If there’s one question on every Revenue Manager’s lips, is this: **what is the price elasticity of my demand?**

It’s a question I hear every week or so. How do I answer it? Are there any good answers? And finally, is it even a good question?

# The beginners naivety

In general, the more mature a company is in terms of Revenue Management, the less they ask themself this question. The more mature they are, the more they have given up trying to find an answer. This is the case for many airlines, which are 10 years ahead of other sectors of the industry in the area of RM, and which are well aware that they are wasting their time.

On the other hand, companies or industries just starting out in Revenue Management (theatres, car parks, etc.) often start by asking us about the subject: «* I’m going to start doing Yield, can you please give me my elasticity?* ».

Given the naivety of the question, you’re almost tempted to reply: «* Yes, yes, two minutes, it’s coming… *». After catching our breath, we gently encourage our interlocutor to consider setting up Yield in the right order and starting with simple things.

Why on earth is it so complicated to measure elasticity?

## The crumbled elasticity

The «* price elasticity of demand* » in itself means nothing. Because there is no single, perfectly uniform and homogeneous demand, but rather a **multitude of demands **that are expressed differently in terms of their appetites and booking methods, their motivations, their choices and their relationship to price.

There is no reason why price elasticity should be the same for a family as for a senior citizen. There’s no reason why it should be the same for all sales channels: Call centres, web, TO, etc. Nor is there any reason why it should be the same over the long or short term, for a May bank holiday or a long August holiday. There’s no reason why it should be the same for every product, whether it’s a standard room or a luxury suite. There’s no reason why it should be the same for French or Spanish customers; in Cannes or Angoulême; a « leisure » customer or a « business » customer.

All these variables (type of customer, destination, product, reservation time, source market, etc.) are obviously not independent, which makes the problem even more complex.

To be fair, demand would have to be analysed for all combinations of all these criteria, which **reduces the analysis sample** to the point where the poor elasticity that was supposed to be measured is crumbled.

### Endogenous and exogenous factors

So, let’s assume that we succeed. We have then identified a perfect segmentation that allows us to have a clean sample of data.

We start by identifying the demand that is usually expressed at a given price level for a given segmentation. We lower the price by 10% on several occasions, for example, and see what happens. Obviously, the same thing never happens…

You won’t have the same impact:

- If the price cut is made via a special offer that is widely publicised or if it remains confidential on page 4 of your website, it won’t have the same impact.
- If the competition follows you or not, you won’t have the same impact.
- If you have substitute products or not, you won’t have the same impact.
- If you advertise in terms of free nights, slashed prices, value or percentages, you won’t have the same impact.
- If the area where your hotel is located is saturated or if there is a lot of availability in the surrounding area, you won’t have the same impact.

That’s a lot.** You’d have to fix a watertight perimeter**, and consider the problem « all other things being equal », which obviously never happens. Perhaps this reminds you of the chemistry lessons in your final year of high school, when we used to think in terms of CNTP (Conditions Normales de Températures et de Pression – Normal Conditions of Temperature and Pressure), which we only find in the lab. But that’s no reason to put customers in test tubes…

#### By the way, what does elasticity do?

Let’s continue: let’s imagine that we’ve found the right segmentation, on a watertight perimeter preventing any cannibalisation, and that the competitors are still doing the same thing to make your life easier. We’re talking about Normal Conditions of Temperature and Pressure.** It never happens**, but let’s be crazy.

So we’re finally going to be able to measure elasticity, which is a generally negative value that depends on a number of variables (customer type, source country, booking lead time, etc.).

The elasticity e is generally given the definition :

*e = Δd/ Δp where Δd is a small variation in demand and Δp is a small variation in price.*

One detail at this stage of our study: the formula holds true for a small variation in price and a small variation in demand. When we measure price jumps of 25%, it no longer holds. But, at this stage, we’re not even close to an approximation…

So what do we do with this value? ????

If the elasticity for a Spanish family booking standard rooms at the Hotel du Bonheur in Cannes in August 4 months in advance, using their preferred TO, is -1.8. What to do ????

There is a formula that gives the optimum discount percentage for a given elasticity (see the box at the bottom of the article). Do we simply apply the formula for the Spanish family who booked in August-4-months-in-advance on the standard rooms at the Hotel du Bonheur by going through their favourite TO? And we repeat the operation for each combination of criteria?

Absurd. Useless. The level of segmentation required, the impact of communication on prices, exogenous effects, the difficulty of measurement itself, the operational use of elasticity…

All these factors make elasticity impossible to encapsulate in a formula, which would be **unusable anyway**.

##### Putting an end to elasticity

Let’s get back to reason. There are many other ways of identifying whether it is appropriate to raise or lower your price. For example, with simple alerts based on good old-fashioned, seasonally adjusted demand. Without knowing elasticity, but with a little common sense and good forecasting.

Whoever makes a significant breakthrough on this subject one day will obviously win the Nobel Prize in Economics. Because the subject is extremely important, far beyond hotel yield. There are a few publications, from MIT for example, where you’ll see algorithms described, you’ll hear about frat 5, Q-forecasting, Marginal Revenue Transformation, hybrid models and so on. Very interesting. A little technical, but not without meaning.

Elasticity is an R&D subject, not an operational one, even if some firms promise you the magic study for a few hundred thousand euros.

What are they offering? Firms deliver this kind of study? I can see your eyes shining. You’re tempted. You never know, it might work.

**I beg you, give up**. Set up simple, robust mechanisms, step by step, without burning your wings. When it comes to Yield, it’s the tortoise that wins, never the hare.

Elasticity is a reality, but an elusive one. The Grail of the Revenue Manager.

e = Δd/ Δp where d is demand and p is price. If P0 is the initial price and D0 is the initial demand, we get :

CA(x) = P0 * D0 *(1-x)(1-e x) where x = price variation (if my price varies by x%, my demand varies by e x%).

CA(x) is a second-degree equation that reaches its maximum when the derivative cancels out. The derivative of CA(x), known as CA'(x), is zero when the derivative of

e x 2 – (e +1) x +1 = 0, i.e. when x = (e+1)/2e

For example, for an elasticity of -2, the discount value that maximises CA (subject to having the available capacity to meet demand) is 25% (because x is ¼ if e is -2)

*Keywords: Elasticity, Revenue Management, segmentation, variation, forecasting *