Question

Consider a demand curve represented as

• A. \(b/a\)
• B. \(a/b\)
• C. \(b\)
• D. \(a\)

Hint:

For multiplicative demand functions like \[ q^ap^b=c, \] logarithmic differentiation directly gives elasticity values.

Answer 1

The Correct Option is A

Step 1: Start from the demand equation.
\[ q^ap^b=c \]
Take natural logarithm on both sides:
\[ \ln(q^ap^b)=\ln c \] \[ a\ln q+b\ln p=\ln c \]

Step 2: Differentiate with respect to \(\ln p\).
\[ a\frac{d\ln q}{d\ln p}+b=0 \]
Thus,
\[ \frac{d\ln q}{d\ln p}=-\frac{b}{a} \]

Step 3: Recall elasticity formula.
Own price elasticity of demand is
\[ E_p=\frac{dq}{dp}\cdot\frac{p}{q} \] But,
\[ \frac{d\ln q}{d\ln p} = \frac{dq}{dp}\cdot\frac{p}{q} \] Hence,
\[ E_p=-\frac{b}{a} \]

Step 4: Find absolute value.
\[ |E_p|=\frac{b}{a} \]

Step 5: Final conclusion.
Therefore, the absolute value of the own price elasticity of demand is
\[ \boxed{\frac{b}{a}} \]
Hence, the correct option is (A).