Make more money (by understanding price elasticity)

The best price to charge is the one where you make the most money (profit). There is a simple formula for this. To calculate the price elasticity, you simply have to have two data points.

How much product was sold at P1 and how much product is sold at Price 2?

Price elasticity (PE) is basically the relationship between the change in quantity and change in price. If you imagine that as a straight line between two points, it is the slope of the line.

 (PE) PE = [(Q2-Q1) / ((Q1+Q2) / 2 )] / [(P2-P1) / ((P1+P2) / 2]

Where Q1 = initial quantity; Q2 = final quantity; P1 = initial price; P2 = final price

• If the PE > 1 (i.e. positive) the product is said to be relatively elastic. An increase in price would result in a decrease in revenue, and a decrease in price would result in an increase in revenue.
• If the PE < 1 (i.e. negative) the product is relatively inelastic. An increase in price would result in an increase in revenue, and a decrease in price would result in a decrease in revenue. (Think products like petrol.) 

To illustrate, assume that:

(a) The product costs $50.

(b) You have calculated the elasticity of a product to be -2.4005.  (This would be a product that is very inelastic – meaning that this product can tolerate price increases without sacrificing quantity.)

The simple formula for the optimum price is this:

Profit maximizing RSP

price elasticity x cost

price elasticity +1

-2.4005 x $50

-2.4005 +1

$85.70 

This means that the price at which you would sell your product to make the most profit is $85.70.

(There is one technical assumption that is unlikely to make a difference, but for the sake of completenes: This calcualtion assumes that the conditions that applied (competitors, discounts, etc) when you collected your price sensitivity data continues to apply after you have set your price.)

Comments

[P]

Not sure of my math, but the result is undesirable and unrealistic...

Q1 52
Q2 62

P1 40
P2 36

PE = -1.6667

Cost = $35.05

Profit Maximizing RSP = $87.62. Will not sell any and would go broke Dennis. Maybe I've missed something...

[DennisPrice]

Your math is impeccable. You have to appreciate though that the underlying assumption (as per closing para) is that the trend (the straight line relationship between price and quantity continues. REALITY prevails and the relationship is a CURVE (or another irregular shape) as people have price ceilings and perceived value is attributed to the items.

So you have not missed anything. Just remember that the equation holds true for a range of prices - which may not stretch to DOUBLE (as in this case) as consumers baulk at the new price point.

[TM]

Dennis, is there anything we can do with this scenario above?

I can add a dose of reality check and common sense, but is there nothing more scientific that we can do?

Also, does Pe assume no competitors? Is there a variation of Pe that shows how to handle a competitive "bench mark" price?

Does comparing a price rise and a promotional price drop on the same product change the calculation outcome? How do we use this info then? Which scenario is better for measuring Pe?
Thanks

[DennisPrice]

YOU SAID: I can add a dose of reality check and common sense, but is there nothing more scientific that we can do?

I SAY: There is modelling software (price optimization) that can be used. From memory the underlying maths relies on linear programming which allows you to nominate constraints (availability of stock, shelving capaicity etc) but I could not explain the intricacies of it.

YOU SAID: Also, does Pe assume no competitors? Is there a variation of Pe that shows how to handle a competitive "bench mark" price?

I SAY: Does not mean no competition - just that the competition level strays the same ; i.e. they do not respond to your price changes OR they always respond in the same way.

YOU SAID: Does comparing a price rise and a promotional price drop on the same product change the calculation outcome? How do we use this info then? Which scenario is better for measuring Pe?

I SAY: No it does not. It is simply the relationship between Price and Quantity. As you can see the assumption being that price drives quantity, and it ignores other factors as already discussed.

You use this info by recognizing that INELASTIC relationships allow you to raise praises without dropping quantity. As long as the relationship remains inelastic, you can keep raising prices. Also, as before, the relationship typically holds true in a certain range and is not indefinite.

In an organisation with 1000s of SKUs you will struggle to make sense of this without specialized software. The purpose of the blog post was to demonstrate the principle and its importance.

As a practical next step I would suggest talking to the suppliers of your key product(s) and get them to provide more information & have a collaborative relationship that will allow you to share the results/ info.