Growth has fallen in the U.S. amid a rise in firm concentration. Market share has shifted to low labour share firms, while within-firm labour shares have actually risen. We propose a theory linking these trends in which the driving force is falling overhead costs of spanning multiple products or a rising efficiency advantage of large firms. In response, the most efficient firms (with higher markups) spread into new product lines, thereby increasing concentration and generating a temporary burst of growth. Eventually, due to greater competition from efficient firms, within-firm markups and incentives to innovate fall. Thus our simple model can generate qualitative patterns in line with the observed trends.