Question

4. Consider the cost function c(y) = 42 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

a. AC(y)= c(y)/y= 4y+16/y

AVC(y)= TVC/y= 4y

b. MC(y)=dc(y)/dy= 8y

c. To find the minimum average cost of production, differentiate AC and then equate it to zero.

dAC/dy= 4-(16/(y^2))= 0

4y^2=16

y^2=4

y= 2

At output level 2 average cost of production is minimum.

d. AVC=MC

4y=8y

So when y=0, AVC=MC