A Multi-Product Lerner Index and Elasticity Aggregation

A method is proposed to aggregate product-by-product elasticities over groups of products so as to obtain aggregate group-by-group elasticities. It is shown that price-cost margins charged by multi-product firms can be written as minus an aggregate inverse elasticity, just as the traditional Lerner formula expresses the margin charged by a single-product firm as minus an inverse elasticity. Expressing the margins charged by multi-product firms in terms of elasticities is not new. What is new in this article is the recognition that the expressions can be interpreted as aggregate elasticities and that the shape of the Lerner formula survives aggregation