A monopolist can produce at a constant average and marginal

A monopolist can produce at a constant average (and marginal) cost of AC-MC-5. It faces a market demand curve of Q=65-P Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its profits. The monopoly would produce 30 units of output at a price of s 353, (Enter numeric responses using real numbers rounded to two decimal places,) In turn, the monopoly would eam profit of S90 Suppose a second firm enters the market. Let Q1 be tho output of the ris·inm and O2 bo the output or tho ooonid. Matkot amnand inwoven by Q1 +Q2 -65-P Assuming that this second firm has the same costs as the first, wite the profits of each firm as a function of Q1 and Qz The profit functions for Firm 1 (I11) and for Firm 2 (112) are

Solution

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Answer

We can write demand as

P = 65-Q

TR = Q×P

=65Q - Q^2

MR = dTR\\dQ = 65 - 2Q

Fro quantity MC = MR

65 - 2Q = 5

Q = 30

P - 65 - 65 - 30

P = 35

Monopoly will produced Q = 30 and price is P = $35