Although we cannot analytically characterize the transitional dynamics of a system with three non-linear differential equations, we can say that a continuing rise in trade freeness would raise 0K until the core-periphery outcome is the only stable long-run equilibrium. Of course, southern knowledge never disappears entirely, so the core-periphery outcome is only reached asymptotically (the number of southern varieties remains fixed, but the value of these drops forever towards zero due to the ceaseless introduction of new northern varieties).
Once the core-periphery outcome is reached – or more precisely, once we can approximate 0K as unity – the world economy enters a third distinct phase. For trade costs lower than this point, the world economy behaves as it did in the first phase. That is to say, making trade less costly has the usual static effects, but no location effects.
Plainly, the location equilibrium in this world would appear as a punctuated equilibrium. In the first and third phases, lower trade costs have no impact on the distribution of world industry, but in the second phase, the north’s share of world industry increases rapidly.
Our paper focuses mainly on the three phases described above, however, the model can also generate a fourth stage in which the south industrializes. The key to this fourth stage is to suppose that ёф slows as it approaches some natural upper bound, but international integration continues in the form of a rise in the internationalization of knowledge spillovers- namely dA>0. Since dA>0 weakens agglomeration forces (by facilitating technology transfers), we can identify a critical value of A. beyond which core-periphery outcome becomes unstable and the symmetric outcome is stable. As we shall see, the emergence of southern industry slows global growth somewhat and forces a relative de-industrialization of the north.