Using the price elasticity of demand to solve for a percent change in quantity

Figuring out how to calculate the price elasticity of demand can be one of the most abstract concepts for students. However, it is a very useful measure, and businesses and the government are very interested in price elasticity of demand measures for all sorts of goods. Imagine, if netflicks knew the price elasticity of demand for their product, they would have never raised their price as they did, and the following fallout could have been avoid.

For this post on economics, we consider the following question relating to the price elasticity of demand:


Assume the industry price elasticity of demand for widgets is equal to -1.2. If the quantity supplied by the industry is expected to increase by 20%, what is the expected change in equilibrium price?
a- it will not change
b- it should fall by 20%
c- it should fall by 16.67%
d- it should rise by 16.7%
e- it should rise by 20%

The trick here is to remember the equation for price elasticity of demand, and to be able to manipulate in such a way that gives us the % change we are looking for instead of the elasticity measure itself.

We know that the equation for the price elasticity of demand is:

PEoD = % change in quantity demanded / % change in price

For the above problem we are given PEoD (price elasticity of demand) and the % change in quantity is positive 20%.  Right away we can cancel out "d", and "e" because we know that the price has to decrease (because of the law of demand and the fact that the PEoD is negative) and since the PEoD measure is not 0, we know "a" cannot be the answer.

We can then use the equation for PEoD to fine out what the actual percent change is:

PEoD = -1.2 = % change in quantity demanded/ % change in price = 20 / X

or

-1.2 = 20/X

Where X is our % change in price, which is what we are trying to figure out.  So we can multiply both sides by X, and divide both sides by -1.2 to get:

X = -16.667%

So the price would have to drop by 16.667% in order to see quantity increase by 20%.  This makes sense, because if our PEoD measure is <-1 (or |PEoD|>1) then it is elastic, which means that a relatively small price change will have a large effect on quantity.  And we can see this in the problem itself, because the % change in price is a smaller number (magnitude wise) then the % change in quantity.