Determine price elasticity of demand and marginal revenue if $q = 30-4p-p^2$, where q is quantity demanded and p is price and p=3.
I solved it for first part-
Price elasticity of demand = $-\frac{p}{q} \frac{dq}{dp}$
on solving above i got answer as $\frac{10}{3}$
But on solving for Marginal revenue i am getting -10. But the correct answer given is $\frac{21}{10}$
Any hint is appreciable please help.
Best Answer
Try this. Total Revenue TR is $pq$. Marginal revenue is the change in TR with change in $quantity$ (not price, as I incorrectly stated in my comment) so marginal revenue is $\frac{\partial TR}{\partial q}$ or $$\frac{\partial (pq)}{\partial p}\frac{\partial p}{\partial q}$$ Revenue is $pq$, or $30p−4p^2−p^3$ so marginal revenue is $30−8p−3p^2$ = 30−24−27=−21. But then, as OP correctly calcualted, $\frac{\partial q}{\partial p}=-10$ so $$\frac{\partial (pq)}{\partial p}\frac{\partial p}{\partial q}= -21/-10.$$