Three price elasticities of demand

Elasticity of demand is a measure of market response to a change in price. Three definitions of elasticity of demand are commonly found in the literature: (1) ε_p = point elasticity, defined for a given point on the demand function and relies on the derivative of the function at that point; (2) ε_a = arc elasticity, defined for the midpoint of an arc connecting two points, irrespective of the shape of the demand function; (3) ε = relative change elasticity, defined for two given points as minus the ratio of the relative volume increment to the relative price increment. Of the three, ε_p is the most widely cited and has the merit that marginal revenue is zero at ε_p = 1. It is also convenient when curves with ε_p = constant can be fitted to price-demand data. In practice, apart from the fact that ε_p is often difficult to determine, management is mainly concerned with discrete increments and not marginal changes, and in this respect ε_a is regarded as more useful. However, the relative change elasticity ε is preferable in all practical applications, both because relative increments refer to a given base period (instead of a midpoint, as in the case of ε_a), and because of the simplicity of using it in the analysis of company performance.