Model Parameters — Elasticities and Cross Elasticities

Elasticity of Demand and Cross Elasticity of Demand

• Elasticity refers to the degree of responsiveness of one variable to another. Price elasticity of demand is a measure of the responsiveness of demand (sales quantity) to a change in price, and it is determined by the following equation:
• $$\varepsilon = Price \,Elasticity$$ $$Q = Sales \,Quantity$$ $$\varepsilon = \frac{\%\,Change\,in\,Sales}{\%\,Change\,in\,Price} = \frac{dQ/Q}{dP/P} = \frac{P}{Q}\frac{dQ}{dp}$$
• In the context of in-store promotions, the relevant parameter is discount price elasticity. The impact on sales due to a temporary price reduction (price discount) is much greater than that due to a permanent reduction in price.
• Cross price discount elasticity is a measure of the responsiveness of sales quantity of a product to a (temporary) change in price of another product:
• $$\epsilon_{A,B}=\frac{\%\,change\,in\,quantity\,of\,product\,A}{\%\,change\,in\,price\,of\,product\,B} = \frac{dQ_A/Q_A}{dP_B/P_B} = \frac{P_B}{Q_A} \frac{dQ_A}{dP_B}$$
• The notion of elasticity of demand, applies similarly for elements of promotions including displays and co-operative advertising. Display elasticity for instance is the percentage change in sales volume due to the incidence of in-store displays. Similarly co-operative advertising elasticity is the percentage change in sales volume due to the incidence of co-operative advertising.
• In the discount price elasticity table the elasticities are placed along the diagonals (shaded beige). For instance, the discount price elasticity of demand for Koko Krunch is −3.2. This implies that a 10% reduction in the item’s price will result in 32% increase in sales.
• The table also depicts the cross discount elasticities. It tells us that a 10% discount in the price of Koko Krunch will result in 8% drop in the sales volume of Milo. Similarly a 10% discount in the price of Milo will result in 3% reduction in sales of Koko Krunch.
• Display and feature elasticities are positive. The incidence of a regular display for Koko Krunch will result in 12.4% increase for Koko Krunch and 2.6% decrease for Milo. And the incidence of a regular feature for Koko Krunch will result in 5.8% increase for Koko Krunch and 1.4% decrease for Milo.
• The impact of endcap displays is 50% greater than that for regular displays, and the impact of special displays is 100% greater. In other words, a special display of Koko Krunch will result in 2 × 12.4% increase in the brand’s sales.
• The impact of large features is 50% greater than that for regular features.