Should you care about customer satisfaction if you have the monopoly?

no

Definitely, because customer loyalty is must for the confirm market. if not if it is a monopoly market for particular product, loose demand on it if it is not very essential product to existance.

Customer satisfaction  should be the motto of you company. if you fail to follow this rule, then the chances are that you will be gradually wiped out of the market even if you enjoy a position of monopoly.

Its sad but true, companies that has the monopoly do not care about customer service.

I personally believe good customer service, though, is like integrity: I suppose you could sacrifice it, but it will come back and bite you later. Even a so-called “monopoly” can be put out of business tomorrow by some new idea. Wherever customers are just waiting for an opportunity to jump ship, there is someone out there who is trying to find a way to take them from you.