It's a Bertrand Triopoly - hence we know there are 3 firms in the industry-in-question, who competes in "price". The inverse demand functions for Firm 1, 2, and 3 are as follows: q1 = 40 - 1.5p1 +0.5p2 +p3 q2 = 40 + 1.5p1 - 3p2 + p3 q3 = 40 + 2p1 + 1.5p2 - 4p3 For each firm, the marginal cost of production is $2.50/unit produced and sold.

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Problem 1. HHI in the Bertrand Triopoly Equilibrium
It's a Bertrand Triopoly - hence we know there are 3 firms in the industry-in-question, who
competes in "price". The inverse demand functions for Firm 1, 2, and 3 are as follows:
q1 = 40 - 1.5p1 +0.5p2 +p3
q2 = 40 + 1.5p1 - 3p2+p3
q3 = 40 + 2p1 + 1.5p2 - 4p3
For each firm, the marginal cost of production is $2.50/unit produced and sold.
Apparently, the firms' products are differentiated. You cannot impose symmetry across firms.
Therefore, please solve each firm's profit maximization problem, impose equilibrium, and solve
for each firm's "action" in equilibrium. After that, please calculate the Herfindahl-
Hirschman Index (HHI) in the industry in equilibrium.
Transcribed Image Text:Problem 1. HHI in the Bertrand Triopoly Equilibrium It's a Bertrand Triopoly - hence we know there are 3 firms in the industry-in-question, who competes in "price". The inverse demand functions for Firm 1, 2, and 3 are as follows: q1 = 40 - 1.5p1 +0.5p2 +p3 q2 = 40 + 1.5p1 - 3p2+p3 q3 = 40 + 2p1 + 1.5p2 - 4p3 For each firm, the marginal cost of production is $2.50/unit produced and sold. Apparently, the firms' products are differentiated. You cannot impose symmetry across firms. Therefore, please solve each firm's profit maximization problem, impose equilibrium, and solve for each firm's "action" in equilibrium. After that, please calculate the Herfindahl- Hirschman Index (HHI) in the industry in equilibrium.
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