As pointed out above, our model is an example of uneven development in the sense that the agglomeration of industry in the north produces immediate divergence with the south. However, because agglomeration generates a take-off which materializes itself into an acceleration of the world rate of innovation, the take-off also produces benefits for the south. The tension between the negative effect of agglomeration and the positive effect of the increase in the rate of innovation is what makes the welfare effect of the take-off ambiguous for the south. Northern and southern steady-state welfare (i.e., the present value of the utility flow’s) as functions of ф are, respectively: Retailing in rural
where g and 0K depend upon ф as described above, and c0 captures terms that do not depend upon ф. Notice that while a rise in g is welfare enhancing in both regions, raising 0K raises northern welfare, but lowers that of the south. As discussed above, the impact of raising the steady-state 0K is twofold: it shifts wealth from south to north and it low’ers the northern price index relative to the southern price index, as long as ф< 1.
Figure 6 plots the levels of welfare corresponding to the higher arm of the pitchfork represented in Figure 4. We have simulated these levels of welfare as a function of trade costs and found three generic cases (again considering only steady states). Two elements are constant in all cases. First, both regional welfare levels rise as ф rises (imports get cheaper) during stage-one (the pre-modern growth phase), and second the north’s welfare is insensitive to ф in the final stage. Symmetry explains the first element and the fact that 0K=1 in the final phase accounts for the second element. The cases differ only in the south’s welfare level in the third phase. In particular, the levels are simulated for three different expenditure shares on manufactured goods, namely a=0.17, a=0.3, and a=0.9; the other parameter values assumed, viz. A=0.7, o=3, p=0.1 and L=l, are common to the three cases.