Slight Correction: Modern pigments used in house (and Barn) paints are almost all synthetic, containing zero minerals or organic substances. The pigments that fade the quickest are Red, Orange, Yellow and Violet; because of this, these pigments need more engineering and production time than the other colors to help make them more fade resistant, so they are actually MORE expensive to produce (red tints are the most expensive per ounce).
Deeper/darker colors require a lot more tint in the can than lighter colors and the tints are expensive. Darker colors use a base gallon can that is less full than a can used for a lighter color. This is so there is more room for the additional tint needed to create the darker color. Less contents in the can is less expensive, but more tint is more expensive. That being said, there is no difference in cost of one color paint over another because the cost is averaged out across the whole color range.
Red paint costs the same as any other color. You can buy cheap red paint, but that has nothing to do with it being red, just with it being of poor quality.