The specific production and marginal cost functions assumed are:
where QK and L, are I-sector output and employment, F is I-sector marginal cost (in equilibrium F is the M-sector’s fixed cost), KwsK+K* where К and K* are the northern and southern cumulative I-sector production levels, and A, (a mnemonic for learning spillovers) is a parameter governing the internationalization of learning effects. Southern technology is isomorphic with a,*=l/A*Kw and A*=A0K+1-0K. Finally, following Romer and Grossman and Helpman, depreciation of knowledge capital is ignored, so К =QK. The regional K’s therefore represents three quantities: region-specific capital stocks, region-specific cumulative I-sector production (i.e. learning), and region-specific numbers of varieties (recall that there is one unit of К per variety).
The early trade-and-endogenous-growth literature (eg, Grossman and Helpman 1991) considered only the extreme cases of A=1 and A=0. However recent empirical studies – such as Eaton and Kortum, and Cabellero and Jaffee – indicate that international learning spillovers are neither perfect nor nonexistent. We therefore assume partially localized learning externalities, i.e. 0<A,<1. When A,<1, regional I-sector labour productivities, 1/a, and 1/a,*, depend on a common global element K” and a regional element, namely A=0K+X(1-0K) for the north and A*=A0K+1-0K for the south.
Given, the growth rate of north’s К is related to L,, A, and 0K according to: The corresponding expression for K*’s growth is g*=L, *A*/(1-0K).
To keep the analysis tightly focused on key issues, we assume an infinitely-lived representative consumer (in each country) with preferences:
where p is the time preference parameter, Q is a consumption composite of Сx and CM (these are, respectively, consumption of T and a CES composite of M-varieties), and Cj is consumption of variety i. Each regional representative consumer acts atomistically even though she owns all her region’s L and K. Northern income, Y, is wL+nK. Southern income is w*L+ti:*K* (recall that L=L*).
While goods (M and T) are traded, factors (L and K) are not.* For goods, we adopt the standard simplifying assumptions (Krugman 1991; Krugman and Venables 1995) that T-trade is costless but trade in M is impeded by frictional (i.e., ‘iceberg’) import barriers (see Fujita, Krugman and Venables 1997 for detailed discussion of this assumption). Specifically, т> 1 units of M must be exported to sell one unit abroad, т is viewed as reflecting all costs of doing business abroad. These include everything from the mundane – shipping costs and trade policy barriers (tariffs, etc.) – to more exotic factors such as the difficulty of dealing with cultural and language differences, the cost of providing after-sales services, and the costs of communicating with customers and sales agents.