Note first that when transaction costs are sufficiently high (ф is below the threshold level), a decrease in transaction costs has the usual static effects in both the south and the north. It raises welfare because it lowers the real price of traded manufactured goods. At the point of the take-off, north and south welfare diverge. The north benefits from agglomeration and a higher growth rate. The south benefits only from higher growth; agglomeration actually harms the south. This explains why post-take-off welfare is always lower in the south. Sales personnel
The positive growth effect of the take-off explains why the comparison of welfare before and after the take-off is ambiguous. If the share of manufacturing goods is low enough, the increase in the growth rate of the manufacturing sector does not have a large welfare impact. In this case, the south loses due to agglomeration and its welfare never reaches the level it had before the take-off. In the intermediate a case, the south first loses but eventually attains a welfare level that exceeds its pre-take-off level. Finally, when manufacturing is sufficiently high, the positive growth effect dominates and the take-off benefits both the south and the north. Similar results are obtained when we vary other parameters: the welfare impact is more favourable to the south the higher the growth effect of agglomeration, that is the larger the market size (the higher L), the more local the spillovers (the lower A), the more the economies of scale (the lower a) and the lower the subjective discount rate p.
Importantly, after the take-off, lowering transaction costs always improves welfare in the south because it decreases the price of goods imported from the north. Thus, even though the south may have been made worse off by agglomeration in the north, resisting further reductions in transaction costs is not welfare improving.