A general linear demand function has the form to follow. $q = k p + b$ (k and b constants, with $k \neq 0$ )

Obtain a formula for the elasticity of the demand at a unit price p.

A) $E = - \frac { p } { k + b }$
B) $E = b + k p$
C) $E = - \frac { k p } { k p + b }$
D) $E = \frac { k p } { b }$
E) $E = - \frac { p } { p + b }$

Question

A general linear demand function has the form to follow.   $q = k p + b$ (k and b constants, with $k \neq 0$ )
 
Obtain a formula for the elasticity of the demand at a unit price p.
 
A) $E = - \frac { p } { k + b }$
B) $E = b + k p$
C) $E = - \frac { k p } { k p + b }$
D) $E = \frac { k p } { b }$
E) $E = - \frac { p } { p + b }$

Quizplus · Accepted Answer

The elasticity of demand, $E$, is defined as the percentage change in quantity demanded divided by the percentage change in price. For a linear demand function $q = kp + b$, the elasticity formula is derived as $E = \frac{dq/dp \cdot p}{q}$. Given $dq/dp = k$, and substituting $q = kp + b$ into the formula, we get $E = \frac{k \cdot p}{kp + b}$, which simplifies to $E = - \frac { k p } { k p + b }$, since $k$ is negative for a downward-sloping demand curve, indicating that the correct answer is C.

A General Linear Demand Function Has the Form to Follow q=kp+bq = k p + bq=kp+b

A General Linear Demand Function Has the Form to Follow $q = k p + b$