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 relation.
The demand is given by $q^a p^b=c$. Take logs of both sides,
\[ a\ln q+b\ln p=\ln c \]

Step 2: Differentiate in log terms.
Holding $c$ fixed and differentiating with respect to $\ln p$,
\[ a\frac{d\ln q}{d\ln p}+b=0\;\Rightarrow\;\frac{d\ln q}{d\ln p}=-\frac{b}{a} \]

Step 3: Recognise the elasticity.
The quantity $\dfrac{d\ln q}{d\ln p}$ is exactly the price elasticity $E_p$, so $E_p=-\dfrac{b}{a}$.

Step 4: Take the size.
The absolute value is
\[ |E_p|=\frac{b}{a} \]
\[ \boxed{\dfrac{b}{a}} \]