Avoid Arc Elasticities
Most textbooks computer so-called arc elasticities and us the midpoint method to derive percentages for that purpose. In my view, this is a very silly and confusing process. Unfortunately, the midpoint method is used for arc elasticities of demand in the Minnesota Ebook Ch 5: Sec 1. For that reason, I do not suggest that section as a reference reading. You are free to read the section if you want, but keep in the that we will not computer percentages that way in this course.
In case you are interested, this is what the Minnesota Ebook says about the midpoint method:
Notice that in the arc elasticity formula, the method for computing a percentage change differs from the standard method with which you may be familiar. That method measures the percentage change in a variable relative to its original value. For example, using the standard method, when we go from point A to point B, we would compute the percentage change in quantity as 20,000/40,000 = 50%. The percentage change in price would be −$0.10/$0.80 = −12.5%. The price elasticity of demand would then be 50%/(−12.5%) = −4.00. Going from point B to point A, however, would yield a different elasticity. The percentage change in quantity would be −20,000/60,000, or −33.33%. The percentage change in price would be $0.10/$0.70 = 14.29%. The price elasticity of demand would thus be −33.33%/14.29% = −2.33. By using the average quantity and average price to calculate percentage changes, the arc elasticity approach avoids the necessity to specify the direction of the change and, thereby, gives us the same answer whether we go from A to B or from B to A.