Question

A competitive firm has the short-run cost function C(y) = 12y3  - 8y2+30y+12. At what price will the firm agree to produce in the short-run? What is the shutdown condition for this firm?

 

Answer 1

Let the selling price be p

$TR=p\times y\\TR=py$

We can derive MR from this, $MR=\frac{dTR}{dy}=p$

$TC=C(y) = 12y\\^3−8y\\^2+30y+12$

Now, $MC=\frac{dTC}{dy}=48y\\^2-16y+30$

The firm will agree to produce in the short run when $MR>MC p>48y2-16y+30$  The shutdown condition for this firm is when $MR<MCp<48y2-16y+30$