In the 1970s the government of Mexico City repainted the highway lane lines on the Viaducto to transform a four-lane highway into a six-lane highway. The government announced that the highway capacity had increased by 50 percent (equal to 2 divided by 4). Unfortunately, the number of collisions and traffic fatalities increased, and one year later, the government restored the four-lane highway and announced that the capacity had decreased by 33 percent (equal to 2 divided by 6). The government announced that the net effect of the two changes was an increase in the highway capacity by 17 percent (equal to 50 percent minus 33 percent).
This anecdote reveals a potential problem with using the simple approach to compute percentage changes. Because the initial value (the denominator) changes, the computation of percentage increases and decreases are not symmetric. In contrast, if the government had used the midpoint method, the percentage increase in capacity would be 40 percent (equal to 2 divided by 5), the same as the percentage decrease. In that case, we get the more sensible result that the net effect of the two changes is zero.