My Best Frenemy: Price Elasticity

This wouldn't be much of a pricing blog if I didn't discuss elasticity. I typically write for two audiences: 1) analysts who want to learn a few pricing tips and tricks to make their lives easier, and 2) executives who have been tasked with improving pricing within their organization.

Group 2 is one of the big reasons elasticity turns into a dumpster fire. Typically they have an MBA, meaning they took Econ 101, and they remember at least something about elasticity. C'mon, it was in a textbook and was easy to apply, so their company should of course be using it!

Well, it's not that simple. In the next few posts I want to help both groups. For Group 2, I want to show some of the nuance as to why elasticity is tricky to find and perhaps why it isn't the unimpeachabe metric it was made out to be. For Group 1, I will show alternate methods to find elasticity because the execs won't quit badgering you about using it.

A Refresher On Elasticity
Elasticity (many times referred to as the price elasticity of demand in economics) is a metric that shows the ratio of a percent change in quantity relative to the percent change in price. This is pretty much the Econ 101 textbook definition. In case it has been a while since that class, the formula for price elasticity is:

ε = %ΔQ/%ΔP

Where Q = Quantity and P = Price. That little ε is epsilon and is used as shorthand for elasticity.

You may remember something about the terms elastic, inelastic, and unit elastic.

• If ε > 1, then it is considered elastic. It implies that the item is relatively sensitive to a change in price. A 1% change in price will result in a greater than 1% change in quantity. Proceed with caution when changing prices!
• If ε < 1, then the item is inelastic. It's not really that sensitive to a price change. A real world example is gasoline. If it goes up by 1% in price, people still pretty much buy at the same rate. This is a great place to be from a business perspective!
• If ε = 1, the the item is unit elastic. A 1% change in price equals a 1% change in quantity. On the surface this isn's super interesting, but in a future post I will talk about why it can help maximize revenue.

In general, elasticity makes intuitive sense. If the price of something goes up, then the quantity purchased should go down. This is how the real world works, right? I don't buy as many hamburgers if they become more expensive. The whole trick is to figure out if, as a company, you can stand the change in volume associated with a price change. Elasticity helps us do that.

(A quick note about notation: Due to habit I'm typically going to refer to elasticity as a positive number, whether thinking about a price increase or decrease. As we just discussed in the paragraph above, a price increase will typically correspond to a decrease in quantity and vice versa.)

Putting Some Numbers Out There
Let's work through some numbers. In Example 1 our burgers went from $6.99 to $7.99, and the corresponding quantity of burgers that we sold went from 10,000 to 8,800.

A curious thing has happened! We raised our price, sold fewer units, and made more money (which we can see on the Total Revenue line). The reason we made more money is because this item is inelastic. Using the data from the table, we can see that Elasticity = %ΔQ/%ΔP = -12%/14% = -.84. If we take the absolute value of -.84, we get .84 and that is definitely less than 1.

How about another example? Same scenario (burgers from $6.99 to $7.99) but the quantity sold has changed. Uh oh, we're making less revenue in this example. Why? Because in this example hamburgers are elastic. The elasticity is greater than 1 (-15%/14% = -1.07. The absolute value is 1.07, which is greater than 1).



How can we apply this to future decisions?
What a time to be alive! I've quantified the interaction between a change in price and a change in quantity. Now I can apply that logic to future decisions. I bet there's a slight tweak to a formula somewhere in this very blog post that can help us do so. Yep, there sure is! It looks like:

%ΔQ =  ε * %ΔP

 Let's revisit Exaple 1. Elasticity is .84. We're at $7.99, and we sell 8,800 burgers. What if we want to raise prices to $8.99? Ok, that is a % change in price of ~12.5%.

%ΔQ =  ε * %ΔP = (.84) * 12.5% = ~10.5%

Because we're raising our prices, we should expect quantity to fall. Our new quantity sold is:

8,800 * [1 + (-10.5%)] = 7,876

We do a little bit of math to figure out our future revenue based on the price change ($8.99 * 7,876 = $70,805).

So that's it, right?
Numbers don't lie, so obviously we should raise the price AGAIN, right? Not so fast, my friend. An extra buck moves the price point up quite a bit, and 12.5% on top of a previous increase of 14% is quite a bit of an increase to stomach (yesssss, another pun!). Would I really risk that much of a drop in volume for an extra $500? Probably not.

In addition to the above, in my experience there are three broad issues with the elasticity equation we used:

1. False Numerical Exactitude - It doesn't give any indication as to how good a measure it is. Put another way, we don't know if the elasticity we computed has any explanatory/predictive power, or how big a confidence interval it has.
2. Doesn't Account for Exogenous Factors - It doesn't account for factors that are happening outside of the simplistic view of quantity and price. For example, it doesn't know that I stopped advertising in the local paper, or that a new competitor opened up across the street, or that I started offering chicken sandwiches on the menu.

Tread carefully if you decide to use the Econ 101 formula. You are very likely to end up exactly wrong. There's a reason that companies like Nielsen and IRI make hundreds of millions of dollars per year providing this information. It's tricky to do well, but when it is done well it is worth the price.

This post has gotten quite lengthy, so let's draw it to a close. In the next post I will show how to use simple linear regression to begin to address some of the issues above, although it is far from a perfect solution.