If the price elasticity of demand for used cars priced between $3,000 and $5,000 is –1.2 (using the mid-point method), what will be the percent change in quantity demanded when the price of a used car falls from $5,000 to $3,000?

the decrease in price of used cars from $5000 to $3000 will lead to a rise in the demand of used cars by 60%

Explanation:

Mid-point method

The midpoint formula for calculating elasticity calculates change in quantity demanded and divides it by the change in the the price

The original formula is

(Q2-Q1) / (Q2-Q1)/2   / (P2-P1)  / (P2-P1/2)

Q2 is new Quantity

Q1 is old quantity

P2 is new price

P1 is old price

Since we already have the Price elasticity of demand as -1.2

the formula changes to

Percentage Change in QUantity = Price Elasticity of demand x ( (P2-P1)  / (P2-P1/2)

= -1.2 x (P2-P1)  / (P2-P1/2)

= -1.2 x (3,000-5000)  / (5000-3000/2)

-1.2 x (-2000/4000) x 100

= 60%

Therefore, the decrease in price of used cars from $5000 to $3000 will lead to a rise in the demand of used cars by 60%