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The dairy processing industry is the largest subsector in the EU food industry and is characterised by high concentration. We investigate the extent of output market power exerted in EU dairy processing, applying an advanced stochastic frontier approach to estimate firm‐level markups of price over marginal cost using data for France, Italy and Spain from 2008 to 2017. We further relate markups to firm characteristics to identify what type of dairy processors possess the highest power in the sector. Our findings only reveal small average deviations from perfect competition but we find considerable heterogeneity of markups within and between the three countries. We identify a strong positive relationship between markup and profitability, though we find firm size and markups to be inversely related. This indicates that small firms operating in differentiated niche markets are able to charge higher markups, thereby ensuring their profitability. This result can serve EU dairy processors for future strategic alignment, and is particularly interesting from a policy perspective as large firms are mostly blamed in the exercise of market power in public and policy debates. [ABSTRACT FROM AUTHOR]