joint cost curve

[Target MA]

You have two plants. Plant A has costs c(y) = y^2 and Plant B has costs c(y) = 2y^2. What is the
joint cost curve?
a) y^2 c) 5y^2/9
b) 2y^2 d) 3y^2

[maahi]

d

[Mauli]

i think it should be A

[Amit Goyal]

It is none of them.
If you have access to these two plants and you want to produce y units, then you would like to produce it in a way that minimizes cost of production:
min a^2 + 2b^2
subject to a + b = y

Solving the above optimization problem with respect to a and b, where a is the number of units produced in Plant A and b is the number of units produced in Plant B, we get
a = (2/3) y and b = (1/3) y
and joint cost is a^2 + 2b^2 = [(2/3) y]^2 + 2[(1/3) y]^2 = (6/9) y^2 = (2/3) y^2

[Mauli]

sir so shouldnt the question be in this way
c(y1)=y1^2 and c(y2) = 2y2^2..?
and y1 +y2 = y
is the framing of this question proper?

[Akshay Jain]

sir there is no option like "none of dese"....wat to do in dis case????