The first and third term are positive, so they represent the destabilizing forces, namely the demand-linked and growth-linked circular causalities (respectively). The negative second term reflects the stabilizing local-competition effect. Clearly, reducing trade costs ^ф>0) erodes the stabilizing force more quickly than it erodes the destabilizing demand-linkage. Moreover, trade free-ness ф does not affect the strength of growth-linkage (third term).
To isolate the two distinct cycles of circular causality, suppose, for the sake of argument, that the demand-linkage is cut, so d0E/d0K=O. In this case, 3q/d0K is positive and the system is unstable when А.<2ф/(1+ф2). This shows that growth-linked circular causality can by itself produce total agglomeration when trade costs are low enough. (Recall that 0<ф< 1 is a measure of the free-ness of trade, so ф=1 indicates costless trade). To see the dependence of growth-linked circular causality on localized knowledge spillovers, note that with A=1 and d0E /d0K=O, the symmetric equilibrium is always stable. At the other extreme, w’hen spillovers are purely local (A=0), the symmetric equilibrium is never stable even without the demand linkage.
Finally the critical level of ф at which the symmetric equilibrium becomes unstable is defined by the point where switches sign, namely 3q/<30K=O. This expression is quadratic in ф, so it has two roots. The economically relevant one is:
Observe that the range unstable (J)’s, (фса1,1], gets smaller as the internationalisation of learning effects (as measured by A.) increases. Since the growth-linkage becomes weaker as A rises, it is easy to understand why the range of trade costs that leads to instability shrinks as A rises. Additionally the instability set expands as the discount rate p rises since this amplifies the demand linkage. That is, the equilibrium return to capital rises with p, so a higher p amplifies the expenditure shifting that accompanies production shifting.