We adopt a three-country framework, in which firms from Home country (H) would invest in either North country (N), or South country (S), or both, to explore the role of uncertainty on locating manufacturing units overseas. Each firm is willing to serve not only the domestic market but also the foreign markets via either local production or exporting from other country. In this model, each firm engaging in production activities faces an array of integration strategies that include choices of production locations and final consumption destinations. While an additional set-up cost is incurred by establishing a production facility overseas, there is an “iceberg”
transportation cost for a firm to serve a specific market through exporting from other place.
Households consume goods produced by n firms. Each firm supplies one single differentiated goods. Consumers share the same preferences that can be represented by the CES utility function
V = (
ni 1qi ）
/
1 , 0＜ ＜1 (1)
where qi is the consumption of the goods produced by firm i ∈﹛1,..., n﹜. Given the CES utility function, the demand function of goods produced by firm i in country j is derived as:
qij= Yj pij (2)
where = 1/ (1- )> 1 represents the elasticity of substitution between any pair of goods, and Yj = Ej / Pj is a measure of the total expenditure in country j, Ej, divided by the price index for all products in country j, j. Here the price index for all goods
in country j is represented as: j =
country to country. Let the subscript j indicates the country: Home (H), North (N) and South (S). Following Ekholm et al. (2003) and Yeaple (2003), we assume that one of the host countries, South, has a low production cost and a relative small market size while the other one, North, has a higher wage rate and a larger market.Moreover, the average wage rate in Home country is “sandwiched” between North and South, which is the same as Aw and Lee (2008). For expositional simplicity, let us assume for the time being unit wage in Home country, i.e. WH = 1. Then WS < WH
= 1 < WN. Furthermore,firms differ in their productivity level i, which is the ownership advantage for individual firm i so that there is no difference in the productivity level between a domestic manufacturing facility and an overseas one as long as both production units belong to the same firm. Specifically, the production function for each firm takes the following form:
qi = i Li
(3)
where Li units of local laborare the only inputs, which are required in the production process. Given this production technology, the constant marginal cost of an output produced by firm i with productivity level i in country j is given by MCij = Wj /i.
The optimal pricing strategy for CES-induced demand function is pij =MCij / . Here MCij depends on the pattern how MNCs engage in foreign activities. That is,
MCij = MCij if firms serve overseas markets through their local manufacturing facilities. While firms choose to access foreign markets via exporting and the transportation cost would be taken into consideration, MCij = MCij t, where t > 1 and
symmetric. This pricing strategy then yields the following profit for firm i in country j:
ij = (pij -MCij) qij - Fj = (1- ) YjMC 1ij (1/ )1 - Fj
= (1- ) Yj (1/ )1 (Wjt /i)1 - Fj (4) For expositional simplicity, let Sj = (1- )Yj (1/ )1 and i = i1
. Then we can rewrite equation (4) as:
ij = Sj W 1j i - Fj (5)
where Wj = Wj t. If the output is sold to the overseas market via exporting, t > 1, and if otherwise, t = 1.
Until now, we have been concerned with the situations, which a firm would encounter under conditions of certainty. In contrast to previous studies, our work is designed to highlight how the choice of locating production overseas is affected by the role of uncertainty. Hence we assume that firm i in country j would make a profit, ij, with probability (1-ij) and get zero revenue with probability ij. Firm i must pre-commit to whether or not to locate production in country j prior to the realization of shocks. While each firm is risk-neutral, it will choose the integration strategy, which maximizes its expected profit
E(ij) = (1-ij) [Sj (
Wj)1 i] - Fj , ij ∈ [0, 1] (6) To simplify notations, we rescale the market sizes of two host countries relative to that of the parent country by SH = S, SN =N S, and SS =S S. (a, b, c) is defined as the choice set from serving the local markets of Home, North and South in manufacturing locations a, b and c respectively. That is, if a firm locates his manufacturing units in North and South, and it serves the domestic market by
exporting from South, it is described as (S, N, S) in our framework.
Although there are a large array of integration strategies that includes options of production locations and consumption destinations, i.e. 3×3×3= 27, many of them would not be taken into account by the decision maker of a firm. Given the presence of the “sandwiched” domestic wage rate, the symmetric transportation cost of exporting final goods, and moreover, the impact of uncertainty, neither the Home market nor the South market would be served by the factory located in the North.
As a result, there are 12 strategies left over, i.e. 2×3×2= 12. Besides, since locating production overseas incurs an additional fixed cost and shipping entails an “iceberg”
transportation cost, the existence of locating production in either North, or South, or both can be inferred that to serve the local market through the local plant is the most profitable than that through the overseas plant. So among these 12 strategies, (H, H, H), (H, H, S), (H, N, H), (H, N, S), (H, S, H), (H, S, S), (S, H, H), (S, H, S), (S, N, H), (S, N, S), (S, S, H), and (S, S, S), we can eliminate 5 strategies, in which firms have established manufacturing units, but these plants are not used to serves the local markets. In short, there should be the following 7 ones taken into consideration: (H, H, H), (H, H, S), (H, S, S), (H, N, H), (H, N, S), (S, S, S) and (S, N, S).
The expected profit functions of the remaining 7 strategies are as follows:
E(HHH) = S[1+N t1 +S t1]
(7)
E(HHS) = S[1+N t1 +(1-S)SWS1 ] - FS
(8)
E(HSS) = S[1+(1-S)N(WS t)1 +(1-S)S WS1 ] - FS (9) E(HNH) = S[1+(1-N)N WN1 +S t1 ] - FN
(10)
E(HNS) = S[1+(1-N)N WN1
+(1-S)S WS1
] - FS - FN (11)
E(SSS) = S[(1-S)(WS t)1 +(1-S)N(WS t)1 + (1-S)S WS1
] - FS
(12)
E(SNS) = S[(1-S)(WS t)1 +(1-N)N WN1
+ (1-S)S WS1
] - FS - FN
(13)
According to the above strategies, we recognize that firms may not locate their manufacturing units in Home country all the time. In Eqs. (7)- (11), plants are established domestically, and then they are used to serve domestic customers and even foreign ones. In Eq. (7), final goods produced in Home country are not only used to serve domestic customers but also exported to both North and South. The combination of “horizontal” FDI and “export-platform” FDI is found in Eq. (9): firms locate production in South not only to serve the local market but also to export some parts of final outputs to another host country, namely North countries. Eq. (8) and Eq. (11) provide a pattern of “pure” horizontal FDI. The market-access incentive FDI is described in Eq. (10), where firms locate production in North to serve the local customers even though there is a sovereign risk in North and the labor force provided there is such expensive. Eq. (12) appears a mixed strategy of “vertical” FDI and
“export-platform” FDI, whereby firms are headquartered in Home country and manufacture in South. Another mixed strategy, which is a pattern combining
“vertical” FDI and “horizontal” FDI, is presented in Eq. (13): firms are headquartered in Home country and manufacture in both North and South.
Due to the impact of the uncertainty incurred by FDI, the relative cost advantage of South becomes indefinite though the wage rate in Home country is sandwiched
between North and South. In sum, the profitability of the above strategies depends crucially on the sovereign risks of each host country. In addition to all of the above, as the transport of final goods is costly, the shipping cost also plays a role in firms’
decisions of locating their manufacturing units overseas. We will discuss each condition in turn.