Midpoint Method
What is Midpoint Method?
The midpoint method calculates elasticity using the average of the two prices and quantities, so it gives the same value in either direction.
It fixes the problem that ordinary percentage changes differ depending on the starting point. The change is divided by the midpoint (average) of the start and end values. The College Board uses it for AP elasticity calculations.
Midpoint Method: a worked example
Price rises from $8 to $12 while quantity demanded falls from 60 to 40. The midpoint quantity is (60 + 40)/2 = 50, so the quantity change is -20/50 = -40 percent. The midpoint price is (8 + 12)/2 = 10, so the price change is 4/10 = 40 percent. Elasticity is -40/40 = -1, unit elastic, an absolute value of 1. Compare the ordinary route: starting from $8 you get 33.3 percent over 50 percent = 0.67, and starting from $12 you get 50 percent over 33.3 percent = 1.5. Same two points, two answers.
The mistake students make with midpoint method
The frequent slip is using the midpoint in one half of the ratio and the starting value in the other, usually the midpoint for price and the original figure for quantity. That produces a number close enough to look plausible and still wrong; both percentage changes have to sit on their own midpoints. A second slip is averaging the two ordinary elasticities instead, which is not the same operation: 0.67 and 1.5 average to about 1.08, not the 1 the midpoint method gives.
Midpoint Method questions
Why does the midpoint method give a different answer than the regular percentage change?
The midpoint method divides by the average of the starting and ending values instead of by the starting value, so the denominator stops depending on which end you began at. An ordinary percentage change counts the same $4 move as 50 percent going up from $8 and as 33.3 percent coming down from $12. Dividing by the midpoint of $10 gives 40 percent in both directions, so the pair of points yields one elasticity.
Does the midpoint method change whether demand is elastic or inelastic?
The midpoint method can change the verdict near the boundary, which is the practical reason it matters. In the worked example the ordinary calculation gives 0.67 in one direction, which reads as inelastic, and 1.5 in the other, which reads as elastic for the very same two points. The midpoint answer of 1 says unit elastic and does not flip. Well away from the boundary, the two approaches usually agree on the category.
Can you use the midpoint method for elasticities other than demand?
The midpoint method works for any elasticity, not just price elasticity of demand. Price elasticity of supply, income elasticity and cross-price elasticity are all ratios of percentage changes, so each percentage change can be taken against the average of its own two values. Only the variables in the numerator and denominator swap; the structure stays the same, and so does the payoff of getting one answer regardless of direction.
Formula / Example
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Common comparisons
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