on technology adoption by the competing firms. 6 Alternatively, one may assume that the producers are not producing any product which is in competition with the innovated product.

interpretation of our framework, assume that a developed-country producer has invented a new product and can enter a developing country only through technology licensing (due to higher costs of exporting and foreign direct investment) and licenses the technology to the producers in the developing country, which has a unionized labor market. Assume that the outputs of the producers are perfect substitutes, and the inverse market demand function for the product is P = a−q;

ð1Þ

for a > q and P = 0 for a ≤ q, where P is price and q is the total output. We assume that each producer requires one labor to produce one unit of output. We consider a right-to-manage model of labor union, such as in Bughin and Vannini (1995), Vannini and Bughin (2000), López and Naylor (2004) and Mukherjee (2008), to name a few, where the producers and the unions bargain for the wage rates and the producers demand workers according to their need.7 The producers and the unions determine the wage rates through a generalized Nash bargaining procedure, where α and (1−α) are the bargaining power of the labor union and the producer respectively. We assume that the reservation wage rates of the workers are zero. We will consider two-types of bargaining between the firms and the unions: decentralized bargaining and centralized bargaining. Under decentralized bargaining, firm-specific labor unions bargain with the respective producers to determine the wage rates. Under centralized bargaining, a representative of the firms bargains with a representative of the unions to determine the wages for all firms. The objective of the firms' representative is to maximize the total profits of the firms and the objective of the unions' representative is to maximize the total utility of the unions. We will consider following licensing contracts designed by I: (i) Auctioning k licenses, 1 ≤ k ≤ n, by I through a sealed bid English auction. The highest bidders get the license. The ties are resolved by I. (ii) Fixed-fee licensing, where a flat pre-determined license fee F is charged by I, and any producer that wishes to can purchase the license at this fixed-fee. (iii) Royalty licensing, where a fixed royalty payment r per-unit of output is charged by I, and any producer that wishes to can purchase the license at this royalty rate. We will also discuss the implications of licensing with both fixed-fee and per-unit output royalty where the fixed-fee can be determined either by the innovator (i.e., fixed-fee plus royalty licensing) or it can be the winning bids of the licensees if the innovator auctions off licenses (i.e., auction plus royalty licensing). We assume that licensing is costless. It is immediate from Kamien et al. (1992) that the essential difference between auction and fixed-fee licensing stems from the difference in the producers' opportunity costs of having a license. Since we are considering a situation with zero opportunity costs of the producers, it is then immediate that auction and fixed-fee licensing give the same solution in this situation. Therefore, we focus on auction and do not consider the case of fixed-fee licensing separately in the following analysis. We consider the following games for our analysis. Under royalty licensing, at stage 1, I announces the uniform royalty rate r. At stage 2, the producers simultaneously and independently decide whether or not to purchase a license. At stage 3, the wage rates are determined simultaneously. At stage 4, the producers choose their outputs simultaneously. If only one producer purchases a license at stage 2, he produces like a monopolist at stage 4. 7 The “efficient bargaining” model, which stipulates that the firms and unions bargain over wages and employment, is an alternative to the right-to-manage model. See, Layard et al. (1991) for arguments in favor of right-to-manage models.

A. Mukherjee / Labour Economics 17 (2010) 735–742

Under auction, at stage 1, I announces to auction k licenses, where 1 ≤ k ≤ n. At stage 2, the producers simultaneously and independently decide whether or not to purchase a license, and how much to bid. At stage 3, the wage rates are determined simultaneously. At stage 4, the producers choose their outputs simultaneously. If I auctions only one license, the licensee produces like a monopolist at stage 4. We solve these games by backward induction. 2.1. Decentralized bargaining Let us first determine the product market equilibrium. If the innovator I licenses the technology to k firms, where 1 ≤ k ≤ n, and each of the k firms pays a per-unit output royalty r, where r < a, the ith licensee, i = 1,2,…,k, chooses his output to maximize the following expression: Max ða−q−wi −rÞqi ;

ð2Þ

qi

where wi is the wage rate paid by firm i. The equilibrium output of the k

a−kwi −r + ∑ wj j=1 i≠j

. Note that r is 0 under ith licensee can be found as qi = k + 1 auction, while r will be positive under royalty licensing. Since a very high wi will make the equilibrium output of the ith firm zero, setting a high wi is not optimal for either firm i or for the labor union as both will obtain zero in that case. Hence, wi should satisfy that k

a−r + ∑ wj

12

0

j=1 i≠j

. wi < k The equilibrium profit of the ith firm is

Ba−kwi −r + B B πi = ðqi Þ2 = B B k + 1 B @

k

∑ wj C j=1 i≠j

C C C C C A

and the ith labor union's utility (which is the labor income from firm i) is k

wi ða−kwi −r + ∑ wj Þ j=1 i≠j

wi qi = . k + 1 Under decentralized bargaining, at stage 3, the wage rate wi is determined by maximizing the following expression:

the following expression to determine the equilibrium royalty rate: Max r

1α 0

k

Bwi ða−kwi −r + ∑ wj ÞC B C j=1 B C i≠j B C MaxB C wi B C k+1 B C @ A

k

2 2

I;d

πr =

n a ð2−αÞ : 4ðn + 1Þðnð2−αÞ + αÞ

ð5Þ

If bargaining power of the labor union increases, it reduces the payoff of I. A higher bargaining power of the labor union increases the wage rate and reduces the total outputs of the licensees. Since the royalty rate does not depend on the bargaining power, the equilibrium payoff of I reduces with higher bargaining power of the labor union. 2.1.2. Auction Let us now consider the game under auction. If I auctions k licenses, where 1 ≤ k ≤ n,8 it follows from Lemma 1 that, under decentralized bargaining, the equilibrium wage rate for the ith licensee is wi = 2k−ka + 1 ; i = 1; 2; …k, since r is 0 under auction. α

The profit of each licensee is π1 = π2 = ::: = πk =

a2 k2 ð2−αÞ2 . ðk + 1Þ2 ðkð2−αÞ + αÞ2

Therefore, in the Nash equilibrium of the bidding game, each potential a2 k2 ð2−αÞ2 . If k = n, I can guarantee this licensee bids ðk + 1Þ2 ðkð2−αÞ + αÞ2 equilibrium bid by specifying a minimum bid. However, for k < n, the producers bid these amounts even if I does not specify the minimum bid. a2 k3 ð2−αÞ2 If I auctions k licenses, his payoff is πI;d a = ðk + 1Þ2 ðkð2−αÞ + αÞ2 , and the number of licenses to auction is determined by maximizing the following expression: Max

a2 k3 ð2−αÞ2 : ðk + 1Þ2 ðkð2−αÞ + αÞ2

ð6Þ

The equilibrium number of licenses is given by :

ð3Þ

ðkð2−αÞ + αÞð3 + kÞ−2kðk + 1Þð2−αÞ = 0:

ð7Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 + 1 + 3αð2−αÞ . The solution of Eq. (7) which satisfies k≥1 is k*;d = 2−α Therefore, in our setup, the equilibrium number of auction under decentralized bargaining is k*,d if n≥k*,d, while it is n if n
2k α −k

If bargaining power of labor union (i.e., α) increases, it increases the equilibrium wage rate. The following lemma is immediate from the above discussion. Lemma 1. Consider a Cournot oligopoly with k firms where firm i pays the per-unit royalty r. Under decentralized bargaining, the wage a−r rate for firm i is wi ðk; rÞ = 2k−k ; i = 1; 2; …k. + 1 α

2.1.1. Royalty licensing Under royalty licensing, each producer always prefers to purchase a license for r < a, since the producers always have the option to produce nothing after purchasing a license, thus earning 0, which is the opportunity cost of having a license. With n licensees, it follows from Lemma 1 that, under decentralized bargaining, the equilibrium wage rate for the ith licensee is a−r wi = 2n−n ; i = 1; 2…n. + 1 α

Due to symmetry, the outputs of the licensees are q1 = nð2−αÞða−rÞ ðn + 1Þðnð2−αÞ + αÞ.

ð4Þ

1ð1−αÞ

Bða−kwi −r + ∑ wj Þ2 C B C j=1 B C i≠j B C B C 2 B C ðk + 1Þ B C @ A

The equilibrium wage rates are w1;r = w2;r = ::: = wk;r =

q2 = ::: = qn =

n2 rð2−αÞða−rÞ : ðn + 1Þðnð2−αÞ + αÞ

The equilibrium royalty rate is r *;d = 2a, and the equilibrium payoff of I is

k

0

737

Hence, the innovator I maximizes

πI;d a =

;d

;d

ðk*

a2 ðk * Þ3 ð2−αÞ2 ;d

+ 1Þ2 ðk* ð2−αÞ + αÞ2

for n ≥k*,d and πI;d a =

a2 n3 ð2−αÞ2 ðn + 1Þ2 ðnð2−αÞ + αÞ2

for n
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A. Mukherjee / Labour Economics 17 (2010) 735–742

2.1.3. Comparing auction with royalty licensing Before comparing I's profit under royalty licensing and under auction, let us compare the wage rates under these licensing schemes, since it will help us to understand the intuition for our result. Proposition 1. Consider decentralized bargaining. A licensee pays lower wage rate under royalty licensing than under auction (or fixedfee licensing) for α > 0. Proof. Under decentralized bargaining, a licensee pays the wage rate a−r *;d under royalty licensing but it pays the wage rate +1 a under auction when there are k*,d licenses under auction. ;d 2k* −k*;d + 1 2n α −n

α

The comparison of these wage rates shows that the wage rate is higher under auction than under royalty licensing if (2n−k*,d)(2−α) +α > 0, which always holds, since the equilibrium number of auction is less than or equal to the number of potential licensees. Q.E.D. Under royalty licensing, the positive royalty rate creates a distortion in the production stage, whereas this type of distortion is absent under auction, since each licensee pays a lump-sum amount while purchasing a license under auction. Therefore, for a given wage rate, the demand for labor is lower under royalty licensing than under auction, thus generating lower equilibrium wage rate under the former than the latter. Since the wage rate is lower under royalty licensing compared to auction, the innovator earns higher profit under the former than the latter if the wage effect dominates the distortion created by output royalty. We show below that this can indeed be the case if bargaining power of the labor union is sufficiently high. Proposition 2. Consider decentralized bargaining. If n > 1 and bargaining power of the labor union is sufficiently high, the innovator earns higher profit under royalty licensing than under auction (or fixed-fee licensing). Proof. If n ≥ 3, there are k*,d ≤ n auctions for α [0,1]. If there are n licenses under royalty licensing but k*,d licenses under auction, the profit of I is higher under the former than the latter if ðk*;d ð2−αÞ + αÞ2 4ðk*;d Þ3 ðn + 1Þ − > 0: ð2−αÞðnð2−αÞ + αÞ n2 ðk*;d + 1Þ2

ð8Þ

Left hand side (LHS) of Eq. (8) is convex in α [0,1]. Since n ≥ 3, LHS of Eq. (8) is negative at α = 0, where k*,d = 1, and LHS of Eq. (8) is positive at α = 1, where k*,d = 3. Hence, the principle of continuity implies that I's profit is higher under royalty licensing than under auction for sufficiently higher values of α. Now, consider the case for n < 3. Straightforward calculation shows that if n = 1, the equilibrium profit of I under auction, which a2 ð2−αÞ2 , cannot be lower than its profit under royalty licensing, is 16 2 a ð2−αÞ , for α∈½0; 1. which is 16 Next, consider the case of n = 2. In this situation, the profit of I under a2 ð2−αÞ a2 . However, the profit of I under auction is royalty licensing is 3ð4−αÞ 4 8a2 for α = 1 (where k*,d =n = 2). for α = 0 (where k*,d = 1) and it is 81 Straightforward calculation shows that I's profit is higher (lower) under auction than under royalty licensing at α = 0 (α = 1). Hence, the principle of continuity implies that I's profit is higher under royalty licensing than under auction for sufficiently higher values of α. This proves the result. Q.E.D. For a given wage rate, auction creates higher total outputs and total profits of the producers compared to royalty licensing, since royalty creates distortion in the output choice. However, higher total

output, and therefore, higher total demand for labor under auction creates higher wage rate under auction compared to royalty licensing, as long as the labor unions have positive bargaining powers. Hence, in the presence of labor unions, whether the total profit of the innovation is higher under auction or under royalty licensing depends on the relative distortion created by the output royalty and the wage rate. If the bargaining power of the labor union is sufficiently high, it strengthens the wage rate effect, which dominates the royalty effect for n > 1, thus crating higher profit of the innovator under royalty licensing compared to auction. On the other hand, if the bargaining power of the labor union is small enough, the wage effect is dominated by the royalty effect for any n, and the profit of the innovator is higher under auction than under royalty licensing. At the extreme, where bargaining power of the labor union is zero, the abovementioned wage effect does not arise, and the distortion created by the output royalty generates lower profit of the innovator under royalty licensing compared to auction, as in Kamien et al. (1992). Note that the wage effect mentioned above is not due to our assumption of the linear demand curve. It is well known that, under Cournot competition, marginal cost reduction of a firm increases its equilibrium output. Hence, given the demand function and the wage rate, royalty licensing reduces the equilibrium outputs of the producers compared to auction, thus creating lower labor demand under the former than the latter. As a result, the above-mentioned positive wage effect of royalty licensing remains under non-linear demand functions, and may create higher profits of the innovator under royalty licensing compared to auction. There is an interesting implication of our analysis. It follows from the above analysis and also from the previous studies such as Kamien et al. (1992) that, under auction, the innovator extracts entire profits generated in the product market, whereas, under royalty licensing, the net profits of the producers are positive. However, we have shown that, for n > 1, the innovator prefers royalty licensing than auction if the unions have full bargaining power. However, for any n, the innovator prefers the opposite if bargaining power of the union is zero. Hence, if the innovator can license either through royalty or through auction (or fixed-fee), the innovator does not extract the entire profits of the producers if the unions have full bargaining power, but he extracts the entire profits of the producers under no bargaining power of the unions. Therefore, the producers can be better off under relatively higher bargaining power of the labor unions since it can change the innovator's licensing policy. It is also worth mentioning that if licensing is costly, the cost of licensing may induce the innovator to restrict the number of licensing contracts, and the cost of licensing may be more binding under royalty licensing compared to auction (or fixed-fee licensing), since the number of licenses are not less under the former than the latter. However, even with costly licensing, royalty licensing may not be inferior for the innovator compared to auction if the number of licensing are the same for different licensing schemes. For example, if n ≥ 3, α = 1 and the number of licenses is 3 under both royalty licensing and auction, the payoff of the innovator is higher under the former than the latter. So far, we have considered that the innovator does not use royalty and fixed-fee together. It is immediate from the above analysis that the net profits of the producers are positive under royalty licensing. Hence, it is trivial that the innovator prefers to use fixed-fee along with royalty to extract the profits of the producers. While royalty provides the beneficial wage effect, auction helps to extract the entire surplus from the licensees. It is then intuitive that the innovator prefers auction plus royalty licensing (or fixed-fee plus royalty) over royalty only licensing and auction for higher bargaining powers of the unions. Under auction plus royalty (fixed-fee plus royalty), the innovator determines the number of licenses to auction (fixed-fee) and the uniform royalty rate r. Since the dominance of the auction plus royalty licensing is straightforward from the above analysis, we skip the mathematical details for this result.

A. Mukherjee / Labour Economics 17 (2010) 735–742

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An interesting implication of the optimality of auction (or fixedfee) plus royalty licensing is that even if there is only one potential producer, the innovator may prefer to charge a positive royalty rate to reduce the wage rate charged by the labor union. If I auctions the a2 ð2−αÞ2 , which is technology to the monopolist licensee, its profit is 16 lower than its payoff under auction (or fixed-fee) plus royalty a2 ð2−αÞð6−αÞ , for α > 23. licensing to the monopolist producer, i.e., 16 This is in contrast to the earlier works where, in the absence of labor unions, the innovator charges only up-front fixed-fee in the presence of a single producer (see, e.g., Sen and Tauman, 2007).

Due to symmetry, the outputs of the licensees are q1 = q2 = ::: = qn = ð2−αÞða−rÞ 2ðn + 1Þ . Hence, the innovator I maximizes the following expression to determine the equilibrium royalty rate:

2.2. Centralized bargaining

If bargaining power of the labor union increases, it reduces the payoff of I. Straightforward comparison shows that the equilibrium wage rate under royalty licensing is higher under centralized bargaining (which is w = ;c ;d αða−r * Þ ) than under decentralized bargaining (which is w = a−r* ).

Let us now consider the case of centralized bargaining. Suppose the innovator I licenses the technology to k firms, where 1 ≤ k ≤ n, and each licensee pays a per-unit output royalty r, where r < a. If the wage rate under centralized bargaining is w, the ith licensee, i = 1,2,…,k, chooses his output to maximize the following expression: Max ða−q−w−rÞqi :

ð9Þ

qi

The equilibrium output of the ith licensee can be found as . Note that r is 0 under auction, while r will be positive qi = a−w−r k + 1 under royalty licensing. If the wage rate, w, which is determined under centralized bargaining, is very high, the equilibrium outputs and the profits of all firms are zero. Hence, setting such a high w is not optimal for either the firms or the unions and the equilibrium wage rate should satisfy w < a−r.  2 The equilibrium profit of the ith firm is πi = ðqi Þ2 = a−w−r and k + 1  2 the total profit of the licensees is π = kπi = k a−w−r . The labor k + 1 income from the ith firm is wqi =

wða−w−rÞ . k + 1

Therefore, the total labor

Max r

nrð2−αÞða−rÞ : 2ðn + 1Þ

ð11Þ

The equilibrium royalty rate is r *;c = 2a, and the equilibrium payoff of I is I;c

πr =

na2 ð2−αÞ : 8ðn + 1Þ

ð12Þ

i

2

2n α −n

+ 1

However, the equilibrium profit of I under royalty licensing is lower under na2 ð2−αÞ 8ðn + 1Þ ) than that n2 a2 ð2−αÞ 4ðn + 1Þðnð2−αÞ + αÞ).

centralized bargaining (which is πI;c r = tralized bargaining (which is πI;d r =

of under decen-

2.2.2. Auction Let us now consider the game under auction. If I auctions k licenses, where 1 ≤ k ≤ n, it follows from Lemma 2 that, under centralized bargaining, the equilibrium wage rate is w = αa 2. 2 2 The profit of each licensee is π1 = π2 = ::: = πk = a ð2−αÞ 2 . There4ðk + 1Þ fore, in the Nash equilibrium of the bidding game, each potential a2 ð2−αÞ2 . If k = n, I can guarantee this equilibrium bid licensee bids 4ðk + 1Þ2 by specifying a minimum bid. However, for k < n, the producers bid these amounts even if I does not specify the minimum bid. 2 ka2 ð2−αÞ Hence, if I auctions k licenses, his payoff is πI;c a = 4ðk + 1Þ2 , and the number of licenses to auction is determined by maximizing the following expression:

kwða−w−rÞ . k + 1

income is kwqi = Under centralized bargaining, at stage 3, the wage rate w is determined by maximizing the following expression:

Max

!ð1−αÞ   kwða−w−rÞ α kða−w−rÞ2 Max : wi k+1 ðk + 1Þ2

The equilibrium number of licenses is given by k*,c = 1. Therefore, in our setup, the equilibrium number of auction under centralized bargaining is 1. The profit of the innovator I is

ð10Þ

The equilibrium wage rate is w = αða−rÞ 2 . If bargaining power of the labor union increases, it increases the equilibrium wage rate. The following lemma is immediate from the above discussion. Lemma 2. Consider a Cournot oligopoly with k firms where firm i pays the per-unit royalty r. Under centralized bargaining, the wage rate is wðk; rÞ = αða−rÞ 2 . Due to symmetry, the total profits of the licensees are simply k times the profit of each licensee. Similarly, the total labor income is simply k times the labor income from each firm. Therefore, there is no conflict between the individual utility and the total utility, either from the firms' point of view or from the unions' point of view. As a result, the equilibrium wage under centralized bargaining is independent of the number of licensees. 2.2.1. Royalty licensing Under royalty licensing, each producer always prefers to purchase a license for r < a, since the producers always have the option to produce nothing after purchasing a license, thus earning 0, which is the opportunity cost of having a license. Under n licensees, it follows from Lemma 2 that, under centralized bargaining, the equilibrium wage rate is w = αða−rÞ 2 .

k

I;c

ka2 ð2−αÞ2 : 4ðk + 1Þ2

πa =

ð13Þ

a2 ð2−αÞ2 : 16

ð14Þ

If bargaining power of the labor union increases, it reduces the payoff of I. Straightforward comparison shows that the equilibrium wage rate under auction is higher under centralized bargaining (which is w = αa a ). 2 ) than under decentralized bargaining (which is wi = 2k*;d *;d + 1 α −k However, the equilibrium profit of I under royalty licensing is lower under centralized bargaining (which is πI;c a = under decentralized bargaining (which is πI;d a

=

a2 ð2−αÞ2 ) 16

than that of

;d

;d

ðk*

a2 ðk* Þ3 ð2−αÞ2 ;d

+ 1Þ2 ðk* ð2−αÞ + αÞ2

).

2.2.3. Comparing auction with royalty licensing Proposition 3. Consider centralized bargaining. A licensee pays lower wage rate under royalty licensing than under auction (or fixed-fee licensing) for α > 0. Proof. Under centralized bargaining, a licensee pays the wage rate αða−rÞ under royalty licensing but it pays the wage rate αa 2 2 under

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auction. Straightforward calculation shows that the wage rate is higher under auction than under royalty licensing. Q.E.D. Proposition 3 is qualitatively similar to Proposition 1 and the intuition for this result is similar to the wage rate comparison under decentralized bargaining. Proposition 4. Consider centralized bargaining. If n > 1 and bargaining power of the labor union is sufficiently high, the innovator earns higher profit under royalty licensing than under auction (or fixed-fee licensing). Proof. If there are n licenses under royalty licensing but 1 license under auction, the profit of I is higher under the former than the latter if na2 ð2−αÞ a2 ð2−αÞ2 > 8ðn + 1Þ 16

Fig. 1. The value of G at α*,c for n over [3,100].

or α>

2 ;c ≡α* : n+1

ð15Þ

LHS of Eq. (15) is less than right hand side (RHS) of Eq. (15) at α = 0, but LHS of Eq. (15) is greater than RHS of Eq. (15) at α = 1 for n > 1. If n = 1, the profit of I cannot be lower under auction than under royalty licensing. Q.E.D. Proposition 4 is qualitatively similar to Proposition 2 and the intuition for the above result is similar to Proposition 2. Like decentralized bargaining, the relative profitability of royalty licensing and auction under centralized bargaining depends on the trade-off between the wage effect created by the labor union and the distortion created by the output royalty. Hence, if n > 1 and bargaining power of the union is very high, the innovator is better off under royalty licensing than under auction, irrespective of the type of bargaining between the firms and the unions. As in the case of decentralized bargaining, it is immediate that, since royalty licensing leaves positive profits to the producers, the innovator may earn higher profit under licensing with royalty plus fixed-fee (where the fixed-fee is either determined by the innovator or it is determined by the equilibrium bid of the producers under auction by the innovator) compared to royalty only licensing and auction. We have seen that the profits of the innovator are higher under decentralized bargaining than under centralized bargaining, for both royalty licensing and auction. Hence, it is not immediate whether the innovator's incentive for royalty licensing over auction is higher under decentralized bargaining or under centralized bargaining. Let us now consider this issue. Since we cannot determine the closed form solution for α that makes the innovator indifferent between royalty licensing and auction under decentralized bargaining, we cannot compare the respective critical values of α directly for different types of bargaining. We take the following approach for this comparison. If n ≥ 3, we know from subsection 2.1.2 that the number of auctions under decentralized bargaining is k*,d. Evaluate the innovator's profit difference between royalty licensing and auction under n2 decentralized bargaining (i.e., evaluate G≡ 4ðn + 1Þðnð2−αÞ + αÞ − ;d 3 ðk* Þ ð2−αÞ 9 ,c ,c ) at α = α* , where α* is given in Eq. (15). ;d ;d ðk* + 1Þ2 ðk* ð2−αÞ + αÞ2 Fig. 1 plots G for n over [3,100] where G is evaluated at α = α*,c. Fig. 1 shows that G is positive at α = α*,c for n over [3,100]. Since the innovator's incentive for royalty licensing over auction increases with higher α, it is then immediate that, the innovator's incentive for royalty licensing compared to auction is higher under decentralized 9 Since the innovator's profits under royalty licensing and under auction consist of a common positive term a2 (2−a), we take out this common term from G.

bargaining than under centralized bargaining, if there is at least three potential licensees. Now consider the case for n < 3. The case of n = 1 is not relevant here since the innovator cannot be better off under royalty licensing than under auction in this situation, irrespective of the bargaining structure. Next, consider the case of n = 2. In this situation, I is indifferent between auction and royalty licensing under centralized bargaining at α = α*;c = 23. If α = 23, the equilibrium number of auction under decentralized bargaining is 2, since k*,d > 2 at α = 23. Straightforward calculation shows that, if there is decentralized bargaining and α = 23, 2a2 , is lower than its the profit of I under royalty licensing, which is 15 32a2 profit under auction, which is . Therefore, if n = 2, I's incentive for 225 royalty licensing compared to auction is higher under centralized bargaining than under decentralized bargaining. The above discussion is summarized in the following proposition. Proposition 5. If there is at least three potential licensees and the opportunity costs of the licensees are zero, the innovator's incentive for royalty licensing over auction (or fixed-fee licensing) is higher under decentralized bargaining than under centralized bargaining. 3. The implications of positive opportunity costs of the licensees We have developed a simple model to show that an outside innovator may prefer royalty licensing over fixed-fee licensing and auction in the presence of labor unions. We have shown this result under the assumption of zero opportunity cost, which is a reasonable assumption for certain cases (e.g., when the innovation is drastic), it may worth discussing the implications of positive opportunity costs on our analysis. We take up this issue in this section. To discuss the implications of positive opportunity costs of the licensees, let us consider an economy with n firms, each producing a product x with its own technology. The innovator I invents a new product, called product y. To make our points in the simplest way, assume that x and y are not in direct competition. Of course, there could be other possibilities such as competition between the products. Following Kamien et al. (1988), we assume that the firms produce either x or y. This may be due to diseconomies related to production of more products. Also assume that productions of both x and y require workers and the labor market is unionized. Given the usual negative relationship between the number of firms and the per-firm profit (even after considering the effects of more firms on the equilibrium wage rates), as more firms switch their productions from x to y, the profit of each firm producing y reduces and the profit of each remaining firm producing x increases. It is then

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immediate that, unlike the case of zero opportunity costs of the licensees, even if there is royalty licensing and k firms has switched from x to y, the (k + 1)th firm may not find it profitable to switch from x to y. This happens if the (k + 1)th firm's benefit from producing x and competing with (n − k − 1) firms is greater than its benefit from producing y and competing with k firms. Due to the positive opportunity costs of the licensees, there is a difference between auction and the fixed-fee licensing. If there is a fixed-fee licensing and k firms take the license, each licensee's opportunity cost of having the license is its profit from producing x and competing with (n − k) firms. However, if there are k auctions, each licensee's opportunity cost is its profit from producing x and competing with (n − k − 1) firms. Given that the profit of each firm producing x with (n − k − 1) competitors is higher compared to the situation with (n − k) competitors, the opportunity costs of the firms are higher under auction than under fixed-fee licensing. Since the profits of a licensee under k auctions and under fixed-fee licensing with k licenses are the same, it is then immediate that, for the same number of licenses under auction and under fixed-fee licensing, each producer's willingness to pay for the license is higher under fixed-fee licensing than under auction. Hence, fixed-fee licensing dominates auction for innovator I. This is in contrast to the existing works on licensing of process innovation by an outside innovator (Kamien and Tauman, 1984, 1986; Kamien et al., 1992; Sen, 2005a). In our case of a product innovation with no competition between x and y, the positive externality of licensing on the non-licensees (i.e., the remaining producers of x) is the reason for higher profit of I under fixed-fee licensing compared to auction. In contrast, the existing literature with process innovation creates a negative externality on the nonlicensees, thus reducing the profit of the innovator under fixed-fee licensing compared to auction. Competition between x and y in our analysis will reduce the positive externality effect and will start creating a negative externality, thus reducing the possibility of higher profit of I under fixed-fee licensing compared to auction. Hence, in contrast to the case of zero opportunity costs of the licensees, positive opportunity costs of the licensees create the following differences. Unlike zero opportunity cost, positive opportunity cost may not induce all firms to buy license even under royalty licensing. Positive opportunity costs of the licensees constrain the innovator's profit extraction for all types of licensing contracts by reducing the licensees' gain from licensing. Further, for a given number of licenses, the innovator can be better off under fixed-fee licensing compared to auction. However, it must be noted that the wage effects under different licensing contracts will be similar under zero opportunity cost and under positive opportunity cost. Unlike royalty licensing, neither fixed-fee licensing nor auction distorts the outputs of the licensees through per-unit royalty. Hence, for a given number of licenses, the outputs of the licensees are higher under fixed-fee licensing and under auction compared to royalty licensing. Therefore, the corresponding wage rates are higher under the former contracts than the latter. Further, since the innovator gets lump-sum up-front fees under both fixed-fee and auction, the licensing fees under these contracts do not affect the equilibrium outputs of the licensees and the wage rates. Therefore, given the same number of licenses, the equilibrium outputs of the licensees are the same under both fixed-fee licensing and auction. The wage effect tends to reduce the distortionary effect of royalty, thus helps to increase the innovator's incentive for royalty licensing compared to fixed-fee licensing and auction. Further, the wage effect increases with higher bargaining power of the union. Therefore, sufficiently higher bargaining power of the union may make the innovator better off under royalty licensing compared to fixed-fee licensing and auction. It is also worth mentioning that since the royalty licensing leaves surplus to the licensees which can be extracted through fixed-fee, a licensing contract with both fixed-fee

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and royalty can be used to extract more profits from licensing compared to royalty only licensing. These effects are similar to the case of zero opportunity cost. The above discussion shows possible implications of positive opportunity costs on different licensing contracts. However, a formal analysis showing the effects of labor unions on the innovator's preference for a particular licensing contract in the presence of positive opportunity costs of the licensees is worth considering. We leave this issue for future research. 4. Conclusion We show that if the labor market is unionized and the labor union has significant bargaining power, an innovator, which is not a producer, can be better off under royalty licensing than under both auction and fixed-fee licensing. Though positive royalty rate creates distortion in the product market, the wage rates are lower under royalty licensing compared to auction and fixed-fee licensing. The benefit of a lower wage rate can outweigh the negative impact of a distortionary output royalty if the labor union has significant bargaining power, thus allowing the innovator to earn higher profits under royalty licensing than under auction and fixed-fee licensing. Since royalty licensing leaves positive surplus to the producers, a combination of fixed-fee and royalty can be preferable to the innovator compared to royalty only licensing and auction (or fixed-fee licensing). Our results hold for both decentralized and centralized bargaining. Our formal analysis considers the case of zero opportunity costs of the licensees, which correspond to the case of drastic innovation. We have also discussed the implications of positive opportunity costs of the licensees. Our analysis suggests that, under technology licensing by an outside innovator, more licensing contracts with output royalties are expected in economies with strong labor unions, thus providing a testable hypothesis for empirical works. Acknowledgements I would like to thank two anonymous referees of this journal for helpful comments and suggestions. The usual disclaimer applies. References Arrow, K., 1962. Economic welfare and the allocation of resources for invention. In: Nelson, R. (Ed.), The Rate and Direction of Inventive Activity. Princeton University Press, Princeton. Beggs, A.W., 1992. The licensing of patents under asymmetric information. International Journal of Industrial Organization 10, 171–191. Bousquet, A., Cremer, H., Ivaldi, M., Wolkowicz, M., 1998. Risk sharing in licensing. International Journal of Industrial Organization 16, 535–554. Bughin, J., Vannini, S., 1995. Strategic direct investment under unionised oligopoly. International Journal of Industrial Organization 13, 127–145. Choi, J.P., 2001. Technology transfer with moral hazard. International Journal of Industrial Organization 19, 249–266. Faulí-Oller, R., Sandonis, J., 2002. Welfare reducing licensing. Games and Economic Behavior 41, 192–205. Filippini, L., 2001. ‘Process innovation and licensing’, Mimeo, Università Cattolica. Flanagan, R.J., 1999. Macroeconomic performance and collective bargaining: an international perspective. Journal of Economic Literature 37, 1150–1175. Fosfuri, A., 2004. Optimal licensing strategy: royalty or fixed fee? International Journal of Business and Economics 3, 13–19. Gallini, N.T., Wright, B.D., 1990. Technology transfer under asymmetric information. Rand Journal of Economics 21, 147–160. Iversen, T., 1998. Wage bargaining, central bank independence and the real effects of money. International Organization 52, 469–504. Kabiraj, T., 2004. Patent licensing in a leadership structure. Manchester School 72, 188–205. Kabiraj, T., 2005. Technology transfer in a Stackelberg structure: licensing contracts and welfare. Manchester School 73, 1–28. Kamien, M.I., 1992. Patent licensing. In: Aumann, R.J., Hart, S. (Eds.), Handbook of Game Theory. Elsevier, Amsterdam, pp. 331–355. Kamien, M.I., Tauman, Y., 1984. The private value of a patent: a game theoretic analysis. Journal of Economics. Supplementum (Zeitschrift für Nationalökonomie) 4, 93–118.

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