Math question

[Susan Ballinger]

Okay, maybe this seems trivial to some, but I'm curious as to how you would figure this example of a commission.

Say you charge $1,000 for a portrait, plus 20% for a lot of detail (clothing or background), plus 50% for each additional person. A person asks you what it would cost for two people with a highly detailed background. Would you simply multiply it all together 1,000 x 1.5 x 1.2 = $1,800 or would you add the percentages to multiply it off the original starting commission $1,000 x (1+.5+.2) = $1,700.

Since it does make a difference, which way would you compute it?

Susan

[Chris Saper]

Hi Susan,

I would probably figure my price for two subjects first, then apply the complexity premium to the total, but that's just because it seems logical to me that way. Frankly, I think you can go either way, as long as you are consistent in the way you calculate your pricing approach. Otherwise, you may forget how you quoted a price, and find that the client who asks you to remind him of the quote finds himself with two different numbers.

After all, the only sensible basis (in my view) upon which a painter would adjust charges, once his or her basic prices are established, is how much more time (and time here can also be aggravation), relatively speaking, is needed to complete the adjusted piece.

[Tarique Beg]

Susan

I think it would be disingenuous to calculate the percentage as 1000 x 1.5 x 1.2. This is because, in effect, the base on which you are calculating the percentage increments becomes variable, instead of fixed. A mathematically inclined client would assume a fixed base. The reason you get 1800 is because 50 percent of the first base (1000) is 500 plus 20 percent of the second base (1000 + 500) is 300 making a total percentage increment of 800. If your base stayed at 1000, then you'd have 50 percent of 1000 = 500 plus 20 percent of 1000 = 200 for a total increment of 700. In any business transaction as far as I am aware, we always assume a fixed base. Otherwise, the client won't know what they're paying 20 or 50 percent of. Therefore, the calculation of 1000 x (1 + (0.5 + 0.2)) = 1000 x 1.7 is correct. Just my opinion (which could be wrong).