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.
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.
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| 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.
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