ch4

Microeconomics Study Notes

Chapter 4: Elasticity

Introduction

• After studying this chapter, you will be able to:

  • Define, calculate, and explain the factors that influence the price elasticity of demand.

  • Define, calculate, and explain the factors that influence the income elasticity of demand and the cross elasticity of demand.

  • Define, calculate, and explain the factors that influence the elasticity of supply.

Price Elasticity of Demand

Understanding Price Elasticity of Demand

• Price elasticity of demand indicates how responsive the quantity demanded of a good is to a change in its price, holding all other influences constant.

• When supply decreases, the equilibrium price rises and the equilibrium quantity decreases.

  • The degree of change in price and quantity is determined by the responsiveness of quantity demanded to the change in price.

Importance of Elasticity

• The slope of the demand curve reflects the relationship between price and quantity demanded.

  • A steep demand curve indicates that price rises significantly while quantity decreases only slightly.

  • A flat demand curve suggests that price barely rises and quantity dramatically increases.

• Since the slope can vary with units of measurement, elasticity provides a unit-free measure of responsiveness.

Formula for Calculating Price Elasticity of Demand

• The formula for price elasticity of demand: $E_d = \frac{\%\Delta Q}{\%\Delta P}$ where:

  • $\%\Delta Q$ is the percentage change in quantity demanded.

  • $\%\Delta P$ is the percentage change in price.

Example Calculation

1. Initial price of pizza: $P_1 = 20.50$

   • Quantity demanded: $Q_1 = 9$

2. New price of pizza: $P_2 = 19.50$

   • New quantity demanded: $Q_2 = 11$

3. Changes:

   • Change in price: $\Delta P = P<em>2 - P</em>1 = -1$

   • Change in quantity: $\Delta Q = Q<em>2 - Q</em>1 = 2$

4. Average price:

   • $P<em>{ave} = \frac{P</em>1 + P_2}{2} = \frac{20.50 + 19.50}{2} = 20$

5. Average quantity:

   • $Q<em>{ave} = \frac{Q</em>1 + Q_2}{2} = \frac{9 + 11}{2} = 10$

6. Percentage changes:

   • $\%\Delta Q = \frac{\Delta Q}{Q_{ave}} \times 100 = \frac{2}{10} \times 100 = 20\%$

   • $\%\Delta P = \frac{\Delta P}{P_{ave}} \times 100 = \frac{-1}{20} \times 100 = -5\%$

7. Price elasticity of demand:

   • $E_d = \frac{20\%}{-5\%} = -4$

   • Interpretation: The demand is elastic since the elasticity is greater than 1 (absolute value).

Concepts of Elasticity

• Elasticity classifications:

  • Perfectly Inelastic Demand: Demand does not change with price changes (elasticity = 0).

  • Graph: Vertical demand curve.

  • Elastic Demand: Quantity demanded changes significantly with price changes (elasticity > 1).

  • Unit Elastic Demand: Percentage change in quantity equals percentage change in price (elasticity = 1).

  • Inelastic Demand: Quantity demanded changes less than price changes (elasticity < 1).

  • Perfectly Elastic Demand: Quantity demanded is infinitely responsive to price changes (elasticity = ∞).

Factors Influencing Elasticity of Demand

1. Closeness of Substitutes:

   • Closer substitutes lead to more elastic demand (e.g., luxury goods).

   • Necessities (e.g., food, housing) generally have inelastic demand.

2. Proportion of Income Spent:

   • Higher proportion of income spent on goods leads to more elastic demand.

3. Time Elapsed Since Price Change:

   • Longer time allows consumers to adjust demand, increasing elasticity.

   • Goods that can be stored without losing value also exhibit increased elasticity.

Elasticity Along a Linear Demand Curve

• Demand's elasticity varies at different points along a linear demand curve:

  • Above the Mid-point: Demand is elastic.

  • At the Mid-point: Demand is unit elastic.

  • Below the Mid-point: Demand is inelastic.

Total Revenue and Price Elasticity

• Total revenue (TR) from sales is calculated as:
  $TR = Price \times Quantity$

• Effects of price changes with regard to elasticity:

  • Elastic Demand: Price cut increases quantity sold more than 1%, leading to increased TR.

  • Inelastic Demand: Price cut increases quantity sold less than 1%, leading to decreased TR.

  • Unit Elastic Demand: Price cut increases quantity sold by exactly 1%, leaving TR unchanged.

Your Expenditure and Your Elasticity

• Elastic Demand: A 1% price cut increases quantity bought by more than 1%, increasing expenditure.

• Inelastic Demand: A 1% price cut increases quantity bought by less than 1%, decreasing expenditure.

• Unit Elastic Demand: A 1% price cut increases quantity bought by exactly 1%, leaving expenditure unchanged.

More Elasticities of Demand

Income Elasticity of Demand

• Measures the responsiveness of quantity demanded to changes in income, calculated as: $E<em>y = \frac{\%\Delta Q</em>d}{\%\Delta Income}$

  • Greater than 1: Demand is income elastic (normal good).

  • Greater than 0 but less than 1: Demand is income inelastic (normal good).

  • Less than 0 (negative): Demand is for an inferior good.

Cross Elasticity of Demand

• Measures responsiveness of demand for one good to changes in the price of another good, calculated as: $E<em>{xy} = \frac{\%\Delta Q</em>x}{\%\Delta P_y}$

  • Positive: Good x and y are substitutes.

  • Negative: Good x and y are complements.

Elasticity of Supply

Understanding Elasticity of Supply

• Elasticity of supply measures the responsiveness of quantity supplied to price changes, under constant influences.

Formula for Elasticity of Supply

• Formula:
  $E<em>s = \frac{\%\Delta Q</em>s}{\%\Delta P}$

Factors Influencing Elasticity of Supply

1. Resource Substitution Possibilities:

   • Greater ease in substituting resources leads to higher elasticity of supply.

2. Time Frame for Supply Decision:

   • Momentary Supply: Perfectly inelastic, constant quantity post price change.

   • Short-run Supply: Somewhat elastic.

   • Long-run Supply: Most elastic.

Glossary of Elasticities

• Table 4.1 contains a compact glossary summarizing various measures of elasticity:

  • Income Elasticities of Demand:

  • Elastic: Greater than 1 (normal good)

  • Inelastic: Less than 1 (but greater than 0, normal good)

  • Negative: Less than 0 (inferior good)

  • Cross Elasticities of Demand:

  • Substitutes: Positive

  • Complements: Negative

  • Unrelated Goods: Zero

  • Elasticities of Supply:

  • Perfectly Elastic: Infinity

  • Elastic: Less than infinity (greater than 1)

  • Unit Elastic: 1

  • Inelastic: Greater than 0 (but less than 1)

  • Perfectly Inelastic: 0

• These study notes capture the essential concepts and calculations of elasticity as presented in the provided transcript, ensuring a comprehensive understanding of microeconomic principles related to elasticity.