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March 18th, 2014, 06:03 AM   #1
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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
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March 18th, 2014, 07:25 AM   #2
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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.
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March 21st, 2014, 08:07 AM   #3
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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
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March 21st, 2014, 08:27 AM   #4
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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.
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March 21st, 2014, 09:57 AM   #5
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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
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March 21st, 2014, 01:00 PM   #6
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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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