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##### There are two identical rm which are playing the innite horizon Bertrand

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**Question**

1. There are two identical rm which are playing the innite horizon Bertrand;game in a market with the inverse demand function p = 16 3q. Firms marginal cost;of production is constant and equal to 4. The discount factor for the rms is the same;and 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 they;always set the price equal to the monopoly price.;Now suppose there is a informational lag for the price change. In particular, think about;a situation in which a price change would not be observed (and therefore) punished by;the opponent until three periods after.;c. Show that in this case there is no SPNE for this game in which all rms set the price;equal 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 three;identical 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 equal;to 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 the;assumptions which was introduced on the class is satised. In particular, rms nd out;the 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 which;are 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 monopoly;prot for these two markets.;b. Show that if the state of the market was always good, then using a grim trigger;strategy 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 trigger;strategy 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 all;the periods.;e. Intuitively explain why collusion is not achievable in the presence of uctuation in;the market?

Paper#18201 | Written in 18-Jul-2015

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