Question

8. Suppose that the demand for bentonite is given by Q = 40 − 0.5P, where Q is in tons of bentonite per day and P is the price per ton. Bentonite is produced by a monopolist at a constant marginal and average total cost of $10 per ton. How much profit is earned per day if the profit-maximizing quantity of bentonite is sold at the profit-maximizing price?

Answer 1

Answer:

The total profit is  612.5

Explanation:

First we need to find the profit maximizing quantity. Since the monopolist faces the entire demand his profit ($\Pi$)equation would be

$\Pi=Q\times P- 10 Q$

where PxQ is his revenue and 10Q is his total cost.

We can replace P in the above equation from the equation demand$Q=40-\frac{P}{2}\rightarrow P=80-2Q$

Then

$\Pi=Q\times (80-2Q)- 10 Q=80Q-2Q^2-10Q$

taking derivatives with respect to Q

$\frac{\partial \Pi}{\partial Q}=80-4Q-10=0$

then Q=17.5 and P=45.

The total profit is then 612.5