Question

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?

Answer 1

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.