Elasticity of Demand

CFA Level I
#1

If the price elasticity of demand is –1.5 and a change in the price of the product increases the quantity demanded by 4%, then what is the percent change in price?

A)

–0.375%.

Failed

B)

–6.000%.

Failed

C)

–2.667%.

Achieved

Explanation

Price elasticity of demand is calculated by dividing the percent change in quantity demanded by the percent change in price. The percent change in price is, therefore, the percent change in quantity demanded divided by the price elasticity of demand = 4 / –1.5 = –2.667.

If Elasticity = (%ChangeQuantity/%ChangePrice) why is this problem not solved by -1…5 = 4%/X so X = -1.5 * 4% = -6%. Why do they start with -1.5 = 4%/X then…-1.5X=4%…X=4%/-1.5 = -2.6667%?

Am I forgetting basic algebra?

#2

Probably.

Elasticity = %ΔQ / %ΔP

Elasticity × %ΔP = %ΔQ

%ΔP = %ΔQ / Elasticity

#3

Thanks! It clicked haha

#4

My pleasure.

#5

1.5 = 4/x

Simplify the expression
Multiply all terms by the same value to eliminate fraction denominators
Cancel multiplied terms that are in the denominator
Re-order terms so constants are on the left
1.5 = 4/x
1.5x = 4

Divide both sides by the same factor
1.5x = 4
1.5x/1.5 = 4/1.5

Simplify the expression
Cancel terms that are in both the numerator and denominator
Divide the numbers
1.5x/1.5 = 4/1.5
x = 2.6666667

Solution
x = 2.6666667