Finally a use for calculus: bidding to maximize profits!


sleepLast week, Google released a video talking about profit maximization and AdWords.  Having studied in Applied Economics, watching Hal Varian talk about incremental costs and revenues reminded me of a few important economic concepts (not to mention the few painful memories of studying up until dawn for next morning's math exam).  These concepts should help anyone visualize what costs and revenues look like under an auction for clicks.

Before we get in the details, let's build the model first.  We'll just use a simple 2-dimensional graph, with the number of clicks on the x-axis and price/revenues on the y-axis.  If you've been using the Bid Simulator tool, you'll notice that the click/price relation isn't usually linear but rather concave: the incremental value of acquiring clicks is positive.  In other words, the more clicks you want, the higher the cost/click you must be willing to pay.  Hypothetically, the revenues curve should have about the opposite trajectory; the more revenues you want, the harder it gets, therefore the more clicks you will need to get that extra buck (those are sometimes called irrelevant keywords).  The result is a graph that looks like this:


The difference between total cost and revenues is a Delta value. What Dr Varian was explaining is how to get the Maximum Delta value on the graph: that is the bid price where revenues and costs are as far away from one another as possible.  This is where we achieve profit maximization.  In other words, the point where marginal costs = marginal revenues (remember those calculus classes?)!  If we plot the Delta value from the figure above, it would somehow look like this:


Ideally you are looking for the threshold value where increasing your total spending would only start decreasing your ROI.

What does this mean for your business?

I always like to finish my posts by returning to reality, where we must put away the theory and think of how we can use the concepts in our everyday lives (or rather work).  The point of this blog is, when you've got tons of data, you can start to make bigger life decisions with your accounts.  Always keep in mind there comes a time when increasing Adwords spending (by adding more keywords, increasing budgets, bids and such) can increase your revenues, but not your return on investment.

In reality, drawing curves like the ones I've just shown you would be extremely difficult & time consuming.   What you can do however, is look at the ROI section in Google Analytics while paying attention to your Change history in AdWords.  Look for spikes in the ROI graph and analyze what changes you've made to your AdWords account around that period.  See if you can spot any patterns. Another indicator to look at is the cost/conversion value.  If you've been recently betting on new keywords and noticed your cost/conversion values going up, maybe you're heading in the wrong direction.  Wake up before you slide too far down the right side of the Delta curve.

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