Answer to Question #88499 in Macroeconomics for Didi

Question

market demand is P=64-Q/7. A multiplant monopolist operates three plants with marginal cost functions:
MC1(Q1) = 4Q1
MC2(Q2) = 2+2Q2
MC3(Q3) = 6+Q3
i) find the monopolist's profit maximizing price and output at each plant
ii)how would your answer to part (i) change if MC2 (Q2) = 4?

Answer 1

i) If market demand is P = 64 - Q/7, then MR = TR' = 64 - 2/7Q.

In equilibrium MR = MC:

MC1(Q1) = 4Q = 64 - 2/7Q,

Q = 64×7/9 = 49.78 or 50 units.

P = 64 - 49.78/7 = 56.9.

MC2(Q2) = 2 + 2Q = 64 - 2/7Q,

Q = 62×7/16 = 27.1 or 27 units.

P = 64 - 27.1/7 = 60.1.

MC3(Q3) = 6 + Q = 64 - 2/7Q,

Q = 58×7/9 = 45.1 or 45 units.

P = 64 - 45.1/7 = 57.6.

ii) If MC2 (Q2) = 4, then:

64 - 2/7Q = 4,

Q = 60×7/2 = 210 units.

P = 64 - 210/7 = 34.