(Monopoly with Multi-plant) suppose that Gillette has a monopoly in the market f
ID: 1108401 • Letter: #
Question
(Monopoly with Multi-plant) suppose that Gillette has a monopoly in the market for razor blades in Mexico. The market demand curve for blades in Mexico is P=1000 - 10Q (in thousands). Gillette has two plants, one in Mexico city and one in LA where marginal cost for the LA plant is MC1(QLA) = 2 + QLA and marginal cost for the Mexico city plant is MC2(QMC) = 1 + 0.5QMC. (15) a. Find Gillette’s profit-maximizing price and quantity of product for the Mexican market overall. b. How will Gillette allocate production between its Mexican plant and its LA plant?
Explanation / Answer
let Q1 = output of LA plant
Q2 = output of mexico city plant
MC1 = 2 + Q1
MC2 = 1 + 0.5Q2
so total marginal cost is the horizontal sum of MC1 and MC2
MC1 = 2 + Q1
Q1 = MC1 - 2
MC2 = 1 + 0.5Q2
0.5Q2 = MC2 - 1
Q2 = 2MC2 - 2
Q1+ Q2 = MC1 - 2 + 2MC2 - 2 Q1 + Q1 = Q
Q = MC1 + 2MC2 - 4 MC1 = MC2 = MCT
Q = 3MCT - 4
Q + 4 = 3MCT
MCT = (Q +4)/3
P = 1000 - 10Q
TR = PQ
= Q(1000 - 10Q)
= 1000Q - 10Q2
MR = dTR/dQ
= 1000 - 20Q
at optimal point
MR = MCT
1000 - 20Q = (Q + 4)/3
3000 - 60Q = Q + 4
3000 - 4 = Q + 60Q
2996 = 61Q
Q = 2996/61
= 49.11
P = 1000 - 10(49.11)
= 508.9
b)
MCT = (49.11 + 4 )/3
= 17.70
so Q1 = 17.70 - 2
= 15.7
Q2 = 2(17.70) - 2
= 33.4
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.