Price Elasticity of Demand

The Price Elasticity of Demand is the percentage change of demand when the price increases by 1%. $$\eta = \frac{d Q_D}{d P} \frac{P}{Q_D}$$

Example

The demand for cookies follows the equation `Q_D = 10 - 2 P`.

The price elasticity of demand is $$ \eta = \frac{d Q_D}{d P} \frac{P}{Q_D} = - 2 \frac{P}{Q_D} = - 2 \frac{P}{10 - 2 P} $$

If the price of a cookie is $1, the price elasticity of demand is `- \frac{2}{8} = -0.25`.

A 1% price increase (`P = $1.01`) leads to a 0.25% decreases of the number of cookies demanded (`Q_S = 7.98`).

Question

The demand for cookies follows the equation `Q_D = 31 - 15 P`.

What is the Price Elasticity of Demand?

The price elasticity of demand is $$ \eta = \frac{d Q_D}{d P} \frac{P}{Q_D} = - 15 \frac{P}{Q_D} $$