Alchem (L) is the price leader in the polyglue market. All 10 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 function (Qt = Ql + Qf):
P = 20,000 -4Qt
Alchem's marginal cost function for manufacturing and selling polyglue is
MCl= 5,000 + 5Qt
The aggregate marginal cost function for the other manufacturers of polyglue 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 in Part (a)? How much of the total demand do the follower firms supply?