## Definition

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 for that product.

### 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 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, no analytical solution is easily available. Because a share of the sales that are lost if the price of one product is increased 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 changes with the price change of another, pricing theory offers the concept of the 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.

Price elasticities are widely used in practice, because they reduce the complexities of market dynamics into a single number that can easily be used for pricing decisions. There are different ways to determine price elasticities ranging from survey to sales data analysis. Most common are regression-based analyses of the price-sales relationship using historical sales data.

### What to watch out for 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, in practice such price elasticity analyses are often tweaked to support the expected result.