$2.(40$ points$)$ Suppose there are two firms in a market who each simultaneously choose a quantity. Firm $1$s quantity is q$1,$ and firm $2$s quantity is q$2.$ Therefore the market quantity is Q $=$ q$1+$ q$2.$ The market demand curve is given by P $=1004$Q$.$ Also, each firm has constant marginal cost equal to $28.$ There are no fixed costs. The marginal revenue of the two firms are given by:

MR$1=1008$q$14$q$2$

MR$2=1004$q$18$q$2.$

A$)(8$ points$)$ How much output will each firm produce in the Cournot equilibrium?

B$)(8$ points$)$ What will be the market price of the good?

C$)(8$ points$)$ What is the deadweight loss that results from this duopoly?

D$)(8$ points$)$ How much profit does each firm make?

E$)(8$ points$)$ Suppose Firm $2$ produced $10$ units of output. How much output should Firm $1$ produce in order to maximize profit? $($Hint: Use Firm $1$s Reaction Function$)$