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Answer on Microeconomics Question for Anthony

Question #41198
A monopolist can produce at constant average and marginal costs of AC = MC =
9. The firm faces a demand curve given by:

q = 75 &ndash; p

a. Calculate the profit‐maximizing price quantity combination for the
monopolist. Also calculate the monopolist&rsquo;s profits.

b. What output would be produced by this industry under perfect competition?
Show that PM &gt; PC and QC = 2QM.
AC = MC = 9, q = 75 &ndash; p

a. The profit‐maximizing quantity can be found in the point where MR = MC, and the price we can find from the demand curve:
MR = TR&#039; = (p*q)&#039; = (75q - q^2)&#039; = 75 - 2q
MR = MC = 75 - 2q = 9
2q = 66
q = 33 units
p = 75 - 33 = $42 Monopolist&rsquo;s profit = (p - AC)*q = (42 - 9)*33 =$1089

b. Under perfect competition monopolist will produce output in the point, where demand equals marginal cost:
p = MC = \$9
q = 75 - 9 = 66 units
So, PM &gt; PC and QC = 66 = 2QM.

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