> No. I have a monopoly on faucets made to my design, not on faucets generally.

You can try to subdivide any particular market but you still can't get yourself out of the second half of the post: If the products were actually substitutes then the prices would approach the marginal cost. If they're not, they're not.

College textbooks are an obvious example of this. Anybody can make "math textbook" but only one of them will have the homework problems your professor will assign in them, so you need that one and the publisher has a monopoly.