Although an equal division of M-varieties is always an equilibrium, it need not be stable, as the economic geography literature has emphasised. Indeed, in our model two cycles of’circular causality’ tend to de-stabilize the symmetric equilibrium.
The first is the well-known demand-linked cycle in which production shifting leads to expenditure shifting and vice versa. The particular variant present in our model is based on the mechanism introduced by Baldwin. To see the logic of this linkage, consider a perturbation that exogenously shifts one M-sector firm from the south to the north. Firms are associated with a unit of capital and capital-earnings are spent locally, so ‘production shifting’ leads to ‘expenditure shifting’*. Other things equal, this expenditure shifting raises northern operating profits and lowers southern operating profits due to a market-size effect. This tends to raise q and lower q* thereby speeding north’s accumulation and retarding south’s. The initial exogenous shift thus leads to another round of production shifting and the cycle repeats. As w’e shall see, if trade costs are sufficiently low, demand-linked circular causality alone can de-stabilize the symmetric equilibrium.
The second link is the growth-linked circular causality introduced by Martin and Ottaviano (1996a). When I-sector technological externalities are transmitted imperfectly across borders, production shifting leads to ‘cost shifting’ in the I-sector. For instance, suppose an exogenous perturbation increased 0K slightly. Given localized knowledge spillovers, this shock lowers the northern I-sector’s marginal cost and raises that of the south. Other things equal, this raises q and lowers q*, so the initial production shifting raises north’s rate of investment and low’er south’s. Of course, this ‘growth shifting’ further increases 0K and the cycle repeats. Again, if trade costs are low enough, grow’th-linked circular causality alone can yield to total agglomeration.
The sole force opposing agglomeration here is the local competition effect. Namely, raising 0K (north’s share of varieties) tends to raise local competition in the north and lower it in the south. Since competition is bad for profits, raising 0K tends to lower q and raise q*.