Let P₀ = original price.
Let Q₀ = the initial demand.
After a 20% drop in price, the new price is
P₁ = 0.8P₀.
Because of the drop in price, the new demand increased by 50% to
Q₁ = 1.5Q₀
The price elasticity of demand is
[tex]\eta = ( \frac{Q_{1}-Q_{0}}{Q_{1}+Q_{0}} )( \frac{P_{1}+P_{0}}{P_{1}-P_{0}} ) =( \frac{Q_{1}/Q_{0} - 1}{Q_{1}/Q_{0}+1} )( \frac{P_{1}/P_{0}+1}{P_{1}/P_{0}-1} )[/tex]
Note that
Q₁/Q₀ = 1.5
P₁/P₀ = 0.8
Therefore the price elasticity is
[tex]\eta = ( \frac{1.5-1}{1.5+1} )( \frac{0.8+1}{0.8-1} )=-1.8[/tex]
This means that a 20% drop in price caused an 80% increase in demand.
Answer: η = -1.8
