Elasticity in Microeconomics: Concepts, Measurement, and Applications

Chapter 4: Elasticity

Introduction to Elasticity

Elasticity is a unitless measure of the responsiveness of one variable to a change in another variable. In microeconomics, elasticity is used to analyze how changes in price or other factors affect the quantity demanded or supplied of a good or service.

• Definition: Elasticity measures the percentage change in one variable (the dependent variable) resulting from a one percent change in another variable (the independent variable).

• In most elasticity measures in microeconomics, the dependent variable is quantity.

Elasticity of Demand

Price Elasticity of Demand

The price elasticity of demand quantifies how much the quantity demanded of a product changes in response to a change in its price.

• Formula:

$\text{Price Elasticity of Demand} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$

• The result is called the elasticity coefficient (Ed).

• Standard percentage change formula:

$\text{Percentage change} = \frac{100 \times (\text{Point 2} - \text{Point 1})}{\text{Point 1 is the base}}$

Calculating Price Elasticity of Demand: The Midpoint Formula

When working with linear or convex downward-sloping demand curves, the price elasticity of demand changes along the curve. To avoid inconsistencies due to different base points, economists use the midpoint formula:

• Midpoint formula for Ed:

$E_d = \frac{(Q_2 - Q_1) / [(Q_2 + Q_1)/2]}{(P_2 - P_1) / [(P_2 + P_1)/2]}$

Or, after simplifying:

$E_d = \frac{(Q_2 - Q_1) \div (Q_2 + Q_1)}{(P_2 - P_1) \div (P_2 + P_1)}$

• This approach uses the average of the starting and ending values as the base for percentage changes.

Example Calculation

• Suppose tuition increases from $4,000 to $5,000.

• Quantity demanded falls from 20,000 to 18,000 students.

• Apply the midpoint formula to find Ed.

Tabular Example: Calculating Elasticity Coefficient

Point	Price	QuantityD	Elasticity Coefficient
A	$25	20	---
B	$20	40	Between A & B
C	$15	60	Between B & C

Types of Elasticity of Demand

Terms Used to Describe Responsiveness

• Elastic Demand (|Ed| > 1): The percentage change in quantity demanded is greater than the percentage change in price.

• Inelastic Demand (|Ed| < 1): The percentage change in quantity demanded is less than the percentage change in price.

• Unitary Elastic Demand (|Ed| = 1): The percentage change in quantity demanded equals the percentage change in price.

• Perfectly Elastic Demand (|Ed| = ∞): Any small change in price leads to an infinite change in quantity demanded.

• Perfectly Inelastic Demand (|Ed| = 0): Quantity demanded does not change as price changes.

Elasticity Along a Linear Demand Curve

Except for vertical and horizontal demand curves (where elasticity is zero and infinite, respectively), the price elasticity of demand changes as you move along a straight-line (linear) demand curve.

• Elasticity is higher at higher prices and lower quantities.

• Elasticity decreases as you move down the demand curve (price falls, quantity rises).

Total Revenue and Elasticity

Relationship Between Total Revenue and Elasticity

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

$TR = P \times Q$

• If demand is elastic, a price cut increases total revenue.

• If demand is unit elastic, a price cut does not change total revenue.

• If demand is inelastic, a price cut decreases total revenue.

Determinants of Elasticity of Demand

Factors Influencing Elasticity

• Availability of Substitutes: More substitutes make demand more elastic.

• Necessities vs. Luxuries: Necessities tend to have inelastic demand; luxuries have elastic demand.

• Share of Budget: Goods that take up a larger share of the consumer's budget tend to have more elastic demand.

• Time Horizon: Demand is more elastic in the long run than in the short run.

Cross Elasticity of Demand

Definition and Calculation

Cross elasticity of demand measures the responsiveness of demand for one good to a change in the price of another good.

$E_c = \frac{\% \Delta \text{Quantity demanded of good A}}{\% \Delta \text{Price of good B}}$

• If Ec > 0, the goods are substitutes.

• If Ec < 0, the goods are complements.

• If Ec = 0, the goods are unrelated.

Income Elasticity of Demand

Definition and Calculation

Income elasticity of demand measures the responsiveness of quantity demanded to a change in income.

$E_y = \frac{\% \Delta \text{Quantity demanded}}{\% \Delta \text{Income}}$

• If Ey > 0, the good is a normal good.

• If Ey < 0, the good is an inferior good.

Elasticity of Supply

Price Elasticity of Supply

Price elasticity of supply measures the responsiveness of the quantity supplied of a product to a change in its price.

$E_s = \frac{\% \Delta \text{Quantity supplied}}{\% \Delta \text{Price}}$

• Calculated using the midpoint formula, similar to demand elasticity.

• Elastic supply: Es > 1

• Inelastic supply: Es < 1

• Unit elastic supply: Es = 1

• Perfectly elastic supply: Es = ∞

• Perfectly inelastic supply: Es = 0

Determinants of Elasticity of Supply

• Resource Substitution Possibilities: Greater ease of substituting resources increases elasticity.

• Time Frame: Supply is more elastic in the long run than in the short run or momentary period.

• Momentary Supply: No time to change inputs or production methods.

• Short-Run Supply: Some inputs can be changed.

• Long-Run Supply: All inputs and technology can be changed.