Comprehensive Study Notes on Elasticity: PED, YED, and XED

Fundamental Definitions of Elasticity

  • Elasticity Concepts:
    • Elastic: Refers to a state where the quantity demanded is highly sensitive or responsive to changes in another variable (most often price).
    • Inelastic: Refers to a state where the quantity demanded is not very sensitive or responsive to changes.

Price Elasticity of Demand (PED)

  • Definition: Measures the responsiveness in the change of quantity demanded following a specific change in the price of the good.
  • Formula:
    • Price Elasticity of Demand=Percentage Change in Quantity DemandedPercentage Change in Price\text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}
    • PED=%ΔQD%ΔP\text{PED} = \frac{\% \Delta \text{QD}}{\% \Delta \text{P}}

Ranges and Classifications of PED

  • Perfectly Inelastic:

    • Numerical Value: 00
    • Calculation Example: %ΔQD%ΔP=0−20%=0\frac{\% \Delta \text{QD}}{\% \Delta \text{P}} = \frac{0}{-20\%} = 0
    • Characteristics: Regardless of price increases or decreases, the Quantity Demanded (QD) remains constant. This is typically seen in the case of monopolies.
    • Example: TNB.
    • Graph Shape: Completely vertical line.

  • Inelastic:

    • Numerical Value: Greater than 00 but less than 11 (in absolute terms).
    • Calculation Example: %ΔQD%ΔP=+5−20%=−0.25\frac{\% \Delta \text{QD}}{\% \Delta \text{P}} = \frac{+5}{-20\%} = -0.25
    • Characteristics: The percentage change in price is much larger than the resulting percentage change in quantity demanded. Consumers are not sensitive to price changes due to necessity, addiction, or lack of alternatives.
    • Examples: Fruits, flowers, cigarettes.

  • Unitary Elasticity:

    • Numerical Value: −1-1 (11 in absolute terms).
    • Calculation Example: %ΔQD%ΔP=+20%−20%=−1\frac{\% \Delta \text{QD}}{\% \Delta \text{P}} = \frac{+20\%}{-20\%} = -1
    • Characteristics: The percentage change in price is exactly equal to the percentage change in quantity demanded. Consumers are equally sensitive to the price change.
    • Example: Picking red grapes over green grapes.

  • Elastic:

    • Numerical Value: Greater than 11 (in absolute terms).
    • Calculation Example: %ΔQD%ΔP=+80%−20%=−4\frac{\% \Delta \text{QD}}{\% \Delta \text{P}} = \frac{+80\%}{-20\%} = -4
    • Characteristics: The percentage change in price results in a much larger percentage change in quantity demanded. Consumers are highly sensitive; small discounts can induce significant increases in purchases.
    • Example: Discounted expensive handbags.

  • Perfectly Elastic:

    • Numerical Value: ∞\infty (Infinity).
    • Calculation Example: %ΔQD%ΔP=+70%0=∞\frac{\% \Delta \text{QD}}{\% \Delta \text{P}} = \frac{+70\%}{0} = \infty
    • Characteristics: Price never changes regardless of the quantity bought. If the price were to change even slightly, demand would theoretically drop to zero because consumers are extremely sensitive.
    • Example: Homogenous goods such as newspapers or bread.

  • Exception (Positive PED):

    • Calculation Example: %ΔQD%ΔP=+50+20%=+2.5\frac{\% \Delta \text{QD}}{\% \Delta \text{P}} = \frac{+50}{+20\%} = +2.5
    • Characteristics: Both price and quantity demanded move in the same direction (positive relationship).
    • Example: Luxury goods or Giffen goods.

Important Observations on PED

  • Graphical Representation: The slope of the demand curve shifts from completely vertical (Perfectly Inelastic) to completely horizontal (Perfectly Elastic).
  • Negative Sign: PED values are almost always negative because price and quantity demanded move in opposite directions (Law of Demand).
  • Position on the Demand Curve:
    • Higher Price Range: Tends to be Elastic.
    • Mid-Range Price: Unitary Elastic.
    • Lower Price Range: Inelastic.

Factors Affecting Price Elasticity

  • Range and Attractiveness of Substitutes: The more substitutes available for a product, the more elastic it becomes.
  • Quality and Accessibility of Information: When consumers are better informed or more information is available, demand becomes more elastic.
  • Time Horizon: The longer the time period available for consumers to adjust their behavior, the more elastic the demand becomes.
  • Percentage of Income Spent on the Good: A product that takes up a larger proportion of a consumer's income will be more elastic.
  • Width of Product Definition: A narrower or more specific definition of a product (e.g., "Sunkist Oranges" vs. "Fruit") leads to a more elastic demand.
  • Types of Goods:
    • Addictive Goods: Highly inelastic.
    • Necessity Goods: Inelastic.
    • Luxury Goods: Elastic.

PED and Total Revenue (TR)

  • Total Revenue Definition: The total income from sales made by a company.

    • Total Revenue (TR)=Price×Quantity\text{Total Revenue (TR)} = \text{Price} \times \text{Quantity}
    • Note: Total Revenue for the firm is synonymous with Total Expenditure for the consumer.

  • Revenue Relationship by Elasticity Type:

    • Perfectly Inelastic: Since QD doesn't change, the proportion of change in price equals the proportion of change in revenue. Firms can increase prices to increase revenue.
    • Inelastic: A price increase leads to a drop in QD, but the gain from the higher price outweighs the loss from fewer units sold. Policy: Increase Price to maximize revenue.
    • Unitary Elastic: Revenue remains constant regardless of price changes. Policy: Maintain Price.
    • Elastic: A small drop in price leads to a massive increase in QD and revenue. Policy: Reduce Price to maximize revenue.
    • Perfectly Elastic: Prices cannot change; companies must find ways to sell greater output to increase revenue.

Calculation and Policy Practice

  • Scenario 1 (Price 1010 to 1212; Quantity 5555 to 3535):

    • %ΔP=20%\% \Delta \text{P} = 20\%
    • %ΔQD=−36.3%\% \Delta \text{QD} = -36.3\%
    • PED=−1.8\text{PED} = -1.8 (Elastic).
    • TR Change: Old TR (10×55=55010 \times 55 = 550); New TR (12×35=42012 \times 35 = 420). Revenue decreased.

  • Scenario 2 (Price 2020 to 2525; Quantity 5050 to 4545):

    • %ΔP=25%\% \Delta \text{P} = 25\%
    • %ΔQD=−10%\% \Delta \text{QD} = -10\%
    • PED=−0.4\text{PED} = -0.4 (Inelastic).
    • TR Change: Old TR (20×50=100020 \times 50 = 1000); New TR (25×45=112525 \times 45 = 1125). Revenue increased.

Managerial and Government Use of PED

  • Price Discrimination Policy: Firms use different elasticity classes to maximize revenue from different categories of consumers.
    • Example: Airlines (Business Class vs. Economy Class).
  • Government Tax Implementation:
    • Inelastic/Addictive Goods: The government can impose higher taxes (e.g., cigarette tax) because demand will not drop significantly; consumers purchase out of necessity or addiction.
    • Normal Goods: Taxes are often shared between producers and consumers or borne more heavily by producers to generate government revenue for public spending.

Income Elasticity of Demand (YED)

  • Definition: Measures the responsiveness of quantity demanded to a change in consumer income.

  • Formula:

    • Income Elasticity of Demand=Percentage Change in Quantity DemandedPercentage Change in Income\text{Income Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Income}}
    • YED=%ΔQD%ΔY\text{YED} = \frac{\% \Delta \text{QD}}{\% \Delta \text{Y}}

  • YED by Category of Goods:

    • Normal Goods: Positive relationship (Income up, QD up). Can be elastic (e.g., clothes) or inelastic (e.g., fruit).
    • Inferior Goods: Negative relationship (Income up, QD down). Usually inelastic. Example: Public transport.
    • Luxury Goods: Positive relationship. Highly elastic values. Example: Luxury holiday destinations.
    • Giffen Goods: Positive relationship. Very inelastic values. Example: Near-expiry food.

  • Economic Cycles and YED:

    • Economic Growth: Production should focus on normal and luxury goods.
    • Recession: Production should focus on inferior and Giffen goods.

Cross Elasticity of Demand (XED)

  • Definition: Measures the responsiveness of quantity demanded of Good B to a change in the price of Good A.

  • Formula:

    • Cross Elasticity of Demand=Percentage Change in Quantity Demanded of Good BPercentage Change in Price of Good A\text{Cross Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded of Good B}}{\text{Percentage Change in Price of Good A}}
    • XED=%ΔQDB%ΔPA\text{XED} = \frac{\% \Delta \text{QD}_B}{\% \Delta \text{P}_A}

  • Complementary Goods:

    • Signage: Negative XED.
    • Logic: If Price of Coke increases, Quantity of Coke decreases, therefore Quantity of Fries also decreases (consumed together).
    • Elastic vs. Inelastic Complements:
      • Elastic: Price of Fries increases, Quantity of Fish decreases significantly (commonly consumed together).
      • Inelastic: Price of Fries increases, Quantity of Kebab decreases slightly (Kebab can alternatively be eaten with rice).

  • Substitute Goods:

    • Signage: Positive XED.
    • Logic: If Price of Coke increases, Quantity of Coke decreases, but Quantity of Pepsi increases as consumers switch.
    • Elastic vs. Inelastic Substitutes:
      • Elastic: Price of Coke increases, Pepsi Quantity increases by a large percentage.
      • Inelastic: Price of Coke increases, "100 Plus" Quantity increases by a smaller percentage due to differences in color, appearance, and purpose.

  • Purpose of Knowing XED:

    • To understand competitor goods.
    • To understand related markets.