Calculation of Price Elasticity of Demand:

To calculate the price elasticity of demand, we use the formula:

Price Elasticity of Demand (E) = (% Change in Quantity Demanded) / (% Change in Price)

Step 1: Calculate the percentage change in quantity demanded:

The initial quantity demanded (Q1) is 10 units, and the final quantity demanded (Q2) is 15 units. The change in quantity demanded is:

Change in Quantity Demanded = Q2 - Q1 = 15 - 10 = 5 units

Percentage Change in Quantity Demanded = (Change in Quantity Demanded / Initial Quantity Demanded) * 100

Percentage Change in Quantity Demanded = (5 / 10) * 100 = 50%

Step 2: Calculate the percentage change in price:

The initial price (P1) is Rs. 6, and the final price (P2) is Rs. 4. The change in price is:

Change in Price = P2 - P1 = 4 - 6 = -2

Percentage Change in Price = (Change in Price / Initial Price) * 100

Percentage Change in Price = (-2 / 6) * 100 ≈ -33.33%

Step 3: Calculate the price elasticity of demand:

Price Elasticity of Demand (E) = (% Change in Quantity Demanded) / (% Change in Price)

Price Elasticity of Demand (E) = 50% / -33.33%

Price Elasticity of Demand (E) ≈ -1.5

Explanation of the negative sign:

The negative sign in the price elasticity of demand indicates the inverse relationship between price and quantity demanded. In most cases, when the price of a commodity decreases, the quantity demanded increases, and vice versa. This negative relationship is captured by the negative sign in the price elasticity of demand.

If the price elasticity of demand is greater than 1 (in absolute value), it indicates that the demand for the commodity is elastic. This means that a small change in price leads to a relatively larger change in quantity demanded.

In this case, the price elasticity of demand is approximately -1.5, which means that the demand for the commodity is elastic. A 1% decrease in price would lead to a 1.5% increase in quantity demanded.