Unit 5: Elasticity – Price Elasticity of Demand (Microeconomics Study Notes)

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 vary.

• Definition: Elasticity quantifies the percentage change in one variable in response to a percentage change in another variable.

• General Formula:

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

• Elasticity is unit-free (uses percentages), so it is independent of the units of measurement for quantity and price.

• Elasticity can be applied 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. This is a key concept for understanding consumer behavior and for firms setting prices.

• 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 the responsiveness at a given point or over a range.

Calculating Price Elasticity of Demand

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

• Midpoint (Arc) Formula:

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

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

Interpreting Price Elasticity of Demand

Because the quantity demanded typically decreases as price increases (and vice versa), the price elasticity of demand is usually negative. By convention, economists often refer to the absolute value of elasticity.

• Elasticity is always negative (due to the law of demand), but the absolute value is used for interpretation.

Types of Price Elasticity of Demand

• Inelastic Demand: $0 < |E_d| < 1$ - The percentage change in quantity demanded is less than the percentage change in price. - Example: Necessities such as salt or basic utilities.

• Unit Elastic Demand: $|E_d| = 1$ - The percentage change in quantity demanded equals the percentage change in price. - Example: Some goods at specific price points.

• Elastic Demand: $|E_d| > 1$ - The percentage change in quantity demanded is greater than the percentage change in price. - Example: Luxury goods or goods with many substitutes.

Graphical Representation

• When price changes from $P_1$ to $P_2$, the quantity demanded changes from $Q_1$ to $Q_2$.

• The steepness of the demand curve at a given point reflects the degree of elasticity.

• Flatter curves indicate more elastic demand; steeper curves indicate more inelastic demand.

Example Calculation

• Suppose the price of a product increases from $P_1 = 10$ to $P_2 = 12$, and the quantity demanded decreases from $Q_1 = 100$ to $Q_2 = 80$.

• Using the midpoint formula:

$\text{Price Elasticity of Demand} = \frac{\frac{80 - 100}{(100 + 80)/2}}{\frac{12 - 10}{(10 + 12)/2}} = \frac{-20/90}{2/11} \approx -2.44$

• This result indicates elastic demand (since $|E_d| > 1$).

Summary Table: Types of Price Elasticity of Demand

Elasticity Value	Type	Description	Example
$0 < |E_d| < 1$	Inelastic	Quantity demanded changes less than price	Basic food items
$|E_d| = 1$	Unit Elastic	Quantity demanded changes equal to price	Some mid-range goods
$|E_d| > 1$	Elastic	Quantity demanded changes more than price	Luxury goods

Additional info: The notes reference Hubbard et al. as the textbook source, and the content is structured as lecture slides for an introductory microeconomics course. The graphical examples and formulas are standard in microeconomics education.