ps5_sol_fall'11_(3)

ps5_sol_fall'11_(3) - Department of Economics Columbia...

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Department of Economics W3211 Columbia University Fall 2011 SOLUTIONS TO Problem Set 5 Intermediate Microeconomics Prof. Seyhan E Arkonac 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 ex ante optimal? Is it always ex post optimal? If not then under what circumstances is it not ex post optimal? (c) A “market search” will determine whether he will need a booth or a table. He will ask a series of questions to his friends and gather information about the amount of games he can collect but this will cost him X amount of money (or time in terms of opportunity cost) Illustrate Sinan’s decision problem when he can choose whether or not to run the market search. (d) What is the highest X that Sinan would be willing to pay for the “market search”? Since Sinan is risk neutral, his utility will be a linear function of his profits, so it is sufficient to analyze the expected profit of his store. In order to solve the problem, we need to make some further assumptions: 1. The state space is binary, so there are only two possible outcomes: Sinan gathers 40 games with Prob. = 0.6 and gathers 400 games with Prob. = 0.4 2. The game market will clear, so Sinan will sell all of the games that he has in stock 3. Sinan knows the probabilities of gathering 40 and 400 games
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(a) The timeline is as follows: before knowing how many games he will be able to gather from his friends, Sinan chooses to place his store either at the small booth in the student union or a table in Washington Square. After he chooses, an exogenous choice will be made by “nature” about how many games he will gather (40 with Prob = 0.6 and 400 with Prob = 0.4). Finally Sinan sells all of his games and after paying the fixed and variables costs he will collect his profit.
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This note was uploaded on 01/16/2012 for the course ECON W3211 taught by Professor Elmes during the Fall '09 term at Columbia.

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ps5_sol_fall'11_(3) - Department of Economics Columbia...

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