Question

Suppose a firm's cost function is C (q) = 2q2 + 8.

The output q that minimizes average total cost is: (Hint: At the minimum of the ATC, ATC is equal to MC)

a)4

b) 2

c) 0

d) 8

Answer 1

The output q that minimizes average total cost is where ATC = MC

so we can find q by two ways,

first minimize the ATC or second find the level of q where ATC = MC

Let's find q by second way:

ATC = C(q)/q = 2q + 8/q

MC = d(C(q)) / dq = 4q

2q + 8/q = 4q

8/q = 2q

2q² = 8

q² = 4

q = 2

so at output level q = 2, ATC is minimized.

Ans is b) 2