Before revision:  We quantify for the first time the worst-case profit reduction for the case of two markets with affine price functions and firms with convex cost technologies . We show that the relative loss of the monopoly firm is at most 25\% no matter how many firms compete on the second market.
After revision:  We quantify for the first time the worst-case profit reduction for the case of two markets with affine price functions and firms with convex cost technologies , we show that the relative loss of the monopoly firm is at most 25\% no matter how many firms compete on the second market.