A Better Way to Calculate Percentage Changes Elasticities

If you try calculating the price elasticity of demand between two paints on a demand curve you will quickly notice an annoying problem. The elasticity from point a to point B seems different from the elasticity from point B to point A. for example consider these numbers.

Going from point A to point B the price rises by 50 percent, and the quantity falls by 33 percent, indicating that the price elasticity of demand is 33/50 or 0.66. By contrast going from point B to point A, the price falls by 33 percent, and the quantity rises by 50 percent indicating that the price elasticity of demand is 50/33, or 1.5. The reason this difference arises is that the percentage change are calculated from a different base.

One way to avoid this problem is to use the midpoint method for calculating elasticities. The standard way to compute a percentage change is to divide the change by the initial level. By contrast the midpoint method computes a percentage change by dividing the change by the midpoint (or average) of the initial and final levels. For instance S5 is the midpoint of S4 and $.6. Therefore according to the midpoint method a change from $4 to $6 is considered a 40 percent rise because (6 - 4)/5 * 100=40. Similarly a change from $6 to $5 is considereda 40 percent fall.

Because the midpoint method gives the same answer regardless of the direction of change it is often used when calculating the price elasticity of demand between two points. In our example the midpoint between point A and point B

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