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.
b)
1. find the profit maximizing output for each individual firm when the duopolists behave as cournot competitors.
2. find the profit maximizing output for each individual firm under the stackelberg solution, with firm #1 representing the market leader.
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