Before revision:  We show that the relative loss of the monopoly firm is at most 25\% no matter how many firms compete on the second market. In particular, we show for the setting of Bulow et al. involving affine price functions and only one additional firm on the second market that the worst case loss in profit is bounded by 6.25\%. We further investigate a dual effect: How much can a firm gain from a negative price shock in its monopoly market? Our results imply that this gain is at most 33\% . We complement our bounds by concrete examples of markets where these bounds are attained .
After revision:  We show that the relative loss of the monopoly firm is at most 25\% no matter how many firms compete in the oligopoly. We further investigate the impact of positive price shocks on total profit of all firms as well as on consumer surplus. We find tight bounds also for these measures showing that total profit and consumer surplus decreases by at most 25\% and 16.6\%, respectively .