Lets change the question a bit just to prove a point.

**What would make a painting expensive in a world where you can photocopy anything?**

About now you should see where i'm going right? You can get a painting of Monét fairly cheap (the cost of royalty and frame), but the original would still be  super expensive. And with precious minerals it would be the same, and I'll even have to correct my self here. It is the same.

If you take a look at this article on Wikipedia: [Synthetic diamond][1] you will see that making a diamond is not impossible, in fact it is fairly easy everything considered.

**Conclusion:** 
So what kind of jewlery would be valuable in a world where anything can be produced? The original kind of jewlery.

  [1]: https://en.wikipedia.org/wiki/Synthetic_diamond