Solutions Homework Assignment 2 411

Solutions Homework Assignment 2 411 - Solutions Homework...

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Solutions Homework Assignment 2 4.1 a. Set up Lagrangian £ (1.00 .10 .25 ) ts t s . ! = + " " 0.5 0.5 £ ( / ) .10 £ ( / ) .25 s t t t s s " = # " " = # " £ 1.00 .10 .25 0 t s " = # # = " Ratio of first two equations implies 2.5 2.5 t t s s = = Hence 1.00 = .10 t + .25 s = .50 s . s = 2 t = 5 Utility = 10 b. New utility 10 or ts = 10 and .25 5 .40 8 t s = = 5 8 s t = Substituting into indifference curve: 2 5 10 8 s = s 2 = 16 s = 4 t = 2.5 Cost of this bundle is 2.00, so Paul needs another dollar.
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4.2 Use a simpler notation for this solution: U ( f , c ) = 2/3 f 1/3 c I = 600 a. £ = f c + ! (600 " 40 f " 8 c ) ! £ ! f = 2 / 3( c / f ) " 40 # ! £ ! c = 1/ 3( f / c ) " 8 Hence, 5 2 , 2 5 c c f f = = Substitution into budget constraint yields f = 10, c = 25. b. With the new constraint: f = 20, c = 25 Note: This person always spends 2/3 of income on f and 1/3 on c . Consumption of California wine does not change when price of French wine changes. c. In part a, 2 3 1 3 2 3 1 3 ( , ) 10 25 13.5 U f c f c = = = . In part b, 2 3 1 3 ( , ) 20 25 21.5 U f c = = . To achieve the part b utility with part a prices, this person will need more income. Indirect utility is 21.5 = (2 3) 2 3 (1 3) Ip f ! p c ! = (2 3) I (40) ! (8) ! 1 3 . Solving this equation for the required income gives I = 964. With such an income, this person
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This note was uploaded on 11/22/2010 for the course ECON 411 taught by Professor Ann during the Fall '10 term at University of Oregon.

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Solutions Homework Assignment 2 411 - Solutions Homework...

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