Question

Find the monopolist’s marginal revenue curve given:

a. Demand curve: QD = 50 – ½ P

b. Inverse demand curve: P = 222 – 3QD

Answer 1

a) QD = 50 - 1/2P = 50 - 0.5P

0.5P = 50 - QD

P = (50/0.5) - (1/0.5)QD

P = 100 - 2QD            [inverse demand curve]

TR = P * QD = 100QD - 2QD²

MR is the first order derivative of TR function. So,

MR = 100 - 4QD            [This is marginal revenue curve]

b) P - 222 - 3QD

    TR = P * QD = 222QD - 3QD²

     MR is the first order derivative of TR function. So,

     MR = 222 - 6QD            [This is marginal revenue curve]