1. A monopoly has total cost and marginal cost given by: TC = Q2 + 5Q + 100 MC =

Question

1. A monopoly has total cost and marginal cost given by: TC = Q2 + 5Q + 100 MC = 2Q + 5 The market demand curve is given by P = 65 2Q a) Use the twice-as-steep rule to find the equation of the marginal revenue curve corresponding to the market demand curve. b) Find the profit-maximizing quantity of output for the monopoly and the price the monopolist will set. c) Calculate the monopolists profits. Calculate the value of the Lerner Index. d) Calculate the consumer surplus under monopoly. e) What quantity of output would be produced if the monopolist acted like a perfect competitor and set MC equal to P? f) Calculate profits and consumer surplus corresponding to the competitive equilibrium. g) Find the deadweight loss due to the monopoly.

Explanation / Answer

a)

            P = 65 – 2Q

From the twice as steep rule, we know that the slope of the MR curve must be double that slope of the demand curve. That is,

            MR = 65 – 4Q

b)

Find the profit maximizing quantity of the consumer as follows.

            MC = MR

            2Q + 5 = 65 – 4Q

            Q = 10

which is the profit maximizing quantity.

The price charged is

            P = 65 – 2Q

            P = 65 – 2(10)

            P = 45

c)

Profit = PQ – (Q2+5Q+100)

            = 45(10) – (102+5(10)+100)

            = $200

At the optimal quantity,

            MC = 2(10) + 5 = 25

Lerner Index = (Price – Marginal cost)/Price = (45 – 25)/45 = 0.44

d)

Consumer surplus        = ½(price when quantity is zero – price charged)(Quantity sold)

                                    = ½(65 – 45)(10)

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.