# Optimum Choice of an MNC: Location and Investment

## Article excerpt

The existing literature is quite voluminous on how one country engages in trade relations with another country, how international trade is mutually gainful to each other, what factors determine trade structures, and so on. There has been a substantial exploration on different aspects of multinational corporations engaged in production and transnational trade. Yet there exists an area which seems to have remained quite unexplored, and it is the question of optimum location of production of goods and services and the optimum marketable quantity of output and investment outlay. In this paper, we try to fill in this gap in the literature by way of determining optimum factory location for a multinational corporation (MNC) and ascertaining optimum investment outlay for such a firm.

Consider an MNC that produces only one good (x) by employing two mobile factors, labor (L) and capital (K), which are available at geographic locations of A and B, respectively. Let the market for the product X (which capital and labor can only jointly produce) be at location M. The location triangle ABM [ILLUSTRATION FOR FIGURE 1 OMITTED] depicts the locational situations of factor L at A, factor K at B and the final destination of product X at M. Production of X is a function of capital and labor as follows:

X = f(K,L), [f.sub.i] [greater than] 0, [f.sub.ii] [less than]0, for i = K,L; 0 = f(0,L) = f(K,0)

Let w = (given) price of L at its source A, and

r = (given) price of K at its source B.

Now the choice of the location of production (factory) can be anywhere on, inside or outside of, the locational triangle, but once the MNC's objective is to minimize cost (for a given output) and/or maximize output (for a given expenditure), the location choice is a matter of optimization. Assume, at this stage, that the MNC decides to build its factory away from the market be a given linear distance, say M[a.sub.0]. That means it can build his factory anywhere on the circle u[a.sub.0][n.sub.0][b.sub.0] (whose radius is M[a.sub.0]); but once the transport costs of factors are considered, it is obvious that it would want to locate its factory somewhere on the arc [a.sub.0] [n.sub.0] [b.sub.0]. (1) Let factor A[a.sub.0] distance = [d.sub.1] and B[a.sub.0] distance = [d.sub.2]. If the factory is built at point [a.sub.0], then cost for each unit of factor L and K at the factory location respectively are:

[w.sup.[a.sub.0]] = w + [d.sub.1] [T.sub.L] (1)

[r.sup.[a.sub.0]] = r + [d.sub.2] [T.sub.k] (2)

where [T.sub.L] and [T.sub.K] measure the transportation costs of each unit of labor and capital per unit distance, respectively. Similarly, one can easily ascertain the unit factor cost at location [b.sub.0] as follows:

[w.sup.[b.sub.0]] = r + [D.sub.2] [T.sub.K] (3)

[r.sup.[b.sub.0]] = r + [D.sub.2] [T.sub.K] (4)

where [D.sub.1] and [D.sub.2] are the measures of linear (mile) distances from A and B to [b.sub.0].

If the budgeted expenditure of the firm is [E.sub.0], then availability of the factor units are spelled out by the following equations for location [a.sub.0] and [b.sub.0], respectively:

L [multiplied by] [W.sup.[a.sub.0]] + K [multiplied by] [r.sup.[a.sub.0]] = [E.sub.0] (5)

L [multiplied by] [W.sup.[b.sub.0]] + K [multiplied by] [r.sup.[b.sub.0]] = [E.sub.0] (6)

These equations are plotted in Figure 2:Given the total expenditure [E.sub.0], the MNC can get and employ any capital labor combinations defined by coordinates on the line [[Alpha.sub.0] [[Epsilon].sub.0] if its factory is located at [a.sub.0] in Figure 1, and if [b.sub.0] happens to be the chosen factory location, its available inputs combinations are denoted by the line [[Gamma].sub.0] [[Beta].sub.0]. For obvious reasons, any input mix defined by [T.sub.0][[Epsilon].sub.0] and [T.sub.0] [[Gamma].sub.0] is noneconomic, and thus the kinked locus [[Alpha].sub.0] [T.sub.0] [[Beta].sub.0] is the meaningful iso-cost line for the MNC. …

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