capacity commitment and licensing - fep.up.pt iv/iv.d... · this was challenged by dixit (1980),...

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Commitment and excess capacity: a new look with licensing Arijit Mukherjee * University of Nottingham and The Leverhulme Centre for Research in Globalisation and Economic Policy, UK February 2005 Abstract: This paper provides a new rationale for holding excess capacity. We show that incumbent firms may hold excess capacity not to deter entry but to get more benefit from technology licensing. Our results are robust with respect to capacity commitment by the entrant. We also show that if the entrant commits to a capacity level, the incumbent is better off by licensing its technology after rather than before the entrant’s capacity choice. Key Words: Capacity commitment, Entry, Excess capacity, Incumbent, Licensing JEL Classification: D43, L13, O33 Correspondence to: Arijit Mukherjee, School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K. E-mail: [email protected] Fax: +44-115-951 4159 ___________________________________ * I would like to thank David Greenaway for his comments and suggestions on the earlier version of this paper. I am very much indebted to Arnab Bhattacharjee for providing me with the empirical findings. Discussion with Achintya Ray was also rewarding. Financial support from the Netherlands Technology Foundation (STW) is gratefully acknowledged. The usual disclaimer applies.

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Commitment and excess capacity: a new look with licensing

Arijit Mukherjee*

University of Nottingham and The Leverhulme Centre for Research in Globalisation and Economic Policy, UK

February 2005

Abstract: This paper provides a new rationale for holding excess capacity. We show

that incumbent firms may hold excess capacity not to deter entry but to get more

benefit from technology licensing. Our results are robust with respect to capacity

commitment by the entrant. We also show that if the entrant commits to a capacity

level, the incumbent is better off by licensing its technology after rather than before

the entrant’s capacity choice.

Key Words: Capacity commitment, Entry, Excess capacity, Incumbent, Licensing

JEL Classification: D43, L13, O33

Correspondence to: Arijit Mukherjee, School of Economics, University of

Nottingham, University Park, Nottingham, NG7 2RD, U.K.

E-mail: [email protected]

Fax: +44-115-951 4159

___________________________________ * I would like to thank David Greenaway for his comments and suggestions on the earlier version of this paper. I am very much indebted to Arnab Bhattacharjee for providing me with the empirical findings. Discussion with Achintya Ray was also rewarding. Financial support from the Netherlands Technology Foundation (STW) is gratefully acknowledged. The usual disclaimer applies.

Commitment and excess capacity: a new look with licensing

1. Introduction

The existence of excess capacity in firms has attracted considerable amount of

attention in the industrial organization literature. Previous work has posited entry

deterrence, collusion and demand uncertainty as the motives of incumbent firms for

holding excess capacity. In this paper, we provide a new rationale for holding excess

capacity. We show that the benefit from technology licensing can induce an

incumbent firm to install more capacity than it needs.

In earlier work, Spence (1977) has shown that an incumbent firm may keep

excess capacity to deter entry. This was challenged by Dixit (1980), who argued that

excess capacity cannot occur in a subgame perfect equilibrium.1 In turn that paper

stimulated a large amount of theoretical and empirical research. Many researchers

have shown that the Dixit (1980) result is very much dependent on its assumptions.

Bulow et al. (1985) show that excess capacity may be the equilibrium outcome if we

do not consider each firm’s marginal revenue is decreasing in other firms’ outputs,

which is assumed in Dixit (1980). Spulber (1981) and Basu and Singh (1990) have

found that if the post-entry game is Stackelberg instead of Cournot, excess capacity

might be the outcome in a perfect equilibrium.2

These theoretical works have inspired empirical works, which test entry

deterrence as the motive for holding excess capacity. Though Masson and Shaanan

1 Ware (1984) criticizes the structure of the game considered in Dixit (1980) and extends Dixit’s two-stage game to a three-stage game. Though Ware (1984) shows that capacity commitment by the entrant reduces incumbent’s first-mover advantage, excess capacity does not occur in equilibrium. 2 Ware (1985) shows the role of inventory in order to deter entry.

1

(1986) and Lieberman (1987) confirm the presence of excess capacity, they provide

very little evidence for entry deterrence as the motive.

In this paper we show that the benefit from technology licensing may induce

an incumbent to install capacity that it ends up not using. Significant investment in

capacity reduces the reservation payoff of the entrant and helps the incumbent to

extract a higher price for its technology under licensing. We show that this benefit

outweighs the cost of the excess capacity and provides a rationale for holding excess

capacity in equilibrium. We find that the co-existence of licensing and excess

capacity is more likely to occur in industries with relatively low costs of capacity,

which provides a testable hypothesis. When the cost of capacity is relatively low, it

neither gives the incumbent a significant strategic advantage nor creates large waste.

But, capacity commitment helps the incumbent to extract higher surplus under

technology licensing.

We further show that our result holds only if the industry marginal revenue

curve is downward sloping. This condition is consistent with Dixit (1980). Thus, we

confirm that an incumbent may also hold excess capacity under the demand

conditions considered in Dixit (1980) if it licenses its technology to the

technologically inferior entrant.

As in Ware (1984), we extend our basic model to incorporate capacity

installation by the entrant. We consider two possibilities: first, where the entrant

installs capacity after licensing and second, where the entrant installs capacity before

licensing. We show that the co-existence of excess capacity and licensing may occur

in equilibrium even for these extended games. We further show that the incumbent

earns higher profit if it licenses its technology after the entrant’s capacity installation.

2

This paper falls in the area of theoretical works, which shows that firms may

hold excess capacity even if that does not deter entry. Benoit and Krishna (1987),

Davidson and Deneckere (1990) and Fershtman and Gandal (1994) have shown that

collusion in an oligopolistic industry creates the incentive for holding excess capacity.

Kim (1996), Poddar (1998) and Robles (2001) have shown that excess capacity can

be the equilibrium outcome if market demand is variable.3 In contrast, we show that,

even in a world with certainty and no collusion, excess capacity can be the

equilibrium outcome when it provides benefit to the other non-productive activities

such as technology licensing.

Mukherjee (2001) also considers licensing in an incumbent-entrant

framework. However, the present paper differs in two important ways from

Mukherjee (2001). Firstly, unlike Mukherjee (2001), in this paper the incumbent firm

does not have an advantage after technology licensing. So, Mukherjee (2001) may be

applicable to situations where firms need time-to-build capacity, whereas this paper

looks at the situation where the incumbency advantage comes mainly from earlier

acquisition of technology. Therefore, to exploit the incumbency advantage, the

incumbent firm needs to install capacity before entry and so, before technology

licensing. Secondly, this paper allows the entrant to choose its capacity after the

incumbent, whereas Mukherjee (2001) ignores capacity choice by the entrant.

Though our analysis is theoretical, there is evidence of the co-existence of

excess capacity and technology licensing in many industries. For example, Ericsson

has licensed its technology to other manufacturers and holds excess capacity (see,

e.g., Ericsson’s Annual report, 2001 and First quarter report, 2002). The Draft

3 Ungern-Sternberg (1988) and Marchionatti and Usai (1997) show rationale for holding excess capacity in a vertical structure and in the prospect of voluntary export restraint respectively.

3

Commission Decision of EEC (1994) also provides evidence of the co-existence of

excess capacity and technology licensing in the float glass industry. It shows that

Pilkington licenses its technology to competitors whilst holding excess capacity.

Unfortunately, we know of no empirical study that attempts to sort out the strategic

effects of licensing on capacity installation. Our results provide testable hypothesis

for this topic.

The remainder of the paper is organized as follows. Section 2.1 provides the

basic argument with a geometric representation and proves the main result. This

section also considers lower cost of capacity. Section 2.2 shows the implications of

higher costs of capacity. Section 3 considers capacity installation by the entrant.

Section 4 concludes.

2. Model

2.1 Geometric representation

Assume there is an incumbent firm, firm 1, and a potential entrant, firm 2. Production

requires investment in capacity. We assume the per-unit cost of capacity is and

is the same for both firms. The firms also need to incur a variable cost of production,

which depends on technology. Assume that firm 1 has better technology

0>z

1c

4 compared to

firm 2 and produces its product with the per-unit variable cost of production ,

while firm 2 produces with c , where c .

0>

2 12 c> 5 Think of firm 1 having a patent for its

technology, which corresponds to the variable cost of production , whilst its patent 1c

4 We consider that lower variable cost of production implies better technology. 5 One may refer to Allen et al. (2000) for a distinction between the cost of capacity and the variable cost of production.

4

for the previous technology has expired and creates potential threat of entry.6 So, total

per-unit cost of production or marginal cost of production, which aggregates the cost

of capacity and the variable cost of production, is 1cz + for firm 1 and for firm

2. We further assume that the per-unit costs are such that both always produce

positive outputs in equilibrium. Since, our purpose is not to address the issue of entry-

deterrence, we abstract from other costs such as fixed costs and entry costs. We

assume the post-entry game is characterized by Cournot-Nash competition.

2cz +

q1

q11

1cz +

Assume that the firms produce a homogeneous product. Inverse market

demand function is with P P q q= +( 1 2 ) ′ <P 0 , where P is price of the product

and, and are the outputs of firms 1 and 2 respectively. We assume that market

demand is such that it ensures unique and stable equilibrium output.

q1 q2

We consider the following game. At stage 1, firm 1 invests up to capacity

level x . At stage 2, firm 2 enters the market.7 At stage 3, firm 1 decides whether or

not to license its technology to firm 2. At stage 4, production takes place and the

profits are realized. We solve the game through backward induction. So, in this

section we do not allow firm 2 to install capacity before production. We will relax this

in section 3.

If firm 1’s output is less than its installed capacity level (i.e., ), its

marginal cost of production at the output stage is c . But, if it produces , its

marginal cost of production at the output stage is

x≤

x>

.

6 There may be other justifications for the differences in the variable costs of production. The technologies may require different types of inputs and the competitive prices for the inputs show the variable costs of production. Or, the technologies may require same inputs but with different combinations and therefore, creates difference in the variable cost of production. 7 Since in this analysis we do not consider the possibility of entry-deterrence, entry always occurs even with different marginal costs of production.

5

Figure 1 shows equilibria of the above game. For expositional convenience,

we draw the reaction functions as linear. The reaction functions are downward

sloping when the industry marginal revenue is downward sloping, which we will

show as a necessary condition for our results.

Figure 1

Let’s first consider the situation under no licensing. In Figure 1, the lines AB

and CD show the reaction functions for firms 1 and 2 respectively when the firms

produce with the marginal costs 1cz + and 2cz + respectively. Point S shows the

equilibrium outputs if firm 1 is a Stackelberg leader. It is well known that firm 1’s

capacity commitment will shift its reaction function to the right and it will try to

commit its output corresponding to point S through its capacity installation. However,

this amount of capacity commitment is subgame perfect provided firm 1’s

Stackelberg leader’s output with its marginal cost 1cz + is less than its Cournot-Nash

output with its marginal cost . Otherwise, subgame perfect capacity commitment is

equal to firm 1’s Cournot-Nash output with its marginal cost c . To prove our result

in the simplest way, we assume that firm 1’s Stackelberg leader’s output with its

marginal cost is more than its Cournot-Nash output with marginal cost . It

follows from Ware (1984) that this will be the outcome for sufficiently low values of

.

1c

1

1cz +

1c

1c

z 8 Therefore, firm 1 installs capacity up to its Cournot-Nash output level with

marginal cost , i.e., up to B′ in Figure 1. A′EB′ shows the reaction function for firm

1 when it installs capacity up to B′ and A′EB′ corresponds to the marginal cost of

8 If the inverse market demand is qaP −= , firm 1’s Stackelberg leader’s output with its marginal

cost is more than its Cournot-Nash output with the marginal cost provided 1cz + 1c

5)21 c

z+

<2( ca −

.

6

production . So, equilibrium output is at E where firm 1 produces 0B′ and firm 2

produces B′E. This equilibrium shows outputs when the firms produce with their own

technologies and provides the benchmark for our licensing game.

1c

Now, suppose that firm 1 installs capacity up to B′ and decides to license its

technology to firm 2. Following Katz and Shapiro (1985), Marjit (1990), Mukherjee

(2001) and others, we focus on a fixed-fee licensing contract. The possibility of

imitation by the licensee or lack of information needed for a provision of royalty in

the licensing contract could be the reason for licensing with an up-front fixed-fee only

(see, e.g., Katz and Shapiro, 1985 and Rockett, 1990). We assume that, in case of

licensing, firm 1 extracts the entire surplus generated from its technology through a

licensing fee.9

If firm 1 licenses its technology to firm 2, firm 2’s per-unit variable cost of

production is . Hence, firm 2’s marginal cost of production under licensing is

. Suppose the new reaction function of firm 2 is C′D′ in Figure 1. Therefore, if

firm 1 licenses its technology, equilibrium in the product market is at L. So, under

licensing, firms 1 and 2 produce 0L′ and LL′ respectively. Hence, ( shows the

amount of excess capacity.

1c

1cz +

)LB ′−′

The above has assumed that firm 1 installs capacity up to B′ and also licenses

its technology. Since equilibrium in the product market is at L, another possibility

may be to install capacity up to L′. In that case, there exists no excess capacity and

firm 1 can save the waste of zLB )( ′−′ . However, if capacity installation is up to L,

equilibrium under no licensing is at E′ and firm 2’s profit at E′ is greater than at E.

Hence, the reservation payoff (i.e., the profit under no licensing) of firm 2 is higher

7

under firm 1’s capacity commitment up to L′ than under firm 1’s capacity

commitment up to B′. Therefore, in the case of capacity commitment up to L′, the

licensing fee is lower compared to the situation where firm 1 installs capacity up to

B′. Thus, capacity installation up to B′ helps firm 1 to extract a higher licensing fee.

However, it creates waste from excess capacity under licensing. If the benefit from

the higher licensing fee outweighs the loss from wastage, it is better for firm 1 to

install more capacity than L′.

Note that due to the trade-off between a higher licensing fee and waste from

excess capacity, it may be that it is better for firm 1 to install capacity between L′ and

B′. Capacity installation below B′ reduces the licensing fee but saves waste from

excess capacity. However, for any capacity installation more than L′, there exists

excess capacity if firm 1 licenses after capacity installation.

2.1.1 Analytical result

Consider the structure as specified in the previous subsection. The per-unit cost of

capacity is sufficiently small that credible commitment by firm 1 without licensing is

up to its Cournot output level with the marginal costs and 1c 2cz + for firms 1 and 2

respectively. Since we solve the game through backward induction, let us first we see

when licensing is profitable, given the capacity commitment up to B′. Then we will

consider the incumbent’s decision on capacity installation.

Licensing is profitable if it increases industry profit. Given the capacity

installation, the decision on licensing should not consider firm 1’s cost of capacity

installation since that investment is sunk at the time of licensing. Therefore, with

9 Our qualitative results will hold for other types of pricing for the technology (e.g., pricing through

8

capacity installation up to B′, Cournot equilibrium without licensing corresponds to

marginal costs and for firms 1 and 2 respectively but, under licensing, it

corresponds to and for firms 1 and 2 respectively. So, the joint profit ex-post

firm 1’s capacity installation is

1c

1c

2cz +

1cz +

2112121 ))(( cqqcqqqqP −−++ (1)

where c without licensing and 2cz += 1czc += under licensing.

Proposition 1: Suppose firm 1 cannot credibly commit to its Stackelberg leader’s

output when both firms produce with their own technologies.

(i) Licensing is profitable only if the industry marginal revenue is downward sloping.

(ii) Given that the industry marginal revenue is downward sloping, licensing is

profitable if the own technologies of the firms are sufficiently close and the per-unit

cost of capacity installation is sufficiently small.

Proof: (i) First, consider the effect of on industry revenue, i.e., 2c

))(( 2121 qqqqPR ++= . We find after rearranging that

22

)(cqPqP

cR

∂∂′+=

∂∂ . (2)

Next, we consider the effect of c on total cost at the stage of production, i.e.,

. We find after rearranging that

2

2211 )( qczqcC ++=

2

12

2122

2

)(cqc

cqcczq

cC

∂∂

+∂∂

−++=∂∂ . (3)

Therefore, the effect of on industry profit (excluding the cost of capacity of firm 1)

is

2c

Nash bargaining).

9

22

212

22

2

)( qcqccz

cqPq

c−

∂∂

−+−∂∂′=

∂∂π . (4)

The reduction in increases industry profit (excluding the cost of capacity of firm

1), i.e.,

2c

02

<∂∂cπ if and only if

2

212

22 )()1(

cqccz

cqPq

∂∂

−+−>∂∂′− . (5)

Differentiating the first order condition of profit maximization for firm 2 with respect

to c , we get that 2 02

2 <∂∂

cq . So, condition (5) holds only if

2cqP

∂1 ∂′> .

Adding the first order conditions of profit maximization for both firms, ex-

post firm 1’s capacity installation, we get

02 21 =−−−′+ czcPqP . (6)

Differentiating (6) with respect to c and after rearranging we find 2

0)2()1(22

=∂∂′′+′+−

∂∂′

cqPqP

cqP . (7)

Since, the absolute slope of the reaction function of firm 1 ex-post capacity

installation and up to the installed capacity level is less than 1,10 we get

0)1(2

1

2

2

2

<∂∂

+∂∂

=∂∂

qq

cq

cq , since 0

2

2 <∂∂

cq . Therefore, it follows from (7) that

2cqP

∂∂′>1

only if 02 <′′+′ PqP , i.e., industry marginal revenue is downward sloping.

10 Ex-post capacity installation by firm 1, the reaction function of firm 1 up to the installed capacity level is given by the first order condition of profit maximization 011 =−′+ cPqP . Differentiating

this first order condition by and after rearranging, we find that 2q 1<1 1

2

1

′′′

+=∂∂

−PPq

qq

.

10

(ii) When , (5) holds if 02 <′′+′ PqP )( 12 ccz −+ is sufficiently small, i.e., when

and c is sufficiently close, and is sufficiently small.1c 2 z 11 Q.E.D.

Proposition 1(i) shows the necessary condition for profitable licensing when

firm 1 invests up to B′. If the necessary condition holds, i.e., if the industry marginal

revenue is downward sloping, licensing occurs when condition (5) holds. Licensing

has two effects on industry profit. On the one hand, licensing increases cost efficiency

of firm 2 and increases its profit excluding licensing fee. This benefit of cost

efficiency is transferred to firm 1 through the licensing fee. On the other hand,

licensing reduces firm 1’s profit in the product market (i.e., profit excluding licensing

fee) as it makes firm 2 more competitive. When the marginal cost of firm 2 at the

output stage (i.e., ) is very close to the variable cost of firm 1, which is c , the

effect of competition due to licensing is sufficiently small. In this situation, the cost

efficiency effect in firm 2 dominates the competition effect and makes licensing

profitable. As is getting larger compared to , the effect of competition is

becoming stronger compared to the cost efficiency effect in firm 2 and makes

licensing unlikely.

2cz +

2c+

1

z 1c

The conditions for profitable licensing shown in the above proposition are

similar to the conditions shown in Katz and Shapiro (1985) with an additional

restriction on the cost of capacity. Unlike Katz and Shapiro (1985), we consider a

situation where the licenser (the incumbent) commits to a capacity level before

production and saves the cost of capacity installation, i.e., , at the stage of

production. Thus, capacity commitment makes the licenser more cost efficient at the

z

11 Note that we have already assumed that the per-unit cost of capacity, , is sufficiently small to z

11

stage of production and the cost of capacity becomes important for profitable

licensing. If the per-unit cost of capacity is sufficiently small, capacity commitment

does not provide much benefit to firm 1 and the conditions for profitable licensing are

more like the conditions shown in Katz and Shapiro (1985). But, given the difference

between and c , as increases, the benefit from capacity commitment increases

and makes licensing less likely to be profitable. It is clear from (5) that as

increases, the right hand side of (5) gets bigger and makes it less likely to satisfy

condition (5).

1c 2 z

z

z

Given that the industry marginal revenue is downward sloping, the per-unit

variable costs are sufficiently close and the per-unit cost of capacity is sufficiently

small, subgame perfect capacity installation is up to B′ and firm 1 licenses its

technology to firm 2. Hence, it creates excess capacity of ( )LB ′−′ in equilibrium.

Though, investment up to B′ increases the licensing fee, it creates waste of

. So, it remains to check whether firm 1 is willing to invest more than L′.LB )( ′−′ 12

Proposition 1 shows that ‘investment up to B′ and licensing’ dominates

‘investment up to B′ and no licensing’. So, given the capacity installation up to B′,

firm 1 is better off at L than at E. It is also well known that profit increases from its

Cournot-Nash equilibrium up to its Stackelberg leader equilibrium. Hence, firm 1 is

better off at E than at E′. Therefore, ex-post capacity installation, firm 1 is better off at

L with capacity installation up to B′ than at E′ with capacity installation up to L′. So,

ensure equilibrium under no licensing at E. 12 It is important to note that capacity commitment is helpful with the possibility of licensing if L′ is to the right of K. Otherwise, commitment up to L′ does not reduce reservation payoff of firm 2 compared to the Cournot-Nash equilibrium G. If the difference in variable costs is sufficiently small, it satisfies that L is to the right of G.

12

if firm 1 was to install capacity up to L′ in equilibrium, it would have to license its

technology ex-post capacity installation. So, investment up to L′ saves investment

costs of . But, investment up to L′ instead of B′ increases firm 2’s

reservation payoff from to

, where is the optimal output of firm 2 when

firm 1 produces at and

zLB )( ′−′

())(*2 zL −′

L

)())())((( *22

*2 BqczBqBP ′+−′+′

(.)*2)())(( *

22 LqcqLP ′++′

q

B′ respectively.

Proposition 2: Suppose condition (5) holds. Excess capacity occurs if and only if the

per-unit profit in firm 2 is greater than the per-unit cost of capacity, i.e.,

. zzcLqLP >−−′+′ ]))(([ 2*2

Proof: If firm 1 invests up to L′ instead of B′, its net gain is

. )]()))((()()))(([()( *22

*2

*22

*2 BqczBqBPLqczLqLPzLBH ′−−′+′−′−−′+′−′−′=

(8)

Under Cournot conjectures, the marginal gain to firm 1 by increasing capacity from L′

is

)())(( *2

*2 LqLqLPz

LH ′′+′′−−=′∂

∂ . (9)

Due to the profit maximization of firm 2 and after rearranging, condition (9) reduces

to

zzcLqLPLH

−−−′+′=′∂

∂ ]))(([ 2*2 . So, 0>

′∂∂LH if and only if

zzcLqLP >−−′+′ ]))(([ 2*2 . (9’)

Since [ , (9’) holds for sufficiently small . Q.E.D. 0]))(( 2*2 >−−′+′ zcLqLP z

13

The above result is very intuitive. If the cost of capacity is sufficiently small,

excess capacity is not costly to firm 1 but it helps firm 1 to extract a higher price for

its technology. Since, price must exceed the marginal cost of firm 2, i.e.,

, firm 1 invests up to B′ than up to L′ when the per-unit cost of

capacity is sufficiently small.

zcLqLP +>′+′ 2*2 ))((

Hence, combining Propositions 1 and 2, we get the conditions required for the

co-existence of licensing and excess capacity.

Proposition 3: Suppose firm 1 cannot credibly commit to its Stackelberg leader’s

output when both firms produce with their own technologies.

(i) Licensing and excess capacity occurs only if the industry marginal revenue is

downward sloping.

(ii) Licensing and excess capacity occurs if and only if (5) and (9’) hold.

The above results show the necessary and sufficient conditions for the co-

existence of licensing and excess capacity. If these conditions are violated, we can get

results similar to previous works. If the industry marginal revenue is not downward

sloping, it follows from Proposition 1 that licensing does not occur. However, when

the industry marginal revenue is not downward sloping, excess capacity occurs only if

it deters entry, as shown in Bulow et al. (1985).

Excess capacity does not occur if either condition (5) or condition (9’) does

not hold.13 In the event of the former, ex-post capacity installation up to B′, firm 1

does not license its technology to firm 2. Hence, firm 1’s profit at E is greater than its

profit both at L with licensing and at E′. Further, it is easy to understand that,

14

following capacity installation, firm 1’s profit under licensing is higher for capacity

installation up to B′ than for capacity installation up to L′, since the licensing fee will

be lower in the latter situation while the profit in the product market remains the

same. Therefore, in this situation, firm 1’s optimal capacity installation is up to B′ and

there will be no excess capacity in equilibrium, which is similar to Dixit (1980).

If licensing after capacity commitment is profitable but condition (9’) is not

satisfied, we again do not observe the co-existence of licensing and excess capacity. If

(9’) is not satisfied then firm 1’s marginal gain from increasing its capacity above L′

is negative and therefore, it has no incentive to install capacity above L′, given that

licensing is profitable after capacity installation. In this situation, firm 1’s optimal

capacity installation is up to L′. So, as the per-unit cost of capacity increases, it

reduces the possibility of excess capacity simultaneously. Though, here excess

capacity does not occur in equilibrium, the possibility of licensing after capacity

installation induces firm 1 to reduce its capacity installation compared to the situation

without licensing, which is again similar to Dixit (1980).

Hence, the following corollary is immediate from the above discussion.

Corollary 1: Even if the industry marginal revenue is downward sloping, we are less

likely to observe excess capacity for relatively larger cost of capacity (i.e., ). z

We have considered licensing with up-front fixed-fee only, which is the

optimal licensing contract when the licensee (firm 2) can imitate the licensed

technology costlessly (see, Rockett, 1990). On the other hand, if imitation is not a

credible threat, following Rockett (1990) and Mukherjee and Balasubramanian

13 As the cost of capacity increases, it is less likely to satisfy (5) or (9’).

15

(2001), we find that it is optimal for the licenser (firm 1) to charge a per-unit output

royalty only and the optimal rate of royalty is . Hence, the reaction

function of firm 2 is similar under licensing and no licensing. Therefore, excess

capacity does not occur in equilibrium when imitation is not a credible threat. But, if

the threat of imitation is credible and imitation costly, it follows from the above-

mentioned two papers that the optimal licensing contract consists of royalty and up-

front fixed-fee, where the optimal royalty rate is less than . In this

situation, licensing shifts the reaction function of firm 2 rightwards and excess

capacity occurs in equilibrium. Though, the assumption of costless imitation helps us

to prove the results in the simplest way, the above argument implies that our

qualitative results hold as long as imitation is a credible threat.

)( 12* ccr −=

r )( 12* cc −=

2.2 Higher values of z

Now consider the implications of the situation where firm 1 can credibly commit to

its Stackelberg leader’s output when both firms produce with their own technologies.

This is shown in Figure 2.

Figure 2

AB shows firm 1’s reaction function before its capacity installation and CD firm 2’s

reaction function without licensing. If S" is firm 1’s Stackelberg leader’s output

without licensing, firm 1’s optimal capacity installation is up to B" without licensing.

If licensing is not profitable after capacity installation, the equilibrium is at S". But, if

licensing is profitable after capacity installation, it shifts firm 2’s reaction function to

C"D".14 Following Proposition 1, we can find the condition required for profitable

14 We consider that licensing occurs with up-front fixed-fee.

16

licensing with the exception that now the output of firm 1 does not change with c .

To avoid repetition, we are omitting the details here.

2

15 However, it is clear from

Figure 2 that excess capacity does not occur in equilibrium since firm 2’s reaction

function after licensing intersects the vertical segment of firm 1’s reaction function

A"B". So, even if licensing is profitable, we find that here excess capacity does not

occur in equilibrium.

If S"', rather than S", is firm 1’s Stackelberg leader’s output without licensing,

firm 1’s optimal capacity installation is up to B"' without licensing. If licensing occurs

after capacity installation, it shifts firm 2’s reaction function to C"D". In this situation,

excess capacity of L"'B"' occurs in equilibrium.16 We need the per-unit cost of

capacity to be sufficiently small for the co-existence of licensing and excess capacity.

However, now we are considering the situation for relatively higher per-unit costs of

capacity. So, it is less likely to satisfy the conditions required for the co-existence of

licensing and excess capacity, and it may be more likely to observe capacity

installation up to L"'.

So, there are two factors that make excess capacity less likely when firm 1 can

credibly commit to its Stackelberg leader’s output when the firms produce with their

own technologies. As the cost of capacity increases, it increases the value of waste

due to excess capacity and makes it less likely to occur. Further, higher cost of

capacity installation gives firm 1 a large strategic advantage in the product market due

to its pre-commitment to the capacity installation. In this situation, even if firm 2 gets

a license and becomes more cost efficient in the product market, it does not affect

15 Here licensing is profitable provided

2

212 c

qPqq

∂∂′> .

16 Since the procedures of Propositions 1 and 2 can be used to find the required conditions for the co-existence of licensing and excess capacity, we are omitting details to avoid repetition.

17

firm 1’s pre-committed output level and does not generate excess capacity in

equilibrium.

So, the implication of higher cost of capacity installation for which firm 1 can

credibly commit to its Stackelberg leader’s output without licensing is immediate and

is given in the following proposition.

Proposition 4: If the per-unit cost of capacity installation is such that firm 1 can

credibly commit to its Stackelberg leader’s output when both firms produce with their

own technologies, the co-existence of licensing and excess capacity is less likely to

occur.

Thus, the analysis of this section shows that the co-existence of licensing and

excess capacity is more likely to hold in industries with relatively lower cost of

capacity. This finding may provide a testable hypothesis.

3. Capacity commitment by the entrant

We have so far assumed that the entrant (firm 2) cannot install capacity prior to

production. However, as pointed out by Ware (1984), capacity installation by the

entrant may affect the incumbent’s optimal capacity installation and may change

industry profits. In this subsection we extend the model of the subsections 2.1 and

2.1.1 to incorporate capacity installation by firm 2.17 We will consider two scenarios:

(i) where firm 2 installs capacity after the decision on licensing, and (ii) where firm 2

17 We have shown that licensing and excess capacity is more likely to observe in the situations considered in these subsections.

18

installs capacity before the decision on licensing. So, our analysis in this section is a

useful check on the robustness of our results.

3.1 Firm 2’s capacity installation after licensing

We consider the following game. At stage 1, firm 1 invests up to capacity level x . At

stage 2, firm 2 enters the market. At stage 3, firm 1 decides whether or not to license

technology to firm 2. At stage 4, firm 2 installs capacity. At stage 5, production takes

place and profits are realized. We again solve the game through backward induction.

Since firm 1 cannot credibly commit to its Stackelberg leader’s output when

the firms produce with their own technologies, it follows from Ware (1984) that, if

firm 2 commits to the capacity level before production, equilibrium under no

licensing is not at E of Figure 1 but it is somewhere between G and E of Figure 1.18

Let us consider Figure 3 where we allow firm 2 to install capacity before

production.

Figure 3

Assume that equilibrium under no licensing is at E". So, firm 1 and firm 2 produce B"

and B"E" respectively. Industry profit under no licensing is

)()())())((( *221

*2

*2 BqczBcBqBBqBP ′′+−′′−′′+′′′′+′′ . (10)

Now, assume that firm 1 licenses its technology ex-post capacity installation

up to B". So, firm 2’s marginal cost of production after licensing is . Since, firm

2 can install capacity before production, it will try to commit its capacity level to its

Stackelberg leader’s output with its marginal cost of production and firm 1’s

marginal cost of production is c . In other words, firm 2 will choose its capacity level

1cz +

1cz +

1

18 Refer to Ware (1984) for the details.

19

to maximize its profit given the reaction function A'OB". However, firm 2’s

Stackelberg leader’s output with its marginal cost of production and firm 1’s

marginal cost of production c is greater than firm 2’s Cournot-Nash output when

both firms’ marginal cost of production is . Hence, firm 2’s credible capacity

commitment cannot exceed the value corresponding to point W, i.e., J. So, ex-post

licensing, capacity installation by firm 2 generates the equilibrium in the product

market at W. Hence, under licensing, firm 1 produces

1cz +

1

1c

I and firm 2 produces

corresponding to its marginal cost of production , i.e., .

)(*2 Iq

1c

)I

IW

(*2q)) −

z

)) − (*2q I

2c

z

Therefore, industry profit under licensing is

)(())((( 11*2

*2 czIcIqIIqIP +−++ . (11)

Now, we are in a position to examine whether licensing is profitable to the

firms and capacity installation up to B" is better for firm 1 compared to its capacity

installment up to I.

Proposition 5: If the own technologies of the firms are sufficiently close, licensing is

profitable when 2

2

cqP∂∂′>1 and is sufficiently small.

Proof: The industry profit at W is

(12) )(())((( 21*2

*2 czIcIqIIqIP +−++ )

with . Differentiating (12) with respect to and following the procedure used

in Proposition 1, we can show that, if c and c is sufficiently close and is

sufficiently small, industry profit over WO in Figure 3 reduces with higher if and

only if

12 cc =

2 1

2c

20

)(12

1

2

2

cq

cqP

∂∂

+∂∂′> . (13)

Since 02

1 >∂∂cq , (13) holds if

2

2

cqP∂∂′>1 .19

Now consider the effect of on the industry profit over B"E". If is very

small and, and is sufficiently close then q

2c z

1c 2c 21 q≈ . In this situation, we find that

industry profit reduces with higher if and only if 2c

2

21cqP∂∂′> . (14)

Q.E.D.

Proposition 6: Capacity installation more than I makes firm 1 better off when the

per-unit cost of capacity is sufficiently small.

Proof: If firm 1 invests up to I instead of B", its net gain is

. )]()))((()()))(([()( *22

*2

*22

*2 BqczBqBPIqczIqIPzIBH ′′−−′′+′′−−−+−−′′=′′

(15)

Following the proof of Proposition 2, it is easy to show that 0>∂′′∂

IH , when is

sufficiently small. Q.E.D.

z

Combining Propositions 5 and 6, we get the following result immediately.

19 It follows from Proposition 1 that (13) holds if the industry marginal revenue is downward sloping.

21

Proposition 7: Assume that firm 2 installs capacity after licensing and prior to

production. Licensing and excess capacity co-exist when 2

2

cqP∂∂′>1 , the own

technologies of the firms are sufficiently close and is sufficiently small. z

Proposition 7 shows that our qualitative result of subsections 2.1 and 2.1.1

showing the co-existence of licensing and excess capacity is robust even if firm 2 (the

entrant) installs capacity after licensing and before production.

3.2 Firm 2’s capacity installation before licensing

Now, we consider another possibility where firm 2 installs capacity before licensing.

So, the game is as follows. At stage 1, firm 1 invests up to capacity level x . At stage

2, firm 2 enters the market. At stage 3, firm 2 installs capacity. At stage 4, firm 1

decides whether or not to license the technology to firm 2. At stage 5, production

takes place and the profits are realized.

It is easy to understand that if there is no licensing after capacity installation

of firm 2, both firms’ capacity installation is like subsection 3.1. Given the capacity

installation by firm 1 up to B", firm 2 has no incentive to change its capacity

installation from Y, since any deviation reduces firm 2’s payoff under no licensing.

Since, under licensing, firm 2 receives its reservation payoff, firm 2 installs capacity

to maximize its reservation payoff. Hence, given that firm 1’s capacity installation is

up to B", firm 2’s optimal capacity installation is up to Y. Further, since, under no

licensing, firm 2’s reservation payoff is minimized when firm 1 installs capacity up to

B", firm 1 also has no incentive to install capacity different from B". So, firm 1

22

installs capacity up to B", firm 2 installs capacity up to Y and the equilibrium is at E"

(see Figure 4).

Figure 4

Now, assume that firm 1 licenses its technology ex-post capacity installation

by both firms. If licensing ex-post capacity installation shifts the reaction function of

firm 2 in a way to create equilibrium between W and O then firm 1 has excess

capacity in equilibrium. This is shown in Figure 4 with the reaction function

D"UM"N" of firm 2 and the equilibrium is at W". But, if equilibrium after license is

between E" and O, say at W"', as shown in Figure 4 with the reaction function

D"UM"'N"' of firm 2, firm 1’s capacity is fully utilized and there is no excess

capacity.20 So, if firm 2 installs capacity before licensing, it reduces its flexibility

about capacity installation and production and may help firm 1 to utilize its full

capacity.

The above argument however assumed that licensing is profitable after

capacity installation and firm 1 has no incentive to install its capacity in a way to

eliminate excess capacity in equilibrium, if ex-post licensing, equilibrium is between

W and O. It can be shown, following the arguments of subsections 2.1.1 and 3.1, that

both assumptions are satisfied when the per-unit cost of capacity installation is

sufficiently small and the own technologies of the firms sufficiently close. To avoid

repetition, we are omitting the details here.

Hence:

20 Difference between and is important in determining whether the equilibrium will be either on the segment OW or on the segment B"O.

z )( 12 cc −

23

Proposition 8: Licensing and excess capacity may co-exist even if firm 2 installs

capacity before licensing.

3.3 Timing of licensing

The previous two subsections have considered different timing of capacity installation

by firm 2. If firm 1 licenses its technology prior to firm 2’s capacity installation,

excess capacity occurs in equilibrium. But, if firm 1 licenses its technology after firm

2’s capacity installation, equilibrium is different from the previous situation and firm

1 may not have excess capacity in equilibrium. If firm 1 can choose the timing of

licensing, the natural question is to ask whether it prefers to license its technology

before or after firm 2’s capacity installation.

Proposition 9: Suppose firm 2 installs capacity before production and the condition

for profitable licensing holds. If the cost of capacity (i.e., ) is sufficiently small, firm

1 prefers to license its technology after firm 2’s capacity installation.

z

Proof: The profits of the firms under no licensing are same irrespective of whether

firm 1 licenses its technology before or after capacity installation of firm 2. So, firm 1

prefers that situation which gives it higher profit under licensing.

Assume that firm 1 experiences excess capacity irrespective of firm 2’s timing

of capacity installation. Hence, we find from Figures 3 and 4 that firm 1’s profit under

licensing is higher if it licenses after firm 2’s capacity installation than if it licenses

before firm 2’s capacity installation provided21

21 Note that if firm 1 licenses its technology after firm 2’s capacity installation then firm 2’s cost of capacity installation is sunk at the time of licensing and hence, is not included in firm 2’s reservation payoff.

24

,0)(

))(()())((

1

111

>+++++−′′′′+−′′−′′′′+′′′′′′+′′

IWczIcIWIIWIPWIczIcWIIWIIP

(16)

or equivalently

0])())(([

2

21112121 <∂

+−−++∂q

qczqcqqqqP . (17)

Given that is sufficiently small, which also helps to make licensing profitable,

condition (17) always holds. This implies that firm 1 prefers to license its technology

after rather than before firm 2’s capacity installation.

z

Following similar logic, we can show that even if firm 1 does not have excess

capacity in equilibrium when it licenses after firm 2’s capacity installation, it prefers

to license its technology after firm 2’s capacity installation. Q.E.D.

The reason for the above proposition is as follows. If firm 1 licenses before

firm 2’s capacity installation then firm 2 has more flexibility about its output level

compared to the situation where firm 1 licenses after firm 2’s capacity installation.

So, firm 1 can induce firm 2 to produce relatively lower amount of output if it licenses

after firm 2’s capacity installation. This, in turn, increases firm 1’s output and profit

in the product market. Further, licensing after firm 2’s capacity installation increases

firm 1’s capacity utilization and reduces the cost of excess capacity, however small it

is. So, higher strategic advantage in the product market makes firm 1 better off if it

licenses after firm 2’s capacity installation compared to the situation where it licenses

before firm 2’s capacity installation.

25

4. Conclusions

Researchers have paid a considerable amount of attention to the existence of excess

capacity by dominant firms. Though earlier theoretical contributions have argued that

entry deterrence is the motive for holding excess capacity, empirical analysis does not

provide much support for this. More recent work shows that the possibility of variable

demand or price competition in the product market may be the reasons for holding

excess capacity even if it does not deter entry.

This paper provides a new rationale for holding excess capacity. We show that

the dominant firms may hold excess capacity not to deter entry but to get more benefit

from technology licensing. In a model with an incumbent and an entrant we show that

the incumbent firm invests in capacity that it ends up not using completely and the

rationale for this type of investment may be to extract a higher price for its superior

technology when licensing it to the entrant. We show that this result is robust with

respect to the possibility of capacity installation by the entrant. Further, we find that

when the entrant has the option for capacity installation, the incumbent’s profit is

higher when it licenses its technology after the entrant’s capacity installation than

when it licenses before its capacity installation.

26

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29

Figure 1: When firm 1 cannot credibly commit to its Stackelberg leader’s output and

firm 2 does capacity installation and production at the same time

Figure 2: When firm 1 can credibly commit to its Stackelberg leader’s output and

firm 2 does capacity installation and production at the same time

30

Figure 3: When firm 2 installs capacity after licensing but prior to production

Figure 4: When firm 2 installs capacity before licensing

31