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ps1v1a - PROBLEM SET 1 VERSION 1 Economics 201 Georey Jehle...

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PROBLEM SET 1 VERSION 1 Economics 201 Geoffrey Jehle ANSWERS
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1. A consumer has preferences for two goods satisfying Axioms 1 through 4 given in class. Answer the following questions. 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 A D E C B a. Plot and label the following bundles. A (3 , 10) B (7 , 10) C (2 , 1) D (9 , 3) E (5 , 9) b. Assume that A is indifferent to D .On a single line, list all the bundles in descending order of preference using ( P ) to denote strict preference and ( I ) to denote indifference between adjacent pairs as, e.g., in the form A ( P ) B ( P ) C ( I ) D ( P ) E . B ( P ) E ( P ) A ( I ) D ( P ) C or B ( P ) E ( P ) D ( I ) A ( P ) C 2
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2. Consider a person whose preferences are represented by the utility function, u ( x, y ) = u ( x, y ) = x 1 / 5 y 4 / 5 . a. For each pair of bundles A and B , indicate whether A ( P ) B , B ( P ) A or A ( I ) B . A B i. (5 , 8) (8 , 4) A (P) B ii. (3,9) (3,7) A (P) B iii. (3,6) (3,8) B (P) A iv. (5,5) (4,5) A (P) B b. For the eight bundles in (a), construct a “list” starting with the most preferred bundle at the top and ending with the least preferred at the bottom. (If two bundles are indifferent, put them side by side on the same line in your list.) (5, 8) (3, 9) (3, 8) (3, 7) (3, 6) (5, 5) (4, 5) (8, 4) c. Bundle A contains exactly 1/2 unit of x and a certain amount of y . If this consumer is indifferent between bundle A and the bundle (1 , 1), how much y does bundle A contain? Bundle A contains y * = 4 2 , or 1 . 18921 units of y 3
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3. See graphs below.
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