Question

Telsave is one of the mobile phone service providers in the region. It offers different calling plans for different types of users, mainly individual plan and business plan. Telsave’s marginal costs and average costs of providing the calling service are both $5 per hour.

The demand for mobile services by individual users and business users are as follows:

Individual users  Q_I= 9000-100P_I

Business users  Q_B=6000-50P_B

where Q_I and Q_B are, respectively, total calling hours made by individual users and business users;  P_I and P_B are, respectively, the calling rate per hour for individual users and business users.

1. Suppose Telsave can price discriminate between two types of customers. Calculate Telsave’s mobile calling rate per hour for each customer class, output (i.e. total calling time made by all users) and profit levels.                                                

2. Calculate Telsave’s calling rate per hour, output (i.e. total calling time made by all users) and profit levels if there is no price discrimination.                     

Compare the results obtained in part a and part b. Explain which pricing strategy Telsave should choose, and discuss whether the consumers are better off under this strategy.

Answer 1

a) in case of price discrimination, he will charge different price in different market depending on the price elasticity. This is called as 3rd degree price discrimination.

Individual user;

• TR = P*Q

Q1 = 9000 - 100P1

=> P1 = 90 - Q1/100

=> TR = (90 - Q1/100)Q1

=> TR = 90Q1 - Q_{​​​​​​1}^{​​​​​2}​/100

=> MR = differentiate TR wrt Q1

=> MR = 90 - Q1/50

• Profit maximisation condition : MR = MC

90 - Q1/50 = 5 => Q1 = 4250 =>P1= $47.5

Business user;

• Q2 = 6000 - 50P2

=>P2 = 120 - Q2/50

TR = 120Q2 - Q₂²​​​​​/50

MR = 120 - Q2/25

• MR = MC --> Q2 = 2875 --> P2 = $62.5

b) no price discrimination

• Q = Q1 + Q2

=> Q = 9000-100P+6000-50P = 15,000-150P

=> P = 100 - Q/150

=> TR = 100Q - Q^{​​​​​​2}​​​​​/150

=> MR = 100 - Q/75

=> At MR = MC, Q = 7125 --> P = $52.5

• Profit = TR - TC

P*Q - MC*Q = $338437.5

Comparing

• Profit in case of price discrmination

TR = P1Q1 + P2Q2 = 47.5*4250 - 62.5*2875= $381562.5

TC = MC(Q1+Q2) = 5(4250+2875)= $35625

Profit = $381562.5 - $35625 = $345937.5

• Therefore profit under price discrimination is higher, hence Telsave will choose price discrimination.
• But consumer will be worse off especially in Business user market where consumer will face high prices.