Exchange Rates and Foreign Direct Investment in Oligopolies

Transcription

1 Echange Rates and Foreign Direct nvestment in Oligopolies b Benan Zei Orba * and Eren İnci ** Jul 00 Abstract This paper eamines the effects of echange rates on R&D activities and international strateg choices of the oligopolies. We develop a three-stage game-theoretic model in which two firms located in two different countries (a developing and a developed one choose the mode of foreign epansion in the first stage. The decide how much to spend on R&D, and how much to sell in domestic and foreign marets, in the second and the third stages, respectivel. According to the results appreciation of developing countr s currenc ma change the decision of the developed countr firm from eport to foreign direct investment. JEL Classifications Ke Words : F3, L0, O34 : Foreign Direct nvestment, echange rates, R&D. * Corresponding author: stanbul Technical Universit, Facult of Management, Maca - stanbul, TURKEY benan@itu.edu.tr; Fa: ; Tel: (60 lines/008 and 0. ** Boston College, Department of Economics, Chesnut Hill, MA, 067, USA, inci@bc.edu.

2 . NTRODUCTON The relationship between echange rates and foreign direct investment (FD alwas stands as an important question for economists. The issue has been discussed in both theoretical and empirical literature in the area. Baldwin and Krugman (989, Caves (989, Froot and Stein (99, Goldberg and Kolstad (995 can be mentioned as the studies addressing this issue. This paper eamines the effects of echange rates on R&D activities and international strateg choices of the oligopolies. Within our nowledge, there is no stud in the literature focusing on the interaction among echange rates, R&D activities and FD. There eit quite large amount of studies dealing with the issue of R&D strateg choice of the firms especiall in oligopolistic environments. D Aspremont and Jacquemin (988 is the leading stud in that area. Kamien, et al., (99, and Petit and Tolwins (996, Kultti and Taalo (998, Salant and Shaffer (998 can be mentioned as the important studies focusing on the information transfer issues related with the R&D activities of firms. On the other hand, there are studies analzing the firms choice between eport and FD (see Motta and Norman (996 and Sanna-Randaccio (996. However, the studies lie Horstman and Marusen (99 and Either and Marusen (996 investigate the effect of R&D decision on firms epansion mode choice without endogenizing the R&D decision. A more recent stud connecting both issues and considering both R&D decision and the epansion mode decision within the same model is Petit and Randaccio (000. n their three-stage model, the showed that multinational epansion and R&D ependitures are positivel related and the firm that invests more on R&D is the firm with an eporter rival. We tae Petit and Randaccio (000 s model as a basis for this stud. The main etensions that we introduce are demand and cost asmmetries and the echange rates in our model. n the three-stage model, firms are located in two different countries. Countr is a developing countr that has lower demand for the product produced b these firms, less valuable currenc unit and a firm with a less advanced technolog. Countr is a developed countr. The firms choose the mode of foreign epansion in the first stage of the game. The decide how much to spend on R&D, and how much to sell in domestic and foreign marets, in the second and the third stages, respectivel.

3 3 According to the results, despite the asmmetries introduced to the model multinational firms invest more on R&D compared to eporter firms as in Petit and Randaccio (000. We also showed that when spill over level is low the eporter developing countr firm whose rival is a multinational firm invests less on R&D compared to the eporter developing countr firm with an eporter rival. On the other hand, the multinational developed countr firm whose rival is an eporter invests more on R&D compared to the eporter firm with an eporter rival. As stated before the main focus of this stud is on how the echange rate movements affect firms R&D and international epansion choices. We showed that the sensitivit differences of the R&D ependiture levels to echange rates becomes more pronounced with an increase in transportation cost level for both firms. According to the numerical results when there is an appreciation in the developing countr s currenc, the eporter developed countr firm ma change its strateg from eport to FD. This effect is more pronounced with low spillovers. When the developed countr firm spends more on R&D, which is less costl with an appreciation of developing countr s currenc, there will be a substantial increase in its competitive advantage. Therefore, FD will become a more profitable strateg for the this firm. However, when the spillover is high, due to the free-rider problem, developed countr firm will increase R&D ependiture less (it will even decrease R&D ependiture at sufficientl high spillover levels, thus, FD ma not be attractive in this situation. This paper is organized as follows. Section includes our theoretical model and results. Numerical results related with the effects of echange rates on epansion mode choice of the firms are presented in Section 3. Concluding remars are given in Section 4.. THE THEORETCAL MODEL We consider a model with two countries, namel a developing home countr and a developed foreign countr. There are two firms, Firm and Firm located in Countr and Countr, respectivel, producing a homogeneous product. Home countr s firm possesses relativel inefficient production technologies. Marginal cost of production of firm and in home countr s currenc unit are assumed to be as follows:

4 4 MC (, A θ ( + αe, (a MC, ea θ ( α + e. (b ( A and A are the initial marginal cost levels ( ea < A and and represent the R&D ependiture levels of the firms (in each countr s own currenc unit. e represents the echange rate and θ is an R&D efficienc parameter that shows the decline in marginal cost level as a result of an increase in R&D ependiture level. Since it is assumed that the rival firms R&D ependitures are also effective on firm i s marginal cost level, we introduce a spillover parameter [ 0,] α. The demand function of Countr j for this product is assumed to be linear; P a b ( q, j, ( j j j j j where P j is the price level in countr j in its own currenc unit q j and q are the j outputs sold in countr j b firm and firm. Similar to Petit and Randaccio (000, we assume three different mode of foreign epansion: Producing at home and eporting to the other countr (EXP, foreign direct investment which means producing in both countries (FD and no epansion which corresponds to the case where each firm sells onl in domestic maret (NFE. We allow our firms to choose among these strategies, thus, we ma face nine different situations. n this section, we will first focus on two smmetric cases where both firms choose EXP or FD and one asmmetric case where developing countr firm eports the other firm becomes a multionational (FD.. Eporting Duopol: Both firms choose to eport to the other countr s maret, therefore the profit functions of the firm firm can be respectivel written as π π ( a b ( q q + e ( a - sq γ F G ( a b ( q q + e ( a b ( q b ( q q ( A ( ea θ ( + αe θ ( α - e s q eγ ef eg (3b Here, γ / represents the cost of R&D investment (see D Asperomont.. As q ( q + e ( q (3a Since countr is a developing countr e is assumed to be greater one.

5 5 γ increases clearl the cost of R&D will increase. F j and G (j, are countr j specific fied costs. G is considered as the set up cost, however, j F j captures all firm activities such as advertising, management, distribution costs etc. For the rest of the stud, it is assumed for simplicit that b eb, s es, F ef, G < eg and a < ea. The equalities mean that the slopes of demand functions, unit transportation costs and firms activit specific fied costs are equal in terms of the currenc unit of Countr in two countries. G < eg means that the set up cost is cheaper in the developing countr. This assumption based on the observation that the land and the building cost is lower in developing countries. B the assumption a < ea, we sa that the demand for this product in developed countr is higher. Firms in our model pla a three-stage game. n the first stage the choose the epansion mode, in the second stage the decide how much to spend on R&D and finall, in the third stage, the determine how much to sell in domestic and foreign marets. Since in this section, we are considering the case where both firms choose to eport, we can compute the last stage Cournot equilibrium output levels as follows: q q q q a e( a a e( a A + A + A e( A A ( α θ + (α θ ( α θ + e( A 3eb ( α θ 3eb + s + (α θ 3eb + (α θ 3eb + s + (α θ ( es e( α θ + es, + A,, + A. (4 Substituting above equilibrium output levels into the profit functions given in (3a and (3b and maimizing the profit functions with respect to R&D ependiture levels, we obtain the following reaction functions. ( α θ ( a 4A + e( a + A s + (α θ (5a 9eγb 4( α θ ( α θ ( a + ea + A 4A + es + (α θ (5b 9eγb 4e( α θ Solving these reaction functions simultaneousl we get the Nash equilibrium R&D levels as follows;

6 6 m6γb ( ea A m(( a m 4θ ( A eαa + + e( a s (m( α θ 3γb (6a me6γb ( A e m 4θ ( αa e ea ea m(( a + e( a s (m( α θ 3eγb e (6b where m ( α θ and 4 7eγ b 6( α ( α θ γb (4( + e( α θ. > 0 due to the stabilit condition. t must be noted here that the sensitivit analsis of these R&D ependiture level w.r.t. echange rate is quite inconclusive. n other words, an increase in echange rate can either increase or decrease the R&D levels, but the conditions for the sign change of the derivatives of and w.r.t. e are quite complicated for a clear analsis. n the proceeding sections, we will at least compare the sensitivit levels with each other under different foreign epansion modes.. Multi-National Duopol: n this case, both firms choose to invest in the foreign countr. Thus, the profit functions of the firms become π π FF FF ( a b ( q γ F ( a b ( q eγ G ef q q eg + e ( a + e ( a b ( q b ( q q q ( A ( ea θ ( θ ( α + αe (7a + e Solving the game bacwards as described before, we obtain the Cournot output levels. Substituting these levels into the profit function and maimizing w.r.t. R&D levels we get the following Nash equilibrium R&D levels for firm and respectivel: (7b ( q ( q FF FF mes ( ( α mθ 3γb (8a ms ( ( α mθ 3γeb (8b Cournot equilibrium output levels are not given because the are ver similar to the output levels for EXP-EXP. The onl difference is the transportation cost. s 0 for FD-FD.

7 7 Proposition : Multinational firms alwas invest more on R&D compared to eporter firms. Proof: We now that > 0, m ( α θ > 0 and e >. From (6a and (6b FF FF 3γb > ( α mθ ڤ. for > 0 and > 0, therefore, > and > As it can easil be seen from (8a and (8b the differences between R&D levels under these epansion modes increase with transportation cost. t is important to note here that when we introduce demand and cost asmmetries to the model, Petit and Randaccio (000 s result, regarding the R&D ependiture levels under different epansion modes, does not change. FD still motivates R&D. Now, we will loo at how the sensitivities of R&D levels w.r.t. echange rates change with the mode of epansion. The differences between the derivatives of FF j and j ( for j, w.r.t. e can be computed as follows: FF 3 3 8( α θ ( 8m( α ( + α θ 9γb (4( α θ + γb 3 s (9a FF 4( α ( α γbθ ( m( α θ 3γb s 3 (9b As it can easil be seen from (9a and (9b the differences between R&D investment levels sensitivities to echange rates under different epansion modes are directl related to the transportation cost level. The direction of this relationship can be determined b the relative values of efficienc cost parameter of R&D and spillover level. Proposition : The sensitivit differences of the R&D ependiture levels to echange rate under different epansion modes intensif with the transportation cost level for both firms. Proof: Proof is obvious.

8 8 This result is ver intuitive. When both firms are eporting rather than being multinational enterprises, the effect of a change in echange rate on R&D ependiture level obviousl differs through the transportation cost. When transportation cost is zero, there will be no difference between R&D level sensitivities to echange rate under different epansion mode. Additionall, it is possible to sa that the directions of the relationship between these sensitivities depend on R&D cost-efficienc parameters and spillover levels..3 Mied Duopol: Here, we will loo at the situation where onl the firm in Countr chooses to be a multinational firm. Then, we will compare the differences between R&D levels and R&D echange rate sensitivit levels for the case where both firms are eporting. For this asmmetric situation the profit function is as given in (3a for firm and as given in (7b for firm. Solving the game as we did before, we obtain the following R&D equilibrium levels. ems ( mαθ 3γb + (0a ms ( mθ 3eγb (0b Proposition 3: For low spillover levels ( α </ ; i The eporter developing countr firm whose rival is a multinational firm ii invests less on R&D compared to the eporter developing countr firm with an eporter rival. The multinational developed countr firm whose rival is an eporter invests more on R&D compared to the eporter firm with an eporter rival. Proof: We now from (6a that 3γb > ( α mθ. From (0a < if 3γb > mαθ. Obviousl, if ( αmθ > mαθ, which holds when α </. 3γb > mαθ will alwas hold. t is also nown from (6b that 3γeb > ( α mθ. From (0b > if 3 γeb > mθ. Similarl, if ( αm θ > mθ, which again holds when α </,. 3 γeb > mθ will alwas hold. Thus, if α </, ڤ. > < and

9 9 As in Petit and Randaccio (000, if α /, then > and < if and onl if 3γb < mαθ and 3 γeb < mθ, respectivel. When we loo at the sensitivit differences of R&D functions w.r.t. echange rate for the international eporting and mied duopol we obtain the following functions; 3 3 8( α θ (mαθ 3γb (4( α θ 3γb s (a 4( α ( α γbθ (mαθ 3γb s 3 (b Similar with our previous finding, the sensitivit differences become more pronounced for higher transportation cost levels. Proposition 4: : For high spillover levels ( α / ; i The eporter developing countr firm s (whose rival is a multinational firm R&D ependiture level increase more (or decreases less as a result of an increase in echange rate compared to the eporter developing countr firm with an eporter rival, if its R&D investment level is lower than the latter firm ( mαθ > 3γb, ii The multinational developed countr firm s (whose rival is an eporter R&D ependiture level increase more (or decreases less as a result of an increase in echange rate compared to the eporter firm with an eporter rival, if mαθ > 3γb. Proof: Since m αθ > (4( α θ for α /, ( α θ 3γb < 0 when 4 mαθ 3γb < 0, thus, < 0. t can easil be seen from (b that when ڤ. < 0, 0 > 3γb α / and mαθ As we see from the above proposition, when the eporter developing countr firm with the multinational rival has a lower R&D level (compared to the case where its rival is also eporter it responds more pronouncedl to a devaluation in its own

10 0 countr s currenc. This result can be eplained b the relative cost decrease in R&D. When the rival is a multinational firm the competition in the domestic maret is more severe, thus domestic firm whose R&D investment level is low start to spend more on R&D due to cost advantage created b the devaluation. On the other hand, the multinational developed countr firm with the eporter rival responds more intensivel (compared to the case where it is also an eporter to the devaluation of the other countr s currenc for not to loose its eisting competitive advantage. 3. THE FECTS OF EXCHANGE RATES ON FRMS STRATEGES n this section we will analze how firms choose their epansion mode and how the R&D activit parameters and echange rates affect these choices. As we stated before, in our game, each firm has three strategies: eporting, FD or no foreign epansion. n order compute the Nash equilibrium of this epansion mode game we need to compare the profit levels of each firm under each of these epansion modes. Unfortunatel, algebraic comparisons is quite complicated, therefore we are not able to present the analtical solution of this game. However, the numerical results given in the following tables will help us to understand the nature of the equilibrium and the effects of the important parameters on equilibrium. We computed the game matries given in Table, Table and Table 3 for the values of the parameters: a 50, a 55, b, A 8, A 4, s.9, γ, θ0.3, G 0, G, F 0, α {0.0, 0.5, 0.9}, e {.,.5,.9}. Tables are computed at different values of the echange rates and spillover parameter because these are the important parameters affecting the equilibrium. As it is seen from Table when e.9, without depending on the value of α, both firms choose to eport at the equilibrium. Petit and Randaccio (000 showed that when there is a reduction in set up cost levels, equilibrium moves from Eport- Eport to FD-FD. Here, we will focus on the effects of echange rate on the equilibrium. α0.0 Firm Firm Firm Firm EXP FD NFE EXP 40.0* 85.5* FD

11 α0.5 Firm α0.9 Firm NFE EXP 58.* 86.8* FD NFE EXP 65.* 86.0* FD NFE Table. The case for e.9 (* represents Nash equilibrium. We observe from Table that when e. 5 and low α is low then the equilibrium moves to Eport-FD. The reduction in e corresponds to an appreciation of the developing countr s currenc. As a result of this appreciation there will be a decrease in transportation cost and a relative increase in the set up cost in developing countr. At first, one thins that the equilibrium should move from FD-FD to Eport-Eport as a result of such appreciation. However, we now that the original equilibrium is Eport-Eport. We also now from Proposition 3 that when α is low (or α is high and 3 γeb < mθ the multinational developed countr firm whose rival is an eporter invests more on R&D compared to the eporter firm with an eporter rival. Due to the appreciation, R&D becomes relativel less costl for this firm and therefore, it spends more on R&D. As a result of this, its competitive advantage substantiall increases. This effect dominates the other negative effects and therefore, it becomes more profitable for this firm to choose FD strateg. As a result equilibrium turns out to be Eport-FD. n fact, at our numerical values of the parameters 3 γeb < mθ never hold thus, > is valid for all games. But, we can easil obtain from (0a and (0b that the differences between and decrease as α increases. Therefore, it is possible to sa that when echange rate is not sufficientl low, the advantage of R&D increase is not sufficient to change the equilibrium from Eport-Eport to Eport -FD at high α levels. α0.0 Firm Firm Firm Firm EXP FD NFE EXP * 67.* FD NFE

12 α0.5 Firm α0.9 Firm EXP 05.* 70.* FD NFE EXP.* 70.* FD NFE Table. The case for e.5 (* represents Nash equilibrium. When echange rate decreases more, as we observe from Table 3, the equilibrium will alwas move to Eport-FD even at high α levels. This happens due to the relativel less costl R&D ependiture increase which brings a substantial production cost advantage to the developed countr firm. α0.0 Firm α0.5 Firm α0.9 Firm Firm Firm Firm EXP FD NFE EXP * 68.5* FD NFE EXP * 74.5* FD NFE EXP * 75.6* FD NFE Table 3. The case for e. (* represents Nash equilibrium.

13 3 4. CONCLUSON This paper investigated how the echange rates affect R&D activities and international strateg choices of the firms in oligopolies. n our three-stage game, two firms located in two different countries (a developing and a developed one choose the mode of foreign epansion in the first stage, how much to spend on R&D in the second stage, and how much to sell in domestic and foreign marets in the third stage. Results showed that appreciation of the developing countr s currenc could cause the eporter developed countr firm to change its strateg to FD. This effect is stronger when the spillover parameter is low. The reason of this strateg choice is the possibilit of spending more on R&D at a less cost (because e is lower and therefore increasing the competitive advantage. When the spillover is high, due to the free-rider problem, developed countr firm will increase R&D ependiture less (it will even decrease R&D ependiture at sufficientl high α levels, thus, FD ma not be attractive in this situation. Usuall, it is believed that developing countries becomes more attractive for FD as a result of a depreciation of the domestic currenc. However, this paper showed us that situation might be reverse when we endogenize R&D. Because, FD also motivates R&D and the competitive advantage obtained from higher R&D level can mae FD a better choice under appreciation instead of depreciation. t is of course clear that due to the restricting assumptions of our model and compleit of calculations these findings are not ver general. But, at least, the show us there are situations that we can observe such results. RERENCES Baldwin, R., Krugman, P., 989, Persistent trade Effects of large echange rate shocs Quarterl Journal of Economics, 04, Caves, R., 989, Echange rate movements and foreign direct investment in the United State, in Audretsch and Claudon, eds., The nternationalization of United States Marets, New Yor Universit Press. D Aspremont, C., and Jacquemin A., 988, Cooperative and noncooperative R&D in duopol with spillovers, American Economic Review, 78, Either, W.J., Marusen J.R., 996, Multionational firms, technolog diffisuion and trade Journal of nternational Economics, 4, -8.

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