Alchem (L) is the price leader in the polyglue All 10 other manufacturers (follo

Question

        Alchem (L) is the price leader in the polyglue 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 + Ql.

The aggregate marginal cost function for the other manufacturers of polyglue is:    

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?

Explanation / Answer

So.... Given the information, the firm appears to be a monopolistic firm. So the profit maximizing condition for a monopoly is MC=MR. a) you use this to determine the quantity the firm produces MR = partial derivative of TR in terms of q TR = PQ = (20,000 - 4 Qt)Qt = 20,000 Qt - 4Qt^2 MR = 20,000 - 8Qt MCI = 5,000 +Qi MCI = MR ==> 5,000 + QI = 20,000 - 8Qt 9Q = 15,000 Q = 15,000/9 = 1666.66 P = 20,000 - 4(Q) = $13,333.33 b)

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