# A Theory of Joint Venture Life-Cycles.

International Journal of Industrial Organization 19 (2001) 319–343 www. elsevier. com / locate / econbase A theory of joint venture life-cycles Indrani Roy Chowdhury a , Prabal Roy Chowdhury b , * b a Jadavpur University, Jadavpur, India CSDILE, School of International Studies ( SIS), Jawaharlal Nehru University ( JNU), New Delhi, 110067, India Received 1 May 1998; received in revised form 1 February 1999; accepted 1 May 1999 Abstract In this paper we provide a dynamic theory of joint venture life cycle that relies on synergy, organisational learning and moral hazard.

We demonstrate that depending on parameter values the outcome may involve any one of the following: stable joint venture formation, joint venture formation followed by breakdown, or Cournot competition in all the periods. We also provide some interesting welfare results. © 2001 Elsevier Science B. V. All rights reserved. Keywords: Joint ventures; Learning; Synergy; Moral hazard JEL classi? cation: F23; L13 1. Introduction Joint ventures represent one of the most fascinating developments in international business.

They are of particular interest to less developed countries (LDCs), especially to those countries which are pursuing a policy of liberalisation. This is because these LDCs are trying to encourage foreign direct investment, and such investments often take the form of joint ventures. * Corresponding author. E-mail address: prabalrc@hotmail. com (P. Roy Chowdhury). 0167-7187 / 01 / $ – see front matter © 2001 Elsevier Science B. V. All rights reserved. PII: S0167-7187( 99 )00014-4 320 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343

In the last two decades the rate of joint venture formation has accelerated dramatically. 1 Recent studies suggest, however, that joint ventures are prone to frequent breakdowns. 2 Kogut (1988), for example, found that out of the 92 joint ventures studied by him, about half had broken up by the sixth year. Even in India there there have been several well documented cases of joint venture breakdowns. These include those between Procter and Gamble (P& G) and Godrej, General Electric (GE) and Apar, Tata Sons and Unisys Corporation, to name only a few. There have been several studies that examine the question of joint venture formation at a theoretical level. These include, among others, Al-Saadon and Das (1996), D’Aspremont and Jacquemin (1988), Bardhan (1982), Chan and Hoy (1991), Chao and Yu (1996), Choi (1993), Combs (1993), Das (1997), Katz (1986), Marjit (1991), Purakayastha (1993), Roy Chowdhury (1995), Roy Chowdhury (1997), Singh and Bardhan (1991), Svejnar and Smith (1984) etc. The question of joint venture breakdown, however, has received relatively little theoretical attention. In particular there are very few studies that provide a uni? d treatment of both joint venture formation and breakdown. It is one of the goals of this paper to try and provide such a theory. We develop a theory of joint venture life cycle that relies on three basic building blocks, synergy, organisational learning and moral hazard. Synergy arises out of the complementary competencies of the two partner ? rms. In particular, in case of joint ventures involving a foreign multinational company (MNC from now on) and a domestic ? rm (especially from a less developed country) it appears that usually the MNC provides the superior technology, while the domestic ? m provides a knowledge of local conditions etc. 4 In the Indian context, in the alliance between Hewlett and Packard (HP) and HCL in computers, HP hoped for a quick access to the Indian market, while HCL hoped to utilise HP’s competence in business processes, production and quality maintenance. (See Business India, 1992. ) In this paper synergy is formalised through the assumption that the MNC can supply capital relatively cheaply, while the domestic ? rm has cheaper access to labour. Organisational learning, whereby the partner ? rms in a joint venture may acquire the other ? rm’s competencies, provides the second building block of our See Hergert and Morris (1988) and Pekar and Allio (1994), among others, for studies on joint venture formation. 2 See Beamish (1985) and Gomes-Casseres (1987) for surveys of prior research on joint venture stability. 3 See Bhandari (1996–97), Business India (1992) and Ghosh (1996) for a description of these and other cases. 4 See, among others, Dymsza (1988), Miller et al. (1996) and Tomlinson (1970). Tomlinson (1970), for example, studies British joint ventures in India and Pakistan. He ? nds that one of the main reasons behind such ventures is the local resource supplied by the domestic partner.

I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 321 theory. 5 In order to keep things simple we assume that learning is both sided and symmetric. Thus, after learning occurs, the MNC can supply labour more cheaply than before, while the domestic ? rm can supply capital more cheaply. The ? nal ingredient of our theory is moral hazard. We assume that input levels are non-veri? able and hence cannot be contracted upon. Thus, if a joint venture forms, then the partner ? rms cannot write a contract over the quantities of the inputs to be supplied. Hence both the ? ms have an incentive to free ride on the other, leading to a coordination cost for the joint venture. This is analytically crucial since, in the absence of any such costs, a joint venture always forms. 6 We consider a dynamic two period model consisting of two ? rms, an MNC and a domestic ? rm. In every period the ? rms decide whether to form a joint venture, or to compete over the output levels. If, in period 1, a joint venture forms, then the ? rms learn to internalise each others competencies. As a consequence both the ? rms become more ef? cient in the second period. If, however, the ? ms decide to pursue Cournot competition in the ? rst period, then there is no learning. We solve for the subgame perfect equilibrium of this game. We demonstrate that depending on parameter values several outcomes are possible. If the demand level is very high then a stable joint venture forms. Whereas for intermediate levels of demand there is joint venture formation followed by breakdown. Finally, for low levels of demand, there is Cournot competition in both the periods. The intuition for joint venture breakdown is as follows. In the ? rst period the joint venture forms to take advantage of the synergistic cost savings.

Once the joint venture forms, however, organisational learning occurs. Thus in the second period both the ? rms become more ef? cient, reducing the value of the synergistic cost savings to the two partner ? rms. Hence the moral hazard costs of forming a joint venture outweigh the potential synergistic bene? ts, and breakdown occurs. The welfare results are as follows. We demonstrate that for a wide range of parameter con? gurations joint venture breakdown welfare dominates stable joint venture formation. This is likely to be the case if learning effects are large and the demand level is either relatively low, or very high.

Moreover, if learning is close to complete or if the societal discount factor is high, then joint venture breakdown is also likely to welfare dominate the outcome where there is Cournot competition in both the periods. Finally, turning to the theoretical literature on joint venture breakdowns, the paper closest to our own is by Roy Chowdhury and Roy Chowdhury (1998). Roy Chowdhury and Roy Chowdhury (1998) also examine a model with learning. In See Hamel (1991), Hamel et al. (1989), and Beamish and Inkpen (1995), among others, for studies of strategic alliances that take organisational learning explicitly into account. Joint venture formation would involve some exogenous ? xed costs as well. Dymsza (1988), for example, suggests that headquarter costs constitute one component of such costs. 5 322 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 contrast to the present paper, however, they do not allow for any moral hazard problem. Furthermore, it is assumed that learning is one sided and the pro? t sharing rule is exogenously ? xed by the government. In their paper, due to one-sided learning the MNC becomes much more ef? cient over time. Due to the exogenously ? ed sharing rule, however, the MNC still obtains only half the joint venture pro? ts. Hence breakdown occurs. 2. The model There are two ? rms, one multinational (denoted ? rm 1) and one domestic (denoted ? rm 2) who can either form a joint venture, or compete (over quantities) in the domestic market. We formulate a simple two period model where every period is further sub-divided into two stages. 2. 1. Stage 1 The ? rms decide, sequentially, whether to opt for a joint venture, or compete ` over quantities (a la Cournot). Firm 1 moves ? rst and can choose either of the two options, joint venture or Cournot competition.

Firm 2 moves second and again chooses one of two options, joint venture or Cournot competition. A joint venture forms only if both the ? rms opt to form a joint venture, otherwise Cournot competition ensues. 2. 2. Stage 2 If both ? rm 1 and ? rm 2 opt for a joint venture, then they simultaneously decide on how much input to supply to the joint venture. In case the two ? rms opt for Cournot competition, they simultaneously decide on their output levels, q1 and q2 . The inverse domestic demand function is p 5 a 2 f(q), where a . 0. Let d denote the common discount factor of the two ? rms, where 0 , d , 1.

There are two factors of production, capital (K) and labour (L). The production functions of both the ? rms are taken to be identical and of the form q 5 q(K, L). We assume that the demand and the production functions satisfy the following assumptions: A1. a 2 f(q) is twice continuously differentiable, negatively sloped and (weakly) concave. Moreover, lim q>0 f(q) 5 0 and lim q>` f(q) 5 a. A2. q(K, L) is twice continuously differentiable and symmetric. Marginal products are positive and there is diminishing factor productivity i. e. qK . 0, qL . 0, qKK , 0, qLL , 0 and lim K >` qK (K, K) 5 0.

The production function exhibits constant or decreasing returns to scale i. e. q( lK, lL) < lq(K, L) for all l . 1. I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 323 Moreover, we also make the technical assumptions that qKK (x, x) 1 qKL (x, x) < 0 and q(0, 0) 5 0. 7 Consider period 1. Let the per unit wage and rental cost for the MNC be w 1 and r , and those for the domestic ? rm be w 2 and r 2 . We assume that the multinational ? rm has cheaper access to capital, while the domestic ? rm has cheaper access to labour. Thus 1 r 1 , r 2 and w 1 . 2 . Furthermore, assume that the game is entirely symmetric, so that r 1 5 w 2 5 c and r 2 5 w 1 5 b . (1) (2) Next suppose that a joint venture forms in the ? rst period. Then learning takes place, so that the ? rms internalise some of the skills of their partners. Thus in period 2 the ? rms can supply the factors of production more cheaply. If m represents the common learning parameter of both the ? rms, then, in the second period, the per unit wage cost of the MNC declines to m w 2 , and the per unit rental cost for the domestic ? rm reduces to m r 1 , where b /c > m > 1.

Notice that if m 5 1, then there is complete learning, whereas if m 5 b /c, then there is no learning. 8 Given the production function we can perform a standard cost minimisation exercise to obtain the cost function of the i-th ? rm C(w i , r i , qi ). Thus under Cournot competition without any learning the cost function of the i-th ? rm is C(c, b, qi ), while under Cournot competition with learning the cost function of the i-th ? rm is C(c, m c, qi ). Clearly given that the production function exhibits decreasing returns to scale, the cost function must be convex i. e. ? 2 C / ? q i2 > 0. 9 In order to ? simplify the exposition we shall write C(qi ) 5 C(c, b, qi ) and C(qi ) 5 C(c, m c, qi ). Under a joint venture the MNC supplies capital, and the domestic ? rm supplies labour so as to take advantage of the synergistic effects. However, because of moral hazard problems the partner ? rms cannot write a contract over the amounts of labour and capital that are to be supplied to the joint venture. The contract only speci? es that the gross pro? t is to be equally shared between the two partner ? rms. (Since the game is completely symmetric, such a surplus sharing rule is, perhaps, not too unrealistic, and ost symmetric bargaining solutions would yield a These technical assumptions are mainly required in footnotes 10 and 11. We assume that if the ? rms pursue Cournot competition then learning does not take place. This is of course unrealistic. Generally learning would take place under Cournot competition as well. However, it seems natural to assume that in this case learning would proceed much more slowly compared to that under a joint venture. Thus our assumption can be justi? ed as a useful simpli? cation. 9 If, for example, the production function is of the generalised Cobb-Douglas type i. . q 5 (KL)a , 1 1 where a < ] , then the cost function is 2w 1 / 2 r 1 / 2 q 1 / 2 a , which is strictly convex for a , ] . 2 2 8 7 324 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 symmetric pro? t sharing rule. ) The input costs are borne by the ? rm that supplies the input. Hence the pro? t functions of the two ? rms under a joint venture are as follows: 1 J1 5 ] [a 2 f(q(K, L))]q(K, L) 2 r 1 K , 2 and 1 J2 5 ] [a 2 f(q(K, L))]q(K, L) 2 w 2 L . 2 (4) (3) The solution concept used in this paper is that of subgame perfect Nash equilibrium.

Given our simple framework it reduces to a simple backwards induction argument. Thus we start by solving the stage 2 game in period 2 ? rst. 2. 3. Stage 2 – period 2 2. 3. 1. Joint venture Since the input levels under a joint venture cannot be contracted upon, we solve for the Nash equilibrium of the game where the MNC and the domestic ? rm simultaneously decide on how much capital and labour, respectively, to supply. The reaction functions of the two ? rms are given by qK (K, L) 1 J1K 5 ]]] [a 2 f(q(K, L)) 2 q. f 9(q(K, L))] 2 r 5 0 , 2 and qL (K, L) 2 and J2L 5 ]]] [a 2 f(q(K, L)) 2 q. f 9(q(K,

L))] 2 w 5 0 . 2 (6) (5) We restrict attention to the symmetric solution where K 5 L. Therefore Eqs. (5) and (6) reduce to qK (K, K)[a 2 f(q(K, K)) 2 q(K, K). f 9(q(K, K))] 5 2c . 10 (7) We can demonstrate that Eq. (7) has a unique solution. Let us denote this ] ] ] ] ] ] ] solution by (K, L) where K 5L, and let ] 5 q(K, L). If J represents the equilibrium q ] ] ] pro? t of both the partner ? rms, then J 5 Ji (K, L). De? ne A(K) 5 qK (K, K)[a 2 f(q(K, K)) 2 q(K, K). f 9(q(K, K))]. Notice that under our assumptions A(K) is negatively sloped (here we use the assumption that qKK 1 qKL < 0).

Furthermore, A(0) 5 aqK (0, 0) and lim A(K) 5 0 (here we utilise the fact that K >` lim qK (K,K) 5 0). Thus under the assumption that aqK (0, 0) . 2c, Eq. (7) has a unique and interior K >` solution. 10 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 325 2. 3. 2. Cournot competition We then examine the outcome under Cournot competition. There are two different cases depending on whether learning had occurred in period 1 or not. Case 1. First consider the case where there is no learning in period 1. The pro? t function of the i-th ? rm ?

Pi 5 [a 2 f(q1 1 q2 )]qi 2 C(qi ) , (8) ? where recall that C(qi ) 5 C(c, b, qi ). A standard reaction function approach yields the reaction function of the ith ? rm ? a 2 f(q1 1 q2 ) 2 qi . f 9(q1 1 q2 ) 2 C 9(qi ) 5 0 . In the symmetric solution we must have that ? a 2 f(2q) 2 qf 9(2q) 2 C 9(q) 5 0 . (10) (9) It is easy to see that under our assumptions Eq. (10) has a unique solution. 11 Let ? ? ? ? us denote this solution by q1 5 q2 5 q, and let the equilibrium pro? t level be P, ? ? ? where P 5 Pi (q, q ). Case 2. We then consider the case where the ? rms form a joint venture in period 1.

Thus learning occurs and the pro? t function of the two ? rms become ? pi 5 [a 2 f(q1 1 q2 )]qi 2 C(qi ) , (11) ? where recall that C(qi ) 5 C(c, m c, qi ). We can mimic the argument in case 1 to ? ? ? show that a unique symmetric equilibrium where q1 5 q2 5 q exists. Let us de? ne ? ? ? p 5 pi (q, q ). We then assume that under Cournot competition with learning ? rms make larger pro? ts compared to the case where there is no learning. ? ? A3. p . P. For linear demand and cost functions this assumption is always satis? ed. For De? ne ? B(q) 5 a 2 f(2q) 2 qf 9(2q) 2 C 9(q) . ? ?

It is clear that B9(q) 5 2 3f 9(2q) 2 2qf 99(2q) 2 C 99(q) , 0. Furthermore, B(0) 5 a 2 C 9(0) and ? ? lim q >` B(q) 5 2 lim q >` [qf 9(2q) 1 C 9(q)] , 0. If we assume that a . C 9(0) then Eq. (10) has a unique and interior solution. This condition will always be satis? ed if the cost function satis? es the Inada ? condition that C 9(0) 5 0. For linear cost functions though, we have to assume that ‘5’ is greater than the constant marginal cost. 11 326 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 more general demand and cost functions Tirole (1988), exercise 10. 0, argues that in a symmetric Cournot duopoly a small and symmetric reduction in cost increases ? rm pro? ts provided the Cournot equilibrium is stable and the industry marginal revenue curve is downward sloping. We assume that this result holds globally. We then consider the game in stage 1 of period 2. 2. 4. Period 2 – stage 1 There are two cases to consider depending on whether a joint venture had formed in period 1 or not. Suppose that in period 1 there was Cournot competition between the two ? rms. Clearly, in the second period a joint venture forms if and ] ? only if J > P.

Whereas suppose that there was joint venture formation in period 1. ] ? Then, in period 2, a joint venture forms if and only if J > p. 2. 5. Period 1 – stage 2 2. 5. 1. Joint venture The analysis in this case is identical to that for joint venture formation in period 2. 2. 5. 2. Cournot competition We then consider the outcome under Cournot competition. It is clear that in this ? case there would be no learning and the pro? t of both the ? rms would be P. We are now in a position to analyse the ? rst stage game in period 1. 2. 6. Period 1 – stage 1 ] ? ? Case (i). Suppose that J > p . P.

In this case, irrespective of what happens in the ? rst period, in period 2 a joint venture is always going to form. Hence the outcome in period 1 does not affect the outcome in period 2, and thus the ? rst period ] ? problem can be solved in isolation. Notice, however, that since J . P, it is optimal to form a joint venture in period 1 also. Thus there is stable joint venture formation. ] ? ? Case (ii). Next assume that p . J > P. In this case if a joint venture forms in ] ? period 1 then, since p . J, it is going to break up in period 2. Consider the decision facing (say) the MNC in period 1.

Suppose a joint venture forms in period 1. Then learning occurs and the joint venture breaks up in period 2. Hence the ] ? present discounted value of the MNC’s pro? t is (J 1 dp ). If, however, in period 1 the ? rms compete over quantities then, in period 2, a joint venture is going to ] ? form. (This follows since J . P. ) Thus the present discounted value of the MNC’s ] ? pro? t will be (P 1 dJ). Clearly, the MNC would prefer to opt for a joint venture provided I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 327 (12) ] ? ] ? Since d , 1, a suf? ient condition for this to happen is that J 2 P >J 2 p. Given assumption A3, this condition is always satis? ed. Thus, in period 1, the MNC always prefers to opt for a joint venture. Obviously, a symmetric argument holds for ? rm 2. ? ] ? Case (iii). We then consider the case where p . P . J. Clearly, irrespective of what happens in period 1 there would be Cournot competition in period 2. The nature of competition would, of course, depend on whether there was learning in period 1 or not. Note that the expected pro? t to any one ? rm from a ? rst period joint venture ] ? ollowed by Cournot competition in the second period is (J 1 dp ). Whereas the ? expected pro? t from pursuing Cournot competition in both the periods is (P 1 ? ). Thus the ? rms opt for a joint venture in period 1 if and only if dP ] ? ? J 1 dp > (1 1 d )P . (13) ? ? Finally, notice that since p . P, these three cases exhaust the possible parameter con? gurations. Proposition 1 below summarises the above discussion and provides a complete characterisation of the subgame perfect equilibrium outcomes in this model. ] ? ? Proposition 1. (i) If J > p . P, then the ? rms opt for a joint venture in both the periods. ? ? (ii) If p . J > P, then a joint venture forms in the ? rst period, which, however, breaks up in period 2. ] ? ] ? ? ? (iii) Suppose that p . P . J. If J 1 dp > (1 1 d )P, then there is joint venture formation followed by breakdown. Otherwise, there is Cournot competition in both the periods. An example. Let us consider an example where the demand function is linear i. e. q 5 a 2 p and the production function is of the Cobb-Douglas type, i. e. q 5 ? (KL)1 / 2 . Straightforward calculations now yield that ] 5 a 2 4c / 2, q 5 [a 2 q ] ? ? 2(bc)1 / 2 ] / 3 and q 5 [a 2 2m 1 / 2 c] / 3.

Furthermore, J 5 a(a 2 4c) / 8, P 5 [a 2 ? 2(bc)1 / 2 ] 2 / 9 and p 5 [a 2 2m 1 / 2 c] 2 / 9. Observe that this example satis? es assump? ? tion A3, i. e. p . P. We then demonstrate that there exist parameter values such that Cournot pro? ts ] ? exceed that from a joint venture, i. e. P(a) 2J(a) 5 [a 2 2(bc)1 / 2 ] 2 / 9 2 a(a 2 4c) / 8 would be strictly positive. Suppose that 4c . 2(bc)1 / 2 , i. e. 4c . b. It is easy to see that ] 1 ? P(4c) 2J(4c) 5 ] [4c 2 2(bc)1 / 2 ] 2 . 0. 9 ] ? ] ? J 2 P > d [J 2 p ] . 328 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 The intuition is as follows.

A joint venture enjoys two advantages vis-a-vis Cournot competition. First, it can exploit the synergistic effect. Second, it can avoid the rent dissipation that occurs under Cournot competition. Notice, however, that the condition that 4c . b essentially implies that c cannot be too small, so that the synergistic effect cannot be too large. Hence the moral hazard costs of joint venture formation outweigh the potential bene? ts and Cournot competition obtains. 3. Comparative statics In this section we perform some comparative statics exercises with respect to the three parameters, a, m and d.

We begin by analysing the impact of a change in the demand parameter, a, on the outcome. Let us begin by introducing some notations. ] ? Z(a) 5J(a) 2 P(a) , and ] ? Y(a) 5J(a) 2 p(a) . (15) (14) De? ne a and b as the minimum values of a that satisfy the equations Z(a) 5 0 and Y(a) 5 0 respectively. Of course, a and b may not always be de? ned. ] ? ? ? Since p . P, it follows that Z(a) . Y(a). Let ] be the minimum a such that J, P a ] ? ? ? and p are all non-negative. It is simple to show that J, P and p are all increasing ] in a. We therefore restrict attention to demand levels such that a >a, thus ensuring ] ? that J, P and p are all positive. The next proposition follows directly from Fig. 1 and Proposition 1 in the previous section. Proposition 2. Assume that Z9(a) . 0 and Y9(a) . 0. ] ] (i) Suppose Y(a) > 0. Then, for all a >a, there is stable joint venture formation. ] > 0 . Y(a). Then, for all a > b, there is stable joint venture ] (ii) Suppose Z(a) formation, whereas, for all a , b, there is joint venture formation followed by breakdown. ] (iii) Suppose Z(a) , 0. Then, for all a > b, there is stable joint venture formation, whereas if a < a , b, then there is joint venture formation followed by ] ? breakdown. For a , a, if J 1 dp > (1 1 d )P, then there is joint venture formation followed by breakdown. Otherwise, there is Cournot competition in both the periods. Clearly, the important question is under what kind of conditions on the primitive I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 329 Fig. 1. Effects of a change in the demand level on joint venture formation and stability. functions can we expect Z(a) and Y(a) to be positively sloped. To begin with observe that we can decompose Z(a) into three different components ] ? Z(a) 5J(a) 2 P(a) M M ] ? [J(a) 2 ](a)] 1 [](a) 2 p (c)(a)] 1 [p (c)(a) 2 P(a)] 2 2 (16) Here M represents the aggregate monopoly pro? t. Let 2qm , Km and Lm represent the levels of aggregate output, capital and labour respectively under the monopoly ? equilibrium. Moreover, p (c) 5 p u m 51 . Thus p (c) represents the Cournot pro? t of the ? rms when learning is complete. ] ] Consider the ? rst term in square brackets, [J(a) 2 M / 2(a)]. Notice that J represents joint venture pro? ts when moral hazard problems are present and M / 2 represents joint venture pro? ts when no such problems are present. Hence the ? st term is an index of the moral hazard problem. Next consider the second term in square brackets, [M / 2(a) 2 p (c)(a)]. This represents the difference between monopoly and Cournot pro? ts, when Cournot competition involves complete learning. Therefore this term is an index of the rent dissipation effect. ? Finally, consider the last term in square brackets, [p (c)(a) 2 P(a)]. Notice that ? p (c) represents Cournot pro? ts when learning is complete, and P represents Cournot pro? ts in the absence of any learning. Thus this term is an index of the synergistic effect. 330 I. Roy Chowdhury, P.

Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 We then argue that under some additional assumptions all three terms are increasing in a. A4. q(x, x) 2 q( y, y) < x 2 y, ;x > y. This assumption will be satis? ed for example if the production function is of the generalised Cobb-Douglas type, i. e. q 5 (KL)a , where a < 1 / 2. Assumptions A5 to A9 that follow are essentially technical conditions that ensure that the higher order derivatives are well behaved. These are all satis? ed for example, if the demand function is linear and the cost function is of the Cobb-Douglas type. A5. K (K, K)[a 2 f(q(K, K)) 2 q(K, K)f 9(q(K, K))] is (weakly) concave in K. A6. qK (K, K) > 1 / 2, ;K. A7. q. f 9(2q) is (weakly) concave in q. A8. 8f 99(2q) 1 4qf 999(2q) 1 C999(q) 5 0. A9. ? 3 C(w i , r i , qi ) ? 3 C(w i ,r i ,qi ) ]]]], ]]]] < 0 . ?qi ? qi ? w i ? qi ? qi ? r i In Proposition 3 below we argue that if assumptions A4 to A9 hold then Z(a) is increasing in a. A similar argument holds for Y(a) also. 12 Thus under the additional assumptions A4 to A9, the hypothesis of Proposition 2 is valid. Proposition 3. If assumptions A4 to A9 hold then both Z(a) and Y(a) are increasing in a.

The proof, which is somewhat lengthy, has been relegated to the appendix. The example. As an illustration we revert to our earlier example with linear demand and Cobb-Douglas production functions. In this case it is easy to show 1 1 that Z(a) 5 ] [a 2 1 4ah8(bc)1 / 2 2 9cj 2 32bc] and Y(a) 5 ] [a 2 1 4ah8m 1 / 2 c 2 72 72 2 9cj 2 32m c ]. Hence we can write that 12 We can decompose Y(a) as follows: ] M(a) M(a) ? Y(a)5f J(a)2 ]g 1f] 2 p(a)g . 2 2 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 331 1 Z9(a) 5 ][a 1 16(bc)1 / 2 2 18c] , 36 1 Y9(a) 5 ] fa 1 16m 1 / 2 c 2 18cg . 6 (17) (18) 1 Observe that the righthand side of Eq. (17) can be re-arranged as ][16h(bc)1 / 2 2 36 cj 1 (a 2 2c)]. Since b . c and a . 4c (this condition ensures that joint venture output is positive), this is positive. We can similarly argue that Y9(a) . 0. Let us then examine if the decomposition argument works in this case. Observe ] that J(a) 2 M / 2(a) 5 a(a 2 4c) / 8 2 (a 2 2c)2 / 8, M / 2(a) 2 p (c)(a) 5 (a 2 2c)2 / ? 8 2 (a 2 2c)2 / 9 and p (c)(a) 2 P(a) 5 (a 2 2c)2 / 9 2 [a 2 2(bc)1 / 2 ] 2 / 9. It is obvious that the second and the third terms are increasing in a, while the ? st term (the moral hazard effect) is independent of a. Notice that this example uses a linear cost function. Given the fact that some of the assumptions, especially A5 and A6, seem to require linearity (in the sense that the examples we provide lead to linear cost functions) we then examine if Proposition 3 can hold if the cost function is non-linear. To this end we consider another example where the demand function is linear, i. e. q 5 a 2 p, but the production function is of the form q 5 (KL)1 / 4 . Thus in the absence of any learning the cost function of the two ? rms would be 2(bc)1 / 2 q 2 . Now straightforward calculations yield that J 5 a 2 (1 1 6c) / 8(1 1 4c)2 , M / 2 5 a 2 / 2 1/2 ? 8(1 1 2c) and P 5 a (1 1 2(bc) ) /(3 1 4(bc)1 / 2 )2 . It is easy to see that in this ] case the moral hazard effect [J 2 M / 2] is decreasing in the parameter a. Even so it is possible that the other two effects may dominate, so that Z9(a) and Y9(a) turn out to be positive. For example consider the case where c is very small. Observe that ] ? d / da[J 2 P ]u c>0 5 a / 36 . 0. Thus Z9(a) is positive. 13 A similar argument holds for Y9(a). This demonstrates that Proposition 3 may hold even though the cost function may not be linear. 4 We then examine the impact of a change in the learning parameter m. Clearly, ? the greater is the rate of learning (i. e. the smaller is m ), the larger is p going to be. This follows since with learning the absolute, as well as the marginal costs are going to decline. There are three different cases to consider. ] ? ? First, suppose that p . J > P. From Proposition 1(ii) the outcome involves joint ? venture formation followed by breakdown. As p increases the condition that ] ? Of course for other parameter values this term can be negative. For example, d / da[J 2 P ]u b 5c 51 5 2 257a / 4900 , 0. 4 We are indebted to a referee for pointing out the importance of the linearity assumption, especially for the analysis of the moral hazard term. 13 332 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 ] ? ? p . J > P would still hold, and the outcome would still involve joint venture breakdown. ] ? ? Next consider the case where, to begin with, J > p . P. Clearly from Proposition 1(i) the outcome involves stable joint venture formation. With an ] ? ? ? increase in p, however, it may be the case that p . J . P, so that the outcome leads to joint venture breakdown. The intuition is straightforward.

The greater is the learning, the smaller is the worth of the synergistic cost reduction to the two partners. Thus they would be more inclined to breakup the joint venture so as to save on the moral hazard costs. ] ? ] ? ? ? We then assume that p . P . J and moreover, J 1 dp , (1 1 d )P, so that from Proposition 1(iii) the outcome involves Cournot competition in both the periods. ] ? ? With an increase in p it may be the case that J 1 dp becomes greater than ? so that the joint venture breaks down. Essentially, with m increasing, (1 1 d )P, learning becomes more attractive, so that a joint venture may form.

But then ] ? breakup occurs so as to exploit this increased knowledge. If, however, J 1 dp > ? to begin with, then the outcome involves joint venture breakdown in any (1 1 d )P case and a further increase in the discount factor does not affect the outcome. To summarise, an increase in the rate of learning encourages joint venture breakdown. If, however, the rate of learning is large enough to begin with, so that the outcome involves joint venture breakdown in any case, then an increase in the learning rate does not affect the outcome. Finally, consider the impact of a change in the discount factor d.

Clearly, from ? ] ? Proposition 1, d plays a role only if p . P . J. Suppose that indeed is the case. From Proposition 1(iii) it is obvious that the larger is d, the greater are the chances that the joint venture will breakdown. If, however, d is small, then a joint venture will not even form, and there is Cournot competition in both the periods. The intuition is simple. In this case a joint venture forms only to take advantage of the learning possibilities that, however, bear fruit in period 2. The greater is d, the greater is the present discounted value of such learning possibilities, hence the result. . Welfare impact of joint venture breakdown In this section we examine if, from a social (i. e. welfare) point of view, stable joint venture formation is preferable to joint venture breakdown. Notice that in both these cases the outcomes in the ? rst period are identical. It is thus suf? cient to compare welfare levels in the second period only. Clearly, under the assumption that the whole of the MNC pro? ts are repatriated, domestic welfare in the second period is the sum of consumers’ surplus (CS) and the pro? t of the domestic ? rm. Let us denote this by S(q). Lemma 1. S(q) is increasing in q.

I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 333 Fig. 2. Effects of a change in the output level on the sum of consumers’ surplus and the pro? t of the domestic ? rm. The proof follows directly from Fig. 2. 15 We then introduce an assumption that we require for the analysis. A10. The marginal cost c9(q) is bounded above by U. 16 Next notice that from Eq. (7) it follows that as a tends towards in? nity, ] q(a) ? also tends towards in? nity. 17 Thus we can ? nd a such that ] ? )f 9(q(a )) ] ? q(a ]]]] 5 U . (19) 2 Let q and q9 be two aggregate output levels where q9 . . The aggregate output is equally divided among the two ? rms, so that q1 5 q2 5 q / 2 and q 9 5 q 9 5 q9 / 2. Thus the consumers surplus when the 1 2 output level is q, CS(q), equals BXC and the pro? t of the domestic ? rm equals AXDE. Hence S(q) 5 ABCDEA. Arguing similarly S(q9) 5 BFY 1 YGHA 5 ABFGHA. From Fig. 2 it is obvious that S(q9) exceeds S(q) by the amount EDCFGHE. 16 Notice that this assumption allows for strictly convex cost functions. 17 From Eq. (7) it follows that ] is strictly increasing in a. Next assume that ] is bounded above q(a) q(a) by q * . Next de? e a * as satisfying q * [a 2 f(q * ) 2 q * . f 9(q * )] 5 2c . Clearly, for all a . a * , ] . q * , a contradiction. q(a) 15 334 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 The next proposition compares the welfare levels under joint venture breakdown with those under stable joint venture formation. ] ? Proposition 4. (i) If p . J, then joint venture breakdown welfare dominates stable joint venture formation. ? (ii) If a . a, then the consumers9 surplus under joint venture breakdown exceeds that under stable joint venture formation. (iii) If learning is complete, i. e. 5 1, then joint venture breakdown welfare dominates stable joint venture formation. ? ] Proof. (i) Given Lemma 1, it is suf? cient to prove that 2q . q. Suppose not i. e. let ] ] ? ? p . J, but 2q 0. This, however, violates Eq. (23). Next we can mimic the argument in the proof of Proposition 4(i) to demonstrate ] ] ] that Km . K, so that 2qm . q. Hence 2qc . 2qm . q. This completes the proof. Intuitively speaking, the aggregate Cournot output exceeds the monopoly output because of competition, and the monopoly output exceeds the joint venture output because of the moral hazard effect. h Corollary. If the parameter con? urations are such that the outcome involves joint venture breakdown, then joint venture breakdown welfare dominates stable joint venture formation. The proof follows directly from Proposition 1 (which shows that a necessary ] ? condition for joint venture breakdown is that p be greater than J) and Proposition 4(i). The intuition for Proposition 4(i) is as follows. Suppose that the parameter values are such that Cournot competition is more pro? table than joint venture formation. This then implies that, because of moral hazard problems, the output level under the joint venture is much less than the industry optimum.

What we show is that this is suf? cient to ensure that the output level under a joint venture is less than the aggregate output under Cournot competition. Hence the result. Proposition 4, however, leaves some questions unanswered. To begin with ] ? Proposition 4(i) argues that if p . J, then joint venture breakdown welfare dominates stable joint venture formation. Proposition 3 suggests that this is likely 336 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 to be the case if a is not large, and, of course, if the learning effect is large.

If, however, learning is small, then it is possible that even for low levels of demand ] ? the outcome shall involve p ] K 2 ]]]]]]]] 2 Km ] ] ] ] 2 2hJ1KK (K, K) 1 J1KL (K, K)j >0 , where the ? rst inequality follows from assumption A4, the second inequality follows from assumption A6 and the last inequality follows from Eq. (32). Next consider the effect of a change in ‘a’ on [M / 2(a) 2 p (c)(a)]. Let qc denote the Cournot equilibrium output levels of the two ? rms. First note that ? pi (c) d M ] ](a) 2 p (c)(a) 5 qm 2 qc 2]] da 2 ? q j F G U dqc ] q c da (34) Next straightforward differentiation of Eq. 23) yields that 340 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 ?pi (c) ]] ? q j and U qc 5 2 qc f 9(2qc ) , (35) dqc 1 ] 5 ]]]]]]]]] . da 3f 9(2qc ) 1 2qc f 99(2qc ) 1 d 99(qc ) Substituting Eqs. (35) and (36) into Eq. (34) we can write qc f 9(2qc ) d M ] ](a) 2 p (c)(a) 5 qm 2 qc 1 ]]]]]]]]] . da 2 3f 9(2qc ) 1 2qc f 99(2qc ) 1 d 99(qc ) De? ne h(q) 5 qf 9(2q). From Fig. 4 and assumption A7 it now follows that X < qm h9(0) 5 qm f 9(0) , qc f 9(2qc ) . (36) F G (37) (38) Next observe that assumption A8 implies that a 2 f(2q) 2 qf 9(2q) 2 d 9(q) is (weakly) convex in q.

Hence from Fig. 4 we obtain that X qc 2 qm < ]]]]]]]]] 3f 9(2qc ) 1 2qc f 99(2qc ) 1 d 99(qc ) qc f 9(2qc ) , ]]]]]]]]] (from (38)) . 3f 9(2qc ) 1 2qc f 99(2qc ) 1 d 99(qc ) (39) Fig. 4. Effects of a change in the demand level on the rent dissipation effect. I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 341 Next Eqs. (37) and (39) together imply that qc f 9(2qc ) d M ] ](a) 2 p (c)(a) 5 qm 2 qc 1 ]]]]]]]]] da 2 3f 9(2qc ) 1 2qc f 99(2qc ) 1 d 99(qc ) . 0 . (40) F G Finally, we examine the impact of a change in ‘a’ on the synergistic effect ? [p (c)(a) 2 P(a)].

We can mimic the earlier steps to argue that ? pi (c) d ? ][p (c)(a) 2 P(a)] 5 qc 1 ]] da ? q j U qc ? dqc ? Pi ]2q2] ? da ? q j U ? dq ] ? q da 2 2qc f 9(2qc ) 1 2q c f 99(2qc ) 1 qc d 99(qc ) 5 ]]]]]]]]]]] 3f 9(2qc ) 1 2qc f 99(2qc ) 1 d 99(qc ) ? ? ? ? ?? ? 2q f 9(2q ) 1 2q 2 f 99(2q ) 1 qC 99(q ) 2 ]]]]]]]]]] ? ? ? ? ? 3f 9(2q ) 1 2q f 99(2q ) 1 C 99(q ) 2 ? 2qc f 9(2qc ) 1 2q c f 99(2qc ) 1 qc C 99(qc ) . ]]]]]]]]]]] ? 3f 9(2qc ) 1 2qc f 99(2qc ) 1 C 99(qc ) ? ? ? ? ?? ? 2q f 9(2q ) 1 2q 2 f 99(2q ) 1 qC 99(q ) ]]]]]]]]]] , 2 ? ? ? ? ? 3f 9(2q ) 1 2q f 99(2q ) 1 C 99(q ) (41) where the inequality follows from assumption A9.

Straightforward differentiation now yields that 2qf 9(2q) 1 2q 2 f 99(2q) 1 qC99(q) / 3f 9(2q) 1 2qf 99(2q) 1 C99(q) is ? ? increasing in q. 18 Since qc . q,19 it then follows that d / da[p (c)(a) 2 P(a)] . 0. Since all three terms are increasing in a, it follows that Z(a) is increasing in a. A similar argument holds for Y(a) also. h Differentiating this expression with respect to q we ? nd that the numerator equals qf 9(2q)[8f 99(2q) 1 4qf 999(q) 1 C999(q)] 1 (2f 9(2q) 1 C99(q))[3f 9(2q) 1 2qf 99(2q) 1 C99(q)]. From assumption A8 it follows that this term is strictly positive. 19 ? Suppose not i. . let qc < q. We can use Eqs. (10) and (23) to argue that ? ? ? ? ? C 9(q )5a2f(2q )2q f 9(q ) d 9(qc ). 18 342 I. Roy Chowdhury, P. Roy Chowdhury / Int. J. Ind. Organ. 19 (2001) 319 – 343 References Al-Saadon, Y. , Das, S. P. , 1996. Host country policy, transfer pricing and ownership distribution in international joint ventures: A theoretical analysis. International Journal of Industrial Organisation 14, 345–364. D’Aspremont, C. , Jacquemin, A. , 1988. Cooperative and non-cooperative R& D in duopoly with spill-overs. American Economic Review 78, 1133–1137. Bardhan, P. K. , 1982.

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