My Math Forum Asymptotic Retail Pricing Based on Cost
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 March 18th, 2014, 06:03 AM #1 Newbie   Joined: Mar 2014 Posts: 3 Thanks: 0 Asymptotic Retail Pricing Based on Cost I need to find a formula that will allow me to calculate the retail price of an item, based on its cost, with the % markup inversely proportional to the cost. In the past we have used a straight-line method of calculation where we would add a fixed % of the cost to derive the retail price. So, for example, using a 10% markup, every item's retail price would be 110% of its cost. However, the straight-line method is less than optimal because for higher-priced items, we would prefer to use a lower percentage. So, bottom line is that as the cost increases, we want the % markup to decrease. I have a formula called Michaelis-Menten that comes close to what I want, but it still has some deficiencies. This formula is calculated as follows: MA = (MM * C)/(PF + C) where MA = Markup Amount C = Cost MM = Max Markup Amount PF = Plateau Factor Using this formula with MM = $175 and PF = 1500, we find the following: For C =$1000, MA = $70, so effective markup rate = 7% For C =$2000, MA = $100, so effective markup rate = 5% I like the markup rates for the above two instances of Cost, but I'd prefer that the Max Markup be higher than$175. Unfortunately, if I want the above two markup rates (7% and 5%) for Cost = $1000 and$2000, respectively, this formula is deterministic, forcing the above two distinct parameters (MM = $175 and PF = 1500). In terms of the curve produced by this formula, while it passes through the$1000 and $2000 Cost points where I want it to, I'd prefer that the curve between these two points be flattened somewhat to allow a higher Max Markup as the curve extends past the Cost =$2000 point. Can anyone propose any other options for me? Thanks for any help you can give. Wayne
 March 18th, 2014, 07:25 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Asymptotic Retail Pricing Based on Cost Maybe split the markup into two parts, one fixed and one going to 0 with increasing price. For example: 3% of the price, plus $40, with a maximum of (say) 12%. That would give$250 12% $500 11%$750 8.3% $1000 7.0%$1250 6.2% $1500 5.6%$1750 5.2% $2000 5.0%$2250 4.7% $2500 4.6%$2750 4.4% $3000 4.3% which hits the desired points. Of course you could tweak this in any number of ways. March 21st, 2014, 08:07 AM #3 Newbie Joined: Mar 2014 Posts: 3 Thanks: 0 Re: Asymptotic Retail Pricing Based on Cost Quote:  Originally Posted by CRGreathouse Maybe split the markup into two parts, one fixed and one going to 0 with increasing price. For example: 3% of the price, plus$40, with a maximum of (say) 12%.
Thanks for this.

At first I was a bit skeptical, but this might just get me very close to where I want this to be.

Wayne

 March 21st, 2014, 08:27 AM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Asymptotic Retail Pricing Based on Cost If it does, great! If not, figure out what you don't like about the method, and come back with more information. Then I (or someone else) can help you build a better model with the new requirements.
 March 21st, 2014, 09:57 AM #5 Newbie   Joined: Mar 2014 Posts: 3 Thanks: 0 Re: Asymptotic Retail Pricing Based on Cost Thanks, CRG. The one other thing that I might like to control is the Max Markup Amount (so that markup amt cannot be more than, say $1200, no matter how high the cost.) I suppose I could simply add another parameter for Max Markup Amt, and I would have everything I need. Then again, I sell so few items that would be impacted by such a parameter that I might be best to just stick with what you've suggested. Thanks. Wayne March 21st, 2014, 01:00 PM #6 Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Asymptotic Retail Pricing Based on Cost Quote:  Originally Posted by whdyck The one other thing that I might like to control is the Max Markup Amount (so that markup amt cannot be more than, say$1200, no matter how high the cost.) I suppose I could simply add another parameter for Max Markup Amt, and I would have everything I need.
Sure, you could do that. (Though I don't know why you would, from a business perspective.)

More generally, you could split the method into different chunks with the n-th chunk having markup $a_n + price * b_n (of course pasting them together where these come out equal). So in my example you'd have the first region be flat 12% markup, a_1 = 0, b_1 = 0.12 and the second region be a_2 =$40, b_2 = 0.03, with the breakpoint being $444.44. Then your suggestion would add a third region with a_3 =$1200 and b_3 = 0, after a breakpoint of, let's see, \$38,667.

If you wanted you could tweak this by adding more regions with this same behavior. (Mathematicians call this sort of scheme piecewise-linear; it's not elegant, but who cares if it works for you?)

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