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ps5_fall'11

# ps5_fall'11 - Department of Economics Columbia University...

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Department of Economics W3211 Columbia University Fall 2011 Probl e m S e t 5 Int e rm e diat e Mi c ro ec onomi c s Prof . S e yhan E Arkona c 1 . Sinan declares that he is risk neutral andthinking of opening a video game store ” for holidays shopping period. His “store” will either be a small booth in the student union or a table in Washington Square. He is planning to buyused games from friends and resell them. However amount of games his friends have is unknown to Sinan. He will try his group of friends from high school and from college. If his friends kept all the games they ever had, he may be able to gather as high as 400 games, if they already gave away most of the games, the number will go as little as 40 games. Sinan must decide how large his store should be before he can find out how many games he will be able to collect to sell. The booth can handle 400 games at a cost of \$2 a game. In addition he has to pay \$200 rent. The table in Washington Square can only handle 40 games at a cost of \$2 a game. He can rent the table for \$20. Finally, assume that the probability that Sinan will be able to gather 40 games is 60% and that he can sell each game for \$20. (a) Illustrate Sinan’s decision problem in a decision tree. (b) What size “store” is e x an t e optimal? Is it always e x po st optimal? If not then under what circumstances is it not e x po st optimal?

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ps5_fall'11 - Department of Economics Columbia University...

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