This paper analyzes the growth rates of two countries and the bilateral income disparity in relation to North-South trade mainly from the viewpoint of the South. We extend a Ricardian trade model with a continuum of goods in order to consider a situation where the South faces the balance-of-payments constraint while the North is in full employment. Using the model, we show that depending on the size of a technological parameter, two possibilities arise with regard to the growth of the South: (1) the South can catch up with the North in income level by expanding its comparative advantage sectors, and (2) the South, in contrast, fails to catch up with the North in spite of expanding its comparative advantage sectors. Moreover, we show that if the South is in the catching-up process, a policy intended to improve its international price competitiveness exerts a positive effect on its growth, thereby promoting the catching-up process, whereas if the South is in the falling-behind process, such a policy exerts a negative effect on its growth, thereby leading to immiserizing growth.