We analyze the transitional dynamics of an economic model with heterogeneous consumption goods where convergence is driven by two different forces: the typical diminishing returns to capital and the dynamic adjustment in consumption expenditure induced by the variation in relative prices. We show that this second force affects the growth rate if the consumption goods are produced with technologies exhibiting different capital intensities and if the intertemporal elasticity of substitution is not equal to one. Because the aforementioned growth effect of relative prices arises only under heterogeneous consumption goods, the transitional dynamics of this model exhibits striking differences with the growth model with a single consumption good. We also show that these differences in the transitional dynamics can give raise to large discrepancies in the welfare cost of shocks.