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Harry Smith owns a metal-producing company that is an unregulated monopoly. After considerable experimentation and research, total cost and marginal cost curves are: TC = 100 + 60Q + Q2 MC = 60 + 2Q where MC is marginal cost (in dollars) and Q is output. The demand and marginal revenue curves for the product are P = 100 Q MR = 100 2Q where P is the product price (in dollars) and Q is output.

a. If Smith wants to maximize profit, what output should he choose?

b. What price should he charge and what are his profits?

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Darryn D'Souza
Darryn D'SouzaLv10
28 Sep 2019

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Related questions

Your monopoly company exhibits the following costs:

TC=60+6Q+Q2 & MC=6+2Q

And the following market demand and marginal revenue functions:

Qd=598-P; MR=598-2Q

a)Find the profit maximizing level of output for the monopoly

b) At what price does the monopolist sell its good?

c)What are the monopolist profits

d)Is there any dead weight loss in the market? 

 

A small firm faces an inverse demand function of P = 100 - Q. Its total cost function is given by TC = .5Q2. (You should see right away that marginal revenue is thus MR = 100 - 2Q, and it also happens that marginal cost is just MC = Q. Both MR and MC are the first derivatives of total revenue and total cost. And a quick comment on MC: unlike some marginal cost functions we've seen, this one is not constant, because marginal cost is getting $1 higher with each additional unit of output.)

The Chief Executive Officer will manage the firm, choosing output and price. Currently, the CEO is negotiating an incentive-based contract with the shareholders of the company.
(Hint: basing compensation on revenue will motivate revenue maximization rather than profit maximization!)

Hint: since the plan creates incentives for the CEO to maximize revenue rather than profit, you should not set MR = MC at this point. BIG hint: revenue is maximized when selling an additional unit won't increase your revenue, or in math terms, when MR = 0.)

Owners' proposal: CEO keeps 10% of TR.

Firm price:

  

Firm output:

  

Total revenue:

  

Firm profit:

  

CEO compensation:

  

Remaining profit for owners:

  

NUMBER 1.

a. A firm is currently producing 40 units of output. At this level of ouput produced:

. Its average total cost is 130 (ATC = 130)

. The price per unit of output is 150

. MR = 30

. MC = 50

i. Is this firm making profits or losses? How much?

ii. Are they máximum profits? Why?

iii. If your answer to part ii. was no, what does this firm have to do to maximize its profits?

NUMBER 2.

A firm’s total cost and marginal cost functions are

TC = 10 Q2 + 2 Q – 2 ; MC = 20 Q + 2.

Asuming that the market price is 42 and that the marginal revenue (MR) is also 42 (it is constant at all output levels), how much output will this firm sell (produce) to maximize profits?

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