Yeesh. I haven’t used the blog in what, years? I’ve changed the title and the header…and maybe I’ll change the theme too, I’m not sure yet. But the ch4na.wordpress.com domain will stay, as a reminder of this site’s origins. Or maybe because I’m too lazy to migrate to a new domain. Or maybe because I can’t think of a clever domain name. Whatevs.

Anyway. I’ve been selling on Amazon and eBay for some time now, to make some money and to get my feet wet in online selling. And it’s been a fun journey, with more than a few mistakes and a decent trickle of profits. However, to maintain an orderly revenue scheme, you have to get down and dirty into the math. I decided to tackle eBay first, since it’s easier. (Edit: <That is a lie.)

eBay charges 10% of the final selling price; PayPal charges 2.9% of the price plus a flat 30¢ fee per transaction. So initially, I thought the revenue formula simply went like this:

**y** = $0.30 + **x** + .029**x** + 0.1x or ** y **= 0.3 +1.129**x
**

where X is the profit you want to make and Y is the price you should sell at, A is acquisition costs and SH represents shipping charges. Easy enough, right?

Wrong.

The formula was giving me the wrong figures, and it took a while to figure out why. You see, I calculated the fees based off X – the profit. In reality, eBay & PP calculate the fees based off of the *selling price. *If I sold something for, say, $6 to make a profit of $5, the fees are calculated from the $6 selling price So I needed something that would just give me a price to sell at.

The TI-84 Plus SI has an built-in equation solver – but you have to set everything equal to “0” to make it work. So when the above formula wasn’t working, I plugged in this:

0 = (.3 + .129**x** + 5) -X

** ** since I wanted $5 of profit and was looking for X, the selling price. I got my answer and I got the right formula.

But I was still not satisfied. I couldn’t understand why I had to work backwards to get the (quite simple) answer. This made me angry and quite a bit upset. I felt that I had cheated, somehow, by using the calculator. I wanted be able to figure this out the “honest” way, by thinking. Eventually I sat down with my original formula and swore I would get from there to the right one, even if it took me all night.

Over and over again I tried every combo of Ys, .3s, .129s and Xs there was. Nothing was working. I looked at my work for the original formula. I tried thinking about what my objective was – to calculate fees based off the selling price.

*Selling price. *

It hit me like a bolt of lightning. Almost literally. SELLING PRICE! Of course! Y represents selling price…so what the hell am I doing, attaching the .129 fees to X, the profit?! I wrote out my victory, adding the other variables back in.

**y **= 0.3 +.129**y **+ **x **+ **A** + **SH**

0.871**y** = 0.3 + **x **+ **A** + **SH**

**y **= (.3 + **x** + **A** + **SH**)/.871

God, I haven’t been so happy since school let out.

I used the TI-84 to calculate a curve based on postage fees per x ounces (up to the 13oz. max for First Class packages that everyone ships with on eBay because they’re cheap.)

**y **= -0.00103**x**³ + 0.02986**x**² – 0.10172**x** + 2.00566

It’s surprisingly accurate – off by a couple of cents, at worst. Plug all that into “A” in our master formula, and replace x with whatever your package weight is. A bit unwieldy, but handy, since I don’t need to keep a separate table of postage prices.

You can manipulate these formulas to show several details about your sales, like percentage of fees out of the total price. And it’s really easy to add in variables like taxes and other expenses.

That’s it for eBay. In an upcoming post, I’ll (try to) dissect (part of) Amazon’s maze of fees, and (try to) construct some hairy formulas for third-party and FBA (Fulfilled By Amazon) selling costs.

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