Question

Suppose a firm wants to produce 60 units of it product by allocating production into two factories, Factory A and Factory B. If MCA= 4+ 2QA and MCB=4+ QB represent the corresponding marginal cost functions, then what is the likely quantity produced in Factory A?
Find QA and QB such that QA+QB = 60 and MCA = MCB. You will get QA = 20 and QB = 40.

Answer 1

Answer: 20 units

MCA = 4 + 2QA .......(1)

MCB = 4 + QB.......(2)

QA + QB = 60.......(3)

MCA = MCB

As, MCA = MCB,

4 + 2QA = 4 + QB

Or, 2QA = QB

Now, we can write the equation(3) as,

QA + 2QA = 60

Or, 3QA = 60

Or, QA = 60 / 3

Or, QA = 20

Now, putting the value of QA in equation(3), we get,

20 + QB = 60

Or, QB = 60 - 20

Or, QB = 40

  The likely quantity produced in Factory A is 20 units.

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