Rarity is merely a funnel through which the flow of demand gets squeezed. If there's little to no demand to begin with, then the funnel never comes into play and prices remain low. However, if demand is great, then the funnel begins to squeeze demand and the prices increase.
You could think of it like water going through a garden hose. The higher the pressure and the smaller the nozzle, the faster the water shoots out. Rarity is the size of the nozzle on the hose, demand is the water pressure, and the exit velocity of the water is the price.
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