A firm has the long-run cost function C(q)= 3q2 + 27.In the long run, it will supply a positive amount of output, so long as the price is greater than
A)$36.
B)$44.
C)$9.
D)$18.
E)$23.

Question

Quizplus · Accepted Answer

The firm will supply a positive amount of output in the long run only if its price is greater than or equal to its long-run average cost (LRAC). 
LRAC is given by: LRAC(q) = C(q)/q = (3q^2 + 27)/q = 3q + 27/q
To find the minimum value of LRAC, we take its derivative with respect to q and set it equal to zero:
dLRAC/dq = 3 - 27/q^2 = 0
Solving for q, we get q = 3√3. 
Substituting q = 3√3 into LRAC(q), we get LRAC = 18√3. 
Therefore, the firm will supply a positive amount of output in the long run only if the price is greater than or equal to $18√3, which is approximately equal to $31.18. 
Thus, the correct answer is D) $18.

A Firm Has the Long-Run Cost Function C(q)= 3q2