The elasticity of demand if p = 40 - 2q at a price of p = 8 is?
(a) -0.35;
(b) -0.5;
(c) 0.25;
(d) 0.5.
you need to know the price elasticity of demand equation ( they will give it to you in test anyway)
its $\displaystyle \frac{p}{q} \cdot \frac{\Delta q}{\Delta p} $
now since that formula is in terms of p , you want to rearrange it to be in terms of q.
$\displaystyle q = \frac{40-p}{2} =\frac{40-8}{2} = \frac{32}{2} = 16$
So using the given price of 8 you can work what q is. Then work out the derivative of p and q in relation to each other. $\displaystyle p=40-2q $ So derivative of q is 2 and derivative of p is 1.
$\displaystyle \frac{p}{q} \cdot \frac{2}{1} = \frac{8}{16} \cdot \frac{2}{1} $
$\displaystyle \epsilon = 0.25 $
Since elasticity is less than one , changes in price change quantity less than 1 for 1 , so it is inelastic.
Does that help?