In: Economics
A competitive firm has a single factory with the cost function c(y) = 4y2+ 89 and produces 28 units in order to maximize profits. Although the price of output does not change, the firm decides to build a second factory with the cost function c(y) = 8y2+ 39. To maximize its profits, how many units should it produce in the second factory?
For first factory,
C1 = 4y12 + 89 --------------- (1)
dC1/dY1 = MC1 = 8Y1
For second factory,
C2 = 8y22 + 39 ----------------(2)
dC2/dY2 = MC2 = 16Y2
Marginal cost will be equal for both the factory,
So,
MC1 = MC2
8*Y1 = 16*Y2
8*28 = 16*Y2
Y2 = 14 units
So, the second factory should produce 14 units.