In this paper, we set up a simple model that explains the relation between low input price, high exit rates and industrial oncentration. More precisely, we argue that falling input prices force firms with low productivity to exit and induce expansion of more efficient incumbents at the expense of less productive producers. Our model helps reconcile some well‐established empirical results regarding the food processing industry. Indeed, agricultural prices have been declining between the early 1900s until 2006 while, over the same period, concentration and firm productivity have been increasing in the agri‐food industry.