Science:Math Exam Resources/Courses/MATH104/December 2016/Question 06 (b)/Solution 2

Alt Sol: using demand elasticity formula $E={\frac {p}{q}}{\frac {dq}{dp}}$

$p+10q=168$

Consider $q$ is a function of $p$, and we take the derivative of $p$:

$1+10{\frac {dq}{dp}}=0$

${\frac {dq}{dp}}=-{\frac {1}{10}}$

Therefore $E=-{\frac {1}{10}}\cdot {\frac {p}{q}}$

Recall when $E=-1$, we say the good is price unit elastic. This is the optimal price which means it maximizes revenue.

So setting $E=-1$ gives us :

$-1=-{\frac {1}{10}}\cdot {\frac {p}{q}}\rightarrow p=10q\rightarrow p=168-p\rightarrow p=84$

answer: $\color {blue}84$