Elasticity and Its Application – Microeconomics Study Notes

Elasticity and Its Application

Introduction to Elasticity

Elasticity is a fundamental concept in microeconomics that measures how much buyers and sellers respond to changes in market conditions. It quantifies the responsiveness of quantity demanded (Qd) or quantity supplied (Qs) to changes in one of its determinants, such as price, income, or the price of related goods.

• Elasticity: A measure of responsiveness in economic variables.

• Applications: Helps understand consumer behavior, pricing strategies, and policy impacts.

Price Elasticity of Demand

The price elasticity of demand measures how much the quantity demanded of a good responds to a change in its price. It is a key indicator of buyers' price sensitivity.

• Definition: The percentage change in quantity demanded divided by the percentage change in price.

• Formula: $\text{Price Elasticity of Demand} = \frac{\%\,\text{change in } Q^d}{\%\,\text{change in } P}$

• Interpretation: Along a demand curve, price and quantity move in opposite directions, making price elasticity negative. Economists report elasticities as positive numbers (absolute values).

Calculating Percentage Changes

Percentage changes can be calculated using the standard method or the midpoint method. The midpoint method is preferred for accuracy, especially when moving between two points on a demand curve.

• Standard Method: $\text{Percentage Change} = \frac{\text{end value} - \text{start value}}{\text{start value}} \times 100$

• Midpoint Method: $\text{Percentage Change} = \frac{\text{end value} - \text{start value}}{\text{midpoint}} \times 100$ $\text{Midpoint} = \frac{\text{end value} + \text{start value}}{2}$ $\text{Price Elasticity of Demand} = \frac{(Q_2 - Q_1)/[(Q_2 + Q_1)/2]}{(P_2 - P_1)/[(P_2 + P_1)/2]}$

Determinants of Price Elasticity of Demand

Several factors influence the price elasticity of demand for a good:

• Availability of Close Substitutes: More substitutes make demand more elastic (e.g., Cheerios vs. Airfare).

• Narrowly vs. Broadly Defined Goods: Narrowly defined goods have more elastic demand (e.g., Mountain Dew vs. Soda).

• Necessities vs. Luxuries: Necessities have inelastic demand; luxuries have elastic demand (e.g., Insulin vs. Rolex watches).

• Time Horizon: Demand is more elastic in the long run than in the short run (e.g., Gasoline).

Variety of Demand Curves

The price elasticity of demand can vary along different types of demand curves:

• Elastic Demand: $>1$ (quantity demanded changes more than price)

• Inelastic Demand: $<1$ (quantity demanded changes less than price)

• Unit Elastic Demand: $=1$ (quantity demanded changes exactly as much as price)

• Perfectly Inelastic Demand: $=0$ (vertical demand curve; quantity demanded does not change)

• Perfectly Elastic Demand: $=\infty$ (horizontal demand curve; quantity demanded changes infinitely with any price change)

Examples of Elasticities from the Real World

Good	Elasticity	Interpretation
Eggs	0.1	Very inelastic
Healthcare	0.2	Very inelastic
Cigarettes	0.4	Inelastic
Rice	0.5	Inelastic
Housing	0.7	Inelastic
Beef	1.6	Elastic
Peanut Butter	1.7	Elastic
Restaurant Meals	2.3	Very elastic
Cheerios	3.7	Very elastic
Mountain Dew	4.4	Very elastic

Elasticity Along a Linear Demand Curve

The slope of a linear demand curve is constant, but elasticity varies along the curve. Elasticity is higher at higher prices and lower quantities, and lower at lower prices and higher quantities.

• Example: At the top of the demand curve, elasticity is high; at the bottom, it is low.

Total Revenue and Elasticity

Total revenue (TR) is the product of price and quantity sold. The effect of a price change on total revenue depends on the price elasticity of demand.

• Formula: $TR = P \times Q$

• If demand is elastic: A price increase decreases total revenue.

• If demand is inelastic: A price increase increases total revenue.

Income Elasticity of Demand

Income elasticity of demand measures how much the quantity demanded of a good responds to changes in consumers' income.

• Formula: $\text{Income Elasticity} = \frac{\%\,\text{change in } Q^d}{\%\,\text{change in income}}$

• Normal goods: Income elasticity > 0

• Inferior goods: Income elasticity < 0

Cross-Price Elasticity of Demand

Cross-price elasticity of demand measures how much the quantity demanded of one good responds to a change in the price of another good.

• Formula: $\text{Cross-Price Elasticity} = \frac{\%\,\text{change in } Q^d_1}{\%\,\text{change in } P_2}$

• Substitutes: Cross-price elasticity > 0

• Complements: Cross-price elasticity < 0

Price Elasticity of Supply

The price elasticity of supply measures how much the quantity supplied of a good responds to a change in its price.

• Formula: $\text{Price Elasticity of Supply} = \frac{\%\,\text{change in } Q^s}{\%\,\text{change in } P}$

• Elastic supply: Quantity supplied responds substantially to price changes.

• Inelastic supply: Quantity supplied responds only slightly to price changes.

Determinants of Price Elasticity of Supply

The price elasticity of supply is greater when sellers can easily change the quantity they produce. It is typically greater in the long run than in the short run, as firms can build new factories or new firms may enter the market over time.

• Short run: Supply is less elastic.

• Long run: Supply is more elastic.

Summary Table: Types of Elasticity

Type	Formula	Interpretation
Price Elasticity of Demand	$\frac{\%\,\text{change in } Q^d}{\%\,\text{change in } P}$	Responsiveness of quantity demanded to price changes
Income Elasticity of Demand	$\frac{\%\,\text{change in } Q^d}{\%\,\text{change in income}$	Responsiveness of quantity demanded to income changes
Cross-Price Elasticity of Demand	$\frac{\%\,\text{change in } Q^d_1}{\%\,\text{change in } P_2}$	Responsiveness of quantity demanded of one good to price changes of another
Price Elasticity of Supply	$\frac{\%\,\text{change in } Q^s}{\%\,\text{change in } P}$	Responsiveness of quantity supplied to price changes

Applications and Policy Implications

• Drug Interdiction: Reducing supply of illegal drugs increases price and total revenue if demand is inelastic, potentially increasing drug-related crime.

• Drug Education: Reducing demand for illegal drugs lowers price and total revenue, reducing drug-related crime.

• Farming: Increased supply with inelastic demand can lower total revenue for farmers.

• OPEC and Oil Prices: Supply and demand elasticity affect the impact of supply changes on price in the short and long run.

Key Takeaways

• Elasticity is crucial for understanding market responses to changes in price, income, and other factors.

• Price elasticity of demand and supply inform pricing strategies and policy decisions.

• Income and cross-price elasticities help classify goods and predict consumer behavior.