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VashaNatasha [74]
3 years ago
6

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 p

er 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?
Business
1 answer:
Keith_Richards [23]3 years ago
3 0

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 demandQ=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

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