Question

Suppose Sify broadband is enjoying a monopoly in Delhi as a id is enjoying a monopoly in Delhi as a cable internet provider. They found that there are two primary groups of cust ere are two primary groups of customer identified as businesses and households. The market demand function for business customers Q = 1000-2P, and for households are Q. = 1500-5P, and respectively. They also observed that cost of providing internet is Rs. 100 per customer. a) If the cable internet provider exercises multimarket price discrimination to these two customer groups, determine equilibrium output quantity and price of each group and total profit. b) If Sify decides to charge one price for all, what changes in the volume of profit will you observe?

Answer 1

(a)

$Q_B = 100-2P_B \\ MC=100 \\ 2P_B=1000 -Q_B \\ P_B = 500 -0.5Q_B \\ MR_B = 500 -Q_B \\ MR_B = MC \\ 100 = 500-Q_B \\ Q_B = 400 \\ P_B = 500-200 \\ P_B=300 \\ Π_B = P_BQ_B -100Q_B \\ = 300 \times 400 -100 \times 400 \\ = 200 \times 400 \\ = 80000 \\ Q_H = 1500-5P \\ MC=100 \\ 5P_H = 1500-Q_H \\ P_H = 300 -0.2Q_H \\ MR_H = 300 -0.4Q_H \\ MR_H=MC \\ 100 = 300 -0.4Q_H \\ 0.4Q_H = 200 \\ Q_H = 500 \\ P_H = 300- 0.2 \times 500 \\ P_H = 200 \\ Π_H = P_HQ_H-100Q_H \\ = 200 \times 500 -100 \times 500 \\ = 100 \times 500 \\ = 50000 \\ Total \; profit = Π_B+Π_H \\ = 130000$

(b)

$Q_B=1000-2P_B \\ Q_H=1500-5P_H \\ Q = Q_B+Q_H \\ P=P_B+P_H \\ Q = 2500 -7P \\ 7P = 2500 -Q \\ P = \frac{2500}{7} - \frac{Q}{7} \\ MR = \frac{2500}{7} - \frac{2Q}{7} \\ MR=MC \\ 100 = \frac{2500-2Q}{7} \\ 700 = 2500 -2Q \\ 2Q=1800 \\ Q = 900 \\ P = \frac{2500-900}{7} = 228.57 \\ Π = PQ-100Q \\ = 228.57 \times 900 -100 \times 900 \\ = 115713$

Profit decreased by 13000 -115713 = 14287