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collusion_prob

# collusion_prob - Problem set on Collusion 1 Collusion...

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Problem set on Collusion 1. Collusion between two °rms is possible no matter what their marginal cost di/erence is. True or False. Explain. 2. Explain why a long detection lag (the time it takes for a °rm to detect a deviation by other °rms) may limit the possibilities of collusion. Relate your answer to the model of collusion discussed in class.Collusion is more likely in industries where individual sales are large and take place ocassionaly than in industries where individual sales are small but frequent. True or False. Explain. 3. r = 1% ; c 1 = 5 ; c 2 = 0 ; demand function Q = 10 ° p: It is not possible to have collusion where °rm 1 gets a positive share. True or False. Explain. 4. The demand function is given by p = 100 ° Q and the constant marginal cost of produc- tion is denoted by c = 20 : Assume °rms engage in Bertrand competition. There are 16 °rms in the industry. If these °rms could collude, they would set the monopoly price and equally share the monopoly output. By deviating from this collusive agreement, a °rm undercuts the rest by a tiny bit and gets all the market. Assume that in this case the °rm gets during the period of undercutting the full monopoly output at essentially the monopoly price (this corresponds to an in°nitesimally small price reduction) and thus the total pro°ts of a monopolist. The °rms will confront each other for in°nite time and the interest rate is r: (a) If the rate of interest in this market is 10%, could you support cooperation at the monopoly level with trigger strategies? (b) Answer the same as above but at an interest rate of 5%. 5. Two °rms can produce either low (L), medium (M) or high (H) quantity. The payo/ matrix is given by: L M H L 10,10 2,10 0,20 M 10,2 5,5 2,6 H 20,0 6,2 3,3 (a) What is the outcome of this game if °rms play only once? (b) Suppose the game is played for in°nite periods and interest rate is 100% ( r = 1) : Is it possible for °rms to collude and choose ( L; L )? Is it possible for °rms to collude and choose ( M; M )?

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