6. [14] Two identical firms that have the cost function C;(q;) = 4q;, where j E {1,2} are competing in a homogenous good market. The two firms make simultaneous decisions on price, and they face industry demand Q(P) = 20 -p. a. [2] What is the Bertrand-Nash equilibrium profit of each firm? Hints for (b) and (c): Solve for each firm j's output (q; ) and use the fact that II; = p;q; - C; (q;). b. [4] Now, suppose the two firms are deciding whether to set a collusive market price of $6 (this means that they would both charge $6). Solve for their profits under this pricing scheme. c. [4] If one of the firms decides to deviate from the collusive scheme and undercut its rival's price by $1, how much profit would it earn