Question

A monopolists who owns a music streaming service must decide on a price for its yearly subscription. He knows that the demand for music streaming subscription is ??(??)=400−2??PA(QA)=400−2QA for adults and ??(??)=300−??2PT(QT)=300−QT2 for teenagers. The marginal cost of providing music is $10$10

a) (8) Find the profit-maximizing monopoly pricing if they cannot differentiate between teenagers and adults.

b) (7) Find the profit-maximizing monopoly pricing if they can give a discount to teenagers.

Answer 1

Price Discrimination
P_A = 400-2Q_A                     P_T = 300-Q_T²

Given MC = $10

a) Without price discrimination (P= P_A = P_T )
thus, P =(700 –2Q -Q²)
MR = (700-4Q-3Q²)

For profit maximization MR = MC
                      (700-4Q-3Q²)=10
                      3Q²+4Q-690 = 0
Q = 14.51 thus the optimum level of production is 14.51 unit
                                        P = 700 –2(14.51) –(14.51²) =$460.44

b) With price discrimination (P_A is not equal to P_T)
Thus for adults,
P_A = 400-2Q_A                     
MR_A= 400-4Q_A
For profit maximization MR_A = MC
                               400-4Q_A = 10
required Q_A= 97.5 thus the optimum level of production for adult is 97.5 unit
   required P_A = (400-(2*97.5)) =$205

Thus for teenagers,
P_T = 300-Q_T²
MR_T= 300-3 Q_T²
For profit maximization MR_T = MC
  300-3 Q_T²=10
                required Q_T= 9.83 thus the optimum level of production for teenagers is 9.83 unit
                required P_T= (300-9.83²)= $203.37