Step 1: Understanding the Concept:
Price Elasticity of Demand (\(E_d\)) measures the degree of responsiveness of the quantity demanded of a commodity to a change in its price.
When the price elasticity of demand is greater than 1 (\(E_d>1\)), it is known as elastic demand.
This indicates that a small percentage change in price results in a relatively larger percentage change in the quantity demanded.
The Total Expenditure (TE) or Total Outlay is the amount spent by consumers on a commodity, calculated as:
\[ \text{Total Expenditure (TE)} = \text{Price (P)} \times \text{Quantity Demanded (Q)} \]
Step 2: Key Formula or Approach:
The Total Expenditure Method (or Total Outlay Method) developed by Dr. Alfred Marshall provides the relationship between price changes and total expenditure based on elasticity:
1. If Price and TE move in opposite directions (e.g., Price $\downarrow$, TE $\uparrow$), then \(E_d>1\).
2. If Price and TE move in the same direction (e.g., Price $\downarrow$, TE $\downarrow$), then \(E_d<1\).
3. If TE remains constant regardless of Price change, then \(E_d = 1\).
Step 3: Detailed Explanation:
When demand is elastic (\(E_d>1\)), the consumer is highly sensitive to price changes.
Suppose the price of a luxury item falls by 10%. Since the demand is elastic, the quantity demanded will increase by more than 10% (say 25%).
Initial Expenditure = \(P \times Q\)
New Expenditure = \((0.9P) \times (1.25Q) = 1.125 \times (P \times Q)\)
In this scenario, the "loss" in revenue from the lower price per unit is more than compensated for by the "gain" in revenue from the massive increase in the number of units sold.
Thus, the total expenditure incurred by the consumers (and total revenue for the sellers) will increase.
The inverse relationship between price and total expenditure is a hallmark of commodities with multiple substitutes or luxury goods.
Step 4: Final Answer:
Therefore, for a commodity with \(E_d>1\), a fall in price leads to a rise in total expenditure.