Methods of Measuring Price Elasticity of Demand

This method, developed by Dr Marshall, looks at how total spending by consumers changes when price changes.

• Total Expenditure Formula:
  Total Expenditure (TE) = Price (P) × Quantity Demanded (Q)

How to Interpret:

Elastic Demand Example (Ed > 1):

• Price of jeans falls from ₹1000 to ₹700
• Quantity bought increases from 10 to 25 units
• Total Expenditure changes from ₹10,000 to ₹17,500 (increases!)
• Conclusion: When price fell, people bought so much more that total spending increased → Elastic Demand

Inelastic Demand Example (Ed < 1):

• Price of salt falls from ₹20 to ₹15
• Quantity bought increases from 5 kg to 6 kg only
• Total Expenditure changes from ₹100 to ₹90 (decreases!)
• Conclusion: When price fell, people didn't buy much more → Inelastic Demand

Data Table:

This method, also called Ratio Method, Percentage Method, or Arithmetic Method, measures elasticity as the ratio of percentage changes.

• Formula:
  \[\mathrm{Ed}=\frac{\text{Percentage change in Quantity demanded}}{\text{Percentage change in Price}}\]
  \[\mathrm{Ed}=\frac{\%\triangle\mathrm{Q}}{\%\triangle\mathrm{P}}\]

Where:

• ΔQ = Change in Quantity Demanded
• Q = Original Quantity
• ΔP = Change in Price
• P = Original Price

This method measures elasticity at a specific point on the demand curve. It's best for understanding how elastic demand is at different price levels.

1) Elasticity On a Straight-Line Demand Curve:

\[\text{ep at point R}=\frac{\text{Lower line segment}}{\text{Upper line segment}}=\frac{\mathrm{RB}}{\mathrm{RA}}\]

2) Elasticity On the Non-linear Demand Curve:

\[\mathrm{e_{P}~at~R=\frac{Lower~line~segment}{Upper~line~segment}=\frac{BR}{RA}}\]

This method measures elasticity between two points on the demand curve. It's called "average elasticity" and is especially useful when there are large price and quantity changes.

• Formula:
  \[\mathrm{E=\frac{Q_{2}-Q_{1}}{Q_{2}+Q_{1}}\div\frac{P_{1}-P_{2}}{P_{1}+P_{2}}}\]
  

Where:

• Q1 = Original Quantity
• Q2 = New Quantity
• P1 = Original Price
• P2 = New Price

• Original Price (P1) = ₹60
• New Price (P2) = ₹50
• Original Quantity (Q1) = 10 units
• New Quantity (Q2) = 13 units

Step 1: Calculate Changes

Step 2: Calculate Averages

Step 3: Apply Formula

This method, developed by Mrs. Joan Robinson, relates elasticity to revenue concepts used by businesses. It connects elasticity with Average Revenue (AR) and Marginal Revenue (MR).

• Formula:
  Ed = AR / (AR - MR)
  or
  Ed = Average Revenue / (Average Revenue - Marginal Revenue)

• How It Works:

  When	MR Value	AR vs MR	Ed Value
  Demand is elastic.	Positive but less than AR	AR > MR	> 1
  Demand is unitary.	Equals AR/2	AR = 2(MR)	= 1
  Demand is inelastic.	Can be zero or negative	AR < 2(MR)	< 1

If at a point:

• AR = ₹100
• MR = ₹60

Then:
Ed = 100 / (100 - 60) = 100 / 40 = 2.5 (Elastic)

Example 1: Coffee Shop Pricing

• If coffee is elastic (Ed > 1): A price drop will increase sales significantly
• Strategy: Reduce price to boost revenue

Example 2: Hospital Medicines

• If a medicine is inelastic (Ed < 1): People will buy regardless of price change
• Strategy: Price increase doesn't hurt sales much

Example 3: Fast Fashion vs Luxury Brands

• Fast fashion: Often elastic (many substitutes available)
• Luxury brands: Often inelastic (brand-loyal customers)

• Total Expenditure Formula:
  Total Expenditure (TE) = Price (P) × Quantity Demanded (Q)
• Revenue Method Formula:
  Ed = AR / (AR - MR)
  or
  Ed = Average Revenue / (Average Revenue - Marginal Revenue)
• Arc Elasticity Demand Formula:
  \[\mathrm{E=\frac{Q_{2}-Q_{1}}{Q_{2}+Q_{1}}\div\frac{P_{1}-P_{2}}{P_{1}+P_{2}}}\]
• Proportionate Method Formula:
  \[\mathrm{Ed}=\frac{\text{Percentage change in Quantity demanded}}{\text{Percentage change in Price}}\]
  \[\mathrm{Ed}=\frac{\%\triangle\mathrm{Q}}{\%\triangle\mathrm{P}}\]