The equation of the demand curve : pq = e, where e is a constant.
Select the INCORRECT statement:
- The demand curve is a rectangular hyperbola.
- The value of p times q is constant.
- The elasticity of demand at all points located on this demand curve is greater than 1.
- At every point of consumption, the expenditure remains the same.
The equation of the demand curve : pq = e, where e is a constant.
Select the INCORRECT statement:
- The demand curve is a rectangular hyperbola.
- The value of p times q is constant.
- The elasticity of demand at all points located on this demand curve is greater than 1.
- At every point of consumption, the expenditure remains the same.
Solution
Option 1 -> The equation pq = e is the standard form of a rectangular hyperbola, which is correct.
Option 2 -> The equation directly states that p × q = e (constant), which is correct.
Option 3 -> For pq = e, the price elasticity of demand Ed = (dq/dp) × (p/q). Since q = e/p, we get dq/dp = -e/p². Therefore, Ed = (-e/p²) × (p/q) = -1. The absolute value is 1, meaning unit elastic demand, NOT greater than 1. This is incorrect.
Option 4 -> Total expenditure = p × q = e, which remains constant at all consumption points, which is correct.
Hence, Option 3: The elasticity of demand at all points located on this demand curve is greater than 1 -> When the demand curve follows pq = e, the price elasticity of demand equals exactly 1 (unit elastic) at all points, not greater than 1. This is because the percentage change in quantity demanded exactly equals the percentage change in price, keeping total expenditure constant. A demand curve with elasticity greater than 1 would be elastic, while this curve exhibits unit elasticity throughout. -> correct
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