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.

An alternative to cost-plus pricing

In my last post, I began a discussion of the shortcomings of a cost-plus pricing system. I also gave a real life example of a Brand Ladder, which we used to rightsize the prices of private label items. In reality, the Brand Ladder is the practical application of a well-trodden, ubiquitous concept within the world of strategic pricing, which is the notion of Value Based Pricing.

My own simplified, colloquial definition of Value Based Pricing is: Understand your customers' needs and how much they value your product, meet those needs and charge accordingly. Sounds easy enough, right?

Let's pretend that we are thinking of opening a hamburger stand/restaurant. There are two locations where we can set up shop.

1. We'll call the first location Cortland, in honor of a former stretch of industrial manufacturers right here in beautiful Chicago, IL. This area is recently defunct, but we will assume that it is still a manufacturing area.
2. The second location we're scouting is called North Face. It sits in the Lincoln Park neighborhood in Chicago, which is yuppie nirvana.

Off the top of your head, who do you think would buy burgers at each location?

1. Cortland - Blue collar types on a short lunch break in search of a quick, cheap meal that will fill them up for the rest of the workday.
2. North Face - Whitecollar millennials getting out of the office that want to eat at a fresh, locally sourced, quirky (i.e. non-chain) option.

Ok, now we're starting to paint a picture! I think the burgers would look something like this:

A burger that takes pride in its craft.

 VS.

In Chicago, a burger is technically a salad anyway.

What would you charge for a burger in each place?

1. Cortland needs to be quick, "good enough" in terms of quality, and provide great value. After looking at similar options to see where they're priced, $7.99 for a cheeseburger, fries, and fountain drink is fair. In and out in 20 minutes or your next burger is free. This is a high volume shop that needs a simple menu for quick customer turns.
2. North Face is has a hand-pressed patty made of a special in-house blended beef. The bun is brioche, because that is a fun word to say. Cheese is organic, usually Havarti. Avocados are extra because we harvest them from the tree we planted on the rooftop. Asparagus instead of fries because of course they have asparagus instead of fries at this place. Drinks are extra. I looked around the neighborhood and somewhere in the $12-$14 (+ drink!) range seems right.

So what is the point of this goofy example? Well, first, you should write about what you know, and I know about eating burgers. Second, I wanted to illustrate the notion of pricing to value. Think of the above example in the following way:

As value goes up, the price charged can/should go up. If you are offering a premium burger at North Face, then you should charge more than Cortland. Similarly, if you're Cortland and are offering a good but not great burger, you can't get away with charging a premium price. Either way, you have to know what your customer values before you can slap a price on it.

(Also, I'd be doing a disservice to my readers if I didn't pause for a moment and point out that this strategy is commonly called Good-Better-Best, or GBB. You have an entry level price for your Good item, a higher price for your Better item, and a premium price for your Best item. You hear this term and acronym getting thrown around all over the pricing world.)

You may be thinking to yourself, uhhhhh, hey Dan, this is a pretty simple concept. I agree. It's straightforward when you understand what your customers value. When you don't you get real-world examples like this:

Pretty obvious that the Steel item is way underpriced.

Why am I belaboring this topic that is found in virtually every pricing strategy book, conference, or course? Because the tricky part is how you actually find what your customers value. I feel that there is a gap in HOW you implement a value-based pricing system. That's actually one of the big reasons I started this blog.

This post has been fairly high level. Over time I'll get into the nitty-gritty of how to actually do some of this stuff. I'll touch on elasticity, competitor data, hypothesis testing, other sources of great pricing information, and all sorts of fun stuff. Drop any specific topics you want me to write about in the comments. Thanks for reading!

Why cost-plus fails and how a Brand Ladder can help fix it

Cost-plus pricing is the grand bete noire of the pricing world. It lurks around every corner, in every spreadsheet, and behind every pricing decision, intent on leaving money on the table and sapping profits.

In case you've never heard of cost-plus pricing, it refers to the practice of slapping a flat rate (whether % or $) onto the cost of an item and making that the price.

Here's the thing: a lot of the time cost-plus works. When costs are increasing, cost-plus will ensure that a company remains whole from a margin % perspective. If your costs go from $100 to $110 and you've always kept a 50% margin, your implied price goes from $200 to $220. Couldn't be simpler, right? (As a side note, I suspect that the simplicity of cost-plus is a big part why so many pricing professionals dislike it, but that's a post for another day.)

So what's the problem with cost-plus when costs are increasing? There are many, but the one that has always stuck out to me is that it doesn't differentiate why a cost went up. If they rose because everyone is facing increased copper prices, well then it makes sense to pass that cost along. What if the cost has gone up because you're not keeping an eye on your scrap/waste numbers, or you're over-scheduling your labor and have idle hours, or you accepted a price increase from your supplier without challenging it? Regardless of the reason, everything you produce is more costly. You're adding price because you can't control your cost. Not exactly a great reason to raise your price.

What about when costs are decreasing? I can go on Ali Baba right now and find literally millions of manufactured goods at a fraction of the cost that I would have paid even a few years ago. (It's a good thing that I don't need 2,000 cast iron skillets.) Six Sigma/Lean/Agile/whatever flavor of the month can significantly cut costs by eliminating defects and/or prioritizing the highest impact work. Perhaps the greatest bogeyman of them all is the threat of a retailer or distributor to go private label. It hangs like the Sword of Damocles over manufacturers worldwide.

Funny, the Sword of Damocles looked bigger in the picture on Amazon.

How does this relate to cost-plus? I'm so glad you asked! The following story is true, only the names and specific details have been changed to protect the innocent.

I worked for a company that was spending a tremendous amount of time and effort to source products around the globe. There were all sorts of smart people working on it. In one specific case, they found the exact factory in China that was producing a nationally branded product. The manufacturer didn't really care if they were stamping Logo A or Logo B onto this product, so they agreed to go down the private label route. This should have been a big win for my company, right?

Well, it didn't work out that way. Although the following are fake-o numbers, I saw thousands of instances where this exact thing happened:

National Brand
Purchased for $5
GM% of 50%
Sold for $10
Gross Margin of $5/unit sold


Private Label
Purchased for $2
Gee, we really like that 50% margin, so let's hold that constant
Sold for $4 (Cost of $2 from above divided by 50% = price of $4)
Gross Margin of $2/unit sold

The issue is pretty straightforward: we're making $3 less per private label unit that we sell! It was a real shame because of how much hard work went into sourcing the product in the first place.

People grasped the problem right away, so we came up with a relatively quick solution that we ended up calling a Brand Ladder.

Standing on a haunted ladder, reaching for floating dollars? This guy gets it.

The Brand Ladder consisted of three steps:

1. Map each private label item to whatever national brand item it is replacing.
2. Hold the GM$ constant instead of the GM%. This would form one boundary of a "good" price.
3. Apply the desired % spread to competition. This would form the second boundary of a "good" price.

Let's take the Private Label example from above and put it through the Brand Ladder logic.

1. We had already mapped this item to the national brand, so that was an easy step. Make no mistake that it was tedious to go through thousands of items that had been private labeled.
2. The national brand was making $5/unit, so let's take that $5 and add it to our private label cost of $2. This gives us one boundary price of $7.
3. Somewhere along the line, it was decided that a 20% spread to the national brand would be enough to entice people to switch to our private label. Ok, so the national brand sold for $10, meaning a 20% spread put us at $8. This is the second boundary price.

Great! Pricing this item between $7 and $8 would be a fair price that would give us a tidy profit for our efforts, would give the consumer a cheaper alternative to the national brand, and would not undercut the national brand to such an extent that it would create ill will.

One additional benefit is that even if we held GM$ flat and charged $7 on a cost of $2, our GM% would go up to 71.4% ($5/$7 = 71.4%). I've never been enamored of GM% as a metric of success because I can't spend a percentage, but you better believe that everyone was thrilled when they saw that they could get a virtually free GM% increase of 2140 bps.

This was a simple solution to a big problem. Organizationally it was an easy sell up and down the line. The devil was in the details when it came time to operationalize the solution across 1,000s of SKUs, but that's half the fun of it.

I hope this example drives home the point that cost-plus can eat up your profits without you even realizing it, especially in a declining cost environment. With a little effort, you can get to a logical, more profitable solution that will make everyone happy. I'm going to get into this Brand Ladder concept in more detail at a later date, so stay tuned.

The Greatest Equation in All of Pricing

I have lost track of the number of times I've heard a salesperson say something like "Let's lower the price and I'll make it up in volume." It's a seductive notion, right? On some level, there's the hope that the only thing keeping you from gobs of sales is that pesky price point. Taken to the extreme, if you lowered the price to $0 (or lower in some loss-leader situations) you'd sure move a lot of volume!

The problem with the above is that it rarely works out that way. In my experience, a price reduction only serves to dilute profit. Certainly, there can be some top line growth or improvement in margin percentage, but my scorecard says that profit is the reason I'm in business.

What about the other side of the coin? What if we want to see what would happen if we raise the price? Wouldn't it be great to have a quick way to set reasonable expectations about what volume we could afford to lose and still make a profit? There must be some sort of formula that can help us, right?!

The Volume Hurdle
We're going to use the Volume Hurdle formula to help illuminate both of the scenarios above. I've used the Volume Hurdle calculation numerous times to quickly show the high-level implications of what a price change could mean. Here's what the formula looks like:

%ΔQ ≥ -ΔCM/(ΔCM + CM_i)

Where Q = Quantity and CM = Contribution Margin (aka Price - Variable Cost). The subscript i = Initial in all subsequent examples (as in what is my initial contribution margin right now without making any price changes), and elsewhere I'm going to use a subscript f to indicate final/future (as in what would my future contribution margin be if I made a price change).

The whole idea is that this equation will show the change in quantity needed to break even based on the change in contribution margin. Let's work through a few examples to illustrate.

The preferred beer of pricing pro's everywhere.

Example: Beer Money
I sell bottles of beer for $4/each, it costs me $1/each to acquire them, and I sell 1,000 bottles on a given night. Beer makes people happy, and I'm a good guy that wants people to be happy. I want to sell MORE beer so I think I want to lower the price to $3/each. The cost remains the same in this example. How many bottles do I need to sell to break even from a profit perspective?

First, let's compute the CM in the initial state ($4 - $1 = $3), and what it will be in the future state once I reduce the price ($3 - $1 = $2).

Great! Because I sell 1,000 beers per night and I made a profit of $3 on each one, looks like my total contribution margin is $3,000.

The next task is to figure out how many bottles of beer I would need to sell at $2/each to break even. The simple math from here is to take the $3,000 profit I made, divide it by the $2 of profit per bottle, and I end up with 1,500.

Holy smokes! If I drop my price by 25% (from $4 to $3) I will need to sell 50% more beer (from 1,000 to 1,500) to break even from a profit perspective! Do I really think I can sell that much more beer? Probably not ethically, so I'd rather not drop my price.

An easier equation
Some of you caught that I pulled a shortcut when computing these numbers. I find the Volume Hurdle calculation a little clunky to use in its generalized format, so rearranged it looks like this:

Q_f ≥ CM_i/CM_f * Q_i

Why is this easier? In most real world applications I know how many units I'm selling now, I know my current price, and I know what price I think I want to charge. Now I can just plug and chug (heh!) to find the hypothetical quantity needed to support a price change.

Pictured above: A bear that would like to improve its profit margin.

Beer Money II: Cruise Control
As we discovered in the previous example, it would be tough for me to drop my prices and make more money. What if I raise my prices? How many fewer beers could I afford not to sell if my price per unit is higher? Assume the same as above (Price = $4/each, cost = $1/each, quantity sold = 1,000) but now I want to raise prices to $5/each. Let's throw that into the simplified equation and see what my future quantity (Q_f ) sold would need to be to break even.

Q_f ≥ ($4-$1)/($5-$1) * 1,000

This reduces to:
Q_f ≥ ($3)/($4) * 1,000
Q_f ≥ 750

Wow! I can afford to sell only 750 beers if I raise my price to $5. Now this is where intuition as a business owner needs to come into play. Do I really think I'm going to sell 250 fewer beers because people need to pay an extra buck? Probably not. So I'm going to move forward with the price increase.

But what about cost?!
I know what you're thinking because I hear it every time I've run through this example. If I sell fewer beers, won't my vendor get mad and jack up the price on me? Or if we consider the first example where we lowered price, couldn't I get a cost reduction if I move more volume? Sure, anything is possible. The beauty of the volume hurdle equation is that it can handle both of those scenarios because we're using Contribution Margin, which is computed with both price and cost.

Let's think about the first example again. Price from $4 to $3. Volume still 1,000. However, after speaking with the vendor about my plans to drive volume for them I can get a cost reduction from $1/each to $0.75/each.

Q_f ≥ ($4-$1)/($3-$0.75) * 1,000
Q_f ≥ ($3)/($2.25) *1,000
Q_f ≥ ~1,334

Ok, now we're getting somewhere. An extra 334 beers a night is still quite a bit, but it's more reasonable than an extra 500 a night in the first example. Maybe I can negotiate harder and get more off per unit, or I can get market funding to broaden my advertising reach to bring in more people, or maybe I can have the supplier front money for a ping pong table to bring in more foot traffic.

The point is I know what I'm up against if I lower my price, and I can bring hard numbers to a negotiation. Perhaps after running this exercise I say that I like where my price is right now and leave it alone. Sometimes the best decision you make is not to change. Cheers!

Practical Pricing Advice

Hi there!

My name is Dan Cakora. I've worked in the pricing world for over a decade. Over that time I've learned many tips, tricks, and tactics that have made my life a lot easier as I strive to drive profit for my employers.

My goal for this blog is to share that knowledge and hopefully help someone that has a pricing problem of their own. There will be some discussion of over-arching strategy, but the real meat and potatoes will be in practical pricing advice that you can use today. Pricing doesn't need to be a Ph.D project, after all. Small improvements can add up quickly!