The demand function for a manufacturer's product is given by p = 20 - 0.02q,where p is the price per unit when q units are demanded.The point elasticity of demand when q = 100 is
A) -
B) -
C) -9.
D) -
E) -

Question

The demand function for a manufacturer's product is given by p = 20 - 0.02q,where p is the price per unit when q units are demanded.The point elasticity of demand when q = 100 is
A) - 
B) - 
C) -9. 
D) - 
E) -

Quizplus · Accepted Answer

The formula for point elasticity of demand is given by

$$
E_p = \frac{p}{q}\cdot\frac{\mathrm{d}q}{\mathrm{d}p}
$$

We can solve for $\frac{\mathrm{d}q}{\mathrm{d}p}$ by taking the derivative of the demand function with respect to $p$:

$$
\frac{\mathrm{d}q}{\mathrm{d}p} = -\frac{1}{0.02} = -50
$$

Plugging in $q=100$ into the demand function, we get

$$
p = 20 - 0.02	imes 100 = 18
$$

Therefore, the point elasticity of demand at this point is

$$
E_p = \frac{18}{100}\cdot(-50) = -9
$$

So the answer is C.

The Demand Function for a Manufacturer's Product Is Given by P