Commitment and excess capacity: a new look with licensing

Transcription

1 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 005 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, L3, O33 Correspondence to: Arijit Mukherjee, School of Economics, University of Nottingham, University Park, Nottingham, NG7 RD, U.K. arijit.mukherjee@nottingham.ac.uk Fax: 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.

2 Commitment and excess capacity: a new look with licensing. 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 (977) has shown that an incumbent firm may keep excess capacity to deter entry. This was challenged by Dixit (980), who argued that excess capacity cannot occur in a subgame perfect equilibrium. In turn that paper stimulated a large amount of theoretical and empirical research. Many researchers have shown that the Dixit (980) result is very much dependent on its assumptions. Bulow et al. (985) 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 (980). Spulber (98) and Basu and Singh (990) have found that if the post-entry game is Stackelberg instead of Cournot, excess capacity might be the outcome in a perfect equilibrium. These theoretical works have inspired empirical works, which test entry deterrence as the motive for holding excess capacity. Though Masson and Shaanan Ware (984) criticizes the structure of the game considered in Dixit (980) and extends Dixit s twostage game to a three-stage game. Though Ware (984) shows that capacity commitment by the entrant reduces incumbent s first-mover advantage, excess capacity does not occur in equilibrium. Ware (985) shows the role of inventory in order to deter entry.

3 (986) and Lieberman (987) 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 (980). Thus, we confirm that an incumbent may also hold excess capacity under the demand conditions considered in Dixit (980) if it licenses its technology to the technologically inferior entrant. As in Ware (984), 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.

4 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 (987), Davidson and Deneckere (990) and Fershtman and Gandal (994) have shown that collusion in an oligopolistic industry creates the incentive for holding excess capacity. Kim (996), Poddar (998) and Robles (00) 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 (00) also considers licensing in an incumbent-entrant framework. However, the present paper differs in two important ways from Mukherjee (00). Firstly, unlike Mukherjee (00), in this paper the incumbent firm does not have an advantage after technology licensing. So, Mukherjee (00) 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 (00) 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, 00 and First quarter report, 00). The Draft 3 Ungern-Sternberg (988) and Marchionatti and Usai (997) show rationale for holding excess capacity in a vertical structure and in the prospect of voluntary export restraint respectively. 3

5 Commission Decision of EEC (994) 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. provides the basic argument with a geometric representation and proves the main result. This section also considers lower cost of capacity. Section. shows the implications of higher costs of capacity. Section 3 considers capacity installation by the entrant. Section 4 concludes.. Model. Geometric representation Assume there is an incumbent firm, firm, and a potential entrant, firm. Production requires investment in capacity. We assume the per-unit cost of capacity is z > 0 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 has better technology 4 compared to firm and produces its product with the per-unit variable cost of production > 0, c while firm produces with c, where c >. 5 Think of firm having a patent for its c technology, which corresponds to the variable cost of production, whilst its patent c 4 We consider that lower variable cost of production implies better technology. 5 One may refer to Allen et al. (000) for a distinction between the cost of capacity and the variable cost of production. 4

6 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 z + c for firm and z + c for firm. 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 entrydeterrence, we abstract from other costs such as fixed costs and entry costs. We assume the post-entry game is characterized by Cournot-Nash competition. Assume that the firms produce a homogeneous product. Inverse market demand function is P = P( q + q ) with P < 0, where P is price of the product and, q and q are the outputs of firms and respectively. We assume that market demand is such that it ensures unique and stable equilibrium output. We consider the following game. At stage, firm invests up to capacity level x. At stage, firm enters the market. 7 At stage 3, firm decides whether or not to license its technology to firm. 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 to install capacity before production. We will relax this in section 3. If firm s output is less than its installed capacity level (i.e., q x ), its marginal cost of production at the output stage is c. But, if it produces q > x, its marginal cost of production at the output stage is z + c. 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

7 Figure 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 Let s first consider the situation under no licensing. In Figure, the lines AB and CD show the reaction functions for firms and respectively when the firms produce with the marginal costs z + c and z + c respectively. Point S shows the equilibrium outputs if firm is a Stackelberg leader. It is well known that firm 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 s Stackelberg leader s output with its marginal cost z + c is less than its Cournot-Nash output with its marginal cost c. Otherwise, subgame perfect capacity commitment is equal to firm s Cournot-Nash output with its marginal cost c. To prove our result in the simplest way, we assume that firm s Stackelberg leader s output with its marginal cost z + c is more than its Cournot-Nash output with marginal cost c. It follows from Ware (984) that this will be the outcome for sufficiently low values of z. 8 Therefore, firm installs capacity up to its Cournot-Nash output level with marginal cost c, i.e., up to B in Figure. A EB shows the reaction function for firm when it installs capacity up to B and A EB corresponds to the marginal cost of 8 If the inverse market demand is P = a q, firm s Stackelberg leader s output with its marginal cost z + c is more than its Cournot-Nash output with the marginal cost c provided ( a c + c ) z <. 5 6

8 production. So, equilibrium output is at E where firm produces 0B and firm c produces B E. This equilibrium shows outputs when the firms produce with their own technologies and provides the benchmark for our licensing game. Now, suppose that firm installs capacity up to B and decides to license its technology to firm. Following Katz and Shapiro (985), Marjit (990), Mukherjee (00) 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, 985 and Rockett, 990). We assume that, in case of licensing, firm extracts the entire surplus generated from its technology through a licensing fee. 9 If firm licenses its technology to firm, firm s per-unit variable cost of production is c. Hence, firm s marginal cost of production under licensing is z + c. Suppose the new reaction function of firm is C D in Figure. Therefore, if firm licenses its technology, equilibrium in the product market is at L. So, under licensing, firms and produce 0L and LL respectively. Hence, ( B L ) shows the amount of excess capacity. The above has assumed that firm 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 can save the waste of ( B L ) z. However, if capacity installation is up to L, equilibrium under no licensing is at E and firm s profit at E is greater than at E. Hence, the reservation payoff (i.e., the profit under no licensing) of firm is higher 7

9 under firm s capacity commitment up to L than under firm 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 installs capacity up to B. Thus, capacity installation up to B helps firm 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 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 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 licenses after capacity installation... 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 without licensing is up to its Cournot output level with the marginal costs and c c z + for firms and 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 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

10 capacity installation up to B, Cournot equilibrium without licensing corresponds to marginal costs c and z + c for firms and respectively but, under licensing, it corresponds to c and z + c for firms and respectively. So, the joint profit ex-post firm s capacity installation is P( q + c q cq () q )( q + q ) where c z + c without licensing and = c z + c = under licensing. Proposition : Suppose firm 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 c on industry revenue, i.e., R = P q + q )( q + ). We find after rearranging that ( q R = ( P + qp ). () Next, we consider the effect of c on total cost at the stage of production, i.e., C = c ( + q q + z c ). We find after rearranging that C = q + ( z + c c) + c. (3) Therefore, the effect of on industry profit (excluding the cost of capacity of firm ) c is Nash bargaining). 9

11 π = qp ( z + c c) q. (4) The reduction in c increases industry profit (excluding the cost of capacity of firm ), i.e., π < 0 if and only if q ( P ) > ( z + c c). (5) Differentiating the first order condition of profit maximization for firm with respect to c, we get that < 0. So, condition (5) holds only if > P. Adding the first order conditions of profit maximization for both firms, expost firm s capacity installation, we get P + qp c z c 0. (6) = Differentiating (6) with respect to c and after rearranging we find ( P ) + (P + qp ) = 0. (7) Since, the absolute slope of the reaction function of firm ex-post capacity c installation and up to the installed capacity level is less than, 0 we get = ( + ) < 0, since < 0. Therefore, it follows from (7) that > P c only if P + qp < 0, i.e., industry marginal revenue is downward sloping. 0 Ex-post capacity installation by firm, the reaction function of firm up to the installed capacity level is given by the first order condition of profit maximization P + q P c = 0. Differentiating qp this first order condition by q and after rearranging, we find that = + <. P 0

12 (ii) When P + qp < 0, (5) holds if z + c c ) is sufficiently small, i.e., when ( c and c is sufficiently close, and z is sufficiently small. Q.E.D. Proposition (i) shows the necessary condition for profitable licensing when firm 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 and increases its profit excluding licensing fee. This benefit of cost efficiency is transferred to firm through the licensing fee. On the other hand, licensing reduces firm s profit in the product market (i.e., profit excluding licensing fee) as it makes firm more competitive. When the marginal cost of firm at the output stage (i.e., z + c ) is very close to the variable cost of firm, which is c, the effect of competition due to licensing is sufficiently small. In this situation, the cost efficiency effect in firm dominates the competition effect and makes licensing profitable. As z + c is getting larger compared to c, the effect of competition is becoming stronger compared to the cost efficiency effect in firm and makes licensing unlikely. The conditions for profitable licensing shown in the above proposition are similar to the conditions shown in Katz and Shapiro (985) with an additional restriction on the cost of capacity. Unlike Katz and Shapiro (985), 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., z, at the stage of production. Thus, capacity commitment makes the licenser more cost efficient at the Note that we have already assumed that the per-unit cost of capacity, z, is sufficiently small to

13 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 and the conditions for profitable licensing are more like the conditions shown in Katz and Shapiro (985). But, given the difference between c and c, as z increases, the benefit from capacity commitment increases and makes licensing less likely to be profitable. It is clear from (5) that as z increases, the right hand side of (5) gets bigger and makes it less likely to satisfy condition (5). 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 licenses its technology to firm. Hence, it creates excess capacity of ( B L ) in equilibrium. Though, investment up to B increases the licensing fee, it creates waste of ( B L ) z. So, it remains to check whether firm is willing to invest more than L. Proposition 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 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 is better off at E than at E. Therefore, ex-post capacity installation, firm 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. 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 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.

14 if firm 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 ( B L ) z. But, investment up to L instead of B increases firm s reservation payoff from ( P ( B + q ( B )) ( z + c )) q ( ) to ( P ( L + q ( L )) ( + c )) q ( ), where q (.) is the optimal output of firm when z L B firm produces at L and B respectively. Proposition : Suppose condition (5) holds. Excess capacity occurs if and only if the per-unit profit in firm is greater than the per-unit cost of capacity, i.e., P ( L + q ( L )) c z] > z. [ Proof: If firm invests up to L instead of B, its net gain is H = ( B L ) z [( P( L + q ( L )) z c ) q ( L ) ( P( B + q ( B )) z c ) q B ( )]. Under Cournot conjectures, the marginal gain to firm by increasing capacity from L is (8) H L = z P ( L + q ( L )) q ( L ). (9) Due to the profit maximization of firm and after rearranging, condition (9) reduces to H = L H P( L + q L ( )) c z] z. So, > 0 L [ if and only if P ( L + q L ( )) c z] > z. (9 ) [ Since [ P L + q ( L )) c z] 0, (9 ) holds for sufficiently small z. Q.E.D. ( > 3

15 The above result is very intuitive. If the cost of capacity is sufficiently small, excess capacity is not costly to firm but it helps firm to extract a higher price for its technology. Since, price must exceed the marginal cost of firm, i.e., P ( L + q L ( )) > c + z, firm invests up to B than up to L when the per-unit cost of capacity is sufficiently small. Hence, combining Propositions and, we get the conditions required for the co-existence of licensing and excess capacity. Proposition 3: Suppose firm 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 coexistence 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 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. (985). Excess capacity does not occur if either condition (5) or condition (9 ) does not hold. 3 In the event of the former, ex-post capacity installation up to B, firm does not license its technology to firm. Hence, firm s profit at E is greater than its profit both at L with licensing and at E. Further, it is easy to understand that, 4

16 following capacity installation, firm 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 s optimal capacity installation is up to B and there will be no excess capacity in equilibrium, which is similar to Dixit (980). 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 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 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 to reduce its capacity installation compared to the situation without licensing, which is again similar to Dixit (980). Hence, the following corollary is immediate from the above discussion. Corollary : 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 ) can imitate the licensed technology costlessly (see, Rockett, 990). On the other hand, if imitation is not a credible threat, following Rockett (990) and Mukherjee and Balasubramanian 3 As the cost of capacity increases, it is less likely to satisfy (5) or (9 ). 5

17 (00), we find that it is optimal for the licenser (firm ) to charge a per-unit output royalty only and the optimal rate of royalty is r = ( c c). Hence, the reaction function of firm 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 abovementioned two papers that the optimal licensing contract consists of royalty and upfront fixed-fee, where the optimal royalty rate is less than r = c c ). In this ( situation, licensing shifts the reaction function of firm 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.. Higher values of z Now consider the implications of the situation where firm can credibly commit to its Stackelberg leader s output when both firms produce with their own technologies. This is shown in Figure. Figure AB shows firm s reaction function before its capacity installation and CD firm s reaction function without licensing. If S" is firm s Stackelberg leader s output without licensing, firm 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 s reaction function to C"D". 4 Following Proposition, we can find the condition required for profitable 4 We consider that licensing occurs with up-front fixed-fee. 6

18 licensing with the exception that now the output of firm does not change with c. To avoid repetition, we are omitting the details here. 5 However, it is clear from Figure that excess capacity does not occur in equilibrium since firm s reaction function after licensing intersects the vertical segment of firm 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 s Stackelberg leader s output without licensing, firm s optimal capacity installation is up to B"' without licensing. If licensing occurs after capacity installation, it shifts firm s reaction function to C"D". In this situation, excess capacity of L"'B"' occurs in equilibrium. 6 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 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 a large strategic advantage in the product market due to its pre-commitment to the capacity installation. In this situation, even if firm gets a license and becomes more cost efficient in the product market, it does not affect 5 Here licensing is profitable provided q > qp. 6 Since the procedures of Propositions and can be used to find the required conditions for the coexistence of licensing and excess capacity, we are omitting details to avoid repetition. 7

19 firm 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 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 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 ) cannot install capacity prior to production. However, as pointed out by Ware (984), 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. and.. to incorporate capacity installation by firm. 7 We will consider two scenarios: (i) where firm installs capacity after the decision on licensing, and (ii) where firm 7 We have shown that licensing and excess capacity is more likely to observe in the situations considered in these subsections. 8

20 installs capacity before the decision on licensing. So, our analysis in this section is a useful check on the robustness of our results. 3. Firm s capacity installation after licensing We consider the following game. At stage, firm invests up to capacity level x. At stage, firm enters the market. At stage 3, firm decides whether or not to license technology to firm. At stage 4, firm installs capacity. At stage 5, production takes place and profits are realized. We again solve the game through backward induction. Since firm cannot credibly commit to its Stackelberg leader s output when the firms produce with their own technologies, it follows from Ware (984) that, if firm commits to the capacity level before production, equilibrium under no licensing is not at E of Figure but it is somewhere between G and E of Figure. 8 Let us consider Figure 3 where we allow firm to install capacity before production. Figure 3 Assume that equilibrium under no licensing is at E". So, firm and firm produce B" and B"E" respectively. Industry profit under no licensing is P ( B + q ( B ))( B + q ( B )) c B ( z + c ) q ( ). (0) B Now, assume that firm licenses its technology ex-post capacity installation up to B". So, firm s marginal cost of production after licensing is z + c. Since, firm 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 z + c and firm s marginal cost of production is c. In other words, firm will choose its capacity level 8 Refer to Ware (984) for the details. 9

21 to maximize its profit given the reaction function A'OB". However, firm s Stackelberg leader s output with its marginal cost of production z + c and firm s marginal cost of production c is greater than firm s Cournot-Nash output when both firms marginal cost of production is c. Hence, firm s credible capacity commitment cannot exceed the value corresponding to point W, i.e., J. So, ex-post licensing, capacity installation by firm generates the equilibrium in the product market at W. Hence, under licensing, firm produces I and firm produces q ( I) corresponding to its marginal cost of production, i.e., IW. Therefore, industry profit under licensing is P I + q ( I))( I + q ( I)) c I ( z + ) ( I). () ( c 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 compared to its capacity installment up to I. q c Proposition 5: If the own technologies of the firms are sufficiently close, licensing is profitable when > P and z is sufficiently small. c Proof: The industry profit at W is P I + q ( I))( I + q ( I)) c I ( z + ) q ( I) ( c () with c =. Differentiating () with respect to and following the procedure used c c in Proposition, we can show that, if c and c is sufficiently close and z is sufficiently small, industry profit over WO in Figure 3 reduces with higher only if c if and 0

22 > P ( + ). (3) Since > 0, (3) holds if > P. 9 c Now consider the effect of c on the industry profit over B"E". If z is very small and, and is sufficiently close then q c c q. In this situation, we find that industry profit reduces with higher c if and only if P c >. (4) Q.E.D. Proposition 6: Capacity installation more than I makes firm better off when the per-unit cost of capacity is sufficiently small. Proof: If firm invests up to I instead of B", its net gain is H = ( B I) z [( P( I + q ( I)) z c ) q ( I) ( P( B + q ( B )) z c ) q B (5) H Following the proof of Proposition, it is easy to show that > 0, when z is I ( )]. sufficiently small. Q.E.D. Combining Propositions 5 and 6, we get the following result immediately. 9 It follows from Proposition that (3) holds if the industry marginal revenue is downward sloping.

23 Proposition 7: Assume that firm installs capacity after licensing and prior to production. Licensing and excess capacity co-exist when P c >, the own technologies of the firms are sufficiently close and z is sufficiently small. Proposition 7 shows that our qualitative result of subsections. and.. showing the co-existence of licensing and excess capacity is robust even if firm (the entrant) installs capacity after licensing and before production. 3. Firm s capacity installation before licensing Now, we consider another possibility where firm installs capacity before licensing. So, the game is as follows. At stage, firm invests up to capacity level x. At stage, firm enters the market. At stage 3, firm installs capacity. At stage 4, firm decides whether or not to license the technology to firm. 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, both firms capacity installation is like subsection 3.. Given the capacity installation by firm up to B", firm has no incentive to change its capacity installation from Y, since any deviation reduces firm s payoff under no licensing. Since, under licensing, firm receives its reservation payoff, firm installs capacity to maximize its reservation payoff. Hence, given that firm s capacity installation is up to B", firm s optimal capacity installation is up to Y. Further, since, under no licensing, firm s reservation payoff is minimized when firm installs capacity up to B", firm also has no incentive to install capacity different from B". So, firm

24 installs capacity up to B", firm installs capacity up to Y and the equilibrium is at E" (see Figure 4). Figure 4 Now, assume that firm licenses its technology ex-post capacity installation by both firms. If licensing ex-post capacity installation shifts the reaction function of firm in a way to create equilibrium between W and O then firm has excess capacity in equilibrium. This is shown in Figure 4 with the reaction function D"UM"N" of firm 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, firm s capacity is fully utilized and there is no excess capacity. 0 So, if firm installs capacity before licensing, it reduces its flexibility about capacity installation and production and may help firm to utilize its full capacity. The above argument however assumed that licensing is profitable after capacity installation and firm 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.. and 3., 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: 0 Difference between z and ( c c) is important in determining whether the equilibrium will be either on the segment OW or on the segment B"O. 3

25 Proposition 8: Licensing and excess capacity may co-exist even if firm installs capacity before licensing. 3.3 Timing of licensing The previous two subsections have considered different timing of capacity installation by firm. If firm licenses its technology prior to firm s capacity installation, excess capacity occurs in equilibrium. But, if firm licenses its technology after firm s capacity installation, equilibrium is different from the previous situation and firm may not have excess capacity in equilibrium. If firm can choose the timing of licensing, the natural question is to ask whether it prefers to license its technology before or after firm s capacity installation. Proposition 9: Suppose firm installs capacity before production and the condition for profitable licensing holds. If the cost of capacity (i.e., z ) is sufficiently small, firm prefers to license its technology after firm s capacity installation. Proof: The profits of the firms under no licensing are same irrespective of whether firm licenses its technology before or after capacity installation of firm. So, firm prefers that situation which gives it higher profit under licensing. Assume that firm experiences excess capacity irrespective of firm s timing of capacity installation. Hence, we find from Figures 3 and 4 that firm s profit under licensing is higher if it licenses after firm s capacity installation than if it licenses before firm s capacity installation provided Note that if firm licenses its technology after firm s capacity installation then firm s cost of capacity installation is sunk at the time of licensing and hence, is not included in firm s reservation payoff. 4

26 P( I + I W )( I + I W ) c I ( z + c ) I W P( I + IW )( I + IW ) + c I + ( z + c ) IW > 0, (6) or equivalently [ P( q + q )( q + q ) cq ( z + c ) q ] < 0. (7) Given that z is sufficiently small, which also helps to make licensing profitable, condition (7) always holds. This implies that firm prefers to license its technology after rather than before firm s capacity installation. Following similar logic, we can show that even if firm does not have excess capacity in equilibrium when it licenses after firm s capacity installation, it prefers to license its technology after firm s capacity installation. Q.E.D. The reason for the above proposition is as follows. If firm licenses before firm s capacity installation then firm has more flexibility about its output level compared to the situation where firm licenses after firm s capacity installation. So, firm can induce firm to produce relatively lower amount of output if it licenses after firm s capacity installation. This, in turn, increases firm s output and profit in the product market. Further, licensing after firm s capacity installation increases firm s capacity utilization and reduces the cost of excess capacity, however small it is. So, higher strategic advantage in the product market makes firm better off if it licenses after firm s capacity installation compared to the situation where it licenses before firm s capacity installation. 5

27 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. 6

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31 Figure : When firm cannot credibly commit to its Stackelberg leader s output and firm does capacity installation and production at the same time Figure : When firm can credibly commit to its Stackelberg leader s output and firm does capacity installation and production at the same time 30

32 Figure 3: When firm installs capacity after licensing but prior to production Figure 4: When firm installs capacity before licensing 3