firm with marginal costs of MC(q) = 60+0.2q is able to engage in third degree pr

Question

firm with marginal costs of MC(q) = 60+0.2q is able to engage in third degree price dis- crimination between two groups of customers, with the following demand curves for the first and second group as follows:

(1) : p1 = 1500 0.5q1 (2):p2 =7002q2

a. How many units does the monopolist sell to each group, and at what price?

b. What would happen if the monopolist were forced to charge all of its customers the same price? That is, how many units are sold, and what is the monopoly price in this case?

Explanation / Answer

a.

1. p1 = 1,500 – 0.5q1

    TR = (1,500 – 0.5q1) × q1

          = 1,500q1 – 0.5q1^2

MR = derivative of TR with respect of q1

        = 1,500 – q1

MC = 60 + 0.2q

The equilibrium condition is MR = MC

1,500 – q1 = 60 + 0.2q

1.2q1 = 1,440

q1 = 1,200

Price = 1,500 – 0.5q1 = 1,500 – 0.5 × 1,200 = 900

2. p2 = 700 – 2q2

    TR = (700 – 2q2) × q2

          = 700q2 – 2q2^2

MR = derivative of TR with respect of q2

        = 700 – 4q2

MC = 60 + 0.2q

The equilibrium condition is MR = MC

700 – 4q2 = 60 + 0.2q

4.2q2 = 640

q2 = 152

Price = 700 – 2q2 = 700 – 2 × 152 = 396

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

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