The modified model has three growth stages as does the Section 2 model, however there are two important differences. In the modified model, the catastrophe is much larger in the sense that once the symmetric equilibrium becomes unstable, the only stable equilibrium is the core-periphery outcome. The second difference is that even though there are no local technological spillovers (since we assumed A=T), we still get a growth take-off because of the pecuniary externalities. Computer usage

To see this, consider the stage-one growth rate of K. Solving for g, using the fact that 0K= 1 /2 and B=l, gsym=[a2LA/(a-a)]-p. Since Д is rising in ф at 0K= 1 /2, we see that g rises as trade costs fall, even in stage-one where 0K is invariant. This brings out the new elements in this modified model; it contrasts with the Section 2 model, where g w’as not directly affected by ф. Intuitively, the point is that given, the marginal cost of new К (i.e. F) falls, as transaction costs decrease. This leads to an incipient rise in each nation’s q, and thereby draws more resources into the I-sectors. Faster К growth (and therefore real income growth) is the result.

The model enters stage-two, the take-off, once ф gets high enough to trigger a collapse to the core-periphery outcome. Since 0K cannot jump, there must be a phase when 0K is moving from 1/2 to 1. As before, we cannot formally characterize growth during this transitional phase.

As in the first model, 0K reaches unity only asymptotically. This means that the third stage of growth when 0K equals one is only reached asymptotically. Of course at that point B=A=1, so the stage-three steady-state growth rate of К is gu =[a2L/(a-a)]-p. This exceeds gsym since Д<1 at 0K=l/2.

To summarize. Figure 8 schematically shows the growth rates in the various phases. Figure 8 plots the growth rates corresponding to the symmetric outcome as long as it is a saddle (ф below фса”) and to the core-periphery outcome afterwards (ф above фса”). When ф crosses фса”, g will asymptotically reach the core periphery level. In the modified model the dynamic system undergoes a subcritical (rather than a supercritical as in the previous model) pitchfork bifurcation as ф crosses фса”: when the symmetric steady state loses stability, the core-periphery steady state becomes the only stable outcome.

*Figure 8*

The model enters stage-two, the take-off, once ф gets high enough to trigger a collapse to the core-periphery outcome. Since 0K cannot jump, there must be a phase when 0K is moving from 1/2 to 1. As before, we cannot formally characterize growth during this transitional phase.