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HW1 - Final Solutions.PDF

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Kathleen Wong

ECO204: Homework I Solutions 1. TrueffalseAjncertain income increasesfromIr to12,onsumption ofgoodY increases (normal a. False.When good),butconsumption ofgoodX decreases asincomes rise.his indicateshatgoodX isiewed asan inferiorood bythis individual.herefore,hestatementthatbothX and so,we shouldobservea higherlevelof Y arenormal goodsisfalse.In orderorthistobe consumptionforboth goods asincome increases. b. False.Ifaren hasconvex preferenceswe know thisbecause theproblem stateshat perfectomplements), her strawberriesnd applesarenotperfectsubstitutes willingnessotradeapplesfor strawberriesorinotherwords,her MRS) isnotgoingto beconstant.Inparticular,sincerutility-maximizingdemand for strawberriesd her appleswill changeith theprices,herMRS inthesummer will beifferentrom MRSin thewinter. By observinganindividual'sevealedpreferencesbetween bundlesofgoods when c. True. pricesandincomes change,we canapproximately traceouttheshape of indifference curves.Revealedpreferencehselpus eliminatepecificregionsofthegraph thatell us curvecannot possiblylie,hich helpsuseliminatedthe where theindifference possibilitythatetwo goods areperfectsubstituteslineaindifferenceurves)orperfect complements (L-shaped indifferenceurves). in when pricesincreaseill d. True. Sincedemand isinelastithepercentagdeecrease Q be lessthanthepercentageincreasein P.o theoveralldecreaseinQ willnotbe enough tooffsethigherprices.As aresult,totalpendituresoninelasticoods (Q x P)will increasewhen Pincreases. e. False.If Mikeismaximizing utility,sindifferencecurvewillbetangenttothe budget line.Or,theslopesofthe twowill beequaltoeach other:*=+. Giventhe MPU PB ^/{rr 4 2 P' 1. informationfrom theproblemw, ecan calculatehat1#=-=- 6 3 a,,dPB= 5' ,o*. M P " P' = Pl-, Nrv v hartMU' ' 'In orderomove towardsthebundle thatguaran"r, *MPu PB MPu PB Mike should consume morc pizzaand lessburgers.fhiscurrentconsumption bundleis hisindifferenceurveisgreaterthantheslope of theudget line atpointA, theslope of ( consuming morcpizzaandless ryr Pu) .Hecan gun ahigherlevelf utility \MPu burger untilereaches pointB,where theslope ofhisindifferenceurve andthebudget linearetangentto eachother.Anotherway to lookatthisistoapply theequalmarginal principle,whichisessentiallycalculationf how much utilitysprovidedby each dollarpenton each ofthegoods.Currently,utility/pricetpizza: 413 1.33 and :615:1.20. SinceMike getsmoreutilityrom spending $1onpizza,he utility/price shouldconsume morc pizza.Eventually,heutilityplirceomconsumingpizzawill fall untilt equalsheutility/priceomconsuming burgers. ,bf;-l_$- l{oP{ Bc.-h* pe 2. I'z* l . . % ' L t Cr,D)" cp = c - D -( f . cf P D -) nI\ / ( c , D , I ) PA.-g-0--, -P - c C = %D =-- O >c ?- vPr-o-> ft'tl ?c Pp p" =^ {vi\s + c - iPo=or t I P.C ' P,D f ) : * @ ( ) v . 3 o o - ) 0 - ) + (r --L - o aA ? " L - D r T : o ? , %b r P"C t PrD --I %c +Po D " -8\f f PcC f F " I H I = T -hA I t PoD L h j I x e . J PoD* FoD = a >Pb D-11-= Q_"fu b) i f P . ' lP p ' 2 - (l-c >+ , ;rritt'a-{t,n"l^ffin^-bu""'dJ* n6D' c *= X : l > D * = 7-r' t? 2tt) c-) i i? ' " t , P o = 3 . ( l>,+) . fr,4rrfun.{wrn'P*'rl-u*'olt*' cF =_t1 D* *, f ' + ,\) ilritiA{wtititj( r'c,60) " l>{6)z Iz -> C" 3) or D' tc hur'pri*>' U4e = t -) LC . s Mrll J = gw
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