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?
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
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