A simple price optimization howto

As many of us already know Predictive Analytics is an extremely useful and powerful toolbox for designing, building and evaluating the effect different pricing levels may have on your sales. In this post I'm going to show a simplified model for calculating the optimal price for a product given very few inputs. Basically you only need a few months history of your sales per week and the price of your specific product for each week. Now there will be a little bit of math included this time, but fear not! It's safe to skip the math if it does not interest you. 

Calculation of the optimal price at different price elasticities

First off we need to define a statistical model for the relationship between sales volume (y) and price (p). Without digging too much into the world of statistics I will boldly claim that sales can be modeled by

lny=βlnp+a


where β and a are unknown to us. These will need to be fitted by your specific data that we mentioned above. How you actually fit this is beyond the scope of this little teaser. 

Now, based on this function we can define a profit function that helps us calculate the optimal price based on price elasticity, cost per product produced along with a profit margin. After some mathematical manipulation it turns out that this function looks like this 

p=ββ+1⋅c−λm

where β is the price elasticity, c the cost of production, m the profit margin and λ the penalty term for the case when β>=−1.0. In this example λ is set to 0. 

What does the price elasticity represent? Well for instance, price elasticities greater than -1.0 indicates that if the price increases by 1% then the loss in sales is less than 1%. This is something you as a sales person should find extremely interesting.  

Let's have a look at an example! Say we want to calculate the optimal price based on different price elasticities. We use a fixed cost of 10 and a profit margin of 0.9.  The optimal prices are shown in the figure. Whether or not this is a realistic scenario I will leave up to you to decide. ;)

This small example has shown you how to give quantitative input to the optimal price based on the current price elasticity. Of course the end product would need a more complicated model but the use case is clear and simple. I hope you've enjoyed it and will start using R to impress your boss with just how operational it can be.

If you're interested and have some basic knowledge of R you can read a more technical blog post of the same scenario at here where code will be provided.

Why predictive analytics is necessary for successful pricing strategies

We've all heard it by now. The business world is being fed more and more buzz words every single day. Words like modeling, predictive analytics, big data, econometrics, fact based marketing and price optimization. Now these are not just buzz words. There's a lot of content behind them. Content that's important to all businesses worldwide. You can easily write a whole book about each and every one of these words, but what's really important is the one thing that unifies them: Facts! Predictive analytics and extraction of knowledge from data has taken a leap from science into the corporate world. This is really good news since questions like:

• How do we minimize markdown?
• How much is our demand affected by competitive prices?
• Which of our products have a strong reaction to changes in price?
• If our strategy is to keep our price below competition, then how much below?
• Are our price reductions just temporary markdowns, or everyday low prices? What is more beneficial?
• How will lowering prices on certain products affect the sales of your other products?
• How much do our products cannibalize on each other?

can now be answered with a much higher confidence than previously. Typically many of these critical questions are answered by rules-of-thumb and/or gut feelings, which might actually work out from time to time. Don't get me wrong, I'm all for gut feeling and taking calculated risks. The point I'm trying to make is here is that they should be calculated. This is precisely what predictive analytics can do for you.

Sounds good right? So, what is predictive analytics? Well it's a set of algorithms and methods that can extract knowledge from data. For example it can identify all the different variables that drive your sales. It can also figure out which media mix you should have as well as what price that will be most beneficial for your specific product.

So even if it seems like the world has gotten a lot more complicated with all these science terms flying around, in reality it's gotten a whole lot simpler. The intelligent algorithms along with a scientific approach to decision making are now able to not only identify cause and effect relationships but also to provide actionable recommendations. The question you should ask yourself today is not whether or not to do predictive analytics, rather it's all about how to get started. Trust me, it will be the smartest decision you'll ever make.