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An oligopoly market's monthly demand is given by the equation: Q = 3,840 – 0.8 P....

An oligopoly market's monthly demand is given by the equation: Q = 3,840 – 0.8 P. In creating a cartel, the four oligopolists agree to the following market shares: Firm a: 35%, Firm b: 20%, Firm c: 30%, and Firm d: 15%. They also agree to charge the same price. Their respective Total Costs functions are:

Firm a T.C. = 600,000 + 0.75 Q2

Firm b T.C. = 300,000 + 0.75 Q2

Firm c T.C. = 500,000+ 0.75 Q2

Firm d T.C. = 180,000 + 0.75 Q2

Please show your work clearly in answering the following questions:

  1. If the four firms live up to their agreement, how many units will each firm produce and what price will each firm charge?
  2. If none of the four firms cheats on the agreement, what will total profits be for each of these firms?
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