Your firm owns two plants that produce chocolate of exactly the same quality. One plant has...
Your firm owns two plants that produce chocolate of exactly the same quality. One plant has a cost function given by cA (y) = 4y2 while the other plant has a cost function given by cB (y ) = y2 + y + 4. Given that you can optimally choose how to distribute the production of chocolate across these two plants, what is your firm's marginal cost function for producing chocolate?
Homework Answers
Let output produced in plant 1 be y1 and in plant 2 be y2.
CA = 4y12
MC(A) = dCA/dy1 = 8y1
y1 = MC(A) / 8 = 0.125 x MC(A)
CB = y22 + y2 + 4
MC(B) = dCB/dy2 = 2y2 + 1
2y2 = MC(B) - 1
y2 = 0.5MC x (B) - 0.5
Setting MC(A) = MC(B) = MC:
y1 = 0.125 x MC
y2 = 0.5 x MC - 0.5
y = y1 + y2
y = 0.125 x MC + 0.5 x MC - 0.5
y = MC x (0.125 + 0.5) - 0.5
y = MC x 0.625 - 0.5
MC x 0.625 = y + 0.5
MC = (y + 0.5) / 0.625 = 1.6y + 0.8
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