Elasticity in Microeconomics: Price, Income, and Cross Elasticities

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Elasticity in Microeconomics

Introduction to Elasticity

Elasticity is a central concept in microeconomics that measures how responsive one variable is to changes in another. In the context of markets, elasticity helps us understand how quantity demanded or supplied responds to changes in price, income, or the price of related goods.

Price Elasticity of Demand: Measures responsiveness of quantity demanded to changes in price.
Income Elasticity of Demand: Measures responsiveness of quantity demanded to changes in consumer income.
Cross Elasticity of Demand: Measures responsiveness of quantity demanded to changes in the price of related goods (substitutes or complements).
Elasticity of Supply: Measures responsiveness of quantity supplied to changes in price.

Price Elasticity of Demand

Definition and Importance

The price elasticity of demand is a units-free measure of the responsiveness of the quantity demanded of a good to a change in its price, holding all other influences constant. It helps explain why prices and quantities change in response to shifts in supply or demand.

Key Question: When supply decreases and price rises, does the price rise by a lot and quantity decrease by a little, or vice versa? The answer depends on elasticity.

Calculating Price Elasticity of Demand

Elasticity is calculated using percentage changes, making it independent of the units used to measure price or quantity.

Formula:

Use average price and average quantity to calculate percentage changes, ensuring consistency regardless of direction of change.

Example Calculation

Initial price of pizza: $20.50; Quantity demanded: 9 pizzas/hour.
New price: $19.50; New quantity demanded: 11 pizzas/hour.
Average price:
Average quantity:
Percentage change in quantity:
Percentage change in price:
Elasticity: (absolute value)

Interpreting Elasticity Values

Perfectly Inelastic Demand: Elasticity = 0; Quantity demanded does not change as price changes.
Inelastic Demand: Elasticity < 1; Quantity demanded changes less than price.
Unit Elastic Demand: Elasticity = 1; Quantity demanded changes by the same percentage as price.
Elastic Demand: Elasticity > 1; Quantity demanded changes more than price.
Perfectly Elastic Demand: Elasticity = ∞; Any small change in price leads to an infinite change in quantity demanded.

Elasticity Along a Linear Demand Curve

Elasticity varies along a straight-line demand curve:

Above the midpoint: Demand is elastic.
At the midpoint: Demand is unit elastic.
Below the midpoint: Demand is inelastic.

Factors Influencing Price Elasticity of Demand

Closeness of Substitutes: More substitutes make demand more elastic.
Proportion of Income Spent: Goods that take a larger share of income have more elastic demand.
Time Elapsed Since Price Change: Demand becomes more elastic over time as consumers adjust.

Total Revenue and Elasticity

Total revenue is the product of price and quantity sold. The effect of a price change on total revenue depends on elasticity:

If demand is elastic, a price cut increases total revenue.
If demand is inelastic, a price cut decreases total revenue.
If demand is unit elastic, total revenue remains unchanged.

Total Revenue Test

Observe changes in total revenue after a price change to estimate elasticity.
If total revenue rises after a price cut, demand is elastic.
If total revenue falls, demand is inelastic.
If total revenue does not change, demand is unit elastic.

Income Elasticity of Demand

Definition and Calculation

Income elasticity of demand measures how the quantity demanded of a good responds to changes in consumer income, holding other factors constant.

If elasticity > 1: Demand is income elastic; the good is a normal good.
If 0 < elasticity < 1: Demand is income inelastic; the good is a normal good.
If elasticity < 0: The good is an inferior good.

Cross Elasticity of Demand

Definition and Calculation

Cross elasticity of demand measures the responsiveness of demand for a good to changes in the price of a substitute or complement.

Positive cross elasticity: Goods are substitutes.
Negative cross elasticity: Goods are complements.

Elasticity of Supply

Definition and Calculation

Elasticity of supply measures the responsiveness of quantity supplied to changes in price, holding other factors constant.

Perfectly Inelastic Supply: Elasticity = 0; Supply curve is vertical.
Unit Elastic Supply: Elasticity = 1; Supply curve passes through the origin.
Perfectly Elastic Supply: Elasticity = ∞; Supply curve is horizontal.

Factors Influencing Elasticity of Supply

Resource Substitution Possibilities: Easier substitution among resources increases elasticity.
Time Frame for Supply Decision:
- Momentary supply: Perfectly inelastic.
- Short-run supply: Somewhat elastic.
- Long-run supply: Most elastic.

Glossary of Elasticities

Elasticity Type	Value Range	Interpretation
Perfectly Inelastic Demand	0	Quantity demanded does not change as price changes.
Inelastic Demand	0 < E < 1	Quantity demanded changes less than price.
Unit Elastic Demand	1	Quantity demanded changes by the same percentage as price.
Elastic Demand	E > 1	Quantity demanded changes more than price.
Perfectly Elastic Demand	∞	Any small change in price leads to an infinite change in quantity demanded.
Income Elasticity (Normal Good)	E > 0	Quantity demanded increases as income increases.
Income Elasticity (Inferior Good)	E < 0	Quantity demanded decreases as income increases.
Cross Elasticity (Substitutes)	E > 0	Quantity demanded increases as price of substitute increases.
Cross Elasticity (Complements)	E < 0	Quantity demanded decreases as price of complement increases.
Perfectly Inelastic Supply	0	Quantity supplied does not change as price changes.
Unit Elastic Supply	1	Quantity supplied changes by the same percentage as price.
Perfectly Elastic Supply	∞	Any small change in price leads to an infinite change in quantity supplied.