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 the good itself. It is a central concept in microeconomics, used to analyze consumer behavior and market outcomes.

• Definition: 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: Elasticity varies along a linear demand curve. It is higher (more elastic) at higher prices and lower quantities, and lower (more inelastic) at lower prices and higher quantities.

• 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: $|E_d| = 1$ (percentage change in quantity equals percentage change in price)

• Perfectly Elastic Demand: Horizontal demand curve, $E_d = \infty$

• Perfectly Inelastic Demand: Vertical demand curve, $E_d = 0$

Example: For $D = 16 - 2p$, at $p = 1$, $Q = 14$; at $p = 2$, $Q = 12$. Elasticity between $p = 1$ and $p = 2$ is: $E_d = \frac{(12 - 14)/14}{(2 - 1)/1} = \frac{-2/14}{1/1} = -0.143$

Elasticity and Expenditure

Elasticity affects total expenditure (or total revenue) in the market. The relationship is given by $E = p \times q$.

• 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.

• At unit elasticity ($|E_d| = 1$), total expenditure is maximized.

Example: For $D = 12 - 2p$, calculate expenditure at different prices to illustrate the relationship.

Elasticity of Supply

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

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

• Formula: $E_s = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}}$ For a linear supply curve: $E_s = \frac{dQ}{dP} \cdot \frac{P}{Q}$

• Perfectly Elastic Supply: Horizontal supply curve, $E_s = \infty$

• Perfectly Inelastic Supply: Vertical supply curve, $E_s = 0$

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

Cross-Price Elasticity of Demand

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

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

• Interpretation:

  • Positive: Goods are substitutes.

  • Negative: Goods are complements.

Example: If the price of good Y rises from $1.50$ to $1.80$ and the quantity demanded of good X increases from $80$to $120$, then: $E_{xy} = \frac{(120 - 80)/80}{(1.80 - 1.50)/1.50} = \frac{0.5}{0.2} = 2.5$

Income Elasticity of Demand

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

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

• Interpretation:

  • Normal Good: $E_I > 0$

  • Inferior Good: $E_I < 0$

  • Luxury Good: $E_I > 1$

  • Necessity: $0 < E_I < 1$

Example: If income increases from $40$to $80$ and demand rises from $20$to $40$, then: $E_I = \frac{(40 - 20)/20}{(80 - 40)/40} = \frac{1}{1} = 1$

Incidence of Tax and Subsidy

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

• 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 vertically upward by $2$units. The new equilibrium can be found by solving $12 - 2p = 5 - 2(p + 2)$.

Supply and Demand Shifts

Shifts in supply and demand curves are caused by changes in determinants other than price, such as income, prices of related goods, expectations, and technology.

• Demand Shift: Caused by changes in income, tastes, prices of substitutes/complements, expectations.

• Supply Shift: Caused by changes in input prices, technology, expectations, number of sellers.

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

Example: If buyers expect the price to rise tomorrow, demand increases today, shifting the demand curve to the right.

Summary Table: Elasticity Types and Interpretation

Elasticity Type	Formula	Interpretation
Own-Price Elasticity of Demand	$E_d = \frac{dQ}{dP} \cdot \frac{P}{Q}$	Responsiveness of quantity demanded to price changes
Price Elasticity of Supply	$E_s = \frac{dQ}{dP} \cdot \frac{P}{Q}$	Responsiveness of quantity supplied to price changes
Cross-Price Elasticity	$E_{xy} = \frac{\%\ \text{change in } Q_x}{\%\ \text{change in } P_y}$	Substitutes ($E_{xy} > 0$), Complements ($E_{xy} < 0$)
Income Elasticity	$E_I = \frac{\%\ \text{change in } Q}{\%\ \text{change in income}}$	Normal ($E_I > 0$), Inferior ($E_I < 0$), Luxury ($E_I > 1$), Necessity ($0 < E_I < 1$)

Applications and Problem Types

• Calculating elasticity using demand and supply equations

• Interpreting elasticity at different points on a curve

• Analyzing the effect of taxes and subsidies on market equilibrium

• Understanding the impact of elasticity on total revenue/expenditure

• Comparing elasticities for different goods (necessities, luxuries, substitutes, complements)

Key Takeaways

• Elasticity is a measure of responsiveness and is crucial for understanding market dynamics.

• Elasticity affects how price changes impact total revenue, tax incidence, and market equilibrium.

• Different types of elasticity (own-price, cross-price, income, supply) provide insights into consumer and producer behavior.

• Graphical analysis and algebraic calculation are both important for mastering elasticity concepts.

Additional info: Some explanations and formulas have been expanded for academic completeness. Graphs referenced in the questions are not reproduced here, but their interpretation is described in the notes.