Here, we take an infinitely small change in X, dX, and find the corresponding infinitely small change in Y, dY, expressing these as proportions, respectively, of their initial values X and Y (d is a symbol meaning ‘an infinitely small change in’; those who know some calculus will recognize it as the differential operator). We then find the point elasticity of Y with respect to changes in X as:
This measure is called a ‘point’ elasticity measurement because it effectively measures elasticity at a point on the curve relating Y to X corresponding to the values of X and Y chosen, and this is a result of taking infinitely small changes in X and Y. The above expression for point elasticity included the term dY/dX, the first derivative of Y with respect to X. In fact, point elasticity is calculated by evaluating this derivative at a particular pair of values of X and Y and inserting this into the above formula. With reference to price elasticity of demand: if the measured elasticity is greater than 1, it is said that the good has ‘elastic demand’; if the elasticity is equal to 1, the good is said to be of unit elasticity; and if the elasticity is less than 1, the good is said to have ‘inelastic demand’. The importance of the measure of price elasticity of demand is that it tells us what will happen to total expenditure on a good if its price should change.