What is the value of price elasticity of demand for the rectangular hyperbola demand curve ?

Question

Accepted Answer

The value of price elasticity of demand for a rectangular hyperbola demand curve is indeed e = 1, as indicated by Option 3. Here's a detailed explanation to justify why this is the correct answer:

1. **Explanation for Option 3 (e = 1):**
   - A rectangular hyperbola demand curve is characterized by a constant elasticity of demand. This means that the percentage change in quantity demanded is exactly equal to the percentage change in price, regardless of the point on the curve. 
   - Mathematically, this is expressed as elasticity (e) being equal to 1. This is because the product of price and quantity (P × Q) remains constant along the curve. As a result, any change in price results in a proportional change in quantity demanded, maintaining the total revenue constant.
   - This property of the rectangular hyperbola is what defines unitary elasticity, where e = 1.

2. **Explanation for why other options are incorrect:**
   - **Option 1 (e > 1):** This would imply that the demand is elastic, meaning that the percentage change in quantity demanded is greater than the percentage change in price. However, for a rectangular hyperbola, the elasticity is constant and equal to 1, not greater than 1.
   - **Option 2 (e < 1):** This would suggest that the demand is inelastic, where the percentage change in quantity demanded is less than the percentage change in price. Again, this does not apply to a rectangular hyperbola, where the elasticity is exactly 1.
   - **Option 4 (e = 0):** This would indicate perfectly inelastic demand, where quantity demanded does not change with price changes. This is not the case for a rectangular hyperbola, as the elasticity is unitary (e = 1), not zero.

In conclusion, the defining characteristic of a rectangular hyperbola demand curve is its unitary elasticity, where the elasticity of demand is always equal to 1. This is why Option 3 is the correct answer, and the other options do not accurately describe the nature of the demand curve in question.