You have the following information:

Price (P) Quantity demanded (Qd)
8 100
10 90

If the price increases from R8 to R10, what is the percentage increase in price?
What is the percentage decrease in quantity demanded if the price increases from R8 to R10?

What is the price elasticity coefficient, using the answers to the above questions?

The increase in price is R2, and the percentage increase in price is R2/R8 x 100 = 25%. The quantity demanded decreases by 10 units (100 – 90), and the percentage decrease in the quantity demand is 10 units/100 units = 10%. In this case, the price elasticity coefficient is:

$${e_p} = {\%∆Q_d \over \%∆P}$$
$${\text{ }} = {\text{10%} \over \text{25%}}$$
$${ } = 0,4$$

If you do the same exercise, but assume that the price decreases from R10 to R8, will you obtain the same price elasticity coefficient as in the previous example that used an increase in the price from R8 to R10?

If you did the calculations correctly, you will see that the percentage change in price is R2/R10 x 100 = 20%, and the percentage change in quantity demanded is 10 units/90 units x 100 = 11,1%. In this example, the price elasticity coefficient is:

$${e_p} = {\%∆Q_d \over \%∆P}$$
$${\text{ }} = {\text{11%} \over \text{20%}}$$
$${ } = 0,55$$

The reason for this difference is that it depends on the starting point (the value we use as the basis for our calculations). It the starting value for price is R8, a R2 increase in price implies a 25% increase in the price. If the starting value for price is R10, a R2 decrease in price implies a 20% decrease in price. The same happens for the change in quantity demanded.

What we are looking for is a measure that is independent of the starting point or direction of change. A R2 increase in the price should give us the same answer as a R2 decrease in price.

To solve this problem, we make use of the midpoint method to calculate the price elasticity coefficient.