The Economic Way of Thinking 13th Edition by David Prychitko, Peter Boettke, Paul Heyne

Exercise 22

Price elasticity of demand can be calculated by dividing the percentage change in the quantity demanded by the percentage change in the price.
(a) What is the coefficient of elasticity between the two points of the Demand schedule in each of the cases shown in Table 3-3?

(b) If you divided 100 percent by 50 percent in the ticket case, and 50 percent by 100 percent in the coffee case, you got very different coefficients (2 and 0.5, respectively) for what are actually identical relative changes. The different results come from using the larger price and the smaller quantity as the base from which to calculate the percentage change in the ticket case, and using the smaller price and the larger quantity as the base in the coffee case. But the coefficient of elasticity should be the same between two points regardless of the direction in which the change is measured. How can this problem be handled?
(c) What is the coefficient of elasticity in each of these cases if you use the average of the prices and quantities between which the change is occurring as the base for calculating the percentage changes?
(d) In both cases, total expenditure (price times quantity) does not change when the price changes. What does this imply about the elasticity of demand between the prices given? Does this implication agree with your answer in (c)? (It should.)