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# S07 Final answers - Econ313-1 Spring 2007 Talia Bar Final...

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Econ313-1 Spring 2007 Talia Bar Final Exam Write your name on this exam form. You need to return it with your exam! This exam consists of three sections. Answer each section in a separate blue book and label each blue book clearly. The exam is worth 145 points. To help you allocate time you can plan on spending about one minute per credit point. The exam is closed-book, but you may use a calculator (answers might not be whole numbers). Show your work. A complete answer to any part of a question must have an argument, explanation or proof. Good luck. 1

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Section I (55 points) Question 1 (35 points) (Consumer theory) Miss Bunting consumes two goods x 1 (bird seeds) and a composite good x 2 : She has an income of \$1200 to spend on these goods. Prices of the two goods are p 1 = \$ 1 2 ; and p 2 = \$1 . Her preferences for the two goods are represented by the utility function u ( x 1 ;x 2 ) = x 1 x 4 2 : (a) Formally write Miss Bunting&s utility maximization problem and ±nd her opti- mal consumption bundle. (b) Suppose a tax is imposed on bird seeds, so that the new price is p 0 1 = \$ 3 4 per unit. What is her new consumption bundle? (c) Numerically ±nd the income and substitution e/ects of this price change. Illus- trate these e/ects graphically. (d) A government economist was asked to assess the impact of the tax on consumers like miss Bunting. The economist who knows her utility function and budget proposed to use CV (compensating variation). De±ne this measure. Find it numerically. (e) Suppose in the economy there are other consumers that have the same utility func- tion as Miss Bunting but di/erent income levels. For a given set of prices, which of the following statements is true: (i) All of these consumers spend the same proportion of their income on good x 1 : 2
(ii) All of these consumers spend the same amount of money on good x 1 : (iii) All of these consumers spend more money on good x 1 than on good x 2 : (f) Mr. Redstart. has a quasilinear utility function of the form u ( x 1 ;x 2 ) = v ( x 1 ) + x 2 where v ( x 1 ) is increasing and concave. His income is \$1400 and he consumes positive Redstart±s CV so that he can compare the e/ect of the tax on Mr. Redstart to the e/ect of the tax on Miss Bunting. The economist (who is also a skilled mathematician) does not knows Mr. Redstart±s utility function (just that it is a quasilinear one), but he does know Mr. Redstart±s entire Marshallian demand for good x 1 when price of good x 2 is p 2

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S07 Final answers - Econ313-1 Spring 2007 Talia Bar Final...

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