INFRASTRUCTURAL DEVELOPMENT , SPILL ... - Semantic Scholar

INTERN ATIONAL ECONOMIC JOURN AL Volume 8, Number 4, Winter 1994

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INFRASTR UCTURAL DEVELOPMENT , SPILL-OVER EFFECTS AND THE STRATEGIC ADOPTION OF NEW TECHNOLOGIES IN THE LDCs PINAKI BOSE State University of New York at Cortland DIPANKAR PURKAYASTHA California State University, Fullerton

Firms in the LDCs need to adopt and indigenize transferred technology before usage. The adoption costs depend on the state of the infra s t ru c t u re and on the l o c a l i zed spillover effects ge n e rated by a rival fi rm. In this context, the pap e r examines the timing of such technological adoption. It shows that strategic decisions regarding time may result in a “waiting game” where, in equilibrium, the efficient firm prefers to adopt after its less efficient rival, thus delaying the speed of technology transfer. The paper also shows that under certain conditions, technology transfer may not take place within the planning horizon. [01, L1, F1]

1. INTRODUCTION An overwhelming majority of industrial innovations occur first in the developed countries. Not all of these innovations are adopted or imitated in the less developed world. For example, the basic technology of computer-aided word processing is well k n own in the LDCs, but there has been a boom in the market for lightwe i g h t typewriters in many developing countries. 1 While researchers ha ve paid attention to strategic innovations and imitations in the developed countries (North), considerably less attention has been paid on the mechanism through which firms located in an underdeveloped country (South) actually adopt and indigenize an already developed technology. Based on product cycle models, existing neoclassical literature assumes that the Southern firms cater to internationally homogeneous consumers with identical tastes and constant elasticity of commodity substitution (Krugman, 1979; Dollar, 1986; Grossman and Helpman, 1991). The Southern firms buy or imitate the innovations made in the North and produce the same products later with lower wages. The North must continuously innovate to keep the Northern wages high. Many other authors such as Atkinson and Stiglitz (1969), Nelson and Winter (1982), Dosi (1988) and Lall 1 In an interview with Business World magazine, Godrej & Boyce Vice president claimed that India was going through a boom period in the typewriter market. The typewriter is still very popular because it does not require an expensive printer and printer papers, it is cheap and it works even if there is a power cut. See Business World, January 15, 1992.

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P. BOSE AND D. PURKAYASTHA

(1992), however, have a different view of the process. They argue that technology cannot be readily bought and adopted because, inevitably, there is a “tacit” and “evolutionary” element to any innovation.2 There are many reasons why a newly developed technology may not be readily bought or transferred to a less developed country. The traditional development economist’s belief about the catalytic role of a critical minimum level of social overhead capital is well known (Nurkse, 1953; Hirschman, 1958). A minimum scale m ay be necessary to ap p ly new tech n o l ogies, or a “demand-pull” rather than a “technology-push” (Gamser, 1988) model may be more appropriate. Technology transfer is shown to cause dualistic development if the infrastructure is not adequate to set in motion the scale-economy benefits of new technology. Most importantly, inputs for a new technology may turn out to be relatively costly for a firm producing an unknown new product for the first time. New inputs may not be available locally and may have to be imported at a high cost. The market size is also limited because the consumers may not be ready to accept the new product. Variables such as literacy rate, number of scientists and engineers, capital goods as percent of total manufacturing, power generation, etc. may also determine whether the new technology is transferable. The appropriateness of the technology thus depends on the relevant demand and supply bottlenecks and the intrasectoral capacity to absorb the new p rocess and the product. The fi rms in LDCs thus do not necessari ly adopt all innovations. The Northern technology, in effect, must be “reinvented” to make it work in a different and less conducive environment (James, 1988). Many processes and products that have long become “standard” in the developed countries, are yet to be introduced in the poorer economies. For example, most carbonated beverages are still sold in glass bottles (not in aluminum cans) in the streets of Calcutta, Lahore and Akra; automatic transmission cars are not manufactured in South Asian countries and compact discs are not produced in Dhaka, N a i robi or Mogadishu. The fi rms in the LDCs sometimes tend to wait for a considerable time before they adopt a new technology for the domestic market. Northern innovations, then, affect the LDCs only indirectly: a complex interplay of what Lall (1992) has called National Technological Capabilities (NTC) and FirmLevel Technological Capabilities (FTC) determine the timing and appropriateness of Southern adoptions of Northern innovations. While the traditional approach generally recognized national capabilities, as defined by the broader aspect of physical and human capital accumulation at a macroeconomic level, the role of sectoral capability has been emphasized by the structuralists. The structuralist approach views the Existing neoclassical models also erroneously assume that once a high quality product is available in the market, producers of low quality products face zero sales and everyone in the South consumes the product of the highest quality. This assumption also can be disputed from casual observation. A large proportion of Southern consumer and intermediate goods are of relatively low quality. One can use a Lancasterian framework to describe the Southern demand for low-quality goods. 2

ADOPTION OF NEW TECHNOLOGIES

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process of innovation and adoption as a consequence of sector-specific skill-formation and market size at a microeconomic level which depends on the critical mass of engineers, physicists, network of laboratories, intertemporal skill-fo rm ation and consequent scale economies in the production of inputs for the new product.3 We recognize in this paper that these two approaches are not contradictory and assume with Ranis (1973) that the development of social overhead capital is a necessary condition for the sector and skill-specific investments to occur. We assume that the Southern firms have full knowledge of the processes available from the Northern “technology shelf” (Ranis, 1973) for adoption, but initially the country lacks the macroeconomic infrastructure to reduce the Ranis-type X-inefficiency associated with a new technology. The first mover must produce the new product with costly inputs within a relatively underdeveloped macroeconomic infrastructure. But the fir m that decides to enter late, not only enjoys a better macroeconomic infrastructure, it also enjoys ch e aper inputs and the spill-over effects of the micro e c o n o m i c i n f ra s t ru c t u re created by the first mover4 and learns from the first mover’s past mistakes. The history of product development in the LDCs is replete with examples that confirm the process described above. Based on high yielding variety seeds originally developed for Iowa farmers, Philippines has developed a particular variety of rice suitable for Asian agriculture. Vietnam has modified the conventional diesel enginepumps to produce low-lift pumps wh i ch are more efficient for rice cultivat i o n (Gamser, 1988). The Vietnamese innovation would not have been possible if local commercial engines and the impeller shafts were not available or if adequate training was not given to the local producers. An LDC-firm that considers a technological adoption has to consider at least three types of costs. First, it must incur variable costs such as wages and raw materials; s e c o n d, it has to take into account the indirect costs of lack of an ap p ro p ri at e macroeconomic infrastructure required to sustain the new product; third, the firm must consider the “first mover” costs of a leader who must pay a premium to obtain the specialized inputs required to produce the new product.5 The Southern adoptionimitation game is similar to the innovation-imitation games in the North with two important differences: (1) timing of Southern adoption depends on the state of the See Halperin and Teubal (1991) and Justman and Teubal (1991) for a survey. Th e traditional approach is primarily based on models with one consumption good sector. This set up precludes the possibility of differential impact of infra s t ru c t u re on “high” and “low” technology products. Empirical tests of significance of the role of sectoral infrastructure have been performed by Antle (1983) and Adams (1984). 4 These are the auxiliary services such as training schools, repair shops, public awareness of the new product etc. that devlop when at least one firm adopts a new technology and produces a higher quality product. 5 Conrad and Duchatelet (1987) construct a game between an incumbent and entrant where the first mover must bear non-firm specific development costs. These costs are typically incurred for advertising and marketing to make the new product known to the consumers. 3

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infrastructure, which, we assume, becomes better with time. (2) Once a firm adopts a new technology, it generates a localized spill-over effect. Scale economies set in when more than one firm demands the specialized inputs. Both firms benefit from the auxiliary services that develop endogenously.6 No attempt has been made in the literature to model this process. Our model attempts to fill this gap and shows that in a Southern duopoly game of adoption and imitation, there is always a disincentive to adopt too early and that the most efficient firm does not necessarily adopt first. It is also possible that both firms may decide on a “fence sitting” strategy and may not adopt at all during a given period of time. Conditions under which a collusion is optimal is discussed. It is also shown that an interventionist policy may have beneficial results. The model, presented in the next section is similar to Reinganum (1981) to the extent that it analyzes strategic choice of time regarding technology adoption, and that the reaction functions are discontinuous.7 However, we focus on the heterogeneity b e t ween the two fi rms with respect to adoption costs, and also incorp o rate the spillover effects. Not surprisingly, this results in important differences in the shape of the reaction functions which crucially affect the issues addressed in this paper. 2. THE MODEL Assume that in an LDC characterized by barriers to entry in the domestic market, there are only two firms (firm 1 and firm 2) that produce and sell their outputs over the continuous time interval [0, T]. Each firm can adopt and indigenize a new process (and consequently improve the product quality) at any point during this interval. The cost of initial indigenization depends negatively on the society’s macroeconomic infrastructure and the indirect microeconomic costs of sectoral X-inefficiency. The cost function, for the firm that adopts first, is assumed to have the explicit form: Cib = µ[α i (T −Φtib ) + σ i (τ−tib )]2

(1)

Cib is the total indigenization costs of firm i; tib is the time of adoption of firm i; µ, αi and σi are parameters; T is the planning horizon; Φi is a parameter that depicts the state of infrastructure. The subscript “ib” signifies that the i-th firm adopts before its rival. The rival’s time of adoption is denoted by τ (τ > tib). The cost of indigenization goes down when the rival enters the market and generates input scale economies. 6 Consequently a firm’s cost function has two additively separable elements that reflect the infrastructure: one that shows the development of the macroeconomic social overhead capital and the other that shows the development of sector specific capital that develops when at least one firm adopts the new technology. 7 A game of technological race with the possibility of preemption is analyzed by Fudenberg and Tirole (1985).


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Entry of the rival also improves the X-efficiencies and firm level technological c ap abilities (FTC) discussed earlier.8 Note that T, tib and τ are all measured in calendar time. Fixed costs go down as soon as the rival enters the market. Thus the parameter σi is a measure of negative spill-over effects. Higher σi signifies a more costly venture for the first mover. If the rival firm has already indigenized the technology, the cost of indigenization is lower for the entrant. After adoption by the first mover, sector-specific microeconomic infrastructure starts developing in the market, and it becomes easier to imitate the indigenized technology. Firm i can thus benefit from such positive externalities if i adopts after j does. The cost function then becomes: Cia = µ[α i (T −Φtia ) − β i (tia −τ )]2

(2)

which is less than the cost of the first mover. Cia is the total indigenization costs of firm i; tia is the time of adoption of firm i. The subscript “ia” signifies that the i-th firm adopts after its rival. The rival’s time of adoption is again denoted by τ. If the rival adopts at time τ < tia, the i-th firm can imitate this process. With improved sectoral infrastructure, it becomes easier to imitate as time goes by. The parameter βi captures two effects: first, it represents the fact that the input costs fall for the second mover; and second, it also captures the fact that it is easier for the second mover to follow the indigenizing process by simply imitating the leader. The parameter βi is thus a measure of beneficial spill-over effects accruing to the imitating firm i. Higher βi signifies higher spill-over effects. We simplify the revenue side of the problem by assuming a generic duopoly situation in a game of technological race. Let Xi be a scalar measure of the level of adoption by the i-th firm, with higher Xi resulting in higher revenue, as Xj remains constant. Thus Ri(t) = R(Xi, Xj) measures the revenue, net of usual variable costs and R&D costs (but gross of the infrastructure-dependent costs Ci), of the i-th firm. For simplicity of exposition assume further that Xi can take either of two values - the original level L (corresponding to low quality product) or level H (corresponding to high quality product) reached after adoption. In other words, there is only one particular adoption available for the firms. Before the i-th firm adopts, its state of the art is described by Xi = L; and after adoption, by Xi = H. Denoting Rpq= R(p, q); p = L, H; q = L, H; where Rpq signifies r evenue of the i-th firm when the firm in question sells the good with quality p, while its rival sells the good with quality q. We also assume that RHL > RHH > RLL > RLH , and that RHL − RLL > RHH − RLH

(A1)

We assume that Cib (or Cia) is phased out over the entire planning horizon and this cost is known with perfect foresight at the time of choosing tib (or tia). 8

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The fi rst part of the assumption fo l l ows from ge n e ral duopoly models with differentiated product qualities. The second part of the assumption is not unduly restrictive. It can be regarded as a consequence of a more familiar assumption that the cross partial derivative of R(Xi, Xj) is negative. We assume that the two firms decide on the timing of adoption simultaneously at t = 0, and with perfect foresight commit to the sunk cost (including indigenizing R&D costs) phased out over the entire planning horizon that is necessary for such adoptions. These decisions, once taken, are irreversible. The firms have a zero time discount rate and the effect of adoption on the earnings of the firms is instantaneous. Timing of Adoption The first step for a firm is to choose its best response (to adopt or not to adopt) as a function of the time of adoption of its rival. If the first firm decides to adopt no later than its rival at time t1b, its profit earned over the interval [0, T] is given by (using (1)): π 1b = RLL t1b + RHL (τ − t1b ) + RHH (T − τ) − C1b

(3)

where π1b is the profit of firm 1 in the interval [0, T], t1b ∈ [0, τ), and τ ∈ (t1b, T]. From the first order conditions of a maximum, we get t1b = min{τ,(α 1T + σ1 τ)/(α 1Φ + σ 1) − ( RHL − RLL )/2µ(α 1Φ + σ 1) 2}

(4)

If the first firm decides to adopt after its rival at time t1a, its profit earned over the interval [0, T] is given by (using (2)): π 1a = RLL τ + RLH (t1a − τ) + RHH (T − t1a ) − C1a

(5)

From the first order condition for a maximum we get t1a = max{ τ,(α 1T + β 1τ)/(α1 Φ + β1 ) − (RHH − RLH )/2µ(α 1Φ + β 1 )2}

(6)

Assuming that these are both interior solutions to the above first order conditions, the profit functions become: π 1b = (RHL − RHH )τ + (RLL − RHL )t1b + RHH T − (RHL − RLL )2 /[4µ(α 1Φ + σ 1) 2 ] π 1a = (RLL − RLH )τ + (RLH − RHH )t1a + RHH T − ( RHH − RLH ) 2 /[4µ(α 1Φ + β 1 )2 ] Firm 1 will adopt before its rival if π1b > π1a. Similarly, firm 2 will adopt before its


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rival if π2b > π2a. Indexing T, µ and Φ to unity9 and using (A1) it can be shown that π 1b > π 1a if τ > 1 −(RHL − RLL )/4α 1(α1 + σ1) − (RHH − RLH )/4α1 (α 1 + β1 ) ≡ t1*

(7)

We can now proceed to outline the reaction function of the first firm. The reaction function of the first firm, Q1(τ), is a discontinuous one, and can be specified as Q1(τ) = t1a if τ ∈ [0, t1*)

(8)

= t1b if τ ∈ (t1* , T] and t1a and t1b are in the interior. Similarly for the second firm , we can derive t2b = min{τ,(α 2 T + σ 2 τ)/(α 2 Φ + σ 2 ) − ( RHL − RLL )/2µ(α 2 Φ + σ 2 ) 2}

(9)

t2a = max{ τ,(α 2 T + β 2 τ)/(α 2 Φ + β 2 ) − (RHH − RLH )/2µ(α 2Φ + β 2 )2}

(10)

and π 2b > π 2 a if τ > 1 − (RHL − RLL )/4α 2(α 2 + σ2 ) − (RHH − RLH )/4α 2 (α 2 + β 2 ) ≡ t2*

(11)

The reaction function is again discontinuous. The reaction function for the second firm can be specified as Q2 (τ) = t2a if τ ∈ [0, t*2 ] = t2b i f τ ∈ [t*2 , T]

(12)

and t2a and t2b are in the interior. Rest of this section explores the various possibilities of the equilibria given by the reaction function Qi(τ). Non-Unique Equilibr ia One possible graph of the reaction functions is represented in figure 1 which assumes that both firms are identical such that α1 = α2 ≡ α; β1 = β2 ≡ β; and σ1 = σ2 ≡ σ. In figure 1 the solid line ABCD is firm 2’s reaction to firm 1’s time of adoption and the solid line EFGH is firm 1’s reaction to firm 2’s time of adoption. Figure 1 This assumption is maintained throughout the rest of the paper.

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shows the possibility of two Nash equilibria: M and N. It can be shown, however, that existence of either one of these equilibria is not assured.

Proposition 1. Even if both firms are identical, an equilibrium to the adoption game may not exist. Consequently, technological transfer may never take place within a given time period. Proof: With identical firms, t1* =t2* =t *. Let tai be the time of adoption of the i-th firm (which moves after its rival) for which the best response of the j-th firm is to adopt first at t jb =t *, i.e., tai satisfies (t jb |τ =tai )= t* . Then, from figure 2, it is apparent that neither of the two equilibria (at M or N) exists if (tai |τ = t* )>tai for i = 1 and 2. For α = 1, β = 1 and σ1 = σ2 = 3, RHL – RLL –RLH = 4 and RHH - RLH = 1, this condition is satisfied, which demonstrates the possibility of non-existence of equilibrium in our model. Proposition 1 represents a game of “chicken” where neither firm adopts. This may be the reason why many LDC firms show little enthusiasm to adopt a new technology. We now provide a sufficient condition for existence of equilibrium. Proposition 2. With identical firms, technological transfer will take place if either one of the spill-over effects does not exist, i.e, if either σ = 0 or β = 0.


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Proof: This is heuristically proved by setting either σ or β, or both equal to zero. The result is shown in figure 1 where σ is set to zero. The line ABCD * (with a broken segment CD*) is now firm 2’s reaction to firm 1’s time of adoption and the line E*FGH (with a broken segment E*F) is firm 1’s reaction to firm 2’s time of adoption. Equilibrium is assured as long as t1* = t2* < T.

Unique “Inef ficient” Equilibr ium So far we have assumed that both firm are identical. This, of course, need not be the case. If α1 < α2, firm 1 is more efficient as an adopter. To avoid messy algebra, assume that σ1 = σ2 = 0. Assume (4) and (9) are such that we get t1b < t2b, which is the case in figure 3. It is possible, therefore, that the two firms can get “locked in” an inefficient equilibrium (represented by N) where the inefficient, high cost firm adopts first, followed by the efficient firm. We inve s t i gate the possibility of existence of this inefficient outcome. Th e equilibrium at N exists if ( t2b |τ = t1a )≤t1*

(13a)

and ( t1a |τ = t2b )≥t2*

(13b)

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According to condition (13a), if firm 2 chooses to adopt first, firm 1, from reaction function (8), will be a follower. (13b) ensures that t1a = Q1(t2b) is high enough to make it optimal for firm 2 to adopt first. When these two conditions are jointly satisfied, t1a a re t 2b a re the best-replies of the two fi rms to each other, and the ineffi c i e n t equilibrium (i.e., N) exists. In addition, this equilibrium is unique if ( t2a |τ = t1b )≤t1*

(13c)

which is a sufficient condition for ensuring that the efficient equilibrium, represented by M in figure 1, is non-existent. Note that since t2b < t2a, (13c) is a stronger condition than (13a), and implies the latter. Using (7) and (10), condition (13c) can be rewritten as ( RHL − RLL )(y2 / α1 x 2 )≤(RHH − RLH )(2 α 1x 1 − x 22 )/ x1 x 22 and from (6), (11) and (13b) we

(14)

get

( RHL − RLL )(y1 / α 2 x1 )≥(RHH − RLH )(2 α 2 x 2 − x 12 )/ x 2 x12

(15)


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where x 1 ≡ α1 +β 1; x2 ≡α 2 + β 2 ;y1 ≡α 1 − β1 ;y2 ≡ α 2 − β 2. If both (14) and (15) are satisfied, the inefficient equilibrium exists and is unique. These two nonlinear constraints do hold over a certain range. For example, α1 = 2.5, α2 = 2.6, β1 = 1, β2 = 6, Φ = 1.1, R HL – RLL =2, RHH – RLH = 1 satisfy both the constraints. The arguments above thus lead to the following: Proposition 3. For appropriate values of the parameters, the Nash equilibrium outcome can be one where the efficient adopter adopts later and follows the less efficient adopter. The above numerical examples also indicate the intuition behind the inefficient outcome. If β2 > β1, the inefficient adopter is the more efficient imitator. In this case, if firm 1 adopts first, firm 2 is likely to follow soon afterwards, thus reducing the former’s rent during the period (t2a – t1b). Since adopting first involves higher cost, firm 1 may then prefer being an imitator since the relative gain from imitation may be high enough to result in the inefficient equilibrium. In any case, the strategic decision to adopt modern technology manifests in a “waiting game” where the efficient fir m finds it profitable to “out-wait” its less efficient rival. The process of technology transfer and upgrading is delayed as a result. Collusion and ec Thnological Transfer We can derive the conditions under which a collusion would facilitate a faster transfer of technology. If both firms collude and work as a monopoly, cost function will be different from the aggregate cost function of these duopolists. Since there is no spill-over effect, we can write the cost function of the monopolist as C m = θ(T − tm ) 2

(16)

where Cm is the indigenizing cost of the monopolist, tm is the monopolist’s time of adoption and θ the relevant parameter. This yields the optimal time of adoption as tm =T −(RH − RL ) / 2θ

(17)

where RH and RL are revenues net of wage and raw material costs of the monopolist for high quality and low quality products respectively. A monopoly definitely leads to a faster transfer of resources if tm