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# Help with profit-maximizing quantity and price

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A monopolist has demand and cost curves given by:
Quantity demand = 10000 - 20P
TC = 1000 + 10Q + .05Q^2

a. Find the monopolist's profit-maximizing quantity and price.
b. Find the monopolist's profit.

I tried to do the problem but kept coming up with a negative number for the monopolist's profit. Are my number's correct?

P = 10 - .05Q
TR = 10Q - .05Q^2
Q = 99.5
P = \$5.03 (nearest cent) or \$5.00 (nearest 10 cents)

What should I use as the wholesale price?

https://brainmass.com/economics/macroeconomics/profit-maximizing-quantity-price-104242

#### Solution Preview

a. Find the monopolist's profit-maximizing quantity and price.

We write the demand into:
P = 500-.05Q
Then TR = P*Q = 500Q - .05Q^2
It should be noticed that the firm is a monopolist and is facing a downward ...

#### Solution Summary

The expert examines profit-maximizing quantity prices.

\$2.19