1. (5points)Twoindividuals,FredandHelen,inaneconomywithnoproduction,each...

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1. (5points)Twoindividuals,FredandHelen,inaneconomywithnoproduction,each havetheutilityfunctionU=10XY.PricesofbothXandYaresetat$1.InitialendowmentsforFredare10unitsofXand6unitsofY.Helenhas8unitsofXand12unitsofY.Showthatthisinitialendowmentisnotonthecontractcurve.2.(5points)Considerasocietyconsistingofjustafarmerandatailor.Thefarmerhas10 unitsoffoodbutnoclothing.Thetailorhas20unitsofclothingbutnofood.SupposeeachhastheutilityfunctionU=F·C.Thepriceofclothingisalways$1.Ifthepriceoffoodis$3,doesacompetitiveequilibriumexist?Ifnot,whatwillhappentothepriceoffood?3. (10points)JackandJillaretheonlytwoinhabitantsonanisland.Jackstartsoutwith10lobstersandfivecoconuts.Jillstartsoutwith10lobstersand15coconuts.AftertradingJackendsupwith5lobstersand7coconuts.JackfeelsneitherbetternorworseoffthanwhenhestartedbutcannotgetJilltoagreetoanymoretrades.Jillfeelsbetteroffthanwhenshestarted.DrawtheEdgeworthboxconsistentwiththisstory.4. (10points)AnneandSpyrosconsumeonlypizza,Z,andcola,C.Anne’sutilityfunctionisUA=ZACA,andSpyros’utilityfunctionisUS=ZS0.5CS0.5.TheirendowmentsareZA=10,CA=20,ZS=20,andCS=10.a. Whatarethemarginalratesofsubstitutionforeachperson?b. Whatistheformulaforthecontractcurve?c. DrawanEdgeworthbox,labelingcarefully,andindicatethecontractcurve.
	
Document Preview: 1. (5 points)Two individuals, Fred and Helen, in an economy with no production, each  have the utility function U = 10XY.  Prices of both X and Y are set at $1.  Initial  endowments for Fred are 10 units of X and 6 units of Y.  Helen has 8 units of X and 12  units of Y.  Show that this initial endowment is not on the contract curve.   2.(5 points) Consider a society consisting of just a farmer and a tailor.  The farmer has 10  units of food but no clothing.  The tailor has 20 units of clothing but no food.  Suppose  each has the utility function U = F·C.  The price of clothing is always $1.  If the price of  food is $3, does a competitive equilibrium exist?  If not, what will happen to the price of  food?   3. (10 points) Jack and Jill are the only two inhabitants on an island.  Jack starts out with 10 lobsters and five coconuts. Jill starts out with 10 lobsters and 15 coconuts. After trading Jack ends up with 5 lobsters and 7 coconuts. Jack feels neither better nor worse off than when he started but cannot get Jill to agree to any more trades.  Jill feels better off than when she started. Draw the Edgeworth box consistent with this story.   4. (10 points) Anne and Spyros consume only pizza, Z, and cola, C.  Anne’s utility function is UA = ZACA, and Spyros’ utility function is US = ZS0.5CS0.5.  Their endowments are ZA = 10, CA = 20, ZS = 20, and CS = 10.    a. What are the marginal rates of substitution for each person?   b. What is the formula for the contract curve?  c. Draw an Edgeworth box, labeling carefully, and indicate the contract curve.

Robert · Accepted Answer

1. (5 points) 
Two individuals, Fred and Helen, in an economy with no production, each   
have the utility function U = 10XY.  Prices of both X and Y are set at $1.  Initial   
endowments for Fred are 10 units of X and 6 units of Y.  Helen has 8 units of X and 12   
units of Y.  Show that this initial endowment is not on the contract curve.    
 
Answer: 
 
Contract curve is the locus of all pareto- optimal allocations. In edge-worth box, it is the 
locus of all points where indifference curves are tangent. 
 
This condition is satisfied where MRSxy (marginal rate of substitution) for Fred = MRSxy 
(marginal rate of substitution) for Helen 
 
MRSxy for Fred = MUx/MUy = 10Y/10X = Y/X 
 
Initial endowment for Fred; X = 10 and Y =6, So MRSxy of Fred at endowment point  = 
6/10 = 0.6 
 
Similarly we derive MRSxy for Helen at endowment point.  
 
MRSxy  = MUx/MUy = 10Y/10X = Y/X 
 
Initial endowment for Helen: X = 8 and Y = 12, so MRSxy for Helen at endowment point 
= 12/8 = 1.5 
 
Since MRS of two consumers (at their respective endowment) are not equal to each 
other, we conclude that initial endowment is not on the contract curve. 
 
 
2. 
(5 points) Consider a society consisting of just a farmer and a tailor.  The farmer has 10  
units of food but no clothing.  The tailor has 20 units of clothing but no food.  Suppose   
each has the utility function U = F∙C.  The price of clothing is always $1.  If the price of   
food is $3, does a competitive equilibrium exist?  If not, what will happen to the price of   
food? 
 
Answer: 
 
Total amount of food = 10. So in general equilibrium, we must have 
 
Ff + Ft = 10  ……….   (1) , where Ff denotes food consumption of farmer and Ft denotes 
food consumption by tailor. 
 
Total amount of clothing = 20,

1. (5points) Twoindividuals,FredandHelen,inaneconomywithnoproduction,each havetheutilityfunction U=10XY .Pricesofboth X and Y aresetat$1.Initial endowmentsforFredare10unitsof X and6unitsof Y...

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