Economics

Price elasticity of demand is the economic term for the negative of the percentage change in quantity demanded divided by the percentage change in price (Katz  Rosen, 1994). It is therefore a measure of the responsiveness of quantity demanded to any given price change. The downward slope of a demand curve accounts for the opposing signs of percentage change in quantity demanded and percentage change in price and hence, their negative ratio. It has been customary to present price elasticity of demand in positive form by multiplying the ratio with -1 for the purpose of avoiding confusion and complexity. Price elasticity of demand (ED) will therefore be positive, given a downward-sloping demand curve (Katz  Rosen, 1994).
   
This formula is used for computing the price elasticity of demand
         ED   _     Q2  Q1                  P2  P1
                       (Q1  Q2)2        (P1  P2)2

where ED is the price elasticity of demand, Q2 is final quantity demanded, Q1 is initial quantity demanded, P2 is the final price and P1 is the initial price. The price elasticity of demand of apples in this example will be computed using the aforementioned formula.

         ED   _     20  30               4.00  3.50         _   -10        0.50     _  (-0.4)      3.00
                       (30  20)2       (3.50  4.00)2              25      3.75           0.1333
   
The price elasticity of demand of apples in this case is 3, indicative of a price-elastic demand. Demand for a good is price-elastic when a 1 increase in price effects in a greater than 1 decrease in quantity demanded. A 1 price hike in the apple case dampened demand by 3 demand was therefore very responsive to the price change. This price-responsiveness of the demand for apples is probably due to the presence of close substitutes, other fruits and foods which will make up for the lost utility.