Suppose firms A, B, and C set prices while facing per-period demand of Q = 200 – P, which yields…

Suppose firms A, B, and C set prices while facing per-period demand of Q = 200 – P, which yields a MR curve MR = 200 – 2Q for a monopolist. When setting prices non-cooperatively, the firms choose their prices simultaneously. All firms have MC = 20. The firms are currently involved in a cartel that sets the monopoly price and divides quantity evenly among the firms. The firms enforce their cartel arrangement with a grim trigger strategy.
The Department of Justice (DOJ) has just started an antitrust division that is designed to break up cartels. The DOJ successfully detects and prosecutes a cartel with probability s, and prosecuted cartels receive the fine F and are prevented from ever colluding again.
The firms believe that their interaction will continue forever (? = 1.0), and they discount future periods at R = 0.80.

I. Which strategic variable are the firms choosing? What type of competition is this?
A) Quantity; Cournot
B) Quantity; Bertrand
C) Price; Cournot
D) Price; Bertrand

II. What are the firms’ per-period profits from:
$______ operating collusively and setting the monopoly price
$______ unilaterally defecting from the cartel
$______ choosing non-cooperative equilibrium prices

III. In the absence of antitrust prosecution, are the three firms able to maintain a cartel while using the grim trigger strategy for the given R and ??
A) Yes
B) No

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