A note on measuring multi-product market power using the lerner index

• We relate product-specific and aggregate Lerner indices for multi-output firms • Cost function related conditions for the aggregation of multi-product Lerner indices • Linear vs linearly homogenous output aggregation functions and aggregate Lerner index In this note we re-examine Shaffer and Spierdijk (2020) conditions for the aggregate Lerner index to be equal to the weighted-average of product-specific Lerner indices and we show that they can be made weaker than assuming a separable cost function with a linear output aggregation function. In particular, we verify that the aggregate Lerner index is equal to the weighted average of the product-specific Lerner indices, with revenue share as weights, if the cost function is separable in outputs and the output aggregation function is linearly homogenous.