Question

If a 21 percent increase in the price of cheerios causes a 14 percent reduction in the number of boxes of cereal demanded, the price elasticity demanded for cheerios is

Answer 1

The price elasticity of demand is given by

`\eta = ((Q_(1)-Q_(0))/(Q_(1)+Q_(0)))/((P_(1)-P_(0))/(P_(1)+P_(0)))`
where
Q₀ = initial demand
P₀ = initial price
Q₁ = new demand
P₁ = new price

The price increased by 21%, therefore
P₁ = 1.21 P₀
P₁/P₀ = 1.21

The reduction in demand is 14%, therefore
Q₁ = (1 - 0.14)Q₀ = 0.86 Q₀
Q₁/Q₀ = 0.86

Therefore
(Q₁ - Q₀)/(Q₁ + Q₀)
= (Q₁/Q₀ -1)/(Q₁/Q₀ + 1)
= (0.86 - 1)/(0.86 + 1)
= - 0.0753
Similarly,
(P₁ - P₀)/(P₁ + P₀)
= (P₁/P₀ - 1)/(P₁/P₀ + 1)
= (1.21 - 1)/(1.21 + 1)
= 0.095

From the formula, obtain
η = -0.0753/0.095 = - 0.7926
Because |η| <1, the demand decreases.

Answer: -0.7926