This paper applies the Jones–Kierzkowski model to the contract manufacturing service industry. Stylized facts of that industry imply a theory of non-convex general equilibrium. The cost structure combines a constant marginal cost and a positive fixed cost; Marshalian free entry-free exit prevails. This implies a distinct market structure (which is neither perfect nor monopolistic competition, nor the usual Bertrand oligopoly) and a generalized equilibrium concept, based on the ‘full employment’ and ‘competitive profit’ conditions.
In a class of examples where the technology is Ricardian for fabrication and Leontief for assembly, with fixed costs for ‘service links’, it is proved that there always exists Pareto optimal allocations, supported by a concept of generalized equilibrium (but–as shown by Koopmans–not by the Walras equilibrium, where the firms with increasing returns operate as price takers). Implications on specialization and cross country income distribution are noted.
Three points may be made, on the observed facts, the future theoretic development and the applications.
First, the ‘service links’ in the JK model of fragmentation is identified with the free-standing firms operating in the manufacturing service industry. In the theoretic model, we presented, under the Marshallian assumption of no entry, no exit, these firms managing the supply chains neither earn positive profit nor wield monopoly power on their own. In real life, those providing manufacturing services mostly operate out of headquarters in high income (or industrialized) economies and may also undertake some fabrication on the side, or vice versa. Hence, the reported high net income of some of these firms and the assumption of a Marshallian industry equilibrium at zero profit are not necessarily mutually contradictory.
Second, due to the highly complementary nature of parts and components, labor inputs across countries often are not readily substitutable to each other, so that income divergence is expected. Costly work in carrying out division of labor will only accentuate the situation and our exercise seems to confirm it.
To concentrate on characterizing the implications of the JK model in a general equilibrium context, we have attempted to avoid technical complexities in our examples. It seems that a simple reinterpretation should allow the input endowment of each country to be a vector and not a number, entering a linear homogeneous production function for each part. But then through the Ricardo–Viner form, studied in Jones (1971), the extension to decreasing returns to scale is obvious, and as Jones and Scheinkman (1977) taught us, an even fuller generalization is in sight. The general approach used here remains valid if the internal scale economy is such that the total cost function does not take the affine form with an additively separable term for fixed cost.14
Our draconian assumption of a single universal consumption good has served this purpose well. For generalization, the natural next step is to allow the presence of different final goods, producible from various parts under constant returns, but consumed by all households sharing the same homothetic utility index, as in a Heckscher–Ohlin–Vanek model. Again, the problem of the social planner can be solved as an exercise of mathematical programming.
Many comparative static studies on the implications of outsourcing can be done at this stage.
Still another round of generalization is to allow households of each country to have their own kind of homothetic utility index. A tentative line of inquiry is as follows. Each normalized price vector in the price simplex generates both a vector of final goods as a supply response, and a corresponding input price vector, then a vector of country-specific incomes, and finally a vector of final goods as a demand response. The agreement between these two quantity vectors in their relative proportions forms a fixed point in some suitably defined mapping, along the work of McKenzie (1954). Further afield lies the task of exploring the limit of supporting Pareto efficient allocations with average-cost pricing.
Last but not least, this theory of trade was developed not merely for its generality and elegance, but for its relevance in policy issues. The JK study has opened the door to analyzing important questions of our day, related to globalization. Like the reduction of artificial impediments to trade when tariff barriers are removed at the formation of customs unions, reduced cost for the service links opens up new supply chains and shifts the pattern of trade within existing ones, with inherent changes to absolute and relative income levels. To clinch such issues, a general equilibrium foundation helps so that over fewer variables and parameters, researchers need to assume their values as staying equal. Although we have not considered applications here, the present study may point to directions where more may be done
