Transnational Licensing in the Presence of Trade Barriers

Wen-Jung Liang

Ching-Chih Tseng

Kuang-Cheng Andy Wang

Overview of the presentation

Introduction: motivation, purpose, related literature, main contributions, the intuition, and game structure.

The benchmark model: licensing is absent. The innovation licensing model: examine the optimal

amount of a lump-sum fixed-fee and optimal number of licenses for the case of a fixed-fee licensing as well as the optimal royalty rate for the case of a royalty licensing.

The optimal licensing contract Concluding remarks

Motivation

Transnational licensing is quantitative significance in international trade.

This quantitative significance becomes evident from the following figures.

Figures on transnational licensing

Nadiri (1993): for Japan and U.K. the total transaction of transnational licensing between 1970’s to the late of 1980’s increased by about 400%, France and the U.S. about 550%, and West Germany over 1000%.

Mottner and Johnson (2000): U.S. income from international licensing had an average annual increase of 12 percent in the 1990s.

Vishwasrao (2007): in 2002, the receipts of royalties and fees collected by U.S. companies from their foreign subsidiaries and unaffiliated firms in foreign countries have roughly doubled over the last decade.

Transnational licensing in the presence of trade barriers is crucial

Kabiraj and Marjit (2003) argue that until 1991, many developing countries have been observed to have encouraged technology licensing, while maintaining tariffs on foreign product.

Thus, transnational technology licensing in the presence of trade barriers, such as tariffs and transportation costs, is crucial and commonly existent in practical applications.

Fee and royalty as well as exclusive and

non-exclusive licensing are popular The survey of firms by Rostoker (1984) shows that roy

alty alone is 39 percent, fixed fee alone is 13 percent, and royalty plus fixed fee is 46 percent.

Caballero-Sanz et al. (2005) point out the survey report published by the Association of University Technology Managers Licensing (AUTM, 2001) that about half of the licenses are exclusive, while the other half non-exclusive.

These figures demonstrate that in the real world, not only fixed-fee and royalty but also exclusive and non-exclusive licensing are popular.

The purpose of the paper

To explore the following two issues by taking into account trade barriers with an outsider patent holder, as firms engage in Bertrand competition in the commodity market with a homogenous product.

Firstly, what is the outsider patent holder’s optimal licensing contract in terms of a fixed-fee and a royalty licensing?

Secondly, whether the outsider patent holder licenses the patent exclusively?

Related literature (1)

Kabiraj and Marjit (2003): explore an issue where a strategic tariff policy induces the foreign firm to transfer its superior technology to the domestic rival.

Mukherjee and Pennings (2006): extend the work of Kabiraj and Marjit (2003) to the discussion of royalty and fixed fee licensing instead of a fixed fee only.

Related literature (2)

Muto (1993): employs a duopoly model with differentiated products and obtains that in a Bertrand competition, the royalty is optimal for small innovations, but the fee is optimal for large innovations.

Poddar and Sinha (2004): utilize a Hotelling’s linear city model and show that offering a royalty licensing is the best policy for the outsider patentee for both drastic and non-drastic innovations.

Kamien and Tauman (1986) and Kamien et al. (1992): fee, royalty and auction, to be equivalent in an n-firm model under Bertrand competition with a homogenous product.

All of the related literature point out that the outsider patentee will license its patent exclusively in a fee licensing.

Main findings of the paper

Firstly, a fixed-fee licensing is superior to a royalty licensing under Bertrand competition as trade costs relative to the innovation size are higher, while the reverse occurs, otherwise.

Secondly, the outsider patentee would like to choose a fixed-fee licensing non-exclusively rather than exclusively, as trade costs relative to the innovation size are higher, while the reverse occurs, otherwise.

The intuition behind the main findings

Bertrand competition in each market with a homogeneous product induces firms to charge an equilibrium price equaling its rival’s marginal production cost plus unit trade costs in each market.

Firm becomes a local monopolist and earns a monopoly profit in the advantageous market.

The higher the degree of trade costs, the larger will be the local monopoly profit.

Thus, fixed-fee licensing is superior to royalty licensing under Bertrand competition, as trade costs are high.

A four-stage game

In stage 1, the outsider patent holder decides to select a fee or a royalty licensing contract.

In stage 2, the outsider patent holder announces how many licenses to be issued and charges a fixed-fee under fee licensing or a royalty rate under royalty licensing.

The third stage marks the decision of the firm of whether to purchase a license or not.

In the final stage, firms engage in Bertrand price competition in each amrket.

The benchmark model

Consider a two-country duopolistic model, where countries, 1 and 2, are located at the opposite endpoints of the line.

Consumers reside only in two countries 1 and 2, where market 1 and firm A are located in country 1 while market 2 and firm B in country 2.

Firms sell a homogeneous product with a constant marginal production cost c. The exports of the product to the other country incur trade costs, t.

Technology licensing is absent in the benchmark model.

The equilibrium prices

The Bertrand game with a homogeneous product in each market has the property “winner-takes-all”. The lower marginal cost firm wins the price competition and captures the whole market. Since firm A is located in market 1, it can use its location advantage to force out its rival from the market. Similarly, firm B has an edge over firm A in market 2.

The winner’s price in its advantageous market would be slightly lower than its rival’s marginal cost, i.e., its rival’s marginal production cost plus trade costs.

Equilibrium prices and profits in each market of the benchmark model

,21 ctpp BNAN

].2/)1[(for ,)1(21 ctcttBNAN

trade barriers

The Bertrand competition operating assumption

Note that any price exceeding the monopoly price, [(1 + c)/2], would lead to a lower profit and would never be charged by firms. Hence, Bertrand competition can not operate in situations where the trade costs are higher than [(1 c)/2].

Assume that this assumption holds throughout the paper i.e., t [(1 c)/2].

The licensing model with an outsider patentee

Assume that there is an outsider patentee, who is located beyond the two countries, having a technology of a cost-reducing innovation.

This innovation decreases both firms’ marginal production cost by the same amount , where 0 < < c.

Three types of an innovation

drastic:

Innovation

with local monopoly:

non-drastic

with global monopoly:

the licensee can drive its rival out of the market and meanwhile charge monopoly prices in both markets

the licensee is unable to drive its rival out of the markets

the licensee can drive its rival out of the markets but could not charge monopoly prices

Restrictions imposed on three types of an innovation

Drastic innovation: occurs as trade costs t relative to the innovation size are small, say, t – (1 – c), measured by the area C in Figure 2.

Non-drastic innovation with a global monopoly: arises as t relative to lies in the medium range, t and t [ – (1 – c)], measured by the sum of the areas Bn and Be.

Non-drastic innovation with a local monopoly: emerges as t relative to is high, say, t , measured by the area A.

Three types of an innovation measured by the areas in Figure 2

The non-drastic innovation with local monopoly: measured A {(t, ): t , t (1-c)/2}. The condition for both firms survival: t , and the Bertrand competition operating assumption t (1-c)/2 .

The non-drastic innovation with global monopoly: measured Bn Be {(t, ): t , t - (1-c), t (1-c)/2}. The condition for the licensee unable to charge monopoly prices is: t - (1-c).

The drastic innovation: measured C {(t, ): t - (1-c), t (1-c)/2}.

Three types of an innovation measured by areas in Figure 2

A fixed-fee licensing – the case of a non-drastic innovation with local monopoly

Assume first that the patent is licensed to firm A only. In the final stage: the licensee’s and non-licensee’s equilibrium p

rices:

p1LAFe = t + c, for (t, ) A,

p2LBFe = t + c - , for (t, ) A.

In stage 3: the licensee’s maximum willingness to pay for the license is the difference between the licensed and unlicensed profit, FL

e.

FLe = 1L

AFe -1AN = (1- t - c).

In stage 2: since the outsider patentee can extract the whole licensee’s benefit from licensing, its profit can be derived as:

LFe = FL

e = (1- t - c).

The number of licenses issued

The difference in the outsider patentee’s profit between a non-exclusive and an exclusive fixed fee licensing is:

Proposition 1.

The outsider patentee would like to license its technology non-exclusively in a fixed-fee licensing under Bertrand competition, as trade costs relative to the innovation size are so high that the innovation is non-drastic with local monopoly.

.)(for 0,)1()1(2 At, ε ctctFeL

FnL

A fixed-fee licensing – the case of a non-drastic innovation with global monopoly

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)}1(2)]1()1(2[{

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The number of licenses issued

Proposition 2.

Assume that trade costs relative to the innovation size lie in the medium range so that the innovation is non-drastic with global monopoly. The outsider patentee would like to license its technology non-exclusively in a fixed-fee licensing under Bertrand competition when trade costs are relatively high, and exclusively when trade costs are relatively low.

Comparison with related literature

Propositions 1 and 2 are significantly different from those derived in Kamien and Tauman (1986), Kamien et al. (1992), Muto (1993) and Poddar and Sinha (2004), in which the outsider patentee always licenses the patent exclusively in a fixed-fee licensing under Bertrand competition.

The intuition behind the result

This paper indicates that the bigger the trade costs, the higher will be the equilibrium price and hence the monopoly profit in each market. As a result, the outsider patentee would like to license its technology non-exclusively to capture the total monopoly profits, as trade costs are relatively high.

On the contrary, the total monopoly profits are so low that the outsider patentee turns to license its technology exclusively, as trade costs are relatively low.

By contrast, there exists no trade barriers in the related literature. Hence, no monopoly profit generated from trade barriers occurs in those papers so that the outsider patentee always licenses the patent exclusively.

A royalty licensing

Note that the outsider patentee would definitely license the patent non-exclusively in a royalty licensing.

In the final stage: since both firms have the technology license, their marginal production costs are reduced to (c － + r). The licensees’ equilibrium prices can be derived as:

p1LAR = p2L

BR = t + c - + r, for t (1-c)/2. In stage 3: the maximum royalty rate is the innovation

size, .

The optimal royalty rate

In stage 2: the outsider patentee’s profit is;

LRn = 2r (1 - t - c + - r), for t (1-c)/2.

The optimal royalty rate is:

The outsider patentee’s profit for a non-exclusive royalty licensing is:

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(17.1) ],1[)/2][(1for ,2/)(1

ctct

ctcctr RnL

(18.2) . )(for ),1(2

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ec

nc

ei

ni

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CBBt, εct

Areas for the interior and corner solutions of the optimal royalty rate in Figure 3

The optimal licensing contract

We first discuss the case where the innovation is non-drastic with local monopoly measured by area A in Figure 3.

In stage 1: the difference in the outsider patentee’s profit between a non-exclusive fixed fee licensing and a royalty licensing can be obtained as:

.),(,02 2 AtforRnL

FnL

The case where the innovation is non-drastic with local monopoly measured by the area A

Proposition 3.

Assume that trade costs relative to the innovation size are so high that the innovation is non-drastic with a local monopoly. The outsider patentee would prefer non-exclusive fixed-fee licensing to royalty licensing under Bertrand competition.

The case where the innovation is non-drastic with global monopoly measured by the area B

From (20.1) that > (<) 0 if t > (<) t1C

(1c+)/5, and from (20.2) that > (<) 0 if t > (<) t2

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RnL

FnG

RnL

FnG

]/2.)1(4)1(2[ 22 cc

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ec

ei

RnL

FeG

Btct

Bt tc

The case where the innovation is non-drastic with global monopoly measured by the area B

Proposition 4.

Assume that trade costs relative to the innovation size lie in the medium range so that the innovation is non-drastic with a global monopoly. The outside patentee would like to choose non-exclusive fixed-fee licensing rather than non-exclusive royalty licensing under Bertrand competition when the trade costs are relatively high, while the reverse occurs when the trade costs are relatively low.

Areas for the outsider patentee’s optimal contracts

Comparison with Muto (1993)

Propositions 3 and 4 are in sharp difference from those derived in Muto (1993), in which the royalty is optimal for an outsider patentee for small innovations, but the fee is optimal for large innovations.

By contrast, in the paper the fee is superior to the royalty for relatively small innovations, while the reverse occurs for relatively large innovations.

The intuition behind the result in the paper

Engaging in Bertrand competition and producing a homogeneous product induce firms to charge a price equaling the rival’s marginal production cost plus trade costs in each market. Thus, each firm becomes a local monopolist and earns the monopoly profit in its advantageous market.

The bigger the trade costs, the higher will be the monopoly profit for a fixed-fee licensing.

As a result, the outsider patentee’s profit for a fixed-fee licensing is higher than that for a royalty licensing, as trade costs relative to the innovation size are higher.

The intuition behind the result in Muto (1993)

There exist no trade costs and corresponding monopoly rents in Muto (1993). Since the degree of competition in a non-exclusive royalty licensing is more intense than that in an exclusive fixed-fee licensing, the aggregate outputs of the former are larger than those of the latter.

Thus, in Muto (1993), the royalty revenue and profit derived in a non-exclusive royalty licensing will be higher than the one derived in an exclusive fixed-fee licensing for small innovations, while the reverse occurs for large innovations.

Comparison with Podda and Sinha (2004)

Our result is also sharply different from that in Poddar and Sinha (2004), in which the non-exclusive royalty licensing is the best policy for an outsider patentee for both drastic and non-drastic innovations.

The intuition behind the result in Poddar and Sinha (2004)

Poddar and Sinha (2004) employ a Hotelling’s linear city model, in which the total output is fixed in the model. Therefore, a rise in the royalty rate does not reduce the total production for the licensees. Given that the outsider patentee charges a royalty rate equals the innovation size, the whole benefits from innovation licensing are completely extracted by the patentee. Thus, the outsider patentee can earn the maximum patent profit by choosing a non-exclusive royalty licensing.

On the other hand, the mill price will fall with the decrease in the marginal cost of the licensee caused by an exclusive fixed-fee licensing. Thus, the patent profit is lower in an exclusive fixed-fee licensing than that in a non-exclusive royalty licensing.

A special case: trade costs are nil, i.e., t = 0

Proposition 5.

Assume that trade costs equal zero. The fee and royalty licensing are equivalent for an outsider patentee under Bertrand competition.

(21.2) .),(for ,0)1( ec

RnL

FeG Btct

= 0, if t = 0.

Concluding Remarks

Firstly, a fixed-fee licensing is optimal for an outsider patentee under Bertrand competition, as trade costs relative to the innovation size are high, while a royalty licensing is optimal, otherwise. This result is significantly different from that

derived in Muto (1993) and Poddar and Sinha (2004).

Concluding Remarks

Secondly, related literature indicates that the outsider patentee licenses a fixed-fee licensing exclusively under Bertrand competition. By contrast, we show that the outsider patentee would choose a fixed-fee licensing non-exclusively, as trade costs relative to the innovation size are high.

Concluding Remarks

Lastly, we show that the fee and royalty licensing are equivalent for an outsider patent holder, as trade costs equal zero. This result is the same as that derived in

Kamien and Tauman (1986) and Kamien et al. (1992).

Thank you