I don't know if your wealth has anything to do with it (it could, but I don't think so). I do believe that the utility you might get out of a resource definitely affects its cost.
For example, it is widely believed (and I've never seen anyhting in my games to contradict it) that the AI will value its luxury by how much happiness it will provide to your civ. Each luxury generates one happy face in each city, sometimes a lot more happy faces when the civ already has control of several luxuries and has constructed marketplaces in most of its cities. The AI's extra gem is worth a lot more to the civ that has 40 cities, with marketplaces in every city, and already has access to 4 luxuries, then it is worth to the civ that has 5 cities, no marketplaces and no luxuries. The AI will price its luxuries accordingly (try it when you're the smaller, backward civ -- you can get quite a deal from the AI).
I'm not certain how the strategic resources are valued.