Microeconomics Study Guide: Elasticity, Supply & Demand, and Incidence

Unit 2: Elasticity

Own-Price Elasticity of Demand

The own-price elasticity of demand measures the responsiveness of quantity demanded to changes in the price of a good, holding all other factors constant. It is a central concept in microeconomics, used to analyze consumer behavior and market outcomes.

• Definition: The own-price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price.

• Formula: $E_d = \frac{\%\,\text{change in quantity demanded}}{\%\,\text{change in price}}$ Alternatively, for a linear demand curve: $E_d = \frac{dQ}{dP} \cdot \frac{P}{Q}$

• Elasticity and Slope: The slope of the demand curve affects elasticity. Steeper curves are less elastic; flatter curves are more elastic.

• Types of Elasticity:

  • Elastic Demand: $|E_d| > 1$ (quantity demanded is highly responsive to price changes)

  • Inelastic Demand: $|E_d| < 1$ (quantity demanded is less responsive to price changes)

  • Unit Elastic: $|E_d| = 1$ (proportional response)

  • Perfectly Elastic: $|E_d| = \infty$ (horizontal demand curve)

  • Perfectly Inelastic: $|E_d| = 0$ (vertical demand curve)

• Examples:

  • If the price of a product increases by 10% and quantity demanded falls by 20%, $E_d = -2$ (elastic demand).

  • For a vertical demand curve, $E_d = 0$ (no response to price).

  • For a horizontal demand curve, $E_d = \infty$ (any price change eliminates demand).

Calculating Elasticity Along a Linear Demand Curve

Elasticity varies along a straight-line demand curve, even though the slope is constant. It is higher (more elastic) at higher prices and lower quantities, and lower (more inelastic) at lower prices and higher quantities.

• Formula: $E_d = \frac{dQ}{dP} \cdot \frac{P}{Q}$

• Application: For $D = 16 - 2p$, at $p = 1$, $Q = 14$; at $p = 5$, $Q = 6$.

• Example Calculation:

  • At $p = 5$, $Q = 6$, $dQ/dP = -2$ $E_d = -2 \cdot \frac{5}{6} = -1.67$

• Elasticity Changes: Elasticity decreases as you move down the demand curve (from high price/low quantity to low price/high quantity).

Elasticity and Total Expenditure

The relationship between elasticity and total expenditure (or revenue) is crucial for understanding how price changes affect seller revenue.

• Formula: $E = p \times q$

• Key Points:

  • If demand is elastic ($|E_d| > 1$), a price decrease increases total expenditure.

  • If demand is inelastic ($|E_d| < 1$), a price decrease decreases total expenditure.

  • Total expenditure is maximized when demand is unit elastic ($|E_d| = 1$).

• Example: For $D = 12 - 2p$, calculate $E_d$ at different prices and observe changes in $E$.

Elasticity of Supply

The price elasticity of supply measures the responsiveness of quantity supplied to changes in price.

• Definition: $E_s = \frac{\%\,\text{change in quantity supplied}}{\%\,\text{change in price}}$

• Formula: $E_s = \frac{dQ_s}{dP} \cdot \frac{P}{Q_s}$

• Types:

  • Elastic Supply: $E_s > 1$

  • Inelastic Supply: $E_s < 1$

  • Unit Elastic Supply: $E_s = 1$

  • Perfectly Elastic Supply: $E_s = \infty$

  • Perfectly Inelastic Supply: $E_s = 0$

• Example: If price rises from $4.00$ to $5.00$ and quantity supplied rises from $500$to $1000$, $E_s = \frac{(1000-500)/500}{(5-4)/4} = \frac{1}{0.25} = 4$

Cross-Price Elasticity of Demand

Cross-price elasticity measures the responsiveness of demand for one good to changes in the price of another good.

• Definition: $E_{xy} = \frac{\%\,\text{change in quantity demanded of } x}{\%\,\text{change in price of } y}$

• Interpretation:

  • Substitutes: $E_{xy} > 0$

  • Complements: $E_{xy} < 0$

• Example: If the price of good Y rises and the demand for good X increases, they are substitutes.

Income Elasticity of Demand

Income elasticity measures the responsiveness of demand to changes in consumer income.

• Definition: $E_I = \frac{\%\,\text{change in quantity demanded}}{\%\,\text{change in income}}$

• Interpretation:

  • Normal Good: $E_I > 0$

  • Inferior Good: $E_I < 0$

  • Luxury Good: $E_I > 1$

  • Necessity: $0 < E_I < 1$

• Example: If income rises from $40$to $80$ and demand rises from $20$to $40$, $E_I = \frac{(40-20)/20}{(80-40)/40} = 2$

Incidence of Tax and Subsidy

Tax and subsidy incidence refers to how the burden or benefit of a tax or subsidy is shared between buyers and sellers, depending on the elasticities of supply and demand.

• Tax Incidence:

  • If demand is more inelastic than supply, consumers bear more of the tax burden.

  • If supply is more inelastic than demand, producers bear more of the tax burden.

• Subsidy Incidence:

  • If supply is more elastic than demand, buyers benefit more from the subsidy.

  • If demand is more elastic than supply, sellers benefit more from the subsidy.

• Example: For $D = 12 - 2p$ and $S = 5 + 2p$, a $t = 2$ per unit tax shifts the supply curve upward by $2$ units.

Elasticity and Shifts in Supply and Demand

Changes in determinants such as expectations, production costs, and related goods can shift supply and demand curves, affecting equilibrium price and quantity.

• Supply Shift: Occurs when factors like input prices, technology, or expectations change.

• Demand Shift: Occurs when factors like income, tastes, or prices of related goods change.

• Elasticity Matters: The impact of a shift depends on the slope (elasticity) of the curve.

• Example: If buyers expect prices to rise, demand increases, shifting the demand curve rightward.

Applications and Problem Solving

Elasticity concepts are applied to solve problems involving changes in price, income, and related goods, and to analyze market outcomes.

• Calculating Elasticity: Use the midpoint formula for discrete changes: $E = \frac{(Q_2 - Q_1) / ((Q_2 + Q_1)/2)}{(P_2 - P_1) / ((P_2 + P_1)/2)}$

• Diagram Analysis: Supply and demand diagrams illustrate the effects of taxes, subsidies, and shifts.

• Revenue Maximization: Total revenue is maximized at unit elasticity.

• Incidence Analysis: Use elasticity to determine who bears the burden of taxes or benefits from subsidies.

Summary Table: Types of Elasticity

Elasticity Type	Formula	Interpretation
Own-Price Elasticity of Demand	$E_d = \frac{dQ}{dP} \cdot \frac{P}{Q}$	Responsiveness of quantity demanded to price
Elasticity of Supply	$E_s = \frac{dQ_s}{dP} \cdot \frac{P}{Q_s}$	Responsiveness of quantity supplied to price
Cross-Price Elasticity	$E_{xy} = \frac{\%\,\text{change in } Q_x}{\%\,\text{change in } P_y}$	Effect of price of one good on demand for another
Income Elasticity	$E_I = \frac{\%\,\text{change in quantity}}{\%\,\text{change in income}}$	Effect of income changes on demand

Additional info:

• Questions in the file cover calculation, interpretation, and graphical analysis of elasticity, supply and demand shifts, and tax/subsidy incidence.

• Diagrams are referenced for graphical illustration but not provided; students should practice drawing supply and demand curves to visualize effects.

• Some questions involve real-world applications, such as changes in equilibrium due to migration or government policy.