Coastal Soda Sales has been granted exclusive market rights to the upcoming Beaufort Seafood Festival. This means that during the festival Coastal will have a monopoly, and it is anxious to take advantage of this position in its pricing strategy. The daily demand function is
p=2-0.0004x
and the daily total cost function is
C(x)=800+0.2x+0.0001x2
where x is the number of units.
(a) Determine Coastal's total revenue and profit functions.
(b) What profit-maximizing price per soda should Coastal charge, how many sodas per day would it expect to sell at this price, and what would be the daily profits?
(c) If the festival organizers wanted to set an economically efficient price of $1.25 per soda, how would this change the results from part (b)? Would Coastal be willing to provide sodas for the festival at this regulated price? Why or why not?