The Basic Model: A Monopoly 1 The Model

To incorporate

exchange rate, R&D competition and firm heterogeneity into an oligopolistic model might make our model too complex to obtain any analytical solution. In order to

derive some analytical results for better understanding of the driving forces behind our theory, in this section, we start with a simple theoretical framework to analyze the interaction of a monopoly firm’s entry mode decision and its relationship with its domestic

2 See Chen, et al. (2006) and Lin, et. al. (2010) among others for recent research about the impact of exchange rate movements on OFDI both theoretically and empirically.

5

R&D spending, and then extend this basic model to cases with duopoly.

We assume that a monopoly firm which produces to serve a foreign market. It can choose to manufacture its product in its home country and exports the product to the foreign market. It can also relocate his production activity to the foreign country to serve the market.

Assume that the firm initially produces at home. When the firm faces an increase of domestic labor cost, it can relocate its production to country with lower labor cost, which strategy can be referred as “moving out” strategy. Alternatively, it can choose increase its R&D spending in order to increase its productivity to reduce the adverse impact of an increase in wage rates, which strategy can be referred as “moving up” strategy (Lu (2007)). In this section, we illustrate that the firm’s OFDI does not necessarily negatively relate to its domestic R&D spending. In other words, its moving-out strategy and moving-up strategy can be either substitutes or complements.

Suppose that a monopoly firm uses labor input only to manufactures a good in the home country or a foreign country to serve the foreign market. The firm can undertake R&D to reduce its production costs before it determines its production level. Let

I be the level of

R&D undertaken by the firm and let

c denote the firms marginal cost. As for the

relationship between the firm’s marginal cost,

c , and its R&D spending, the following

functional form suggested by Chen and Yang (2013), is adopted:

( , )

_j

( ), ,

c w I  w    I j  h f

(1)

where

 is a constant and can be considered as the initial labor requirement per unit of

output, and

w

_jis the wage rate in the home country (j=h) or in the foreign country (j=f) . The parameter θ, with θ>0, represents the productivity of a firm’s R&D activity.

Eq. (1) implies that a firm can reduce its marginal cost of production in two ways, either lowering its labor cost by moving out to a country with lower labor costs or increasing its R&D spending. Consequently, there exists a substitution effect induced by investing in

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low-wage countries on the firm’s domestic R&D spending. In addition, it should be noted that Eq. (1) implies that the returns on a firm’s R&D investment is assumed to be higher if a firm faces a higher wage rate. This suggests that the above-mentioned negative impact of OFDI on R&D will be higher if the gap of the wage rates between home and host countries is larger.

The specification of the marginal cost function in this setting is different from most previous studies in which the return on a firm’s R&D investment is assumed to be independent of the wage rates.

It is assumed that the firm has two entry modes for serving the foreign market: exports or OFDI. There exist sunk costs of exporting, which are typically thought to include fixed costs of research into product compliance, distribution networks, advertising and so on. ³ There also exists a unit cost associated with exporting activities such as transportation costs,

s . The sunk costs and variable costs associated with exporting activities are assumed to be

zero for simplicity. If the firm attempts to take advantage of low-wage labor in the host country and decides to start a new plant there, it will incur additional plant-specific sunk costs

G,, which are usually supposed to be higher than the sunk costs of exporting. For simplicity,

the sunk costs and the trade costs of exports are assumed to be zero.

We consider a linear (inverse) demand function,

p    q

(2)

where

p

is the output price in terms of foreign currency, and

q

denotes the output of the firm. When the firm chooses exports as its international expansion mode, its profits are given by:

   

²

h h 2

R p q w I q I

            

(3)

where

R

is the exchange rate, and(

 I

₂²) / 2 is the cost of R&D investment with



>0, which

3 Greenway and Kneeter ( 2007), p. F151.

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is the inversely related to the cost effectiveness of the firm’s R&D investment. The specification of the cost of R&D investment implies that there exists decreasing returns to R&D activity. Exchange rate is expressed in units of home currency per unit of foreign currency.

By contrast, if the firm decides to set up a new plant in the foreign country instead of exporting, the firm’s profits are then given by:

   

²

f f 2

R p q R w I q I

             

(4)

It is assumed that the firm faces a three-stage decision problem. In the first stage, the firm determines if it will serve the market via exports or FDI. In the second stage, given the entry mode of the firm, it chooses its R&D spending level. In the third stage, given its R&D spending level, the firm then chooses its output level. The model is solved by backward induction. That is, given the firm’s entry mode and R&D decision, the output decision of the firm is solved first. Then the firm’s optimal R&D level is derived. Finally, the choice of the firm’s entry mode is determined.

2.2 Comparative Statics

The Case of Export

The quantity decision problem for the case of export is solved first. For simplicity, the parameters of



and



are assumed to be 1 in this section. From the first-order condition of profit maximization, we obtain the firm’s optimal quantity as follows:⁴



¹



2

R w

h

I

q R



  



. (5)

Substituting Eq. (5) into Eq. (3), we then solve the second stage problem, the R&D decision problem. From the first-order condition, we can solve for the optimal R&D level as

4 The second-order condition,²_h   q² 2R0, holds.

8

follows:⁵

1

2

A w

h

I A



 

, (6)

where

A

₁

  R w

_h and

A

₂

 2 R   w

_h²



². To ensure a positive output or R&D level, we assume that

R w 

_h



0( thus

A

₁



0), and

A

₂



0.

Substituting Eq. (6) into Eq. (5) and then Eq. (3), we can derive the optimal quantity and profits, respectively, as follows:

1

2

q A A



 

(7)

2 1

2

2

A A



^

 

(8)

Proposition 1: The optimal R&D level of the monopoly firm is positively related to its

productivity of a firm’s R&D activity and the exchange rate of the home country, but negatively related to its investment cost of R&D spending. However, the relationship between wage rate and its optimal R&D level is indeterminate.

Proof: Differentiating Eq. (6) with respect to 

, ,

R

and

w , we have

_h



^{2 2}



1 2 2

2 0

h h

w A R w I

A

 







   



2 3 2 2 h

0 w A I

R A







 



1 2 2

2 Rw

^h

A 0 I

A









  





1 3



2 2

2

_h

h

R A w A

I

w A

 





 



, where

A

₃

 2   w

_h



².

5 The second-order condition, ²   I² A₂ 2R0, holds.

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