# Help with profit-maximizing quantity and price

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?

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#### 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