problem7

# problem7 - where the actions are “cooperate” and...

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Problem Set 7 Econ 115a November 14, 2007 Don’t forget to indicate your name and your TAs name! Due Date: Monday, Nov. 26. 1. Deﬁne (a) Prisoners’ Dilemma (b) Grim Strategy (c) Free Rider Problem 2. Consider a Cournot duopoly with identical ﬁrms. Say that in this market monopoply proﬁts would be M whereas duopoly proﬁts are D , with D < 1 2 M . (a) Suppose that the 2 ﬁrms are thinking of colluding so that each produced 1 2 of the monon- poly output, 1 2 Q M . What would proﬁts be if they actually did this? (b) Show, on a graph, what would be the optimal response of ﬁrm 2 if ﬁrm 1 did produce 1 2 Q M . Is the optimal quantity, q * 2 ( 1 2 Q M ), you just graphed greater or less than the Cournot duopoly output? (c) Thinking about your last answer, what would be the best way for ﬁrm 2 to “cheat” if ﬁrm 1 really did try to collude by producing 1 2 Q M ? (d) Denote proﬁts at the best response q * 2 ( 1 2 Q M ) as R , with D < R < 1 2 M . Draw a “prisoners’ dilemma” table that shows the pay-oﬀs of the two possibly colluding ﬁrms,

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Unformatted text preview: where the actions are “cooperate” and “cheat” and the payoﬀs are one of D , R and M . (e) Would the two ﬁrms collude if they competed for only one period? 3. Suppose that 4 roommates are planning to spend a Saturday night in their dorm room watching old movies. They are debating how many to watch. Here is their willingness to pay for each movie: John Eric Brian Adam 1st ﬁlm \$7 \$5 \$3 \$2 2nd ﬁlm \$6 \$4 \$2 \$1 3rd ﬁlm \$5 \$3 \$1 \$0 4th ﬁlm \$4 \$2 \$0 \$0 5th ﬁlm \$3 \$1 \$0 \$0 1 (a) Suppose that renting a movie costs \$4. If each person privately rented a movie to watch on their own, how many would each person rent? (b) Suppose that each roommate enjoys watching movies together just as much as alone. Within a dorm room, then, is the showing of a movie a public good? Why or why not? (c) If it costs \$8 to rent a movie, how many should they rent to maximize total surplus? 2...
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## This note was uploaded on 04/08/2008 for the course ECON 115 taught by Professor Stevenberry during the Fall '07 term at Yale.

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problem7 - where the actions are “cooperate” and...

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