TECHNOLOGY TRANSFER: BARRIERS AND

. In this paper we study technology transfer in a duopoly model with heterogeneous goods under quantity and price competition. We obtain three conclusions: Firstly, under product heterogeneity, technology transfer can take any form. Secondly, the properties found in the homogeneous case generalize to the heterogeneous case with various degrees of generality. Finally, if demand is not symmetric we may ﬁnd full technology transfer between ﬁrms with dif- ferent sizes and that ﬁrms with similar technology do not engage in technology transfer. We ﬁnd evidence of the latter in the market for antidepressants.


1.
Introduction. Technology transfer (TT in the sequel) is a central issue within the economics of technological change and innovation. It has been analyzed from different perspectives (perfect competition, evolutionary models, etc.). In this paper we will be concerned with TT in static oligopolistic markets.
Economic intuition -borrowed from, say, the theory of international trade-suggests that with zero adoption costs the size of TT should be positively related with the technological distance between firms. However, Katz and Shapiro [5] proved that the properties that characterized TT run counter to the this intuition: (i) TT always occurs between similar firms with similar costs.
(ii) TT never occurs if firms have very different costs.
(iii) Under linear demand, joint profits are U-shaped in the marginal cost of the firm receiving TT (Firm 2 in the sequel), (see also Marjit [6]). The explanation of these results is that profits of the firm transferring the technology (Firm 1 in the sequel) decrease with the size of TT because the business stealing effect but profits of Firm 2 increase with the size of TT because costs reduction. When the marginal cost of 2 is high the business stealing effect is dominant because TT entails a large loss of profits of 1 but a small increase in profits for 2. When both firms are similar, business stealing is small and cost reduction dominates.
Katz and Shapiro [5] used several simplifying assumptions, including product homogeneity. This assumption is a useful first approximation but restricts too tightly the scope of the market under consideration. On the one hand, from the empirical point of view, product homogeneity does not allow experiences like the Silicon Valley (where a sizeable part of TT occurs among firms producing different products), the car industry (where six firms produce the blueprints for all engines) or the consumer electronics industry (where the same invention, e.g. cordless appliances, has been applied to a variety of products). Moreover, product homogeneity implies that all firms face the same demand function and this discards the case in which firms sell in different countries. On the other hand, from the theoretical point of view, product heterogeneity allows to consider Cournot and Bertrand competition and to compare the features of both equilibria.
In this paper we study TT in markets with heterogeneous goods. By simplicity we assume that product heterogeneity is exogenous. 1 In Section 2 we present some facts gathered from a specific market, that of a class of antidepressants. We see that under product heterogeneity TT takes a variety of forms that are hard to reconcile with the analysis of Katz and Shapiro [5].
Section 3 explains the model and the main concepts.
In Section 4 we consider two examples. Assuming demand is linear or isoelastic we show that Properties I-III above may not hold: The reason is that if Firm 2 faces a small demand, joint profits are maximized if Firm 1 makes no TT. Similarly, TT may happen between firms with very different costs as long as Firm 2 faces a large demand relatively to the one of Firm 1. These possibilities can not arise under good homogeneity because there, all firms face the same demand. This section prepares the ground for the more general findings of the next section.
In Section 5 we consider TT in general duopoly models of price and quantity competition. We show that, even under strong restrictions on the class of admissible demand functions, industry profits and the marginal cost of Firm 2 can be related in any arbitrary form (Proposition 1). This can not happen under product homogeneity where, for instance, joint profits are maximized when Firm 2 produces zero output. The implication is that under product differentiation any TT can arise. We show that joint profits are increasing in the marginal cost of 2 when the output of 2 is close to zero, if and only if goods are substitutes (Proposition 2). Finally, we show that joint profits are increasing in the marginal cost of 2 when firms have a similar output, under symmetric demand and small cross price effects (Proposition 3).
Summing up, we obtain three conclusions that are robust to the consideration of both quantity and price competition. Firstly, under product heterogeneity, TT can take any form. Secondly, the properties found in the homogeneous case generalize to the heterogeneous case with various degrees of generality. Finally, if demand is not symmetric we may find full TT between very different firms and that firms that are similar in technology do not engage in TT. The next section provides some evidence of that.

2.
A case study: the market for antidepressants. Empirical evidence on the forms of TT is a difficult task. However, we have found useful the insights and lessons to be learn from TT practices in the pharmaceutical industry related to a specific subset of antidepressants, Selective Serotonine Reuptake Inhibitors (SSRI) for several reasons. Firstly, they involve a high level of innovation and rivalry as their market success have been increasing in the last fifteen years. Secondly, SSRI drugs have been the first antidepressants advertised directly to consumers and recognized by their trademark rather than by their molecules, leading to, possibly spurious, product differentiation. 2 And, finally the period covered allows us to compare the TT policies designed by companies before they faced the threat of generic substitutes and the marketing of new competing drugs. 3 The set of products includes the so called N6A: Prozac , Paxil /Seroxat ; Celexa / Cipramil , Zloft , Effexor /Efexor /Vandral /Dobupal and Serzone . The patented active principles behind each product are different but still close substitutes in terms of their treatment, prescriptions and effects, specially for the case of Prozac -fluoxetine-, Paxil /Seroxat -paroxetine-; Celexa /Cipramil -citalopram-and Zloftsertraline-. Here, the molecules are the basic technology while trademarks represent marketing differentiation.
N6A drug makers and technology holders have followed different technology strategies, ranging from exclusive exploitation granted by a series of patents and applications to full TT. In both situations, the products ranked among the top selling drugs in global sales figures and contributed to firms' growth dramatically. Several examples of this follow.
In 2001, Eli Lilly lost the exclusivity for marketing fluoxetine hydrochloride -Prozac -and generic versions became available in the US. In December 2000, paroxetine's global market share was 24%. The threat of generic Prozac prompted to Eli Lilly to find alternative ways to keep ahead in the profitable SRRIs market -USD 17.1 billion in 2002-by licensing in fluoxetine R from Sepracor. Through that agreement the licensor -Sepracor-transferred to Eli Lilly all the rights to market the new active principle under the name of Prozac-R , launched in 2001. However, Sepracor did not market fluoxetine-R on its own. This case illustrates that full TT may occur even when the creator of the technology does not sell it.
In contrast, full TT occurs in the case of Celexa /Cipramil in which the licensor -Lundbeck-a large Danish pharmaceutical company licensed out citalopram in 1995 to Forest Lab, a small US drug company, that largely contributed to their growth. Moreover, following the innovation path in this segment, Cipralex /Lexapro based on citalopram R, are also the outcome of full TT and co-marketing between these companies. Here we observe full TT from a large to a small firm.
The case concerning paroxetine -Paxil /Seroxat -is quite different from the two mentioned above. After the acquisition of the patent by Beecham Pharmaceuticals, paroxetine was marketed by SmithKline Beecham (SB) which was acquired by GlaxoSmithKline. The threat of generic paroxetine in 2001 pushed GlaxoSmithKline to search for SSRIs alternatives. Since 2002 GlaxoSmithKline markets Paxil-CR in a formulation that uses SkyePharma's Geomatrix controlled-release technology. SkyePharma received an undisclosed payment from GSK in addition to royalties on net sales. The effects of TT on Skye Pharma' accounts have been bigger than expected, from 17,7 million sterling pounds in 1999, to 69,6 million in 2002. In this case there was partial TT from a small to a large firm.
The examples above show that TT under product differentiation may take forms that are not possible under product homogeneity and that TT does not always takes place among similar firms as under product homogeneity. We will see that the theoretical model backs these empirical findings.
3. The model. There are two firms selling a product each. Firm 1 can sell to firm 2 a technology that influences its marginal cost. Marginal costs are constant on output. Letc 2 be the value of the marginal cost of firm 2 before transfer of technology (TT) takes place. Let c 2 be a generic value of the marginal cost of firm 2, which belongs to the interval [c 2 ,c 2 ] where c 2 is the minimum marginal cost that can be achieved by TT. Let c 1 be the marginal cost of firm 1. Profits of firm i are Let y i be the action of firm i = 1, 2 where y i ∈ 0,ȳ], someȳ. We consider two scenarios: Price competition, where the firm chooses prices i.e. y i ≡ p i and quantity competition where the firm chooses quantities i.e. 4 We will say that good i is a substitute (resp. complement) of good j if ∂xj ∂pi > 0 (resp. < 0). Under quantity competition payoffs are ( In this case, goods are substitutes (resp. complements) if ∂pj ∂xi < 0 (resp. > 0). Denote by π 1 (y 1 , y 2 ) and π 2 (y 1 , y 2 , c 2 ) the payoff functions of firms 1 and 2. We will assume that they are twice continuously differentiable.
The game has two stages. In the first stage firms decide the value of c 2 cooperatively and in the second stage they set their actions non-cooperatively. We will refer to the second stage as the competition stage that we define below.
Definition 3.1. A Nash Equilibrium (NE) in the competition stage is a pair (y * 1 , y * 2 ) such that y * 1 maximizes π 1 (y 1 , y * 2 ) and y * 2 maximizes π 2 (y * 1 , y 2 , c 2 ). Under price competition, a NE has the form (p * 1 , p * 2 ) and usually is called a Bertrand equilibrium (BE) with first order conditions (FOC) Under quantity competition, a NE has the form (x * 1 , x * 2 ) and usually is called a Cournot Equilibrium (CE) with FOC We assume that the system of FOC fulfills the Gale-Nikaido Property. Formally: Assumption 3.2 has two parts: a) implies that the profit function of i is strictly concave in y i . If part a) holds a sufficient condition for b) to hold is that the effect in absolute value of y i on ∂πi ∂yi is larger than on ∂πi ∂yj j = i i.e. that the matrix with typical element ∂ 2 πi ∂yiyj has a Dominant Diagonal (see Friedman [3], Assumption 7, p. 71). 5 Under quantity competition, Assumption 3.2 reads ∂x1x2 ). Thus, Assumption 3.2 (part a)) holds if inverse demand is concave. Even if it is convex, the assumption may hold if ∂ 2 p 2 /∂x 2 2 is not too large. Assumption 3.2 (part b)) holds if the impact of the own price on marginal revenue is larger than the cross price impact. A similar condition applies under price competition. We now have the following. Proof. The existence of a NE follows from Kakutani fixed point theorem (see, e.g. Friedman [3]) since by A.3.2 π i ( ) is continuous and concave and actions belong to a compact set. Uniqueness and differentiability follows from applying Theorem 4 in Gale and Nikaido [4] to FOC of a NE.
We will assume that Firm 1 is always active in any NE. Letc 2 be the minimum value of c 2 for which the output of firm 2 is zero in a NE. Under our assumptions this value exists.
By Lemma 3.3 we can write y 1 and y 2 as functions of c 2 , i.e. y i = y i (c 2 ), i = 1, 2. Write π 1 (c 2 ) = π 1 (y 1 (c 2 ), y 2 (c 2 )) and π 2 (c 2 ) = π 2 (y 1 (c 2 ), y 2 (c 2 )), c 2 ). Thus, industry profits can be written as Π Finally we assume that in the first stage of the game c 2 is chosen from [c 2 ,c 2 ], to maximize Π. Formally, We finally remark that the model is sufficiently flexible to incorporate alternative interpretations. 1) TT may refer to a product that was previously not produced by Firm 2. In this case we setc 2 =c 2 . 2) Positive adoption costs. Suppose that these costs are a function of the pre-TT output and actual output. Since the former is given, write this as F (x 2 ). Thus, under quantity competition, )/x 2 as the inverse demand function of Firm 2 and carry on as before. These two interpretations do not fit well with product homogeneity: The first result happens because joint profits are maximized when Firm 2 does not produce at all so it is impossible to explain any positive TT. The second one, because product homogeneity implies that the two firms face the same demand function. 6 4. Two examples. In this section we explore what difference product differentiation makes to TT by considering two examples. The first deals with quantity competition and generalizes the linear inverse demand case worked out by Katz and Shapiro [5] and Marjit [6]. The second example considers price competition with linear demand.   We first calculate the CE for a given c 2 . We have that, In order to guarantee that profits are non negative in the CE, we assume that From (1) we get that the sign of dΠ dc2 equals the sign of We now check for the properties I-II-III stated in the Introduction. I : If a 2 is sufficiently small in relationship with a 1 we see from (1) that Π is increasing on c 2 so TT never occurs. The reason is that Firm 2 faces a demand curve that, relative to that of Firm 1, is small so is not profitable to transfer technology to a firm that is relatively inefficient selling the good. We will refer to the question of the relative size of demand as the Marketing Effect. Assuming a 1 = a 2 ≡ a, > 0. Thus, Π( ) is strictly convex and Π( ) attains a minimum at dΠ da2 = 0. We now give sufficient conditions for Π( ) to be U-shaped with a minimum atĉ 2 ∈ (c 1 ,c 2 ). Letting Q ≡ ( (1+α)b2 d1 ) α we get from (1) that the value of c 2 which minimizes Π iŝ Assume substitute goods (if goods are complements (1) implies dΠ da2 > 0 so full TT is optimal) and symmetric demand. Keep the notation introduced in I above. If c 2 ≤ c 1 , we had that . Thus under substitute goods and symmetric demandĉ 2 > c 1 .
7 If goods are substitutes these conditions imply A.3.2b). If goods are complements these conditions always hold for a i > c i . 8 If d 1 = d 2 = 1 demand functions are identical to those in the circular model of Salop [9].
From (3) we get that the sign of dΠ dc2 equals the sign of We now check for the properties I-II-III stated in the Introduction. I) Again, it is easy to see that lack of symmetry may imply dΠ dc2 | c1=c2 > 0. But even under symmetric demand if d 1 = d 2 > 0 and d 1 d 2 ≥ 2, dΠ dc2 | c1=c2 > 0. In this case cross substitution effects are very strong and reductions in c 2 exacerbate competition making TT unprofitable. However if d 1 , d 2 < 1, dΠ dc2 | c1=c2 > 0. So in this case we need symmetry and small cross substitution effects for I to hold.
It is now time to sum up our findings in this section: 1. The assumption of homogeneous product hides two important assumptions: that demand for both firm is the same and that goods are substitutes. If demand functions do not satisfy these assumptions the properties that characterize TT under homogeneous products do not hold. However, once demand is assumed to be symmetric and goods are substitutes these properties also hold in our framework. 2. Quantity competition and price competition yield the same conclusions under similar assumptions. The assumptions necessary for I) to hold are a little bit stronger in the case of price competition. 3. The marketing effect can explain that the owner of a patent does not exploit it, as in the Sepracor/Eli Lilly case in the previous section, or that a large firm licences to a small one, as in the Lundbeck/Forest Lab case. In the first case it may be argued that the success of Prozac gave to Elli Lilly a large advantage in marketing the product. In the second case both firms had relative advantages in marketing the product in different locations, EU and USA. 4. However, as long as demand functions fulfill the properties assumed in this section, partial TT, as in the GlaxoSmithKline/SkyePharma case, can not be explained. Because joint profits are strictly convex on c 2 the TT policy can only be full transfer or no transfer.
Equipped with these findings we are prepared to study the form of Π( ) in a general framework.

General properties of technology transfer.
In this section we investigate the shape of Π( ) in order to derive the implications for the kind of TT that we may expect in general.
Our first result shows that the shape of Π( ) is arbitrary even under strong assumptions on the form of demand/inverse demand functions. All proofs are gather in the Appendix. There are inverse demand (resp. demand) functions p i ( ) (resp. x i ( )) i = 1, 2 that are linear on x i (resp. p i ) yielding payoff functions that satisfy A.3.2 such that; a) There is a unique NE in which Firm 1 is active and Proposition 1 implies that any TT can be rationalized as arising from the maximization of joint profits followed by a competition stage with payoff functions satisfying A.3.2 and demand/inverse demand that are linear in the action controlled by the firm. This result implies that any TT between two firms can be rationalized as arising from these firms playing the previous game with payoff functions satisfying A.1. Thus, we can not expect Properties I-II-III in the Introduction hold when the product is differentiated.
Next, we show that the properties of Π( ) in the boundaries, i.e. in c 2 andc 2 found in the case of homogeneous goods hold in our framework under the appropriate assumptions.
First, we study the form of Π( ) in c 2 =c 2 . In this case, the property found in the homogeneous good case holds under reasonable circumstances. Proposition 2. Under A.3.2, dΠ dc2 | c2=c2 > 0 ⇔ good 2 substitute of good 1. Next, we study the form of Π( ) in c 2 . In this case, some extra conditions are needed in order to prove the result obtained under homogeneous goods. Examples 1 and 2 above give us some clues: Demand functions must are symmetric and cross effects must not be very large. Our next two assumptions deal with symmetry.
There is a y such that ∂π1(y , y ) ∂y1 < 0. Assumption 5.1 (part a) and b)) is a symmetry assumption. Assumption 5.1 (part a)) says that the minimum marginal cost that can be achieved is that of Firm 1. Assumption 5.1 (part b)) says that demand/inverse demand functions are symmetric. Let us now concentrate on Assumption 5.2 (part a)). Consider quantity competition: From (2.2), ∂π1(0,0) ∂x1 = p 1 (0, 0) − c 1 . Thus, Assumption 5.2 (part a)) says that p 1 (0, 0) > c 1 . If x 1 and x 2 are very large we expect that prices fall below marginal costs so ∂π1 ∂x1 = ∂p1 ∂x1 x 1 + p 1 − c 1 < 0 and Assumption 5.2 (part b)) holds. Under price competition from (2.1), ∂π1(0,0) ∂p1 = − ∂x1 ∂p1 c 1 + x 1 > 0. If p 1 and p 2 are very large we expect x 1 0 and ∂π1 ∂y1 ∂x1 ∂p1 (p 1 − c 1 ) < 0, so Assumption 5.2 (part b)) holds. Thus, the behavior of ∂π1 ∂y1 assumed by Assumption 5.2 seems reasonable. Proof. Consider ∂π1(y,y) ∂x1 as a function of y. Let f (y) ≡ ∂π1(y,y) ∂x1 . By Assumption 5.2, f ( ) changes sign when we go from y = 0 to y = y . By the intermediate value theorem, there is a value of y, y * such that f (y * ) = 0. By Assumption 5.1, say y * also solves the FOC of profit maximization for Firm 2 so, under Assumption 3.2 (part a) y * is a symmetric NE. By Lemma 1 NE is unique, so the symmetric NE is the only NE. Now we make assumptions that guarantees that the impact of the action of the competitor on the marginal profit of a firm is smaller than the impact of the action taken by this firm. Let p * (resp. x * ) be the action in the BE (CE) when c 1 = c 2 .
Under homogeneous products, Assumption 5.4 (part b)) is a local version of the so called strong concavity assumption (Corchón [2]). Notice that, as hinted in Examples 1 and 2, the assumption dealing with price competition is, somehow, stronger than the assumption dealing with quantity competition. Assumption 5.  Conclusions. In this paper we have explored the consequences of assuming product heterogeneity by considering quantity and price competition. We proved that the three properties that characterized TT under product homogeneity hold in our framework under suitable assumptions. Our analysis has uncovered the importance of symmetry and small substitution effects for these properties to hold. Symmetry is specially important because, in our case, a small firm is not necessarily one with low productivity: It might be that the demand for this firm is small, i.e. the marketing effect is important here.
We also have found new features of TT, specially that under general demand functions the shape of Π( ) is arbitrary.
Summing up, the answer to the question what difference makes the consideration of heterogeneous products is that we expect here a richer set of interactions between firms regarding TT. In particular, we have to keep a close eye on the following possibilities.
(i) If Firm 1 faces a small demand it might be off business after TT. This resembles the Sepracor/Eli Lilly case in Section 2 where Sepracor licensed the product but it did not market it.
(ii) Even ifc 2 is high, Firm 2 may receive large quantities of TT if its demand is large relative to that of Firm 1 or the markets in which both firms operate are independent. This resembles the Lundbeck/Forest Lab case in Section 2 where the two firms involved had very different sizes. (iii) TT may be partial like in the GlaxoSmithKline/SkyePharma case recorded in Section 2. (iv) Even ifc 2 is close to c 1 , firm 2 may not receive TT at all because its demand is small or because cross price effects are large. The latter could be a potential candidate to explain why TT seldom occurred among the big companies in the market for antidepressants.
6.1. Proof of proposition 1. Let us tackle first the case of price competition. Let be such that < Ψ(c 2 )∀c 2 ∈ [c 2 ,c 2 ]. Define the candidate demand functions: For good 2, x 2 = max(0, b(c 2 − p 2 )) and for good 1, The above demand functions fulfill the desired properties: They are linear and satisfy A1. Since demands are linear in their own price and marginal costs are constant, profit functions are strictly concave on their own price. Therefore, the BE for the above demand functions is found by setting ∂πi ∂pi = 0. This yields, 2p * 2 −c 2 = c 2 ≤c 2 , min(2p * 2 −c 2 ,c 2 ) = c 2 and max(c 2 , c 2 ) = c 2 .