Question

Multichoice company broadcasts to subscribers in Lusaka and Solwezi. The demand for each of these two groups are QSZ = 50 – (1/3) PSZ and QLSK = 80 – (2/3) PLSK, where Q is in thousands of subscriptions per year and P is the subscription price per year. The cost of providing Q units of service is given by C (Q) = 1000 + 30Q, where Q = QSZ + QLSK. Assuming Multichoice is a Monopoly and can engage in third-price discrimination, thenWhat is the profit-maximizing price and quantity in Solwezi Market?What is the profit-maximizing price and quantity in Lusaka Market?Suppose the Monopoly can only charge a single. What price should it charge and what is the total quantity sold?

Answer 1

The demand for each of these two groups are

QSZ = 50 – ($\frac{1}{3}$ ) PSZ 

QLSK = 80 – ($\frac{2}{3}$ ) PLSK,

where

Q is in thousands of subscriptions per year 

P is the subscription price per year.

The cost of providing Q units of service is

given by C (Q) = 1000 + 30Q,

where

Q = QSZ + QLSK. Assuming 

Step 2

1.

In Solwezi market:

Qsz= 50-($\frac{1}{3}$ )Psz

Inverse demand: Psz= 150-3Qsz

TRsz= Psz x Qsz= Qsz(150-3Qsz)

MRsz= $\frac{dTR}{dQ_{sz}}$ = 150-6Qsz

MC= $\frac{dC}{dQ_{sz}}$ = 30

Profit maximizing quantity:

MC= MRsz

30= 150-6Qsz

6Qsz= 150-30

Qsz= $\frac{120}{6}$ = 20 Profit maximizing quantity

Psz= 150-3(20)= 90 Profit maximizing price

 

2.

QLsk= 80-($\frac{2}{3}$ )(PLsk)

Inverse demand: PLsk= 120-1.5QLsk

TR= QLsk x PLsk =(QLsk)(120-1.5QLsk)

MR= 120-3QLsk

MC= 30

Profit maximizing condition:

MC= MR

30= 120-3QLsk

3QLsk= 120-30

QLsk= $\frac{90}{3}$ = 30 Profit maximizing Quantity

PLsk= 120-1.5 x 30= 120-45= 75 Profit maximizing price

 

3.

Total demand: Q= QLsk+Qsz= 130-P

Inverse demand: P= 130-Q

TR= (Q)(130-Q)

MR=$\frac{ dTR}{dQ}$ = 130-2Q

MC= $\frac{dC}{dQ}$ = 30

Profit maximizing condition:

MC=MR

30= 130-2Q

2Q= 130-30

Q=$\frac{ 100}{2}$ = 50 Profit maximizing quantity

P= 130-50= 80 Profit maximizing price