How to know if a price change is profitable?
The profitability of a price change depends largely on how sensitive customers are to that change. To quantify this sensitivity, a metric called price elasticity of demand is used, which measures how much units sold vary when the price changes.
COSTSPRICE ELASTICITYBREAK-EVEN ANALYSIS
Understanding price elasticity of demand
Elasticity is defined as the relationship between the percentage change in units sold and the percentage change in price. For example, if a product costing $70 sells 100 units, and lowering its price to $50 doubles the units sold, then the price drops 29% and units increase 100%, giving an elasticity of 3.5. This means that for every 10% reduction in price, units increase 35%.
However, if elasticity is calculated in the opposite direction—from $50 to $70—the price increases 40% and units fall 50%. In this case, the result would be 1.25. Even though the change is the same, the direction of variation affects the result.
To avoid this asymmetry, midpoint elasticity is used. It is calculated using the midpoint between the two observations as the reference. Thus, the price variation would be 33% and the unit variation 67%, regardless of direction. In this case, the elasticity would be 2, indicating that for every 10% change in price, units change 20% in the opposite direction.
Price determines elasticity
Elasticity is not a fixed value. It depends on the distance between the current price and the fair price, which is determined by perceived value. If the current price is above the fair price, elasticity will be high, and reducing the price makes sense. Conversely, if the price is below the fair value level, elasticity will be low, and increasing the price will be advisable.
In this sense, it is not elasticity that determines the price, but the price that determines elasticity.
The break-even point
Often, the exact elasticity of a product is unknown. In such cases, break-even analysis can be used to determine whether a price change will be profitable.
The break-even point involves calculating the necessary variation in units sold to maintain the initial gross contribution after the price change. To do so, one starts with the initial price (P1) and final price (P2), as well as the units sold before (Q1) and after (Q2), and the product's variable cost (VC).
The break-even condition is reached when the gross contribution of the final scenario (P2 – VC) × Q2 equals the gross contribution of the initial scenario (P1 – VC) × Q1.
The formula resulting from this analysis indicates that the minimum variation in units needed to maintain gross contribution is equal to the negative of the variation in price, divided by the sum of the gross margin and the variation in price.
Examples of application
If a product has a gross margin of 50% and a 10% price increase is considered, the analysis shows that up to 17% of units can be lost while still maintaining the original gross contribution. If the loss in units is smaller, more contribution is generated. But if more than 17% is lost, profitability decreases.
In an opposite case, if the price is reduced by 10%, at least 25% more units must be sold to maintain gross contribution. If the increase in volume is lower, contribution is lost; if it is higher, improvement is achieved.
Differences between types of buyers
Elasticity varies depending on the type of buyer. Price and value buyers tend to be more sensitive to price variations, so their elasticities are usually higher. In contrast, relationship and convenience buyers show lower sensitivity, resulting in lower elasticities.
This difference has important strategic implications for the capabilities a company must have to serve each type of customer profitably.