INTERNATIONAL RESOURCE ALLOCATION: The Basic Model

In the next section of this paper we present our basic model. The equilibrium with complete information in all markets is derived in section III, and in section IV we analyze the solution when producers have incomplete information about potential foreign matches. Group ties are introduced in section V, and their effects in a three-country model are examined in section VI. Section VII concludes.
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The Basic Model

We begin by describing our basic model in the absence of group ties. The model is constructed with two goals in mind. First, we need a simple general equilibrium set-up where the difference in information between domestic and international partnerships can be captured intuitively and be analytically tractable. Second, we want to include an immobile factor, whose different distribution across countries is the origin of gains from trade, as in traditional analyses.

The world is composed of two countries. In each country, there are two sets of agents: workers and producers. Workers are homogeneous, but their number differs across the two countries: there are L workers in the home country, and L* in the foreign country, where L>L*. Producers on the other hand are of different types: in each country a continuum of them is distributed uniformly over a line that extends between -1 and 1. Type i is at location z,, representing the producer’s type. There is an equal mass, 2, of producers in both countries. The difference between labor-producer endowment ratios across countries can therefore be summarized by the ratio L/L*. In all that follows, asterisks will be used to indicate foreign variables.

Output is generated through a joint venture of two producers, and the distance between their locations on the line is an index of the gains from trade that result from their matching. To actively engage in production, a partnership needs to hire labor; thus output is a function of the quality of the producers’ match and the labor employed:

y,j = F(x.z,j) (1)

where z# is the Euclidean distance between the two producers of types i and j, and x is labor. The function F is characterized by constant returns to scale. Producers want to maximize profits.