Question

What is Elasticity of Demand ? Explain percentage method of its measurement.

Hint:

When using the percentage method, be careful to use the original price and quantity as the base for your percentage calculations. A clear, step-by-step numerical example is the best way to explain this method in an exam.

Answer 1

Price elasticity of demand is a measure of the degree of responsiveness of the quantity demanded of a good to a change in its own price. It quantifies how much the quantity demanded changes when the price changes. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

In simple terms, it tells us how sensitive consumers are to a price change.

If a small change in price causes a large change in quantity demanded, demand is elastic (\( |E_d| > 1 \)).

If a large change in price causes a small change in quantity demanded, demand is inelastic (\( |E_d| < 1 \)).

If a change in price causes a proportional change in quantity demanded, demand is unitary elastic (\( |E_d| = 1 \)).

Percentage Method of Measurement:

The percentage method is the most common way to calculate price elasticity of demand. It measures elasticity by dividing the percentage change in quantity demanded by the percentage change in price.

The formula is:

\[ E_d = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} \]

This can be expressed as:

\[ E_d = \frac{\frac{\Delta Q}{Q} \times 100}{\frac{\Delta P}{P} \times 100} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} \]

Where:

• \( E_d \) = Price elasticity of demand
• \( \Delta Q \) = Change in quantity demanded (\( Q_{\text{new}} - Q_{\text{old}} \))
• \( \Delta P \) = Change in price (\( P_{\text{new}} - P_{\text{old}} \))
• \( P \) = Original price
• \( Q \) = Original quantity demanded

The value of \( E_d \) is usually negative due to the inverse relationship between price and quantity demanded, but we often consider its absolute value for interpretation.

Numerical Example:

Suppose the price of a coffee cup increases from \$4 to \$5. As a result, the quantity demanded per day falls from 200 cups to 150 cups.

Original Price (P) = \$4

New Price (\(P_{\text{new}}\)) = \$5

Original Quantity (Q) = 200 cups

New Quantity (\(Q_{\text{new}}\)) = 150 cups

Step 1: Calculate the changes in price and quantity.

\[ \Delta P = 5 - 4 = 1 \text{ (dollar)} \]

\[ \Delta Q = 150 - 200 = -50 \text{ cups} \]

Step 2: Calculate the percentage changes.

\[ \text{Percentage Change in Price} = \frac{\Delta P}{P} \times 100 = \frac{1}{4} \times 100 = 25\% \]

\[ \text{Percentage Change in Quantity Demanded} = \frac{\Delta Q}{Q} \times 100 = \frac{-50}{200} \times 100 = -25\% \]

Step 3: Calculate Elasticity.

\[ E_d = \frac{-25\%}{25\%} = -1 \]

Conclusion:

Since the absolute value of elasticity is 1, the demand for coffee in this price range is unitary elastic. A 25% increase in price led to exactly a 25% decrease in quantity demanded.