Question

PT. MEREKAH is a sole provider of internet cable in BSD. This company levies a price
discrimination policy for the consumers who live in three different areas.
Area 1: P = 100 - 8Q
Area 2: P = 60 - 4Q
Area 3: P = 80 -12Q
The cost function for this company is given by TC = 30 +4Q. As an economist, you are
assigned to calculate some basic information below:
a) Find the function of Total Revenue & Marginal Revenue for each area
b) Find the quantity and price for each area
c) Find the value of Total Revenue, Total Cost and Total Quantity for all area

Answer 1

a) Total revenue is given by Price × Quantity demanded

So, for Area 1 ---> Total revenue (TR1) = P×Q = (100 - 8Q)Q

= 100Q - 8Q²

Marginal Revenue (MR) is given by different TR with respect to quantity.

MR2 = 100 - 16Q

Similarly, for Area 2 ---> TR2 = (60 - 4Q)Q = 60Q - 4Q²

MR2 = 60 - 8Q

for Area 3 ---> TR3 = (80 - 12Q)Q = 80Q - 12Q²

MR3 = 80 - 24Q

b)

The total cost (TC) = 30 + 4Q

Marginal cost is nothing but the differentiation of total cost with respect to quantity.

MC = 4

At profit maximizing condition,

MR = MC

So, for Area 1:

MR1 = MC

=> 100 - 16Q = 4 => Q = 6

Substituting this Q in the inverse demand function we get,

P = 100 - 8Q = 100 - 8×6 = 52

Similarly, for Area 2:

MR2 = MC

60 - 8Q = 4

=> Q = 7.

Substituting Q, we get P = 60 - 4×7 = 32

For Area 3:

MR3 = MC

80 - 24Q = 4

=> Q = 3.17

Substituting Q, we get P = 80 - 12×3.17 = 41.96

c)

Total quantity for all area = 6 + 7 + 3.17 = 16.17

Total revenue for Area 1 = TR1 = 100Q - Q² = 100×6 - 6²

= 564

Total cost for Area1 = TC1 = 30 + 4Q = 30 + 4×6 = 54

Similarly, TR2 = 60Q - 4Q² = 60×7 - 4×7² = 224

TC2 = 30 + 4×7 = 58

TR3 = 80Q - 12Q² = 80×3.17 - 12×3.17² = 133.01

TC3 = 30 + 4×3.17 = 42.68

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