Question

If the price of a good increases by 20% and the quantity demanded changes by 15%, then the price elasticity of demand is equal to

Answer 1

The price elasticity of a demand has the formula 

$Price \ Elasticity= \frac{ \frac{D1-D2}{D1+D2} }{ \frac{P1-P2}{P1+P2} }$

where D is demand and P is price. Based on the given:

D2= 1.15D1  ;  P2 = 1.2P1

Upon simplifying

$Price \ Elasticity= \frac{ \frac{D1-1.15D1}{D1+1.15D1} }{ \frac{P1-1.2P1}{P1+1.2P1} }$

Price Elasticity = 0.7674 or 76.74%

The variables D1 and P1 are cancelled out, and then you can obtain the answer.