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---- Bidding for maximum profit

Tonearm - 1:14 pm on Aug 6, 2012 (gmt 0)

I've been struggling with this for a while. An ROI system tells you how much a click is worth, but it doesn't tell you at what number of clicks your profits are maximized.

0 clicks = 0 profit. x clicks = 0 profit. Clicks greater than 0 and less than x = profit greater than 0. But at what number of clicks (and thereby CPC) is profit maximized?

If CPC increases in a linear fashion along with the number of clicks, I think profit would be maximized at x/2 according to the example above. The graph of profit vs. clicks would slope up to the maximum profit and then slope back down to zero with the same slope on either side of the point of maximum profit.

If CPC increases exponentially along with clicks, I think profit is maximized at a number of clicks greater than x/2. If CPC increases logarithmically along with clicks, I think profit is maximized at a number of clicks less than x/2.

I looked at some macro data in my account and it looks like CPC doubles when the number of clicks quadruples. At this point my lack of mathematical ability really takes its toll and I'm pretty much stumped.

Am I on the right track? Can I use a method like this to figure out what my maximum CPC should be in order to maximize profit?