2. Theoretical Model
2.3 R&D Activities
In order to bring R&D into our discussion, we consider a labor biased production function and rewrite it as
xi= Kiη(θLi)1−η,
where θ is the efficiency index of the final-good producer. Suppose that the final-good producer hires its local labor, and we could rewrite its optimal amount of labor and sales revenue as: On the other hand, there exists a lot of foreign suppliers with different θ1m(θ1m is the efficiency index of the foreign supplier m). To simplify our discussion, we assume that the information of efficiency index is prevalent, and there is no cost to search a suitable foreign supplier. If outsourcing takes place, the final-good producer will screen out its partner with the greatest θ1m, and the foreign supplier hires its local labor to maximize its profit. To simplify notation, we drop out subscript m. We have the optimal amount of labor and sales revenue from first order condition:
Lbi =
In order to capture the efficiency gap between two different countries, we assume that the labor hired by the final-good producer are more skilled than that hired by the foreign supplier (θ > θ1). Again, the final-good producer has to make a decision whether to adopt outsourcing policy. Outsourcing takes place if and only if
D ≥ w1
w θ θ1
. (2.18)
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Note that efficiency gap between two countries will determine the final-good producer’s outsourcing policy. From equation (2.18), we can obtain an intuitive result that out-sourcing will take place if wage rate between two countries is huge but efficiency gap is moderate. Hence, the foreign supplier will not be chosen if it could not upgrade its efficiency to a higher level.
Suppose that there exists a technology, which could improve the efficiency of the foreign supplier immediately (¯θ1 > θ1), and it must cost the foreign supplier a R&D expenditure to acquire such technology. We assume that this expense is equal to F units of labor. For the foreign supplier which has built a relationship with the final-good producer, it would not engage in such R&D to increase its net profit unless the following inequality holds
R¯i−w1L¯i−
Rbi−w1Lbi
≥w1F,
where Rbi and Lbi are sales revenue and labor input when upgrading does not occur, and R¯i and ¯Liare the same as equation (2.16) and (2.17) except that θ1 is replaced by ¯θ1. We simplify previous inequality and yield the following one
F1 ≥w1F , F1 = (1 − Φ) ¯Ri
where F1 is the upper limit of R&D cost for more efficient technology to be adopted.
This equation suggests that if the efficiency improvement ratio (¯θ1/θ1 > 1) is significant, the foreign supplier would engage in R&D to enhance the contribution of each labor, and hence it would make a greater sales revenue and net profit.
In order to explore the relationship between R&D and capital intensity, we take the partial derivative of natural logarithm of F1 with respect to η, and we could yield equation (2.20).
Note that (¯θ1/θ1> 1), and E is a positive constant. E measures the decreasing contribu-tion of labor efficiency when capital share increase. If capital share increases significantly,
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labor input would be less important in production process; therefore, the foreign supplier would not apply R&D to improve the contribution of labor input. The right hand side of equation (2.20) is positive if K/L is large enough. The capital intensity is the function of capital share and capital, so we can find out a positive correlation as follow.
∂ ln
The right hand side of above equation may be negative if K/L is small enough. To avoid this problem, we assume that there exists a lower limit of capital which ensures the capital intensity is greater than one. Above two equations imply that an increase in capital or capital share will lead to an increase in capital intensity, and a higher capital intensity will lead to a positive relation between capital share and R&D in equation (2.20). We can find out that the foreign supplier can bear a higher R&D cost in a higher capital intensity industry than a lower one if its capital intensity is high enough.
Proposition 1. For the foreign supplier, there exists a threshold E, and if its logarithm of capital intensity is larger than E, the supplier would engage in more R&D in a higher capital intensity industry.
This result is similar to what we showed in equation (2.12). The foreign supplier which bears less labor cost and shares the contribution of capital in a higher capital share industry can make a greater profit. Given the same efficiency improvement, the foreign supplier in a higher capital share industry is willing to spend more to increase its labor efficiency and the sales revenue. After R&D is done, not only the foreign supplier is better off but also the final-good producer. The final-good producer receives more output and sales revenue derived from the efficiency improvement. As a result, if the foreign supplier actively engages in R&D, the relationship between two parties would be closer.
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Now let’s assume that there is another growing economy (country C) joining the competition of outsourcing, and these new foreign suppliers from such growing economy possess abound and cheaper labor pool. Because the final-good producer has two kinds of partners to choose, there is now a possibility for the final-good producer to change its outsourcing partner. Let’s follow the previous setting, if the new firm has the opportunity to participate production, it would hire optimal labor amount to maximize its profit. We obtain the optimal labor and sales revenue as following,
Lei = assume θ2 < θ1. It can be explained by the possibility that labors from the growing economy are less educated or that the infrastructure is not adequate, so the labor is less productive. Note that δ is the same in both countries. In a real world, δ is smaller in growing economy because contractual problems are more costly in growing economy due to its political corruption and less legal protection (Antras and Helpman, 2004). To simplify following discussion, we ignore such difference in contractual problems to focus on how difference in wage rate affects R&D decision5. We also assume that the bargaining power β remains the same.
Now the final-good producer has two options, it chooses either the existing partner or another one from the growing economy as its outsourcing partner. It would build a new relationship with the new partner if following inequality holds
[δα+ β (1 − δα)]Rbi(w1, θ1) < [δα+ β (1 − δα)]Rei(w2, θ2) .
5If δ is significantly low, final-good producer will not cooperate with such new supplier. In this case, the potential competition that the existed supplier may be confronted with will disappear, so the existed supplier would not engage in further R&D activities.
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Rearrange this inequality and yield θ1
θ2
w2
w1 < 1. (2.21)
Intuitively, because both foreign suppliers are identical except the wage rate and efficiency index, the final-good producer will outsource its labor works to the new firm as long as the wage rate gap remains huge and efficiency index is close enough. Understandably, there will be some marginal foreign suppliers losing their jobs due to the emerging of the growing economy. If the marginal supplier wants to reverse such difficult situation, it would resort to R&D to improve its efficiency. When the marginal supplier fails to increase its efficiency, the outside option of the firm is always zero; therefore, the maximal spending (F2) in R&D that the firm would like to spend is
F2 ≥w1F , F2= (1 − Φ) ¯Ri w1, ¯θ1 .
Again, to discuss the relationship between R&D and capital share, we take the partial derivative of natural logarithm of F2 with respect to η, and yield equation (2.22).
∂F2
From equation (2.22), given capital intensity is larger than one, we find out that the marginal foreign supplier in an industry with higher capital share is likely to invest more in R&D.
Proposition 2. With fierce competition, the existing marginal foreign supplier is likely to engage in more R&D in a higher capital intensity industry than it in a lower one, or if they are suppliers of capital intensive producers.
Compared with proposition 1, this proposition indicates a fact that for some foreign suppliers, competition from another labor abundant country will drive the existing firms devoting to more R&D activities. With incomplete contract, the profit of the outsourcing firm is related to the capital intensity. The firm in a higher capital intensity industry has
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2. Theoretical Model 16
more profit left to put into R&D. Because F1 < F2, some suppliers invest in R&D only when the level of competition is intensified. Furthermore, within an industry, suppliers of less capital intensive producers or suppliers of less capital intensive industries leave the market. In the suppliers’ countries, factors are reallocated from labor intensive industries to capital intensive industries to invest in R&D and to satisfied the increase of labor demand after productivity is augmented. The suppliers’ of labor intensive industries or labor intensive producers within an industry is replaced by new suppliers in country C.
We therefore have the following proposition.
Proposition 3. If the level of competition is intensified, the capital intensive industries of suppliers’ countries expand and labor intensive industries contract. The new labor abundant country will be the new supplier of labor intensive final-good producers within an industry or producers in labor intensive industries.