Question

Ed's construction company has the following short-run cost function: 2q³ - 41q² + 58q. For what quantity is average cost at its lowest?

Your Answer:

Answer 1

Average cost is the per unit cost of production. It can be calculated as Total Cost divided by the total output/quantity.

Given. TC =  2q³ - 41q² + 58q.

Therefore, Average cost ( AC) =

2q³ - 41q² + 58q / q

= 2q² - 41 q +58

To calculate minimum value of quantity:

1. Differentiate AC with respect to q

d (AC)/ d(q) = 4q - 41

2. Put the first order Derivative equal to zero

=> 4q - 41 = 0

=> q = 41/4 = 10.25 ≈ 10 units

To check if it's minimum, let's take second order Derivative which is equal to d²(AC)/d q² = 4 that positive.

Therefore the Quantity at which AC is minimum = 10.25 ≈ 10 units