# Calculating the profit maximizing price and quantity

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Assume a monopolist with the following demand and cost relationships.

Q = 400 - 20P

TC = 10 + 5Q + Q^2 (Where "^" means "to the power of")

Calculate the following:

Profit maximizing price

Profit maximizing quantity

TR, TC, and Profit at profit maximizing Q and P.

https://brainmass.com/economics/pricing-output-decisions/calculating-profit-maximizing-price-quantity-408996

#### Solution Preview

Demand curve:

Q = 400 - 20P

Rearranging:

20P = 400 - Q

P = 20 - 0.05Q

Total Revenue:

TR = PQ

TR = (20 - 0.05Q)Q

TR = 20Q - ...

#### Solution Summary

Detailed calculations of a monopolist's profit maximizing price and output given its Demand and Total Cost functions.

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