Unit 5: Elasticity – Price Elasticity of Demand

Unit 5: Elasticity

Introduction to Elasticity

Elasticity is a fundamental concept in microeconomics that measures how responsive consumers or producers are to changes in various economic factors, such as price, income, or the price of related goods. Understanding elasticity helps economists and firms predict changes in market outcomes when these factors fluctuate.

• Definition: Elasticity quantifies the percentage change in one variable resulting from a percentage change in another variable.

• General Formula:

$\text{Elasticity} = \frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Factor Examined}}$

• Elasticity is measured in percentages, making it independent of the units used for quantity and price.

• Elasticity applies to both linear and non-linear demand curves.

Price Elasticity of Demand

The Price Elasticity of Demand measures how responsive the quantity demanded of a good is to a change in its price. It is a key tool for understanding consumer behavior and for making pricing decisions.

• Formula:

$\text{Price Elasticity of Demand} = \frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Price}}$

• Elasticity is not the slope of the demand curve, but rather a measure of its responsiveness.

Interpreting Price Responsiveness

When the price of a good changes, the quantity demanded will also change. The magnitude of this change depends on how sensitive (responsive) consumers are to price changes.

• If consumers are highly responsive, a small change in price leads to a large change in quantity demanded (elastic demand).

• If consumers are less responsive, a change in price leads to a small change in quantity demanded (inelastic demand).

Calculating Price Elasticity of Demand

Although the slope of a linear demand curve is constant, the elasticity varies along the curve. To accurately measure elasticity between two points, economists use the midpoint formula.

• Midpoint Formula:

$\text{Price Elasticity of Demand} = \frac{(Q_2 - Q_1) / \left(\frac{Q_1 + Q_2}{2}\right)}{(P_2 - P_1) / \left(\frac{P_1 + P_2}{2}\right)}$

• This formula uses the average of the initial and final quantities and prices to calculate elasticity between two points.

Sign and Interpretation of Price Elasticity of Demand

Because the law of demand states that quantity demanded increases as price falls, the price elasticity of demand is always negative. By convention, economists often refer to the absolute value of elasticity (ignoring the negative sign).

• Elasticity is always negative: $\text{Price Elasticity of Demand} = \frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Price}}$

• Absolute value is used for interpretation.

Classifications of Price Elasticity of Demand

The value of price elasticity of demand determines whether demand is elastic, inelastic, or unit elastic.

• Inelastic Demand: If elasticity is between 0 and -1 (absolute value between 0 and 1), demand is inelastic. The percentage change in quantity is less than the percentage change in price.

• Unit Elastic Demand: If elasticity is exactly -1 (absolute value 1), demand is unit elastic. The percentage change in quantity equals the percentage change in price.

• Elastic Demand: If elasticity is less than -1 (absolute value greater than 1), demand is elastic. The percentage change in quantity is greater than the percentage change in price.

Graphical Representation

Demand curves can have both elastic and inelastic regions, separated by a point of unit elasticity. The responsiveness of quantity demanded to price changes can be visualized on a demand curve, with steeper curves indicating inelastic demand and flatter curves indicating elastic demand.

• Steep demand curve: Inelastic demand

• Flat demand curve: Elastic demand

Summary Table: Price Elasticity of Demand Classification

Elasticity Value	Classification	Description
0 < |E| < 1	Inelastic	Quantity demanded changes less than price
|E| = 1	Unit Elastic	Quantity demanded changes equal to price
|E| > 1	Elastic	Quantity demanded changes more than price

Example

Suppose the price of a product decreases from $10 to $8, and the quantity demanded increases from 100 units to 140 units. Using the midpoint formula:

$\text{Price Elasticity of Demand} = \frac{(140 - 100) / (120)}{(8 - 10) / (9)} = \frac{40 / 120}{-2 / 9} = \frac{0.333}{-0.222} \approx -1.5$

Since the absolute value is greater than 1, demand is elastic in this range.