There are two neighboring vacation islands that differ by their target customers. Each of these islands is managed by a different hotel chain. The island Silentium mainly draws customers who are looking for tranquility and relaxation. The island Gaudium mainly attracts customers who like to party. Because of the small distance between the islands, the hotel on Silentium $($also called Silentium$)$ has to offer a price reduction to its customers if they feel disturbed by the noise emissions from the hotel on Gaudium $($also called Gaudium$).$ To simplify matters, assume that the profit of Silentium drops by $2000$ per $100$ guests on Gaudium. The profits on both islands that would result if there were no interdependencies are illustrated in Table $6\mathrm{.}1.$

$1.$ Is there an externality? If yes, which hotel causes it$?$