# Luke’s utility is U( x 1,x 2)= 2 x 1 + ln x 2.

November 24, 2016

Econ10A:ProblemSet2

(1)Luke’sutility is U(x1,x2)= 2×1 + ln x2.

(a)What is Luke’smarginalrateofsubstitution(MRS)?

UT(xa,xb)=6xa+9xb UD(xa,xb)=8xa+12xb U(xa,xb)=xaxb2

(a)RelativetoTom,doesDickrequiremorebananas,less bananas,orthesame numberof bananasto giveawayanapple?Why?

(b)Suppose Harryhas3 applesand2bananas. Would he be willingtotradeanapplefora banana? Showwhyor whynot.

(3)I needaminimumof 7applesper week tomakeoneapplepieperweek. Idon’t liketoeat applesunlessthey arein a pie.(They’ll justsiton theshelf andgetrotten inaweek ifIget less than7.) I do,however,likebananas,evenif theyarenotinapie.Drawmyindifference curves.

(4)UtilityisU(x,y) = x2 + y.

(a)Derivethe formulafortheindifferencecurvethatgivesmea utilityof exactly8.Draw that indifferencecurve.

(b)DerivethemarginalutilityfunctionsMUx(x,y)andMUy(x,y).DeriveMRS(x,y). (c) Doesthisutilityfunctionsatisfythehypothesis of diminishingMRS?Explain. (d)Namesome commoditiesthesemightbe.

(5)Myutilityfunction U(x1,x2)dependsonthetwocommodities x1, x2. Ifmypreferencesare monotonicandsatisfy the Hypothesis ofStrictlyDiminishing MarginalRateof Substitution, andif MRS(5,5)= –2,whatcanyousayabouthowIcouldrank commoditybundles (4,6)and (6,5)?Drawagraphtoillustrate.(Hint: Howwould eachof thesebundlescomparewiththe bundle (5,5)?)

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