Heterogeneous firms can always collude on a minimum price

•There may not exist a common collusive price that raises all firms’ profits.•There always exists a common minimum price that raises all firms’ profits.•Trade associations have promoted a minimum recommended price.

When firms are heterogeneous, there may not exist a common collusive price that raises all firms’ profits. However it is shown that there always exists a common minimum price that raises all firms’ profits.