Shutting off production in short term could you help me to solve the task, please? The task is following.
Total costs of the сompetitive firm are $TC = Q^3 +6$ (Q in thousands \$). If the production is stopped then monthly costs are 4000\$. At what prices the company that maximising profit should shut off the production?
I know that if $P &lt; minAVC$, then the company should stop producing. 
So $VC = Q^3$ then $AVC = \frac{Q^3}{Q} = Q^2$ and $minAVC = 0$
So I get $P&lt;0$ that sounds stupid. And I don't even know how to use that 4000\$.
The answer should be $P&lt;3$
Could you help me to find out how to solve this? 
Thank you in advance.
I think I understand the problem now, your AVC(Q) is wrong. Your fixed costs are 4000, because it's what the firm will pay after it stops production. VC=TC-4=Q^3+2. Thus AVC=Q^2+2/Q. Now you should use your calculus in order to find where AVC has local positive minimum (because it doesn't have global minimum due to its hyperbolic nature).