Elasticity

Chapter 4: Elasticity

Chapter Objectives

• To explain the concept of elasticities.
• To calculate elasticities of demand (price, income, and cross) and elasticity of supply.

Definition of Elasticity

• Elasticity measures the responsiveness/sensitivity of quantity demanded or quantity supplied due to changes in its determinants.

Elasticity of Demand

• Measures the responsiveness/sensitivity of quantity demanded due to changes in its determinants.
• Three types:
  • Price elasticity of demand
  • Income elasticity of demand
  • Cross elasticity of demand

Price Elasticity of Demand (\varepsilon_d)

• Definition: Measures the sensitivity/responsiveness of the quantity demanded due to a change in its price.
• Formula:
  • \varepsilon_d = \frac{\% \Delta \text{ Quantity Demanded}}{\% \Delta \text{ Price}}
  • \varepsilond = \frac{Q2 – Q1}{Q1} \times \frac{P1}{P2 – P_1}
    • Where:
      • Q_1 = Original Quantity Demanded
      • Q_2 = New Quantity Demanded
      • P_1 = Original Price
      • P_2 = New Price
  • Note: Negative coefficient value turns into positive.

Degree of Price Elasticity

• Elastic Demand: A small percentage change in price leads to a larger percentage change in quantity demanded. \varepsilon_d > 1
• Inelastic Demand: A large percentage change in price leads to a small percentage change in quantity demanded. \varepsilon_d < 1
• Unitary Elastic Demand: Percentage changes in price equal percentage changes in quantity demanded. \varepsilon_d = 1
• Perfectly Inelastic Demand: Quantity demanded does not change as the price changes. \varepsilon_d = 0
• Perfectly Elastic Demand: A small percentage change in price leads to an infinite percentage change in quantity demanded. \varepsilon_d = \infty

5 Degrees of Price Elasticity of Demand

Income Elasticity of Demand (\varepsilon_Y)

• Definition: Measures the sensitivity/responsiveness of the quantity demanded due to a change in income.
• Formula:
  • \varepsilon_Y = \frac{\% \Delta \text{ Quantity Demanded}}{\% \Delta \text{ Income}}
  • \varepsilonY = \frac{Q2 – Q1}{Q1} \times \frac{Y1}{Y2 – Y_1}
    • Where:
      • Q_1 = Original Quantity Demanded
      • Q_2 = New Quantity Demanded
      • Y_1 = Original Income Level
      • Y_2 = New Income Level

Responses of Income Elasticity

• \varepsilon_y < 0: Negative Income Elasticity
  • Type of good: Giffen/Inferior goods (e.g., used car and low-grade potatoes)
• 0 < \varepsilon_y < 1: Inelastic Income
  • Type of good: Normal goods (e.g., food and clothing)
• \varepsilon_y = 0: Zero Income Elasticity
  • Type of good: Necessity Goods (e.g., rice and vegetables)
• \varepsilon_y > 1: Elastic Income
  • Type of good: Luxury goods (e.g., antique furniture and diamonds)

Income Elasticity of Demand (\varepsilon_Y) - Examples

Cross Elasticity of Demand

• Definition: Measures the sensitivity/responsiveness of the quantity demanded of one product due to a change in the price of a related product.
• Formula:
  • \varepsilon_X = \frac{\% \Delta \text{ Quantity Demanded of good X}}{\% \Delta \text{ Price of good Y}}
  • \varepsilonx = \frac{Q{x2} – Q{x1}}{Q{x1}} \times \frac{P{y1}}{P{y2} – P_{y1}}

Responses of Cross Elasticity

• \varepsilon_x < 0: Negative Cross Elasticity
  • Good X and Y are complementary goods.
• \varepsilon_x > 0: Positive Cross Elasticity
  • Good X and Y are substitute goods.
• \varepsilon_x = 0: Zero Cross Elasticity
  • Good X and Y have no relationship.

Cross Elasticity of Demand - Interpretation

Price Elasticity of Supply (\varepsilon_s)

• Definition: Measures the sensitivity/responsiveness of the quantity supplied due to a change in its price.
• Formula:
  • \varepsilon_{ss} = \frac{\% \Delta \text{ Quantity Supplied}}{\% \Delta \text{ Price}}
  • \varepsilon{ss} = \frac{Q2 – Q1}{Q1} \times \frac{P1}{P2 – P_1}
    • Where:
      • Q_1 = Original Quantity Supplied
      • Q_2 = New Quantity Supplied
      • P_1 = Original Price Level
      • P_2 = New Price Level

Degree of Price Elasticity of Supply

• Elastic Supply: A small percentage change in price leads to a larger percentage change in quantity supplied. \varepsilon_{ss} > 1
• Inelastic Supply: A large percentage change in price leads to a small percentage change in quantity supplied. \varepsilon_{ss} < 1
• Unitary Elastic Supply: Percentage change in price equals the percentage change in the quantity supplied. \varepsilon_{ss} = 1
• Perfectly Inelastic Supply: A percentage change in price has no effect on the percentage change in the quantity supplied. \varepsilon_{ss} = 0
• Perfectly Elastic Supply: An almost zero percentage change in price brings a very large percentage change in the quantity supplied. \varepsilon_{ss} = \infty

Degrees of Price Elasticity of Supply

Determinants of Price Elasticity of Demand

1. Existence of Substitutes: Goods with more substitutes have more elastic demand compared to goods with fewer substitutes.
2. Complementary Goods: Goods that are used together normally have more inelastic demand.
3. Importance of the good: Demand for necessity goods is inelastic compared to demand for less essential goods.
4. Income level: Higher-income consumers tend to have inelastic demand because they become less sensitive to price changes.
5. Time dimensions for purchase: The shorter the period to decide on buying, the more inelastic the demand for the goods.
6. Habits: When people develop habits around certain goods or services, their demand becomes more inelastic.
7. Proportion of the good in one’s budget share: Goods that take a higher portion of a consumer’s expenditure or budget will have more elastic demand compared to goods that take a smaller portion.

Determinants of Price Elasticity of Supply

1. Period of the production process: If the production process takes a longer time to complete, then the response to price change will be small (inelastic).
2. Time frame to decide on selling: The shorter the time period to decide on selling, the more inelastic will be supply.
3. Availability and mobility of input for production: When inputs required for production are readily available (e.g., labor, raw materials), producers can easily adjust production levels in response to changes in market conditions. Therefore, more elastic.
4. Degree of Perishability: If the product is easily damaged or has a short expiration date, then the supply will be inelastic.
5. Technology Advancement: If more advanced technology is used in production, supply will be more elastic since producers can easily respond to price changes.
6. Nature of market: If the producer has multiple markets for its product, supply will be more elastic. OR if the market has a low barrier to entry, the supply will be more elastic.

Price Elasticity of Demand (E_d) & Relation to Total Revenue (TR)

• TR = P \text{ (price)} \times Q \text{ (quantity)}
• Sellers can adjust their selling price depending on the price elasticity of demand for their product.
• DD is elastic: Change in Q > change in P, therefore TR follows the direction of Q.
• DD is inelastic: Change in Q < change in P. Therefore, TR follows the direction of P.
• DD is Unitary elastic

Examples

• Elastic demand: Change in Q > change in P, therefore TR follow the direction of Q

  • P0= 5, Q0= 20, TR = 100
  • P1= 6, Q1 = 10, TR = 60

• Inelastic Demand: Change in Q < change in P. Therefore, TR follows the direction of P.

  • P0= 5, Q0= 10, TR = 50
  • P1= 8, Q1 = 8, TR = 64

• Unitary elastic

  • P0= 3, Q0= 4, TR = 12
  • P1= 4, Q1 = 3, TR = 12