Two firms compete as duopolists, producing identical goods in quantities q1 and q2, respectively. assume the inverse market demand function for their product is p = 840 – q1 – q2. firm #1 and firm #2 have the same total cost function: tci = (qi)2 [i. e., mc1 = 2q1 and mc2 = 2q2]. {a} suppose that the duopolists behave as a cartel (and thus produce as a single "multi-plant" firm), with a combined profit function of 840(q1) + 840(q2) – 2(q1)(q2) – 2(q1)2 – 2(q2)2 find the profit maximizing output for each "plant" under this scenario. [3 pts] {b} 1. find the profit maximizing output for each individual firm when the duopolists behave as cournot competitors. [4 pts] 2. find the profit maximizing output for each individual firm under the stackelberg solution, with firm #1 representing the market leader. [5 pts] {c} 1. find the profit maximizing output for each individual firm when the duopolists behave as bertrand competitors. [4] 2. find the profit maximizing output for each individual firm under the competitive fringe solution, where firm #1 represents the dominant firm. [5]