OK, in order for this to make any sense, we have to suppose some limits on the replicator. Let’s pretend that it does not violate the laws of physics, so it cannot produce free energy, make oil out of dirt (or rather that it can make oil out of dirt, but it would take more energy than you would get out of the oil), and that it cannot transmute elements but rather re-arranges the atoms in interesting ways.
So, this machine could make anything, but you would have to shovel in feedstock and it would take huge amounts of energy to run it. Also let’s make the machine slow…you can only make a few cubic meters of new stuff every day. And there should be some sort of imformation required too. You can’t make an exact duplicate of the Mona Lisa unless you have the Mona Lisa on hand for analysis.
Now, obviously the best thing to make is another replicator, but we don’t want to do that. And you don’t want to produce commodity goods, since you have to keep the replicator secret. If everyone knows you have a replicator then the government can just arrest you and take the replicator for themselves.
The big problem with very rare valuable items is that they are only extraordinarily valuable because they are rare. If you produce too much, then the value of the rare items plunges. And the price drop is not neccesarily linear either. If there is only one Mona Lisa and two people want it, then they can bid up the price to ridiculous levels. But if there are two Mona Lisas and only two people want it, then it might be worth a few pennies.
But even so, I imagine that diamonds might be the way to go. They are rare, but there are lots of them, and even if the price crashes people will still want them for various reasons. And the feedstock is cheap, any source of carbon. And diamonds have industrial uses. Even if they are so cheap that people don’t want to use them for jewelry, you can still make diamond engine blocks for race cars, or diamond shuttle rockets nozzles.
