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When we measure Arc Elasticity, we are measuring the PRICE ELASTICITY OF DEMAND between two points on the demand curve. We can also measure the elasticity of any one point on the curve. The formula, because we are measuring only one point on the demand curve, does not have to take account of P1 or P2 or of Q1 or Q2. The formula is
where Point Elasticity will be different at each point of the demand curve. How is it calculated? How is there even a "very small change in Price" or a "very small change in Quantity" if we are measuring at a given point. Depending on the scaling of your graph, each point is, by definition, the sum of many other small points on the curve. Hence, when examining the elasticity of a point, you could establish a microscopic difference in the width of the point. No Calculus (I told you this web site was just for you!) To get a numerical answer under examination conditions without resorting to calculus, this is what you can do. Draw a straight line tangential to, but not cutting, the demand curve at the point (A) whose elasticity you wish to measure. This line should meet both the X and Y axes. Measure the length of the tangential line from your point (A) to the Y axis (point B), and from point (A) to the X axis (point C). Express the two measurements as a ratio to each other AB : AC, and you have the Point Elasticity of Demand at that point (A) of the demand curve.
If the demand curve is linear (as it usually is assumed to be), just get the ratio of the straight line demand curve above and below the point (A) , and this will give you the Point Elasticity of Demand.
The length of the line AC is approximately 3 times that of line AB, therefore Point Elasticity is approximately 3 (in absolute terms) - the curve has a negative slope so the answer would be -3.
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