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# quiz1_key - ANSWéﬁL are 3{i(LEN t\03 homogeneous of...

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Unformatted text preview: ANSWéﬁL are; 3, {i (LEN. t, \03' homogeneous of degree zero in prices and income homogeneous of degree zero in prices homogeneous of degree zero in prices and utility homogeneous of degree one in prices and income homogeneous of degree one in prices homogeneous of degree One in prices and utility decreasing in the price of x increasing in the price ofx decreasing in income increasing in income romp rm 51.0 57.» Carlos’ morn wakes up from her coma and can’t remember all the properties of demand functions, expenditure functions, and indirect utility functions... let alone who she saw Gabrielle sleeping with. Help her out by identifying which of the above properties must hold for each of the following functions. Full credit is given for ﬁnding ALL the properties that must hold. Assume throughout that the individual‘s preferences are such that they will for sure consume some of both it and y. Marshallian demand for x (3pts)? 0K Marshallian demand for y (3pts)? OK Expenditure function (4pts)? 32K Hicksian demand for x (3pm)? Hicksian clemiiiiii f9 y (3pm)? - i 40 1‘) b (Hm,er [q n 0 Gang i1 .- Indirect utility function (4pts)? “:31? 2. Edie is very upset with Susan for burning down her house and demands to be compensated. Susan has to give Edie enough money to reach utility level U. (Edie has no money herself... it was all in the ﬁre) or Edie will tell the police. Edie’s utility function is given by U=2xm+y where x is divorces and y is poker. 3) Calculate Edie’s Hicksian demands for divorces and poker. (Spts) b) Derive Edie’s expenditure function. (3pts) e) Derive Edie’s indirect utility function. (4pts) d) Suppose Susan has \$100. The price ofx is \$2 and the price of y is \$4 and Susan needs to get Edie’s utility level to 10. How much money does Susan have to give Edie? (3pts) 1"- Pxx 1-ij + )\ (lxv‘ +3 -— EN Gabrielle, consoling herself while her husband is in jail, demands gardeners and clothes. Her indirect utility function is given by v=ln(M)-(U4)ln(px)-(3f4)ln(py) where x is gardeners and y is clothes. a) Find Gabrielle‘s Marshallian demands for gardners and clothes. (Spts) b) Show whether or not clothes are a Giffen good. (2pts) c) Show whether or not clothes are an inferior good. (Zpts) d) Show whether or not her preferences are homothetic (2pts) 4. In order to deal with her four crazy kids, Lynette consumes speed and yoga. Her utility function is given by U=(2x+y)U2 where x is speed and y is yoga. a) Find her Marshallian demands for speed and yoga. (Spts) b) Suppose her income is \$100, the price of speed is \$4 and the price of yoga is \$3. How much speed and yoga does she demand? (2pts) c) Suppose now there was a discount on yoga and the effective price of yoga fell to \$1. How much speed and yoga does she demand? (Zpts) d) Graph your answers to b) and c), being sure to label all the relevant points. (31315:) c) How much happier is she because of the yoga discount? (3pts) UI Bree is very upset because her husband is asking for a divorce and is now demanding three goods (Yes, three goodsl). Her utility function is given by U=min{2x.2y}+z, where x is cleaning supplies, y is rubber gloves‘ and z is laundry detergent. 3) Find her Marshallian demands for cleaning supplies, rubber gloves, and laundry detergent. (opts) 13) Suppose her income is \$200, the price ofx is \$3, the price of y is \$5, and the price ofz is \$2. How much of each ofthe goods does she demand? (2pts) 0) Bree becom'es very upset when the price of laundry detergent (z) rises to an astonishing \$6! Calculate here new demands for x, y, and z. (2pts) d) How much happier is she because of the increase in the price of laundry detergent? (4pts) a, N33: as he min 41a, 56+ aw: "in Ice QQQQQ ":7 mm CL'so m N were #3 akaw eta only X teal-j W bay Exactly no on ’/ Gaul Z [ Mu. a" H .C b __,,_, < .L 3+5 ‘1’ 9*) Eng W Z "2.00 X‘: D J 3:0 , 2" “I; ’{°O 3H5” cf é’ 3» 8%‘8 v4.6 X “ma 8' —— .2139 I 2.3 t: x g \/ %?0 (7K LLngjlg—{o} -- U‘O/O/ [03» ...
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## This note was uploaded on 05/13/2010 for the course ECON 105D taught by Professor Cur during the Fall '09 term at Duke.

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quiz1_key - ANSWéﬁL are 3{i(LEN t\03 homogeneous of...

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