Determine how much profit he makes

James’s Carpet Cleaning Service is a small business that acts as a price taker. The prevailing market price of carpet cleaning is $26 per room. James’s costs are given by TC=0.3q2+8q+60 with MC = 0.6q+8 where q is the number of rooms James chooses to clean a day.
a) How many rooms should James choose to clean in optimum?
b) What is the equation of James’s S curve?
c) Can you determine how much profit he makes? If yes, what is it? If no, what other information do you need?
d) Is this carpet cleaning market in long run equilibrium? At what level of q will James arrive at long run equilibrium? What will be the market price then?

Solution: