Suppose that American Borax is a monopolist and that the worldwide demand for borax is Q = 100 – P where Q is tons of borax and P is the price per ton. The total cost function for American Borax is TC = 10Q + 0.5Q2.
a. Write out the firm's total revenue as a function of Q.
b. What is the profit function for American Borax?
c. Find the firm's profit-maximizing quantity by applying calculus to the profit function.
d. Find American Borax's profit-maximizing price and profit.