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5_Solutions

5_Solutions - budget constraint How much food and how much...

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College of Human Ecology Cornell University, Ithaca, New York Department of Policy Analysis and Management PAM 200 Intermediate Micro A. Sinan ¨ Un¨ur – Fall 2007 Quiz 5 – Answers September 20, 2007 Alice’s preferences over food, F , and clothing, C , are given by the utility function: U ( F , C ) = FC + F with MRS F , C given by MRS F , C = C + 1 F . The price of food is P F = \$1 and the price of clothing is P C = \$2. Her income is \$22. ( Q1 ) (1 point) Write Alice’s budget constraint. Her budget constraint is P F F + P C C = I . Substituting the information given, we have F + 2 C = 22 . ( Q2 ) (1 point) What is the opportunity cost of food in terms of clothing? Every time Alice buys another unit of food, she spends \$1. With the \$1, she could have purchased P F P C = 1 2 units of clothing. ( Q3 ) (2 points) The bundle Alice chooses will satisfy the both the tangency condition and the

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Unformatted text preview: budget constraint. How much food and how much clothing will Alice choose to buy? The tangency condition states that, for an interior bundle to be chosen by the consumer, MRS F , C = P F P C must hold. Using the information given, this means C + 1 F = 1 2 must hold. Solving, we get F = 2 C + 2 . Since Alice’s preferences satisfy more is better , her chosen bundle must be on her budget line. Substituting the condition above in the budget constraint yields: F + 2 C = 22 ( 2 C + 2 )+ 2 C = 22 4 C = 20 C = 5 . Substitution this back in the tangency condition yields F = 12. So Alice will choose the bundle ( 12 , 5 ) . 2...
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