How are a firm's size and market power related to one another? Combining micro-data about producers and consumers, we document that while firms mainly grow by selling to more customers, their markups are only associated with their average sales per customer. To study the macroeconomic implications of these facts, we develop a model of firm dynamics with endogenous customer acquisition and variable markups. Relative to a model without customer acquisition, our model generates higher concentration at the top, but a lower aggregate markup. Our quantitative analysis reveals large welfare and efficiency losses due to (mis)allocation of customers across firms. By increasing market concentration among the most productive firms, the efficient allocation achieves 11% higher aggregate productivity and 15% higher output.