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?
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\u22128y\\\\^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"
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