# 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 $$\eta = \frac{d Q_D}{d P} \frac{P}{Q_D} = - 15 \frac{P}{Q_D}$$