Alchem (L) is the price leader in the polyglue market. All ten other manufacturers [follower (F) firms] sell polyglue at the same price as Alchem. Alchem allows the other firms to sell as much as they wish at the established price and supplies the remainder of the demand itself. Total demand for polyglue is given by the following demand function, P = 20,000 - 4QT, where QT = QL + QF. Alchem's marginal cost function for manufacturing and selling polyglue is MCL = 5,000 + 5QL. The aggregate marginal cost function for the follower firms is MCF = 2,000 + 4QF.
a. To maximize profits, how much polyglue should Alchem produce and what price should it charge?
b. What is the total market demand for polyglue at the price established by Alchem? How much of the total demand will the follower firms supply?