Price Elasticity of Supply

The Price Elasticity of Supply is the percentage change of supply when the price increases by 1%. $$\epsilon = \frac{d Q_S}{d P} \frac{P}{Q_S}$$

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 = 22 P + 42`.

What is the Price Elasticity of Supply?

The Price Elasticity of Supply is

$$ \epsilon = \frac{d Q_S}{d P} \frac{P}{Q_S} = 22 \frac{P}{Q_S} = 22 \frac{P}{22 P + 42} $$