Question

10. The total costs of a firm operating in perfectly competitive markets are described by the function C(y) = y2+15y+40, where y denotes the quantity (units) of output Y produced by the firm. The market price per unit of output is 25 euros. Find the profit maximizing output level, the firms profits (or loss) and explain briefly (in max 1 or 2 sentences) whether it would be better for this firm to continue producing or to shut down its production in short-run? (Provide calculations for justification!)

Answer 1

In perfect competitive market P= MR

We have C(y)= y2+15y+40

MC= 2y+15

Profit maximizing output is MR=MC

25=2y+15

10=2y

Y= 5

So profit maximizing output is =5 units.

Profit= TR-TC

Profit= (5*25)-(5²+15*5+40)

Profit= 125-140

Profit= -15

So firm is having loss of 15 euros

The firm shut down in short run if profit is not cover it's average variable cost.

AVC= y+15+40/y

AVC= 20 + 8= 28

So firm should shut down because the profit is not cover it's average variable cost. And since price is also less than averages variable cost.