# Pricing and Substitution

In my previous post on pricing, I showed a way to dramatically reduce the analysis required for a pricing decision. In this post, we will take it a step further and show that, in a significantly more complex example, we can still simplify the decision-making process. As an added bonus (!), we can generalize our result to something that makes intuitive sense and can be applied to quickly generate scenario analyses where needed.

Recall our example where we manufacture cars. We have a high-end offering priced at $40,000. The margin we earn on each sale is $4,000. Now we are considering whether to introduce a lower-end model for $30,000. Let’s assume the costs to produce that model (using cheaper parts) is $28,500. How many units of this new model can we sell? How much will consumers substitute away from our high-end model; in other words, how much of our increased volume will simply be from cannibalization? If all we do is shift demand from a higher margin product to a lower margin product, we only hurt our business. We need a way to think about the trade-offs without getting into unnecessary depths of analysis, which will only slow down our decision and time-to-market.

Here is the current situation:

To illustrate the new scenario, let’s first look at the case where substitution (say 30% for illustrative purposes) away from product A accounts for all volume of the new product B.

The net decrease to our margin is $75,000. That comes from simply selling the same number of units but having lower average margin per unit.

But we strongly believe total volume will increase. How much do we need it to increase to offset the substitution? We can use our model in Google Sheets to look at several scenarios.

This tells us we need to expand our sales by at least 50% to do as well as we were from a margin perspective as before.

Here is a graphical view. The points on the line show the result at different levels of market expansion. The area between the x-axis and the curve is the lost or gained margin. Your business can use this as a tool to discuss the impact of this decision and the magnitude of the impact. Remember, we are not trying to be precise here. The assumptions in the model are impossible to get perfectly, so we should look at the approximate size of the result. If the business believes the market would at least double, we should do this! If the business believes there is no way we would see even a 20% expansion, then we should not proceed. Simple, no further analysis is needed!

What if we want to flip this around and assume a given market expansion and then vary the substitution?

Pretty simple; we need substitution to stay below 10–15%.

What if we want to look at the interaction between volume and substitution? Below is the data visualized using Tableau. Larger, green dots are higher margin, and smaller, red dots are lower margin. This is one simple, visual sheet to facilitate a business discussion.

If we want to geek out a bit, we can look at this algebraically. To proceed with the new option, we need the new margin to exceed the old margin. Or:

`4*100*(1-`*s*) + 1.5*100*(1+*e*)-100*(1-*s*) > 4*100

where *s* = substitution %

and *e* = expansion %

This simplifies to:

*e* > 5/3 * *s*

This makes sense intuitively: expansion increases are good, substitution is bad.

But what if we want to generalize this for any set of margins?

We would choose the new product if:

*Ma***Ua**(1-*s*) + *Mb***Ua**[(1+*e*)-(1-*s*)] > *Ma***Ua*

where *Ma* = margin of product a

*Mb* = margin of product b

*Ua* = units of product a at the start

This simplifies to:

*e* > *s* * (*Ma*-*Mb*)/*Mb*

Hope you enjoyed the math fun! You will note this simple formula describes each line we have seen in this article. More importantly, now we have a way to look at any volume-substitution scenario even where the margins are variable. This particular formulation tells us what expansion needs to be given a substitution level and margins of the two products. One could also look at what the new margin would have to be given different expansion and substitution levels. In other words, how much do we have to push down costs of the lower priced product to benefit from it being introduced? I highly recommend using visualization tools like Tableau for the business discussion, rather than asking people to specify their assumptions upfront so precisely. It is not necessary and the decision can be made without that level of precision!

Note that we have not considered a few market forces here:

- If we do not launch a lower-priced option, will our competitors? It is always better to do the cannibalization ourselves than to have our competitors do it. To think about this, we will want a “do nothing” scenario to compare.
- We may want to consider the effect on the market of a new price point. Are we causing the higher-end market price point to collapse somehow?
- Is this an opportunity to raise the price of our high-end offering? That could drive separation of the product in the market and stabilize our high-end demand? Remember, sometimes raising prices also raises demand, and I am not talking about Giffen goods! Isn’t this what Apple did with the iPhone X launch?

Thoughts? Tools you have used in your business analyses?