Price Elasticity of Demand: Concepts, Calculation, and Applications

Price Elasticity of Demand

Introduction to Elasticity in Economics

Elasticity in economics refers to the responsiveness of one variable to changes in another. In microeconomics, price elasticity of demand measures how much the quantity demanded of a good responds to changes in its price, holding all other factors constant.

• Elasticity: Measures the responsiveness of a consumer to a price change.

• Price Elasticity of Demand (Ed): A unit-free measure of the responsiveness of the quantity demanded of a good to a change in its price when all other influences on buying plans remain the same.

Factors Influencing Price Elasticity of Demand

Several factors determine how elastic or inelastic the demand for a good is:

1. Closeness of Substitutes:

   • The closer the substitutes for the good, the more elastic the demand (e.g., chicken).

   • The fewer the substitutes, the more inelastic the demand (e.g., gasoline).

2. Proportion of Income Spent on the Good:

   • The larger the proportion of income spent, the more elastic the demand (e.g., rent).

   • The smaller the proportion, the more inelastic the demand (e.g., coffee or tea).

3. Time Elapsed Since Price Change:

   • The more time available to find substitutes, the more elastic the demand.

   • The less time available, the more inelastic the demand (e.g., gas for transportation).

4. Type of Good:

   • Luxury goods (e.g., vacations, RVs, restaurant dining) are typically very elastic.

   • Necessity goods (e.g., food, shelter) are typically very inelastic.

5. How Narrowly Defined is the Good:

   • The more narrowly defined, the more elastic the demand.

   • The broader the definition, the more inelastic the demand (e.g., clothing vs. Levi Blue Jeans).

Calculating Price Elasticity of Demand

Price elasticity of demand can be calculated using several formulas:

• Basic Formula: $E_d = \frac{\% \Delta Q}{\% \Delta P}$

• Expanded Formula: $E_d = \frac{Q_1 - Q_0}{P_1 - P_0} \times \frac{P_1 + P_0}{Q_1 + Q_0}$

• Point Elasticity: $E_d = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$

• Average Elasticity: $E_d = \frac{\Delta Q}{\Delta P} \times \frac{\text{Average } P}{\text{Average } Q}$

• Inverse Slope Formula: $E_d = \left| \frac{1}{\text{Slope}} \right| \times \frac{\text{Average } P}{\text{Average } Q}$

Degrees of Price Elasticity of Demand

The degree of elasticity describes how responsive quantity demanded is to price changes:

• Perfectly Inelastic Demand: $E_d = 0$ Quantity demanded does not change with price. Examples: Insulin for a diabetic, heart or lung transplant.

• Inelastic Demand: $0 < E_d < 1$ Quantity demanded changes less than the price change. Examples: Apples, bananas, lettuce, alcohol, cigarettes.

• Unit Elastic Demand: $E_d = 1$ Quantity demanded changes exactly as much as the price change. Examples: Oranges.

• Elastic Demand: $1 < E_d < \infty$ Quantity demanded changes more than the price change. Examples: Grapes, furniture, motor vehicles.

• Perfectly Elastic Demand: $E_d = \infty$ Quantity demanded changes by an infinitely large percentage in response to any price change. Examples: Demand for a good with perfect substitutes.

Elasticity Along a Linear Demand Curve

While the slope of a linear demand curve is constant, elasticity varies along the curve:

• Elasticity is not the same as the slope.

• At higher prices and lower quantities, demand is more elastic.

• At lower prices and higher quantities, demand is more inelastic.

Total Revenue and Elasticity

Total revenue (TR) is the product of price and quantity sold:

• Formula: $TR = P \times Q$

• When price changes, total revenue may increase, decrease, or remain unchanged depending on elasticity:

  • If demand is elastic, a price cut increases quantity sold by more than 1%, and total revenue increases.

  • If demand is unit elastic, a price cut increases quantity sold by exactly 1%, and total revenue remains unchanged.

  • If demand is inelastic, a price cut increases quantity sold by less than 1%, and total revenue decreases.

Graphical Representation of Elasticity

Elasticity can be visualized using demand curves:

• Perfectly elastic: horizontal demand curve

• Perfectly inelastic: vertical demand curve

• Unit elastic: curve where percentage change in quantity equals percentage change in price

• Relatively elastic and inelastic: slopes between the extremes

Summary Table: Degrees of Price Elasticity of Demand

Type	Elasticity Value	Quantity Response	Example
Perfectly Inelastic	0	No change	Insulin for diabetics
Inelastic	0 < Ed < 1	Less than price change	Bananas, cigarettes
Unit Elastic	1	Equal to price change	Oranges
Elastic	1 < Ed < ∞	More than price change	Furniture, motor vehicles
Perfectly Elastic	∞	Infinite change	Perfect substitutes

Additional info:

• Elasticity is always taken in absolute value.

• Elasticity is a key concept for understanding consumer behavior and pricing strategies in microeconomics.