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Unformatted text preview: Economics 101, Problem Set 5 Due 12/7/2006 Alan C. Marco November 30, 2006 Instructions. Due at the beginning of lecture (or beforehand in my box in the economics department). I encourage you to work in groups of 2 or 3. Please turn in only one problem set for each group, with the full names of all the students on the front page. Problem sets must be neat, readable, and concise. I prefer typed. They must be stapled if they are more than one page. 1. Give all the Nash Equilibria for the following games. For each game, explain whether the NE (if any) is socially optimal. Explain your answer. (a) Drop Dead Fred Fred Phoebe Laugh Cry Sleep Fly 1 , 1 6 ,- 1 7 , Swim 2 , 5 , 8 ,- 1 Ouch 3 ,- 1 4 , 1 9 , 1 (b) Quarks [Express your answer for dierent values of x, i.e., If x &lt; blah, then the NE are blank. If x = blab, then...] Amber Buffy Top Charm Bottom Up 6 , 1 6 , 6 3 , 4 Strange x, 2 x, 4 , 3 Down 2 , 7 5 , 9 4 , 4 2. Suppose two rms compete according to Cournot competition. They can produce in discrete units only. If demand is given by p = 20- Q and total costs for each rm are given by c ( q ) = q 2 (so that mc = 2 q with no xed costs), create a payo matrix for the game, and determine the Nash equilibrium(a). (a) Compare the Cournot Nash equilibrium outcome to the rst best and to the monopoly (collusive) outcome. [You may reproduce a partial payo matrix if you wish; i.e., you only need to show enough to calculate the equilibria and the other relevant quantities. Hint: gure out the rst best rst so that you know thethe equilibria and the other relevant quantities....
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