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# ECON201PSet8Answers - WELLESLEY COLLEGE D EPARTMENT OF...

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WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS JOHNSON ECONOMICS 201~03 Answers to Problem Set #8 1. a. See Edgeworth box diagram below. Ifwe put James in the lower left- hand comer (probably easier as his are the L-shaped indifference curves) and put ham on the vertical axis, then the contract curve will be a straight line from origin to origin with a slope of liz. Why? Well, James will always optimize at the kink of his indifference curves, where H = C / 2. NOTE: That condition holds that he'll prefer TWO slices of cheese for every ONE slice of ham [Veri fy that with simple numbers for C and H for James!]. The only price ratio in equilibrium will be Y4 (price of cheese to price of ham). Why? Well, that will be the MRS of Karen, who views the two goods as perfect substitutes. .-~--- OK \ () () -- - '/'2- , ~(--- '2.()O ------~) 1 b. If James has 40 slices of ham and 80 slices of cheese, Karen must have 60 slices of ham and 120 slices of cheese. That point IS on the contract curve and thus is a Pareto efficient allocation of these two goods between these two people. See point A in the diagram above. c. 60 ham and 80 cheese for James is NOT on the contract curve (point B above). Indeed, we could give 20 ham to Karen, not reduce James's utility and increase Karen's! We could also move anywhere in the shaded area above. Pareto efficient equilibria will be on the contract curve somewhere between 40 ham and 80 cheese for James and 48 ham and 96 cheese for James. How did we get this? Well, we need to find point C in the diagram above. Karen's utility at point B ( 40 ham and 120 cheese) is: 4(40) + 3(120) = 520 jollies. This indifference curve: 520 = 4H + 3C intersects the contract curve (where H = C/2) at the point:

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520 = 4H + 3(2H) = 10H H = 52 and C = 104 (for Karen!). Thus, at point C, James would have 48 ham and 96 cheese! Wow! Extra Credit: Best equilibrium for James would BE point C, where his utility would jump from 40 at point B (check this!) to 48 at point C. Karen's utility at B and C is the same (and equal to 520 jollies), so she'll revolt, divorce James and marry Gilligan! t 2, L FtC> L( s.;f : L f t L( = ~t t%\1\Gv~'W\ f-x ~ V?t ls: PPF= !+e 2 =200 M~ T = _ de = f MRS = aUlaf = 0.5 Ulf .!:.. df e aUlae 0.5 Ule 1 a. For efficiency, set MRS = AFT I/e = e/I or 1 = e PPF: 2e 2 = 200, e = 10 = 1= U, RPT= 1. b. Demand: PFIPc = 2/1 = MRS = elf so e = 2f. Budget: 21+ Ie = 30 the value of production. Substituting from the demand equation: 4/= 30 1= 30/4, e = 15. U = .JlS ·30/4 =.j112.5 ; an improvement from (a) c. ~ ~ J ",Ii tvv Sll-t I'J.. f( \" = 2/1.: 1= 2e. ~~" PPF: 5e 2 == 200, e = ~, 1 = ..J160 Budget now is: 2..J160 + 1+40 =5~ =10../lO Spend s../1O on 1 and s../lO on c. e=5 'iO 1 = 5../lO U =..J125: . ~lV, . 2 A further improvement f flJ'#'.- (b) Ttw.s 1'1\ ~t JA."rflM\r\ ktwJ: A: lJ'l', tW--~ ~{QJ, ~ C'I'/IS 1MI'\f}ilfv\ ,
---- - E. t U\J\S IIW'\f ~ '\J\ l/vVI.~W htl 11 rJt If r QvlMetM d'J-s ~. A. ~ c : D~~tI\~ r{OdUc~l\r--lvAkt- tYee iNJIe-, ~~ tM~V\AN\r~~ \MI\Jtr ffet 'ltJt (;V~ D ~ 11 \'IAcJ ~f\) v{~~ ~ . t~ t~ C{l~,t-- ~oJvAt d t)C~t5: ',{ P f <L i2 t:- 1 - ~) 1 L q ~ - 5~ J: ~ J j o. - 1r \ \[~~t!l J~: [S\f1o-d-IYtb):: [3%-] '-.!

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