Multi-plant Monopoly - May 19

[Amit Goyal]

May19_MultMono.png

[aditi5000]

a. For part a I made an error in calculation (if my theory is not wrong i.e. !)
q for both plants = 4.5
Total q = 9
p = 1
profit = -2 ie a loss to the extent of fixed costs

So produce only 4.5 in one plant. Other plant, produce 0 ie no costs
So, q = 4.5
total q = 4.5
p = 5.5
profit = 19.25

b. Monopolist has to bear the fixed cost of 1 even if production is zero
profit = 18.25

[anon_econ]

a) produce only in either of the two plants. q=4.5, p=5.5, fixed cost=1, profit=19.25.
b) fixed cost=2. q=4.5 (allocated in any way b/w the 2 plants), p=5.5, profit=18.25.
c) 2 options-either save on fixed cost in one plant and produce everything in the other or incur a fixed cost of 2 and produce equal amounts in both plants. profits in the first case are 11.5. in the second case q=10/3,p=20/3,profits=14.67. so the second option should be chosen.

[aditi5000]

c.
q = 2.5 from only 1 plant
p = 7.5
profit = 11.5

(not both plants because that leads to lower price and thus lower profit of 10.5)

[AJ]

I'm getting

(a) Q=4.5 , he will produce only in one plant
     P=5.5
(b) Q=4.5 , he can produce in only one plant or in both
     P=5.5
(c) Q=2.5 , with q1=q2=1.25 , i.e. He will necessarily produce in both plants
     P=7.5

[AJ]

@vasudha..

for third part .. how did u find q=10/3
that is indeed giving more profits that 2.5 ...?

[AJ]

Ohhh.. I got it..
Yup.. vasudha's answer for part (c)

[Amit Goyal]

Well done Aditi, Vasudha and AJ. Keep it up. :-)

[Amit Goyal]

Vasudha did all three parts correctly. Good work Vasudha :)

[aditi5000]

Hey Vasudha and/or AJ, please help.. I can't understand the second case in which profit = 14.67... if the monopolist produces equal amounts in both plants, how did you get q = 10/3 ???

[aditi5000]

:) thanks Sir!

[AJ]

By maximizing this:

(10-q1-q2)(q1+q2) - (2+q1^2+q2^2) w.r.t. q1 and q2

[aditi5000]

Hey I got it! Thanks AJ! :)

[Chocolate Frog]

Where AM I when all the cool ones are being uploaded? *headdesk*