A general quadratic demand function has the form to follow. $q = c p ^ { 2 } + l p + r$ (c, l, r are constants, $l \neq 0$ )

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

A) $E = c p ^ { 2 } + l p + r$
B) $E = - \frac { 2 } { p + r }$
C) $E = - \frac { p ( 2 c p + l ) } { c \mathrm { p } ^ { 2 } + l p + r }$
D) $E = - l p$
E) $E = \frac { c p + l } { c p ^ { 2 } + l p + r }$

Question

A general quadratic demand function has the form to follow.  $q = c p ^ { 2 } + l p + r$ (c, l, r are constants, $l \neq 0$ )
 
Obtain a formula for the elasticity of demand at a unit price p.
 
A) $E = c p ^ { 2 } + l p + r$
B) $E = - \frac { 2 } { p + r }$
C) $E = - \frac { p ( 2 c p + l ) } { c \mathrm { p } ^ { 2 } + l p + r }$
D) $E = - l p$
E) $E = \frac { c p + l } { c p ^ { 2 } + l p + r }$

Quizplus · Accepted Answer

The elasticity of demand, $E$, is calculated as the percentage change in quantity demanded divided by the percentage change in price, which can be expressed as $E = \frac{p}{q} \cdot \frac{dq}{dp}$. Given the demand function $q = c p ^ { 2 } + l p + r$, the derivative of $q$ with respect to $p$ is $dq/dp = 2cp + l$. Substituting $q$ and $dq/dp$ into the formula for elasticity gives $E = \frac{p}{c p ^ { 2 } + l p + r} \cdot (2cp + l)$, which simplifies to $E = - \frac { p ( 2 c p + l ) } { c p ^ { 2 } + l p + r }$, considering the negative sign to account for the law of demand (price and quantity demanded move in opposite directions).

A General Quadratic Demand Function Has the Form to Follow q=cp2+lp+rq = c p ^ { 2 } + l p + rq=cp2+lp+r

A General Quadratic Demand Function Has the Form to Follow $q = c p ^ { 2 } + l p + r$