Question

In the short term, a MONOPOLY is capable of differentiating, for the same market, two different demand behaviors: (6)

 Q1 = 24 - 0.20P1

 Q2 = 10 - 0.05P2

If the company faces a cost function CTC = 35 + 40Q

i. What price will the company charge if it applies price discrimination? It shows, for each of the previous situations, that the price established by the MONOPOLY allows you to MAXIMIZE PROFITS

ii. Calculate the value of TOTAL BENEFIT

Answer 1

i) TC = 35 + 40Q

MC = 40

In market 1,

Q1 = 24 - 0.20P1

0.20P1 = 24 - Q1

P1 = 120 - 5Q1

TR = P1 * Q1 = 120Q1 - 5Q1²

MR = 120 - 10Q1

The profit maximizing condition is

MR = MC

120 - 10Q1 = 40

10Q1 = 80

Q1 = 80 / 10 = 8

P1 = 120 - 5(8) = $80

In market 2,

Q2 = 10 - 0.05P2

0.05P2 = 10 - Q2

P2 = 200 - 20Q2

TR = P2 * Q2 = 200Q2 - 20Q2²

MR = 200 - 40Q2

The profit maximizing condition is

MR = MC

200 - 40Q2 = 40

40Q2 = 160

Q2 = 160 / 40 = 4

P2 = 200 - 20(4) = $120

Thus, in market 1, the monopolist will charge a price of $80 and sell a quantity of 8 units. And, in market 2, the monopolist will charge a price of $120 and sell a quantity of 4 units.

ii) Q = Q1 + Q2 = 8 + 4 = 12

TC = 35 + 40Q = 35 + 40(12) = $515

TR = (P1 * Q1) + (P2 * Q2) = ($80 * 4) + ($120 * 4) = $320 + $480 = $800

Total benefit = TR - TC = $800 - $515 = $285