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

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

$p + 10 q = 168$

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

$1 + 10 \frac{d q}{d p} = 0$

$\frac{d q}{d p} = - \frac{1}{10}$

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 :

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

answer: $84$