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

Obtain a formula for the price that maximizes revenue.

A) $p = \frac { b } { n }$
B) $p = - \frac { b } { 2 n }$
C) $p = b n$
D) $p = - \frac { n } { 2 b }$
E) $p = - \frac { 2 n } { b }$

Question

A general linear demand function has the form that follows.   $q = n p + b$ (n and b constants, with $n \neq 0$ )
 
Obtain a formula for the price that maximizes revenue.
 
A) $p = \frac { b } { n }$
B) $p = - \frac { b } { 2 n }$
C) $p = b n$
D) $p = - \frac { n } { 2 b }$
E) $p = - \frac { 2 n } { b }$

Quizplus · Accepted Answer

Revenue $R$ is given by $R = p \cdot q$. Substituting $q = np + b$ into the revenue formula gives $R = p(np + b) = np^2 + bp$. To maximize revenue, take the derivative of $R$ with respect to $p$ and set it to zero: $\frac{dR}{dp} = 2np + b = 0$. Solving for $p$ gives $p = -\frac{b}{2n}$.

A General Linear Demand Function Has the Form That Follows q=np+bq = n p + bq=np+b

A General Linear Demand Function Has the Form That Follows $q = n p + b$