Quiz 5

Q: Suppose a competitive firm has TC=q^{2}+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=8^{2}+2(8)+25.
So profit = TR - TC=39.