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
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.