2. (10 Points) A monopolist faces a demand curve given by: P = 70 – 2Q, where P

Question

2.
(10 Points)
A monopolist faces a demand curve given by:
P = 70 – 2Q, where P is the price of the good and Q is the quantity demanded. The marginal cost of production is constant and is equal to $6. There are no fixed costs of production.
A) (2 points) What quantity should the monopolist produce in order to maximize profit?
B) (2 points) What price should the monopolist charge in order to maximize profit?
C) (2 points) How much profit will the monopolist make?
D) (2 points) What is the deadweight loss created by this monopoly (hint: compare the monopoly outcome with the perfectly competitive outcome).
E) (2 points) If the market were perfectly competitive, what quantity would be produced?

Explanation / Answer

(a) P = 70-2Q MR = 70-4Q MC=MR 6=70-4Q Q=16 (b) P = 70-2(16)=38 (c) Profit = TR - TC = (16)(38) - 6(16) = 512 (d) In perfect competition, firms price their goods at P = MC = $6 Q = 32 Welfare of PC = 0.5*(70-6)*32 = 1024 Welfare of Monopoly = 0.5(70-38)(16)=256 Deadweight Loss = $768 (if you're wondering how i calculated those, draw out the DD and Supply graph. Its the area in between DD, SS and quantity. (e) Q = 32 (calculated)

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