Question

2. Suppose the demand function for a monopolist’s product is given by P = 300 – 3Q and the cost function is given by C = 1500 + 2Q2 (Kindly answer clearly)

A) Calculate the MC.

B) Calculate the MR.

C) Determine the profit-maximizing price.

D) Determine the profit-maximizing quantity.

E) How much profit will the monopolist make?

F) What is the value of the consumer surplus under monopoly?

G) What is the value of the deadweight loss?

Answer 1

Demand is given by

P = 300 - 3Q

Cost Function = 1500 + 2Q^2

A) Marginal Cost = d/dQ (Total Cost) = d/dQ (1500 + 2Q^2) = 4Q

So the marginal cost of the monopolist is 4Q

B) The Marginal Revenue is given as d/dQ (PQ) = d/dQ (300 - 3Q)*Q = 300 - 6Q

So the Marginal Revenue is 300 - 6Q

C) At profit Maximization,

MR = MC

or 300 - 6Q = 4Q

or 10Q = 300

or Q = 30

So the profit maximization quantity is 30 units

D) Profit Maximization Price = 300 - 3Q = 300 - 3*30 = 210

So the profit maximization price is $210

E) Profit made by the monopolist = (P-MC) * Q = (210 - 4Q)*Q = (210 - 4*30) * 30 = (210 - 120) * 30 = 90 * 30 = 2700

So the monopolist will make a maximum profit of $2700

F)

The Market graph can be drawn as

Consumer Surplus = Area of ABE = 1/2 * 30 * (300-210) = 1/2 * 30 * 90 = 1350

G) The deadweight loss is area of BCD

Point C = intersection of P and MC

or 300 - 3Q = 4Q

or Q = 42.86

D = Point of intersection of MR and MC

So At Q = 30, MR = 300 - 6*30 = 120

So Area of BCD = 1/2 * (42.86-30) * (210 - 120) = 578.70

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