Formula Derivations and Formulas in Standard Notation

I have been asked a couple times of how I arrived at the equations shown below. As I suspect many others are also wondering about this, I will try to briefly explain how this was accomplished. Finding a best fit curve is the heart of the process and Excel has this capability built-in.

For the most part, these are ideal rates, but I have used some basic premises and applied them. To create a given price curve, one needs to use three base points. I placed the 1/4 page use of Business Week at approximately $450 which it what they pay for 1/4 space rates. The low end was placed at around $200 because that just seemed reasonable to me. I also kept the high end around $750-800. The math did the rest. Excel has a best fit option for matching lines to points and this is how I originally began this process.

For the assignments. I have in my mind the the lowest one should be paid for an editorial shoot is around $500. I have some student information pages on www.foodphotography.com that go into more detail about how much a photographer should expect to earn in a given day. I also talked to photographers about what Time should be paying and what Business Week will be paying down the line. I then took one of the magazines in the middle that had an average ad rate and average circulation and made it the mid point.

For reprints, I am totally guessing. I read EP fairly regularly and have read many posts about reprints. The $1 minimum per reprint kind of stuck in my mind and I also thought it would be important to also be able to differentiate whether a 1/4, 1/2, or full image was used in the reprint to determine price. Thus, if you look on the low end of reprints, it averages around $1000 for 1000 reprints for the four sizes shown. The higher end magazines were scaled up using a somewhat flatter curve because I thought the price for reprints is based more upon the advertising factor and not which magazine it was printed in. Of course, an article in Time should go for more than a reprint in a 50000 circulation magazine.

I made the web rates similar to the space rates for print. I believe the web should be priced the same as print because someday the web will replace the vast majority of print. I defined a quarter page to 320 x 240 pixels and extrapolated from there. I use 320 x 240 because the standard VGA video screen is 640 x 480 pixels.

For a bigger view of the formulas, click here.


Note: the dots in the formulas represent multiplication.