Calculating the price elasticity of demand using the midpoint theorem

In this question and answer we look at the following question about elasticities in economics:

Suppose that the NZ government increases the taxes on air travel and this increases the price of an airline ticket to NZ from $200 to $280. As a result, the demand for hotel accommodation in NZ decreases . Q1 = 10 Q2 = 6

Using the mid-point formula and the information given, calculate the final price elasticity of demand of hotel services, OR explain why it cannot be determined.

This is a straight forward application of the price elasticity of demand equation.  Remember that the price elasticity of demand  isequal to the percent change in quantity over the percent change in price.  In order to get the percent change in quantity, and the percent change in price, we are going to have to use the midpoint theorem.

First we can find the percent change in price, which is going to be equal to the difference between the two price levels or $280 - $200.  This gives us $80.  We then have to divide this difference by the average of the two price levels which is going to be equal to $280+$200 or $480 divided by 2 which gives us $240.  Then we divide the change ($80) by the average ($240) to get a percent change of 33.33, or 1/3.

We now can find the percent change in quantity by doing the same process as above.  The difference between the two quantity levels is 4, and the average is 8.  When we divide the difference by the average we get  a percent change of 50 or ½.  We now divide the percent change in quantity by the percent change in price so we have ½ / 1/3.  This ends up giving us the price elasticity of demand measure of 3/2 or 1.5 which is elastic. 

To be technically correct, the price elasticity of demand measure is negative but we can see this given the information in the original question because as the price rises, the quantity drops.  This leaves us with a negative percent change in the numerator (which I left out for simplicity) and a positive change in the denominator.  A negative number divided by a positive number leaves us with a negative number.