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Industrial Organization Fall 2014 Problem Set 6

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Question;1. There are two identical rm which are playing the innite horizon Bertrandgame in a market with the inverse demand function p = 16 3q. Firms marginal costof production is constant and equal to 4. The discount factor for the rms is the sameand equal to =.6.a. What is the monopoly price, quantity and prot?b. Using grim trigger strategy show that there is a SPNE for this game where theyalways set the price equal to the monopoly price.Now suppose there is a informational lag for the price change. In particular, think abouta situation in which a price change would not be observed (and therefore) punished bythe opponent until three periods after.c. Show that in this case there is no SPNE for this game in which all rms set the priceequal to monopoly price at all the periods.d. Why collusion is not possible here? Give your intuition.Go back to the situation with no informational lag, but now suppose there are threeidentical rms in the market who are playing Bertrand game.e. Show that there is no SPNE for this game in which all the rms set the price equalto the monopoly price at all the periods.f. Why tacit collusion is possible in the rst case but not in the second? Interpret.2. Consider innite horizon Bertrand game with market uctuation. So all theassumptions which was introduced on the class is satised. In particular, rms nd outthe state of the market at the beginning of each period.There are two rms in the market 1, 2. There are to states for the market whichare translated in two dierent inverse demand functions: p1 = 10 2q, and 10 4q.Both rms have discount factor =.6.a. Find out in which state market is in a better condition by comparing the monopolyprot for these two markets.b. Show that if the state of the market was always good, then using a grim triggerstrategy will imply a SPNE in which rms set the price equal to monopoly price.c. Show that if the state of the market was always bad, then using a grim triggerstrategy will imply a SPNE in which rms set the price equal to monopoly price.d. Show that there is no SPNE of this game in which game use monopoly price at allthe periods.e. Intuitively explain why collusion is not achievable in the presence of uctuation inthe market?

 

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