Example
The supply curve for bananas follows the equation `Q_S = 3 P + 2`.
The Price Elasticity of Supply is
$$ \epsilon = \frac{d Q_S}{d P} \frac{P}{Q_S} = 3 \frac{P}{Q_S} = 3 \frac{P}{3 P + 2} $$If the price of a banana is $1, the Price Elasticity of Supply is `\frac{3}{5} = 0.6`.
A 1% price increase (`P = $1.01`) leads to a 0.6% increase of banana supply (`Q_S = 5.03`).
Question
The supply curve is now `Q_S = 96 P + 72`.
What is the Price Elasticity of Supply?
The Price Elasticity of Supply is
$$ \epsilon = \frac{d Q_S}{d P} \frac{P}{Q_S} = 96 \frac{P}{Q_S} = 96 \frac{P}{96 P + 72} $$