The basic logic of our growth take-off – namely, that catastrophic agglomeration speeds growth in the presence of localized learning externalities – would, w’e conjecture, make sense in a very broad class of models. However, fewr such models could be solved analytically; Fujita, Krugman and Venables show that most models with catastrophic agglomeration must be solved numerically. To illustrate the interplay of economic forces as sharply as possible, we want analytic results and this leads us to adopt explicit functional forms and some severe simplifying assumptions. In particular, our model combines Martin and Ottaviano (1996a) and Baldwin and as such it adopts functional forms and simplifying assumption from the standard product-innovation growth model and from the economic geography literature.
Consider a world economy with two regions (north and south) each with two factors (labour L and capital K) and three sectors: manufactures M, traditional goods T, and a capital-producing sector I. Regions are symmetric in terms of preferences, technology, trade costs and labour endowments. The Dixit-Stiglitz M-sector (manufactures) consists of differentiated goods where production of each variety entails a fixed cost (one unit of K) and a variable cost (aM units of labour per unit of output). Its cost function, therefore, is тс+waMmi, where ж is K’s rental rate, w is the wage rate, and m; is total output of a typical firm. (Numbered notes refer to the attached ‘Supplemental Guide to Calculations’). Traditional goods, which are assumed to be homogenous, are produced by the T-sector under conditions of perfect competition and constant returns. By choice of units, one unit of T is made with one unit of L.
Regional labour stocks are fixed, but each region’s К is produced by its I-sector (I is a mnemonic for innovation when interpreting К as knowledge capital, for instruction when interpreting К as human capital, and for investment-goods when interpreting К as physical capital). The I-sector produces one unit of К with a, units of L. To individual I-firms, a, is a parameter, however following Romer and Grossman and Helpman, we assume a sector-wide learning curve. That is, the marginal cost of producing new capital declines (i.e.. a, falls) as the sector’s cumulative output rises. Many justifications of this learning are possible. Romer, for instance, rationalizes it by referring to the non-rival nature of knowledge.