Question

A firm has the long-run cost function C(Q) = 4Q² + 64.In the long run, it will supply a positive amount of output, so long as the price is greater than

a.	$64.
b.	$72.
c.	$16.
d.	$32.
e.	$37.

Answer 1

In long-run, firm will supply a positive amount of output as long as price is greater than long-run average total cost.

The given total cost function is as follows -

C(q) = 4q² + 64

Calculate average total cost -

ATC = C/q

       = (4q² + 64)/q

       = 4q + (64/q)

In order to calculate value of q we will first take the derivative of q and then equate it with zero.

Taking derivative of ATC with respect to q -

dATC/dq = d[4q + (64/q)]/dq = 4 - 64/q²

Equating derivative of ATC to find value of q -

4 - 64/q² = 0

64/q² = 4

q = 4

Calculating value of ATC -

ATC = 4q + 64/q = 4*4 + 64/4 = 16 + 16 = 32

Thus, ATC is $32.

As stated above, in long-run, firm will supply a positive amount of output as long as price is greater than long-run average total cost.

With long-run average total cost being $32, firm will supply a positive amount of output as long as price is greater than $32.

Thus, the correct answer is option (d).