Optimal Licensing Policy under Vertical Product Differentiation*
Munirul H. Nabin, Xuan Nguyen and Pasquale M. Sgro**Deakin University, Australia
November 16, 2011

Abstract

This paper explores a vertical product differentiation model with licensing
arrangement between a multinational firm with superior technology and a domestic
firm with obsolete technology. When the technology gap between the firms is smallenough, licensing is found to improve the participating firms’ profitability andenhance the domestic country’s welfare. We also extend the analysis to compare fixed
fee and royalty licensing and find that, the firms always prefer fixed fee licensing
whereas the social planner always prefers royalty licensing. These results stand incontrast to earlier results using horizontal product differentiation approach.

JEL classification: F12, F13, L13.
Key words: Licensing, Product Differentiation, Oligopoly, Welfare.

* We would like to thank Jota Ishikawa, Martin Richardson and Hong Hwang forearlier discussions at the APTS 2011 seminar.
** Corresponding author: Pasquale M. Sgro, Deakin Graduate School of Business,
Faculty of Business and Law, Deakin University, VIC 3125, Australia.
Email: pasquale.sgro@deakin.edu.au. Tel: +61 3 9244 5245; Fax: +61 3 9244 5533.

0

Optimal Licensing Policy under Vertical Product Differentiation
1.

Introduction

Licensing between a multinational firm and a domestic competitor is popular invarious industries in many countries. By providing its superior knowledge andexpertise to the domestic firm through a licensing arrangement, the multinational firm
can extract a higher level of rents in the form of the enhanced benefits to the domestic
firm as a result of using the multinational firm’s advanced technology for production. 1
For instance, in July 2011, One-stop China, a venture between Universal Music,
Warner Music and Sony Music set a license fee for Bidu Inc., a Chinese internetsearch engine, to allow the latter access to its music contents. 2 In 2010, Chinese
automaker Geely purchased Ford’s Volvo unit to gain the access to modern
automobile technology. 3 According to the World Development Indicators database,between 1998 and 2009, the licensing fee payments by Chinese firms to foreigncompanies had an annual growth rate of over 34 percent. 4 Grindley and Teece (1997)
also document that firms in high-tech industry such as IBM, Texas Instruments,
Hewlet-Packard consider the use of licensing as an important part of their business. 5

Despite the fact that the burgeoning trend of technology licensing, including licensing
between competing firms from different countries, has been an important feature of1

In a study on partial equity ownership, Ghosh and Morita (2010) present several examples whereby
a multinational firm, after acquiring a certain proportion of shares in its competitor, helps its
competitor with the advanced production know-how and expertise.
2
Available at http://www.businessweek.com/news/2011-07-19/baidu-to-pay-record-labels-forbeyonce-gaga-music-in-china.html.
3
Available at http://autonews.gasgoo.com/blog/be-brave-to-buy-foreign-brands-090616.shtml.
4
Calculated by the authors based on the World Development Indicators database, available at
http://data.worldbank.org/indicator.
5
McGrath (209) presents examples of licensing between international competing firms in the Chinese
automobile industry.

1international trade (Erkal 2005; Ciuriak 2010), to the best of our knowledge, noprevious study has examined optimal licensing between firms competing withdifferent productquality. This paper aims to fill this gap in the literature byincorporating the licensing arrangement between the competing firms into the
traditional vertical product differentiation model (Mussa & Rosen 1978).

In our set up, a multinational firm possessing superior (low-cost) technology
undertakes FDI to compete with a domestic firm with obsolete (high-cost) technology
in the domestic market by producing products differentiated by quality levels. Under alicensing arrangement, the multinational firm licences its technology to the domestic
firm so that the latter can utilise the former’s technology for production to reduce
costs. Two alternative methods of technology licensing have been investigated: fixed
fee and royalty licensing.

We find that, when the technology gap (or production cost difference) between thefirms is small enough, licensing is found to be not just profitable for both firms but
also welfare enhancing for the domestic country. In this context, the firms always
prefer a fixed fee over royalty licensing. The reason is that royalty licensing, whichworks like an additional marginal cost for the licensee, induces the domestic firm tochoose a higher quality level compared to fixed fee licensing. This reduces the
profitability for both firms. However, in equilibrium, we find that the social planneralways prefers royalty over fixed fee licensing.

These results contradict those of Erkal (2005) where in his model, which was basedon Sign and Vives (1984)’s and Katz and Shapiro (1985)’s horizontal product2differentiation framework, an innovator with cost advantages competes with anotherfirm in a Cournot fashion. 6 The firms do not choose their product quality but quantity,
and consumers differentiate their products with a symmetric differentiation parameter.
Erkal finds that royalty licensing always raises the profit for the licensor in thiscontext, and fixed fee licensing raises the licensor’s profit if the technology gaps
between the firms is significantly small, or if the degree of product differentiation issignificantly small. Furthermore, he finds that if the innovation size is large, it issocially optimal to allow licensing while if the innovation size is small and the degreeof product differentiation is small, it is socially optimal to discourage licensing.

Sinha (2010) examines a multinational’s modes of entry into a host country market
between export and FDI after it licensed its technology to a host country firm whocompetes with the multinational in quantity. He shows that, in the case when themultinational chooses FDI, it is optimal for it to choose royalty licensing. When themultinational firm does not change its mode of entry after licensing, licensing does
not affect or it can improve the welfare of the host country. Unfortunately optimal
licensing policy from the welfare standpoint has not been discussed in Sinha’s paper(where he focuses on trade policy’s impact on the multinational firm’s mode of entry).
Therefore, most results in Sinha’s paper and ours are qualitatively different. 7

6

The literature on horizontal product differentiation with licensing has been well developed. For
instance, Kabiraj and Marjit (1993) investigate the relationship between optimal international
technology licensing and trade policy (see also Ghosh & Saha 2008). Arora and Fosfuri (2003) examine
a model with many symmetric firms competing with each other and with potential entrants. Theyshow that the incumbents tend to license their technologies to potential entrants more often if theirproducts are less differentiated. Fess, Hoeck and Lorz (2009) explore the competition effect andbusiness stealing effects of international technology licensing.
7
Mattoo, Olarreaga and Saggi (2004) and Tekin-Koru (2009) explore the impact of trade costs on
optimal technology transfers and entry strategy by a multinational firm into a host country where
there are several competitors and when acquisition of a host country firm is possible.

3

Our paper is also related to the growing literature on vertical product differentiationand trade (Das & Donnenfeld 1987, 1989; Boccard & Wauthy 2005; Toshimitsu
2005, among others). The focus thus far under this approach has been on the impactsof trade restrictions on optimal quality and welfare. An exception is Nabin, Nguyen
and Sgro (2011) who analyse an international oligopoly model of vertical productdifferentiation with technology licensing in which a Northern firm licenses its
technology to one of two Southern competing firms. The firms produce products thatare vertically differentiated in both regions. They find that international technology
licensing promotes trade, product variety and is beneficial for all firms, including theoutside firm. To maximize social welfare in this context, both countries have an
incentive to impose quality standards on the low-quality firm. However, a comparison
between fixed fee and royalty licensing was absent in their analysis.

In summary, this paper extends the traditional vertical product differentiation model(Mussa & Rosen 1978) to analyse the impact of licensing between competing firms.
We have found significant differences to the earlier results in the literature. The restof the paper will proceed as follows. The next section presents a duopoly model ofvertical product differentiation with licensing arrangement between competitors.
Section 3 characterises the equilibrium of the model. Section 4 analyses the welfare
impact of fixed fee versus royalty licensing while section 5 concludes.

4

2. The model

Consider an international oligopoly model in which a multinational firm (firm 1)
competes with a domestic firm (firm 2) in the domestic market in verticallydifferentiated products. The multinational firm possesses an advanced technology
which allows it to supply products at a lower cost compared to the domestic
competitor. Without loss of generality, we assume that the marginal cost is zero andthe quality development cost for the multinational firm is zero while that for thedomestic firm is given by a convex function, 𝐶𝐶2 (𝑞𝑞2 ) = 𝑘𝑘𝑞𝑞22 , where 𝑞𝑞𝑖𝑖 (≤ 1) (𝑖𝑖 = 1,2)
is the quality level for the

product of firm 𝑖𝑖 and 𝑘𝑘 denotes the efficiency of

production. In the subsequent analysis, we assume that 𝑘𝑘 = 1/2 to find a closed form

solution for the model. We then discuss the possibility of generalizing the result for
any value of 𝑘𝑘.

The market of the domestic country consists of a continuum of nonatomic consumersof mass 1, where each consumer 𝑗𝑗 is indexed by a taste parameter, 𝜃𝜃𝑗𝑗 ∈ [0,1], andendowed with a reservation utility equal to zero. Assume that 𝜃𝜃𝑗𝑗 is uniformly
distributed. Each consumer purchases zero or 1 unit of the product. If the consumer

with a taste parameter 𝜃𝜃𝑗𝑗 purchases firm 𝑖𝑖’s product, she obtains a net benefit of𝜃𝜃𝑗𝑗 𝑞𝑞𝑖𝑖 − 𝑃𝑃𝑖𝑖 , where 𝑃𝑃𝑖𝑖 is the price charged by firm 𝑖𝑖.

Under technology licensing, firm 1 allows firm 2 to use its technology for productionof the differentiated product. In return, firm 2 pays firm 1 a licensing fee, which is
given by a lump-sum value 𝐹𝐹 in case of a fixed fee licensing arrangement, and by a5

flat royalty payment 𝑟𝑟 per unit of output for the case of a royalty licensing

arrangement.

We analyse a three stage game, described below:[Stage 1] Firm 1 decides on the licensing fee and firms 1 and 2 decide on thearrangement (licensing or royalty).
[Stage 2] Firms 1 and 2 set the quality level for their product.
[Stage 3] Observing the quality levels set at stage 2, the firms choose the prices fortheir product and consumers make purchasing decisions.

We end this section by two remarks. First, the assumption that the multinational firm
possesses superior technology as compared to the domestic firm is consistent with theliterature. Dunning (1981) points out that for multinational firms to enter a domestic
market, they must possess either ownership advantages, locational advantages, orinternalization advantages (referred to as OLI framework). The multinational’s
technology lead in our model has been considered as an ownership advantage inearlier study (see Markusen 1995; Saggi 2002; and Agarwal & Ramaswami 1992 forrelated surveys). Second, our focus is on the case where the multinational commits toentry into the domestic country even with or without licensing (by undertaking FDI).
Possible extensions include a comparison of outcomes (profitability for firms andwelfare for the domestic country) when the multinational chooses between export,
FDI and acquisition. To focus on the optimal licensing policy, we leave this extension
for future research.

6

3. Equilibrium characterisation

3.1. No licensing

Denote by 𝜃𝜃1 the taste parameter of the marginal consumer who is indifferent aboutbuying firm 2's product and buying zero unit of the product, and 𝜃𝜃2 the taste
parameter of the marginal consumer who is indifferent about firm 2's product and firm

1's product. 8 With uniform distribution of the consumer taste parameter, the demand
for firm 1's product is given by 𝑑𝑑1 = (1 − 𝜃𝜃2 ) and for firm 2 is 𝑑𝑑2 = (𝜃𝜃2 − 𝜃𝜃1 ) as
depicted in Figure 1.

𝑑𝑑2
0

𝑑𝑑1

𝜃𝜃1

1

𝜃𝜃2

𝜃𝜃𝑗𝑗

Figure 1: The market segmentation.

The value of 𝜃𝜃1 and 𝜃𝜃2 can be found from the incentive constraints, 𝜃𝜃1 𝑞𝑞2 − 𝑃𝑃2 = 0
𝑃𝑃

𝑃𝑃 −𝑃𝑃and 𝜃𝜃2 𝑞𝑞1 − 𝑃𝑃1 = 𝜃𝜃2 𝑞𝑞2 − 𝑃𝑃2 . Thus, 𝜃𝜃1 = 𝑞𝑞2 ; 𝜃𝜃2 = 𝑞𝑞1 −𝑞𝑞2 . At stage 3, firm 2 chooses 𝑃𝑃2
2

by solving its problem:

2

𝑞𝑞 2

𝜃𝜃

max[ ∫𝜃𝜃 2 𝑃𝑃2 𝑑𝑑𝑑𝑑 − 22 ]1

81

In the literature, it has been shown that the firm producing the high-quality product makes a higher
level of profit compared to the firm producing the low-quality product even when the firms have
similar cost structures (for instance, see Aoki &Prusa 1996; Boccard & Wauthy 2005). Thus, inequilibrium, firm 1 possessing superior technology always chooses a higher level of quality comparedto firm 2 in our model..

7

while firm 1 chooses 𝑃𝑃1 by solving its problem:1

max ∫𝜃𝜃 𝑃𝑃1 𝑑𝑑𝑑𝑑.
2

Routine calculations yield the solutions 𝑃𝑃1 =2𝑞𝑞 1 (𝑞𝑞 1 −𝑞𝑞 2 )

4𝑞𝑞 (𝑞𝑞 −𝑞𝑞 )4𝑞𝑞 1 −𝑞𝑞 2; 𝑃𝑃2 =

𝑞𝑞 2 (𝑞𝑞 1 −𝑞𝑞 2 )4𝑞𝑞 1 −𝑞𝑞 2

. The

1
2
equilibrium profit for firm 1 is 𝜋𝜋1 = (4𝑞𝑞1 −𝑞𝑞, which is increasing in 𝑞𝑞1 . Thus, firm 1)2
12

chooses 𝑞𝑞1 = 1 at stage 2. Consequently, firm 2 chooses 𝑞𝑞2 = 0.058. It follows that𝜃𝜃1 = 0.24; 𝜃𝜃2 = 0.495, which yield equilibrium profit for firms 1 and 2 of 𝜋𝜋1 =0.242; 𝜋𝜋2 = 0.002, respectively. The consumer surplus is given by 𝐶𝐶𝐶𝐶 =
1

0.495

∫0.495(𝜃𝜃 − 0.48)𝑑𝑑𝑑𝑑 + ∫0.24 (0.058 − 0.014𝜃𝜃)𝑑𝑑𝑑𝑑 = 0.137, and welfare for thedomestic country is given by 𝑊𝑊 = 𝜋𝜋2 + 𝐶𝐶𝐶𝐶 = 0.139.
3.2. Fixed fee licensing

Under fixed fee licensing, since the cost structure does not directly affect the optimal
prices (even though it affects the optimal quality levels), at stage 3, the equilibrium
prices can be found in a similar way as with the case of no licensing. At stage 2, thefixed fee licensing, 𝐹𝐹, does not affect the firms’ choice of optimal quality levels.

Therefore, optimal quality levels for firms 1 and 2 are given by 𝑞𝑞1 = 1; 𝑞𝑞2 = 0.571,
as in Boccard and Wauthy (2005). In equilibrium, we have 𝜃𝜃1 = 0.125; 𝜃𝜃2 = 0.42,

which yield 𝜋𝜋1 = 0.146 + 𝐹𝐹; 𝜋𝜋2 = 0.021 − 𝐹𝐹; 𝐶𝐶𝐶𝐶 = 0.292; 𝑊𝑊 = 0.313 − 𝐹𝐹.

8Lemma 1. The degree of product differentiation under fixed fee licensing is lower
than that under no licensing.

The intuition behind Lemma 1 is straightforward: when the domestic firm utilises themultinational firm’s technology for production, it increases its product quality. Since
the multinational firm chooses a fixed level of product quality for both no licensing
and fixed fee licensing, it follows that products supplied by the firm become moresimilar under fixed fee licensing.

3.3. Royalty licensing

Finally, under royalty licensing, firm 2 incurs a marginal cost of 𝑟𝑟 per unit of output.
At stage 3, firm 2 chooses 𝑃𝑃2 by solving its problem:𝜃𝜃max ∫𝜃𝜃 2 (𝑃𝑃2 − 𝑟𝑟)𝑑𝑑𝑑𝑑
1

and firm 1 chooses 𝑃𝑃1 by solving its problem:1𝜃𝜃2

max[� 𝑃𝑃1 𝑑𝑑𝑑𝑑 + � 𝑟𝑟𝑟𝑟𝑟𝑟 ].
𝜃𝜃1

𝜃𝜃2

Routine calculations yield the solutions 𝑃𝑃1 =2𝑞𝑞 1 (𝑞𝑞 1 −𝑞𝑞 2 )+𝑟𝑟𝑞𝑞 1
4𝑞𝑞 1 −𝑞𝑞 2; 𝑃𝑃2 =

𝑞𝑞 2 (𝑞𝑞 1 −𝑞𝑞 2 )+2𝑟𝑟𝑞𝑞 1
4𝑞𝑞 1 −𝑞𝑞 2.

Replacing these prices in the profit functions for the firms, we can solve for the
optimal quality level at stage 2 for a given value of 𝑟𝑟. Then, with backward induction,9

we can solve for firm 1’s optimization problem at stage 1 to find the optimal licensing
fee, 𝑟𝑟.
At stage 1, the optimal licensing fee should be set by firm 1 such that firm 2 is slightly
better-off compared to no licensing. That is, firm 1 should set 𝑟𝑟 such that firm 2’s

profit with royalty licensing is 𝜋𝜋2 = 0.002 + 𝜖𝜖, where 𝜖𝜖 > 0. Thus, the model can be
simplified by assuming that any additional profits captured by firm 2 from licensing
will be fully (or almost fully) taken by firm 1 (that is, 𝜖𝜖 ≈ 0). Thus the equivalent

problem for firm 1 is to maximize the total profits (of firms 1 and 2) at stage 2. Thus,
it chooses 𝑞𝑞1 which solves:
1

𝜃𝜃2

𝜃𝜃2

1

𝜃𝜃2

max[� 𝑃𝑃1 𝑑𝑑𝑑𝑑 + � 𝑟𝑟𝑟𝑟𝑟𝑟 + � (𝑃𝑃2 − 𝑟𝑟)𝑑𝑑𝑑𝑑] = max[� 𝑃𝑃1 𝑑𝑑𝑑𝑑 + � 𝑃𝑃2 𝑑𝑑𝑑𝑑]
𝜃𝜃1

𝜃𝜃2

𝜃𝜃1

𝜃𝜃1

𝜃𝜃2

and with optimal prices, the problem for firm 1 becomes:

max[

2𝑞𝑞1 (𝑞𝑞1 − 𝑞𝑞2 ) + 𝑟𝑟𝑞𝑞1 (𝑞𝑞2 (𝑞𝑞1 − 𝑞𝑞2 ) + 2𝑟𝑟𝑞𝑞1 )2−(4𝑞𝑞1 − 𝑞𝑞2 )2 𝑞𝑞2
4𝑞𝑞1 − 𝑞𝑞22

�(2𝑞𝑞1 − 𝑞𝑞2 )(𝑞𝑞1 − 𝑞𝑞2 ) + 𝑟𝑟𝑞𝑞1 �−].
(4𝑞𝑞1 − 𝑞𝑞2 )2 (𝑞𝑞1 − 𝑞𝑞2 )The sign of the first order derivative can be found to depend on [4𝑞𝑞12 − 3𝑞𝑞1 𝑞𝑞2 + 𝑞𝑞22 ],which is positive for all 𝑞𝑞1 > 𝑞𝑞2 . Hence, firm 1 chooses 𝑞𝑞1 = 1 in equilibrium.

With this result, the first order condition for firm 2 at stage 2 (choosing optimal
quality) is given by [𝑞𝑞2 (1 − 𝑞𝑞2 )(4 − 7𝑞𝑞2 ) + 𝑟𝑟(−2𝑞𝑞23 + 9𝑞𝑞22 − 18𝑞𝑞2 + 8)] = 0. It can
10be seen that if 𝑟𝑟 = 0 then the solution is 𝑞𝑞2 = 0.571 as was the case of fixed fee

licensing. Furthermore, [𝑞𝑞2 (1 − 𝑞𝑞2 )(4 − 7𝑞𝑞2 )] and [(−2𝑞𝑞23 + 9𝑞𝑞22 − 18𝑞𝑞2 + 8)] areboth negative for all 𝑞𝑞2 ∈ [0, 0.571] as well as for all 𝑞𝑞2 ∈ [0.601, 1], so that thesolution is 𝑞𝑞2 ∈ (0.571, 1), where the exact value depends on 𝑟𝑟. Even though a closed

form solution is not possible, the fact that 𝑞𝑞2 ∈ (0.571, 1) helps us to easily compare

profitability of the firms under royalty licensing and fixed fee licensing.

Lemma 2. The degree of product differentiation under royalty licensing is lower thanthat under no licensing but higher than that under fixed fee licensing.

Similar to Lemma 1, Lemma 2 tells us that royalty licensing makes the products of thefirms more similar. However, since the domestic firm chooses a higher equilibrium
quality level under royalty licensing compared to fixed fee licensing, the degree of
product differentiation is lower. This finding suggests that the firms compete more
fiercely under royalty licensing than under fixed fee licensing.

Proposition 1. When 𝑘𝑘 = 1/2, the combined equilibrium profit of firms 1 and 2
under no licensing is greater than that under fixed fee licensing. The combined

equilibrium profit of firms 1 and 2 under fixed fee licensing is greater than that underroyalty licensing.

Proof. Under no licensing we have that 𝜋𝜋1 + 𝜋𝜋2 = 0.244. Under fixed fee licensing,

we have that 𝜋𝜋1 + 𝜋𝜋2 = 0.167 so that total profit is lower under fixed fee licensing

compared to no licensing. Furthermore, recall that under royalty licensing, if thelicensing fee is zero we have 𝑞𝑞2 = 0.571 and total profit under royalty licensing and11

fixed fee licensing are the same. However, as shown above, a positive royalty fee
induces firm 2 to choose 𝑞𝑞2 > 0.571. It can be verified that𝜕𝜕𝜋𝜋 1𝜕𝜕𝜋𝜋+ 𝜕𝜕𝑞𝑞 2 < 0, so that the
𝜕𝜕𝑞𝑞
2

2

higher the value of 𝑞𝑞2 the lower the total profit. Thus, the total profit under royalty
licensing is always lower than that under fixed fee licensing.

Proposition 1 tells us that when 𝑘𝑘 = 1/2, under a private licensing arrangement, firm

1 would choose no licensing as the outcome. The technology gap allows firm 1 toachieve a much higher profit if it keeps the technology for its own production.

4. Welfare impact of licensing

In this section, we compare social welfare for the domestic country under nolicensing, fixed fee licensing, and royalty licensing. We then identify the optimal
licensing policy.

Proposition 2. When 𝑘𝑘 = 1/2 and only fixed fee licensing is possible, the domestic
government should subsidize firm 1 to induce licensing.

Proof. Comparing the fixed fee licensing and no licensing, it follows that social
welfare under fixed fee licensing is higher if 0.313 − 𝐹𝐹 > 0.139 ⇔ 𝐹𝐹 < 0.174.
When 𝐹𝐹 = 0.174 we have 𝜋𝜋2 = 0.146 + .174 = 0.32 > 0.242.

Proposition 2 tells us that fixed fee licensing should be encouraged. If the firms
cannot conclude on the licensing arrangement, the government should provide a
subsidy to firm 1 to enable licensing. The intuition is that with licensing, technology
12transfer from firm 1 to firm 2 raises production efficiency and thus it is socially
optimal.

Proposition 3. The socially optimal licensing policy is royalty licensing.

Proof. Consider royalty licensing and assume that 𝑟𝑟 = 0. It can be verified that𝜕𝜕𝜕𝜕𝜕𝜕𝑞𝑞 2> 0. Thus, an increase in royalty fee raises 𝑊𝑊 and is socially desirable. Recall thatthe outcome concerning optimal quality and price levels under fixed fee licensing androyalty licensing are the same when 𝑟𝑟 = 0. Hence, royalty licensing is always socially
optimal.

Proposition 3 tells us that royalty licensing yields a better outcome in terms of welfare
for the domestic country compared to fixed fee licensing. From the social planner’s
standpoint, inducing the firms to raise their quality level is always welfare enhancing.
Thus, one policy recommendation is that the domestic government should allow onlyroyalty licensing. This strategic policy choice induces the low-quality firm to raise its
product quality and improves net benefits for the domestic country.

Robustness

Finally, we generalize the analysis for the any value of 𝑘𝑘.
Proposition 4. There exist threshold values 𝑘𝑘1 and 𝑘𝑘2 , 0 < 𝑘𝑘2 < 𝑘𝑘1 , such that inabsence of a government subsidy:

13

(i)

a private fixed fee licensing arrangement raises the combined equilibrium(ii)

profit of firms 1 and 2 if and only if 𝑘𝑘 < 𝑘𝑘1 ; anda private royalty licensing arrangement raises the combined equilibrium

profit of firms 1 and 2 if and only if 𝑘𝑘 < 𝑘𝑘2 .
Proof. The results can be found by showing that firm 1’s profit under no licensing
equilibrium is increasing in 𝑘𝑘 (since 𝑘𝑘 does not affect the firms’ quality level underlicensing). Consider the no licensing equilibrium. Since firm 1 chooses 𝑞𝑞1 = 1 atstage 2, the first order condition for firm 2 is given by:

2𝑘𝑘𝑞𝑞2 (4 − 𝑞𝑞2 )3 + 7𝑞𝑞2 − 4 = 0.
𝜕𝜕𝑞𝑞

It can be established that 𝜕𝜕𝜕𝜕2 < 0. That is, the higher the technology level firm 2
possesses (lower 𝑘𝑘) the higher quality level it chooses in equilibrium. Note that when

𝑘𝑘 increases, firm 2’s profitability decreases for two reasons: (i) its production costs
become higher and (ii) firm 2’s equilibrium quality level becomes lower.
4(1−𝑞𝑞 )𝜕𝜕𝜋𝜋Furthermore, with 𝜋𝜋1 = (4−𝑞𝑞 2)2 , it can be verified that 𝜕𝜕 𝑞𝑞 1 < 0, so that when firm 222chooses a lower quality then firm 1’s profitability increases. In other words, the nolicensing profitability for firm 1 is increasing in 𝑘𝑘. By Proposition 1, we obtain the
results.

Proposition 4 says that a private licensing arrangement is possible when thetechnology gap between the two competing firms is low enough. A low cost gap withthe multinational firm enables the domestic firm to choose a relatively high level ofquality under no licensing, thus reducing the profitability for the multinational firm. In
14

turn, this makes licensing more attractive for firm 1. In other words, even without agovernment subsidy, licensing is still possible if the firms possess similar
technologies.

5. Conclusion

Licensing between competing firms is popular in many countries. A number of papers
have focused on the horizontal product differentiation approach. Using this approach,
Erkal (2005) finds that royalty licensing is always profitable for the licensor
regardless of its technological lead over the competitor. Furthermore, when thetechnology gap between the competing firms is small, it is socially optimal to
discourage licensing. Sinha (2010) shows that when licensing takes place between amultinational and a domestic firm then if FDI is the multinational’s mode of entry into
the domestic market, royalty is more profitable as compared to fixed fee licensing.

This paper develops a vertical product differentiation oligopoly model to investigate
the impact of licensing between a multinational and a domestic firm on the firms’
profitability and domestic welfare. We have identified several results that contradict
to the literature. Specifically, it has been found that licensing is profitable for the
licensor if and only if the technology gap between the firms is small enough.
Furthermore, fixed fee licensing is more profitable as compared to royalty licensing.
Finally, licensing is always welfare enhancing, and the social planner should only
allow royalty licensing to maximize the domestic country’s welfare. These findings
suggest that the countries that wish to encourage inflows of international technology
should take note of the nature of competition to design their optimal licensing policy.

15

References
Agarwal, S. & Ramaswami, S.N. 1992, “Choice of Foreign Market Entry Mode:
Impact of Ownership, Locational and Internalization Factors.” Journal ofInternational Business Studies, Vol. 23(1), 1-27.
Aoki, R. & Prusa, T.J. 1996, “Sequential versus Simultaneous Choice with
Endogenous Quality.” International Journal of Industrial Organization, Vol. 13(2),103-121.
Arora, A. & Fosfuri, A. 2003, “Licensing the Market for Technology.” Journal of
Economic Behavior & Organization, Vol. 52(2), 277-295.
Boccard, N. & Wauthy, X. 2005, “Enforcing Domestic Quality Dominance throughQuotas.” Review of International Economics, Vol. 13(2), 250-261.
Ciuriak, D. 2010, “Trade (and other) Policy Implications of Heterogeneous Firm
Trade Theory.” Working Paper, SSRN Abstract 1728065.
Das, S.P. & Donnenfeld, S. 1987, “Trade Policy and its Impact on Quality of Imports:
A Welfare Analysis.” Journal of International Economics, Vol. 23(1-2), 77-95.
Das, S.P. & Donnenfeld, S. 1989, “Oligopolistic Competition and International Trade:
Quantity and Quality Restrictions.” Journal of International Economics, Vol. 27(3-4),
299-318.
Dunning, H. 1981, International Production and the Multinational Enterprise,
London: George Allen and Unwin.
Erkal, N. 2005, “Optimal Licensing Policy in Differentiated Industries.” The
Economic Record, Vol. 81(252), 51-64.
Fess, E., Hoeck, M. & Lorz, O. 2009, “International Technology Transfers andCompetition.” Review of International Economics, Vol. 17(5), 1038-1052.
Ghosh, A. & Morita, H. 2010, “Partial Equity Ownership and Knowledge Transfer.”
Working Paper, UNSW.
Ghosh, A. & Saha, S. 2008, “Trade Policy in the Presence of Technology Licensing.”
Review of International Economics, Vol. 6(1), 45-68.
Grindley, P.C. & Teece, D.J. 1997, “Managing Intellectual Capital: Licensing andCross-Licensing in Semiconductors and Electronics.” California Management
Review, Vol. 39(2), 8-41.
Kabiraj, T. & Marjit, S. 1993, “International Technology Transfer under Potential
Threat of Entry.” Journal of Development Economics, Vol. 42(1), 75-88.
Katz, L. & Shapiro, C. 1985, “On the Licensing of Innovations.” The Rand Journal of
Economics, Vol. 16(4), 504-520.
Markusen, J.R. 1995, “The Boundaries of Multinational Enterprises and the Theory ofInternational Trade.” Journal of Economic Perspectives, Vol. 9(2), 169-189.
Mattoo, A., Olarreaga, M. & Saggi, K. 2004, “Mode of Foreign Entry, Technology
Transfer, and FDI Policy.” Journal of Development Economics, Vol. 75(1), 95-111.
McGrath, T. 2009, China's Geely buys Ford's Volvo for $2bn, viewed 28 January2011,
http://www.theaustralian.com.au/business/city-beat/chinas-geely-buys-fordsvolvo-for-2bn/story-fn4xq4cj-1225846738739.
16

Mussa, M. & Rosen, S. 1978, “Monopoly and Product Quality.” Journal of Economic
Theory, Vol. 18(2), 301-317.
Nabin, M.H., Nguyen, X. & Sgro, P.M. 2011, “Technology Transfer, Quality
Standards, and North-South Trade.” Working Paper, Deakin University, Australia.
Saggi, K. 2002, “Trade, Foreign Direct Investment, and International Technology
Transfer: A Survey.” The World Bank Research Observer, Vol. 17(2), 191-235.
Sign, N. & Vives, X. 1984, “Price and Quantity Competition in a DifferentiatedDuopoly.” Rand Journal of Economics, Vol. 15(4), 546-554.
Sinha, U.B. 2010, “Strategic Licensing, Exports, FDI, and Host Country Welfare.”Oxford Economic Papers, Vol. 62(1), 114-131.
Tekin-Koru, A. 2009, “Technology Transfers and Optimal Entry Strategies for theMultinational Firm.” The Journal of International Trade & Economic Development,
Vol. 18(4), 553-574.
Toshimitsu, T. 2005, “Tariffs, Quality Choice, and Cost Functions: A Foreign
Monopoly Case.” Review of International Economics, Vol. 13(2), 376-384.

17