1. 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. The total demand for polyglue is given by the following function ( = + ), = output of Alchem, and = total output of 10 small firms:

P = 20,000 4Q

Alchem's total cost for manufacturing and selling polyglue is:

= 5,000 + 2.5^( 2)

Alchem correctly estimates that EACH of the other manufacturers of polyglue has a marginal cost of the form

MCf = 40qf + 2000, where is the output of each small firm.

(i). What is each small firm's supply function? What is total supply of 10 small firms.

(ii). To maximize profits, how much polyglue should Alchem produce and what price should it charge?

(iii). What is Alchem's profit? (iv). What is the total market demand for polyglue at the established price by Alchem in part

(ii)? How much of the total demand do the follower firms supply? How much Each follower firm supply?