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# 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.

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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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