Question

Please show all your work step by step

4. Consider the cost function c(y) = 4y2+16. (a) What's the average cost function AC(y) and the average variable cost function AVC (y)?? (b) What's the marginal cost function MC(y)? (c) What's the level of output that yields the minimum average cost of production? (d) At what level of output does average variable cost equal marginal cost?

Answer 1

AC = C/y = 4y^2/y + 16/y = 4y + 16/y

VC = 4y^2 (the part of the cost function which depends on output)

AVC = VC/y = 4y^2/y = 4y

MC = dC/dy =8y (The first order derivative of the cost function)

for minimum average cost we take first order derivative of the AC function and equate it to zero

dATC/dy = 4-16/y^2 = 0

16/y^2 = 4

y^2 = 4 or y = 2 (output at which average cost is minimum)

If AVC=MC

4y = 8y, this means that AVC=MC at y=0