The US labor share has declined, especially in manufacturing and retail. Yet, the labor share of a typical median firm in these sectors has risen. This paper introduces a model where firms incur fixed costs to automate tasks. In response to lower capital prices, the model reproduces the labor share patterns observed in the data: large firms automate more tasks, reducing the aggregate labor share; while the median firm continues to operate a labor-intensive technology with a rising labor share. Using our model, we decompose the labor share decline and the rise in sales concentration in each sector into a part driven by lower capital prices and a part driven by reallocation to higher-markup firms. Lower capital prices played a prominent role in explaining the labor share decline in manufacturing and a smaller role in retail and other sectors from 1982-2012.