On Teaching Price Elasticity of Demand and Change in Revenue due to Price Change -- A Synthesis with and without Calculus

Price elasticity of demand measures how much, in terms of percentage change, the quantity demanded responds to a change in price. In this pedagogical note, first we intuitively introduce the very first notion of price elasticity, which is a directional measure because it describes the impact of an arbitrary change in price from one to another on the percentage change in quantity demanded. Next, we show how this measure becomes "point" price elasticity of demand when demand is linear. Finally, with help from calculus, we show how it leads to the development of (point) price elasticity of demand in general. At each stage, qualitative results concerning changes in total revenue and price are given and compared with what are in textbooks. A quantitative result regarding predicting the percentage change in total revenue from the price elasticity of demand and the percentage change in price is also given for the case of linear demand. By working progressively from the directional measure to the linear case followed by the general case, and from non-calculus approach to calculus approach, with precise definitions and 6 propositions, we intend to provide a unified framework for teaching the notion and applications of price elasticity in principles of economics as well as intermediate microeconomics. Flaws in textbooks are identified and resolved as well.