Quiz 5

Q: Suppose a competitive firm has TC=q²+2q+25.  Find the breakeven price?  What would be the profit to this firm if Pe=18?

A: To find the breakeven price we need to know where MC crosses ATC.  (By competitive assumption MR=P, profit maximization gives MR=MC, and 0 profit implies P=ATC).
MC=2q+2 and ATC=q+2+25/q.  Setting these equal we get q=25/q or q=5.  At q=5 MC is 2(5)+2=12.  Notice that ATC is 5+2+25/5=12 as well.  So the breakeven price is 12.

If P=18 then MR=18 as this is a competitive firm.  The firm sets MR=MC so we have 2q+2=18 or q=8.  The firm's TR=P*q=18*8 and TC=8²+2(8)+25.  So profit = TR - TC=39.