# Elasticity-based Pricing

## What is elasticity-based pricing?

Price elasticity measures how demand changes (∆Q/Q) with price changes (∆P/P):

ε=(∆ Q∕Q)/(∆ P∕P)

If a pricing manager knows a product's price elasticity, they can easily model the effects of a price change on sales, revenue, and profit.

#### Explanation

Furthermore, if only the price of one product needs to be optimized, the profit optimum can be calculated using this formula:

ε∙m=-1,

where ε is the product's price elasticity, and m is its margin (p-c)/p. For example, if a product's price elasticity is -2, then a margin of 50% maximizes the profit. With unit costs of €100, the profit-maximizing price is then €200. Further, the revenue-maximizing price is at a price elasticity of -1.

Price optimization using price elasticities in a portfolio, for example, in a good-better-best offer, where prices and sales between products interact, is much more difficult.

In most cases, an analytical solution is only sometimes available. Because a share of the lost sales if one product's price increases will stay within the portfolio, prices in a portfolio can be higher than if products are optimized individually. Therefore, in a portfolio

ε∙m≤-1

for all portfolio products. To measure cross effects between two products, that is, how the sales of one product change with the price change of another, pricing theory offers the concept of cross-price elasticity. However, in practice, the cross-price elasticity is very difficult to measure, and it changes massively with price changes in either product.

Companies widely use price elasticities because they reduce the complexities of market dynamics into a single number that they can easily use for pricing decisions.

Different ways to determine price elasticities exist, from surveys to sales data analysis. The most common are regression-based analyses of the price-sales relationship using historical sales data.

#### What are the disadvantages of elasticity-based pricing?

Some of the challenges with this pricing method include the choice of the demand function (e.g., linear or exponential), the identification and exclusion of "outliers" that do not support the expected relationship between price and sales, and the way the price elasticity is computed from the regression line – as the price elasticity varies along the curve.

Such models often suffer from poor fit quality, as typical regression models – linear or otherwise – do not capture well the dynamics and customer choices that determine sales in a market. Therefore, such price elasticity analyses are often tweaked to support the expected result.

###### Further reading

October 26, 2022