Power laws in productivity and firm size are well-documented empirical regularities. As they are upper right-tail phenomena, this paper shows that assuming asymptotic power functions for various model primitives (such as demand and firm heterogeneity) are sufficient for matching these regularities. This greatly relaxes the functional-form restrictions in economic modeling and can be beneficial in certain contexts. We demonstrate this in a modified Melitz (2003) model which embeds an innovation mechanism in order to endogenize the productivity distribution and generate both of the above-mentioned power laws. We also investigate the model’s welfare implications with regard to innovation by conducting a quantitative analysis of the welfare gains from trade.