This paper presents a New Economic Geography model of structural change, agglomeration and growth. By assuming the same non-homothetic preference structure as Murata (2008), we obtain similar results in that a progressive reduction of trade costs allows the economy to pass from a pre-industrialized to an industrialized stage and then, within the latter, from a dispersed to an urbanized regime. However, the introduction of capital accumulation and the dynamic setting of our model open the door to a richer set of implications. First, an additional stage is introduced as, for some intermediate values of trade costs, a multiple equilibria regime emerges with the symmetric and the core-periphery equilibria stable at the same time. Second, the introduction of non-homotheticity introduces a new channel through which growth is affected by trade costs and agglomeration. In particular, integration is always growth-enhancing while agglomeration is growth-detrimental.