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# Calculating profit maximizing output level and price

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Suppose a company has just introduced a new line of ceramic insulators for which it has received patent protection, effectively granting the company monopoly status in the industry. The company's revenue and cost relations are given as:

TR = \$300Q - \$0.001Q2

TC = \$9,000,000 + \$20Q + \$0.0004Q2

where TR is total revenue, Q is output, and TC is total cost.

a) As a monopolist, calculate this firm's optimal output (Q) and price per unit (P).
b) Calculate the level of total profit at this output level and also the value of per unit profit at this output level.

##### Solution Summary

The solution describes the steps for calculating profit maximizing price and output level for a monopoly firm. It also calculates profit at this level.

##### Solution Preview

a) As a monopolist, calculate this firm's optimal output (Q) and price per unit (P).

TR=300Q-0.001Q^2
Marginal Revenue=dTR/dQ=300-0.002Q

TC=9000000+20Q+0.0004Q^2
Marginal Cost=d(TC)/dQ=20+0.0008Q

A monopolist sets his ...

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###### Education
• BEng (Hons) , Birla Institute of Technology and Science, India
• MSc (Hons) , Birla Institute of Technology and Science, India
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