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 multiply by Q to find Total Revenue since P*Q=TR TR=70Q-2Q^2 first derivative of TR gives Marginal Revenue MR=70-4Q To maximize profit find Q where MR=0 0=70-4Q Q=17.5 B) Plug Q into demand function to find monopoly price P=70-2(17.5) P=35 C) Since Profit=TR-TC and TC=MC*Q Profit=70Q-2Q^2-6Q Profit=70(17.5)-2(17.5)^2-6(17.5) Profit=$507.5 D)DWL=1/2(Price Change)(Quantity Change) We know price at perfect competition will be 6 since P=MC in a perf competition. We need to find perfect competition Q. Since P=MC in perfect competition, 70-2Q=6 Q=32 so change in quantity is 32-17.5=14.5 change in price is 35-6=29 so, DWL=.5(14.5)(29)=210.25

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