范微觀濟學(xué)現(xiàn)代觀點課后習(xí)題詳解

第1 市125個消費者租用商品房的保留價格為500第1 市125個消費者租用商品房的保留價格為500美元，第Supposethattherewere25peoplewhohadareservationpriceof$500,andthepersonhadareservationpriceof$200.WhatwouldthedemandcurvelookpQ200p50p 2124套住房可以出租，均衡價格是多少?26Intheaboveexample,whatwouldtheequilibriumpricebeiftherewere24torent?Whatiftherewere26apartmentstorent?Whatiftherewere25apartmentsto1-2A點所示，特1-21-1由同（1），如圖1-2C點所示。1 Ifpeoplehavedifferentreservationprices,whydoesthemarketdemandcurvePP越高，保留價PPP的消費者逐漸增多，P下降時，市場需求會不斷增加。當(dāng)消費者足夠多，互相Inthetextweassumedthatthecondominiumpurchaserscamefromtheinner-ringpeople—peoplewhowerealreadyrentingapartments.WhatwouldhappentothePriceofinner-ringapartmentsifallofthecondominiumpurchaserswereouter-ringpeople—thepeoplewhowerenotcurrentlyrentingapartmentsintheinnerring?來的需求曲線D11-3 2SupposenowthatSupposenowthatthecondominiumpurchaserswereallinner-ringpeople,butthateachcondominiumwasconstructedfromtwoapartments.Whatwouldhappentothepriceofapartments?供給曲線由S向左移動至S′。新的均衡價格P′高于原來的均衡價格P。 Whatdoyousupposetheeffectofataxwouldbeonthenumberofapartmentsthatwouldbebuiltinthelongrun? 7．假設(shè)需求曲線是D(p)=100-2p，如果壟斷者有60套住房，他會定什么價格?他可以租出多少套?如果他有40套住房，他會定什么價格?他可以租出多少套?SupposethedemandcurveisD(p)=100–2p.Whatpricewouldthemonopolistsetifhehad60apartments?Howmanywouldherent?Whatpricewouldhesetifhehad40apartments?Howmanywouldherent?3maxq(5012qmaxq(5012qq＝506050 Ifourmodelofrentcontrolallowedforunrestrictedsubletting,whowouldendupgettingapartmentsintheinnercircle?WouldtheoutcomebeParetoefficient?第2 預(yù)算約1p1x1p2x2=m112的價格提高了7倍，收入增加了3倍。根據(jù)原來的價格和收入寫出新預(yù)算線的方程。Originallytheconsumerfacesthebudgetlineplxl+p2x2=m.Thenthepriceofgooddoubles,thepriceofgood2becomes8timeslarger,andincomebecomes4timeslarger.Writedownanequationforthenewbudgetlineintermsoftheoriginalpricesandincome.答：p1x1+p2x2=m，則新的預(yù)算線方程是2p1x18p2x24m'21p'8p；m'4m212以新的預(yù)算線為p'pxm，即2pxx1 2124Whathappenstothebudgetlineifthepriceofgood2increases,butthepriceofgoodandincomeremain答：預(yù)算線會變得更為平坦，橫截距仍然不變。理由如下：假設(shè)原來的預(yù)算線為mpxWhathappenstothebudgetlineifthepriceofgood2increases,butthepriceofgoodandincomeremain答：預(yù)算線會變得更為平坦，橫截距仍然不變。理由如下：假設(shè)原來的預(yù)算線為mpxpxm，將預(yù)算線重新整理為xx21 221 31122倍，預(yù)算線是變平了還是變Ifthepriceofgood1doublesandthepriceofgood2triples,doesthebudgetbecomeflatterorm答：預(yù)算線變得更為平坦。理由如下：由預(yù)算線xx221 211倍，那么預(yù)算線的斜率將從p1變?yōu)?p1p3pWhatisthedefinitionofanumeraire繪出同一個預(yù)算集。因此這條預(yù)算線為：p1x1+p2x2=m，就與下列的預(yù)算線是相同的 mx2x1+x2 ppm22。入限定為5假設(shè)政府對每加侖汽油征稅157假設(shè)政府對每加侖汽油征稅157Supposethatthegovernmentputsataxof15centsagallonongasolineandthendecidestoputasubsidyongasolineatarateof7centsagallon.Whatnettaxisthiscombinationequivalentto?p1x1+p2x2=mu1Supposethatabudgetequationisgivenbyp1x1+p2x2=m.Thegovernmentdecidestoimposealump-sumtaxofu,aquantitytaxongood1oft,andaquantitysubsidyongood2s.Whatistheformulaforthenewbudget答：(p1t)x1p2s)x2muIftheincomeoftheconsumerincreasesandoneofthepricesdecreasesatthesametime,willtheconsumernecessarilybeatleastaswell-off? 第3 l．如果在(x1，x2)和(y1，y2)同時可以得到的情況下，消費者選擇(x1x2)能否得出x1x2)﹥（y1，y2）的結(jié)論Ifweobserveaconsumerchoosing(x1,x2)when(y1,y2)isavailableonetime,arewejustifiedinconcludingthat(x1,x2)﹥(y1,y2)?6答：不能得出(x答：不能得出(x1x2)﹥（y1y2）的結(jié)論。理由如下：從最優(yōu)化原理(下選擇了(x1x2)，那么就可以得出結(jié)論(x1x2)>（y1y2。但就一般的情費者的最優(yōu)商品束并不一定是惟一的，消費者在(y1y2)可得的情況下選擇了(x1，x2)時消費者也可能對二者是無差異的。因此對于一般的情況只能得出結(jié)論(x1，x2（y1，y2ConsideragroupofpeopleA,B,Candtherelation“atleastastallas,”asin“AisatleastastallasB.”Isthisrelationtransitive?Isitcomplete?說A不會比B矮，BC矮，所以AC矮，即AC至少一樣高。Takethesamegroupofpeopleandconsidertherelation“strictlytallerthan.”Isthisrelationtransitive?Isitreflexive?Isitcomplete?喜愛Y消費束勝過Z，那么可以認(rèn)為消費者喜愛X消費束勝過。一個。這種偏好關(guān)系是傳遞的嗎?完備的嗎AcollegefootballcoachsaysthatgivenanytwolinemenAandB,healwaysprefersonewhoisbiggerandfaster.Isthispreferencerelationtransitive?Isit無差異曲線自身能相交嗎?3-1能繪成一條單獨的無差異曲線嗎Cananindifferencecurvecrossitself?Forexample,couldFigure3-9depictaindifference7 CouldFigure3-1beasingleindifferencecurveifpreferencesare圖 Ifbothpepperoniandanchoviesarebads,willtheindifferencecurvehaveapositiveanegative情況下，無差異曲線離原點越近，代表的效用就越高。如圖3－3所示。8圖3－3 圖3－3 Explainwhyconvexpreferencesmeansthat“averagesarepreferredtoextremes.”3－4所示，在凸?fàn)畹钠弥?，X、Y位于同一無差異曲線上，ZXY的加權(quán)平均，由3－4Z位于比X、Y更高的無差異曲線上，即Z比X、Y更受消費者的偏愛。XZ是X和YY圖 915美元鈔票的邊際替代率是多少Whatisyourmarginalrateofsubstitutionof$1billsfor$5美元的鈔票，那么需要5張1美元的鈔票來補償，因此x55x11151Ifgood1isa“neutral”,whatisitsmarginalrateofsubstitutionforgood03－59圖 圖 Thinkofsomeothergoodsforwhichyourpreferencesmightbe第4 效1.一個效用函數(shù)自乘奇數(shù)次是單調(diào)變換。那么該效用函數(shù)自乘偶數(shù)次還是單調(diào)變換嗎?(提示：考慮f(u)=u2這種情況)Thetextsaidthatraisinganumbertoanoddpowerwasamonotonictransformation.Whataboutraisinganumbertoanevenpower?Isthisamonotonictransformation?(Hint:considerthecasef(u)=u2.)（1）u2（2）u1/（3）u1/（4）u（6）u（7）u2,（8）u2,Whichofthefollowingaremonotonictransformations?(1)u=2v－13;(2)u=－l/v2;(3)u=l/v2;(4)u=lnv;(5)u=－e－v;(6)u=v2;(7)u=v2forv>0;(8)u=v2forv<0.3．如果是單調(diào)偏好的話，經(jīng)過原點的射線就只會同每條無差異曲線相交一次。請嚴(yán)格）Weclaimedinthetextthatifpreferencesweremonotonic,thenadiagonallinethroughtheoriginwouldintersecteachindifferencecurveexactlyonce.3．如果是單調(diào)偏好的話，經(jīng)過原點的射線就只會同每條無差異曲線相交一次。請嚴(yán)格）Weclaimedinthetextthatifpreferencesweremonotonic,thenadiagonallinethroughtheoriginwouldintersecteachindifferencecurveexactlyonce.Canyouprovethisrigorously?(Hint:whatwouldhappenifitintersectedsomeindifferencecurvetwice?)x1y1x2y2x1y1x2y2x1y1差異曲線相交一次，如圖4－1所示。4．哪種偏好可用形如u(x1x2v(x1x213x113x2x1x2Whatkindofpreferencesarerepresentedbyautilityfunctionofthe?Whatabouttheutilityfunctionv(xl,答：（1）完全替代的偏好可用形如u(x1,x2) x1x2的效用函數(shù)表示。理由如下u(x1x2x1x2做單調(diào)變換f(u)u2u'(x,x)x 2代表的偏好的類型，所以，u(x1,x2) x1x2也代表完全替代的偏好（2）v(x1x213x113x21v(x,x)13x13x做單調(diào)變換f(v) v，得v'(x,x)xx和（1）的理由 12 同，可知v(x1x213x113x2這種形式的效用函數(shù)表示?效用函數(shù)5．哪種偏好可用形如u(x1x2x11v(x,x)13x13x做單調(diào)變換f(v) v，得v'(x,x)xx和（1）的理由 12 同，可知v(x1x213x113x2這種形式的效用函數(shù)表示?效用函數(shù)5．哪種偏好可用形如u(x1x2x1v(x,x) x2x2是u(x1x22 11Whatkindofpreferencesarerepresentedbyautilityfunctionoftheformu(x1,x2)?Istheutilityfunctionv(x1,x2)=x21+u(x1,+x2amonotonictransformation答：（1）線性偏好可以用形如u(x1x2x1 （2）效用函數(shù)v(x,x) 2x1x2x2是u(x1,x2)的單調(diào)變換。理由如下：2 16．考慮效用函數(shù)u(x1x2)x1x2。它表示哪種偏好函數(shù)v(xx)x2是212)x 是u(xx的單調(diào)變u(xxw(x22 2122Considertheutilityfunctionu(x1,x2).Whatkindofpreferencesdoesrepresent?Isthefunctionv(x1,x2)=x21x2amonotonictransformationofu(xl,x2)?Isfunctionw(x1,x2)=x2lx22amonotonictransformationofu(x1,答：（1）用函數(shù)u(x1x2v(xx)xx不是2u(xx（2）函數(shù) 調(diào)變換不改變它代表的偏好，所以如果v(xxxx是u(xx2的單調(diào)變換，那么這2 1個效用函數(shù)代表相同的偏好，從而它們的邊際替代率相同，但是計算發(fā)現(xiàn)，效用函數(shù)xu(x,x)xx的邊際替代率MRSv(xxx2x的邊際替代率 1 21MRS)x2x肯定不是u(xx，這兩個邊際替代率不相等，所以v(x x1（3）函數(shù)w(x,x)x2 是u(x,x)的單調(diào)變換。理由如下：對效用函2 2u(x,x)xxf(uu4w(xxx2 1 7．請解釋為什么效用函數(shù)的單調(diào)變換不會改變邊際Canyouexplainwhytakingamonotonictransformationofautilityfunctionchange7．請解釋為什么效用函數(shù)的單調(diào)變換不會改變邊際Canyouexplainwhytakingamonotonictransformationofautilityfunctionchangethemarginalrateof假設(shè)對一個效用函數(shù)作單調(diào)變換，比如說，v(x1x2f(u(x1x2f/u/MRS=v/ f/uu/ 222第5 選Iftwogoodsareperfectsubstitutes,whatisthedemandfunctionforgoodp20xppm0到m/pp 1 pm/1 maxx1x10,x2s.t.p1x1p2x2mp1，2p2mp1x00xm/p211p2/mp1(1p1mmp1x00xm/p211p2/mp1(1p1mmax11ppp0x1m/222p20xppm0到m/pp 1 pm/1 圖 Supposethatindifferencecurvesaredescribedbystraightlineswithaslopeof-Givenarbitrarypricesandmoneyincomepl,p2,andm,whatwilltheconsumer’soptimalchoiceslooklike?答：如圖5－2所示，比較預(yù)算線與無差異曲線的斜率可知， b時，消費者 b時5－2糖Supposethataconsumeralwaysconsumes2spoonsofsugarwitheachcupofcoffee.thepriceofsugar5－2糖Supposethataconsumeralwaysconsumes2spoonsofsugarwitheachcupofcoffee.thepriceofsugarisplperspoonfulandthepriceofcoffeeisp2percupandtheconsumerhasmdollarstospendoncoffeeandsugar,howmuchwillheorshewanttopurchase?m和。分析如下x12p1 2p1mpxpxm；。1 2122p2p 4p1，p2并有m美元可支出。那么他的最優(yōu)消費束是Supposethatyouhavehighlynonconvexpreferencesforicecreamandolives,likethosegiveninthetext,andthatyoufacepricespl,p2andhavemdollarstospend.Listthefortheoptimalconsumption ）或者為（m,0。這是因為：在凹性偏好的m最優(yōu)選擇為只消費兩種商品中的一種商品。即消費者的最優(yōu)消費束為）（m,045．如果一個消費者有效用函數(shù)u(xxxx，她會將她收入的多少比例花在商品 1上Ifaconsumerhasautilityfunctionu(xl,x2)=x1x42,whatfractionofherincomewillspendongood斯效用函數(shù)，對其進(jìn)行單調(diào)變換，可得u(x,x) x/。關(guān)于柯布—道格拉斯效用函1/54spendongood斯效用函數(shù)，對其進(jìn)行單調(diào)變換，可得u(x,x) x/。關(guān)于柯布—道格拉斯效用函1/54 xx10,x21s.t.p1x1p2x2由拉格朗日乘子法有：maxxx1(mpxpx11 2x1(1)xx 112p px111 。所以消費者會把 )的收入花費在商品則p p (1)x122145Forwhatkindofpreferenceswilltheconsumerbejustaswell-offfacingaquantitytaxasanincome5－3所示，在征稅后，無論在哪種稅收條件下，消費者的最優(yōu)選擇都不變，5－3第6 需Iftheconsumerisconsumingexactlytwogoods,andsheisalwaysspendingallofhermoney,canbothoftheminferiorx1(p1,p2,圖 px1(p1,p2,圖 p1x1p2x2m，因為消費者總是花光她的全部收入，所以此式恒成立。預(yù)算線兩邊對收入求導(dǎo)得：dx1dx2pp12Showthatperfectsubstitutesareanexampleofhomothetic果消費者對(x1x2的偏好甚于y1y2，則對任意的t0，該消費者對(tx1tx2的偏于(ty1ty2下面來證明完全替代是相似偏好的一個特例。由于完全替代偏好的效用函數(shù)是ux1x2x1x2，如果ux1x2uy1y2x1x2y1y2的正值t，都會有tx1tx2ty1ty2，可得utx1tx2uy1y2，所以完全替代是相似偏3．證明柯ShowthatCobb-Douglaspreferencesarehomothetic答：關(guān)于相似偏好的概念見第2題。由于柯布道格拉斯效用函數(shù)為：uxxx utxtxtxtuxxaatxa 2 1 ux1x2ux1x2uy1y2 ，那么對于任何正 ，就一定utx1tx2tux1x2tuy1y2uty1ty2成立，從而得到utx1tx2uty1ty2AstheincomeoffercurveistotheEngel,whichcurveisthepriceoffercurve6－26-3圖 Ifthepreferencesareconcavewilltheconsumereverconsumebothofthegoods圖 Arehamburgersandbunscomplements圖 ArehamburgersandbunscomplementsorWhatistheformoftheinversedemandfunctionforgood1inthecaseofm p2。理由如下：首先x1完全互補品的效用函數(shù)是：min{x1x2更一般的這種類型的效用函數(shù)是：min{ax1,，但這種特殊形式并不影響分析)，在預(yù)算約束下，消費者選擇效用最大x10,x2min{x1,s.t.p1x2p2x2x10,x2min{x1,s.t.p1x2p2x2少 mmp1x1p2x1mx1，pp m進(jìn)而得到商品1的反需求函數(shù)為p1 p2x18．如果需求函數(shù)是x1p1，那么反需求函數(shù)就是x p1Trueorfalse?Ifthedemandfunctionisx1=－p1,thentheinversedemandfunctionis第7 顯示偏1．當(dāng)價格是p1p2=（1，2）時，消費者需求是(x1x2=(1，2)，當(dāng)價格(q1q21)時，消費者需求是)=(2，1)。這種行為同最大化的行為模型相一致y1,Ifpricesare(pl,p2)=(1,2),thecombinationofconsumerdemandis(x1,x2)=(1,2),andifpricesare(ql,q2)=(2,1),thecombinationofconsumerdemandis(y1,y2)=(2,1).Isthisbehaviorconsistentwiththemodelofmaximizingbehavior?答：這種行為同最大化的行為模型不一致。p1x1p2x25p1y1p2y24(x1x2被顯示偏好于y1y2。同樣的，由于q1x1q2x24q1y1q2y25從中可知y1y1被顯示偏好于x1x2所以這種行為違背了顯示偏好弱公理，與最大化的行2．當(dāng)價格是(p1p2=(2，1)時，消費者需求是(x1x2=(1，2)，當(dāng)價格是(q1q22)時，消費者需求是(y1,y2)=(2，1)。這種行為同最大化行為模型相一致嗎Ifpricesare(pl,p2)=(2,1),thecombinationofconsumerdemandis(x1,x2)=(1,2),andpricesare(ql,q2)=(1,2),thecombinationofconsumerdemandis(y1,y2)=(2,1).Ispricesare(ql,q2)=(1,2),thecombinationofconsumerdemandis(y1,y2)=(2,1).Isthisbehaviorconsistentwiththemodelofmaximizingbehavior?(x1,x2)(y1,y2)O32xIntheprecedingexercise,whichbundleispreferredbytheconsumer,thex-bundleor答：xWesawthattheSocialSecurityadjustmentforchangingpriceswouldtypicallyrecipientsatleastaswell-offastheywereatthebaseyear.Whatkindofpricechangesleavethemjustaswell-off,nomatterwhatkindofpreferencesthey這是因為，對于指數(shù)化的保險金，當(dāng)價格從（pbpb）變?yōu)?qq qxqxqxb1 2 1 2(q,q)t(p,p pbxpbxpbpb1 2 1 2InthesameInthesameframeworkastheabovequestion,whatkindofpreferenceswouldleavetheconsumerjustaswell-offaswasinthebaseyear,forallprice7－2所示。7－2中，AB第8 斯勒茨基方SupposeaconsumerhaspreferencesbetweentwogoodsthatareperfectWillthethingthattheentiredemandresponseequalstothesubstitutioneffecthappenifpricesSupposethatpreferencesareconcave.Isitstillthecasethatthesubstitutioneffectis8－18－1等于A-8－2x向消費者退稅，情況會發(fā)生什么變化Inthecaseofthegasolinetax,whatwouldhappeniftherebatetotheconsumersbasedontheiroriginalconsumptionofgasoline,x,ratherthanontheirfinalconsumptiongasoline,pxymp代表石油價格，x表示花在其他商品上的貨幣，m表示總收入，從而消費者的最優(yōu)選擇為x* ，特別的px*y*px*y*ptxym圖形分析見圖8－3。圖 43題中，政府支出比它得到的稅收更多還是更少Inthecasedescribedintheprecedingquestion,wouldthegovernmentbepayingoutmoreorlessthanitreceivedin_8－3政府的稅收補貼，所以政府支出比它得到的稅收Inthiscasewouldtheconsumersbebetterofforworseoffifthetaxwithrebatebasedonoriginalconsumptionwereineffect?第9 購買和銷Ifaconsumer’snetdemandsare(5,-3)andherendowmentis(4,4),whatareher（9，1（9，當(dāng)商品價格是(pl，p2)=(2，3)時，消費者的消費是(x1，x2)=(4，4)買賣是沒有成本的。那么消費者一定偏好商品束y1,y2=(3，5)嗎?品束(y1，y2)嗎Thepricesare品束(y1，y2)嗎Thepricesare(pl,p2)=(2,3),andtheconsumeriscurrentlyconsuming(x1,x2)=(4,Thereisaperfectmarketforthetwogoodsinwhichtheycanbeboughtandsoldcostlessly.Willtheconsumernecessarilypreferconsumingthebundle(y1,y2)=(3,5)?Willshenecessarilypreferhavingthebundle(y1,y2)?（2）消費者肯定選擇擁有商品束(y1y2)=(3，5)時，消費者出售稟賦的收入是費者的更多的收入也即更大的預(yù)算空間，因此他一定會偏好擁有商品束(y1,)，但是在有商品束(y1,y2)的情況下，消費者的最優(yōu)選擇卻未必還是該商品束，因此他未必偏好3．當(dāng)商品價格為p1p2(2,3時，,消費者的消費是(x1x2(4,4)為(q1q22,4)，那么在新的價格下，消費者的境況會變得更好一些嗎Thepricesare(pl,p2)=(2,3),andtheconsumeriscurrentlyconsuming(x1,x2)=(4,4).Nowthepriceschangeto(q1,q2)=(2,4).Couldtheconsumerbebetteroffunderthesenewprices?更好（如圖9－1中的無差異曲線S1所示），也有可能變的更差（如圖9－1中的無差異曲線S2所示。圖 圖 TheU.S.currentlyimportsabouthalfofthepetroleumthatituses.Therestofitsaremetbydomesticproduction.CouldthepriceofoilrisesomuchthattheU.S.wouldbemadebetteroff?__pxmpw__p，預(yù)算線是最優(yōu)選擇位于ABAB段位于油價上漲前的預(yù)算集內(nèi)，這就是說，油價上漲前，美國在消費得起ABB點對應(yīng)的消費束，由顯示偏好原理，BAB段對應(yīng)的消費束，所以，如果油價上漲后，美國的選擇位于AB段上，那么他的境況必然變差。但是如果美國在石油價格上升后從石油進(jìn)口國轉(zhuǎn)變?yōu)槭统隹趪葱碌淖顑?yōu)選擇位于BC段，那么美國的情況有可能變好（如圖S2）也有可能變差（9－2中的S1）這要視具體的效用函數(shù)來決定圖 2430時(碰巧發(fā)生在考試周的前夕)，這將Supposethatbysomemiraclethenumberofhoursinthedayincreasedfrom24tohours(withluckthiswouldhappenshortlybeforeexamweek).Howwouldthisaffectthebudgetconstraint?2430時，預(yù)算線會平行地向外移動。Ifleisureisaninferiorgood,whatcanyousayabouttheslopeofthelabor替代效應(yīng)＋（RR)(RR)項恒為正替代效應(yīng)＋（RR)(RR)項恒為正，從而等式右邊的后一項，也即收入效應(yīng)恒為負(fù)。由于替代效應(yīng)恒為負(fù)第10 跨時期選1．如果利率是20%，那么20年后交付的100萬美元在今天的價值是多少Howmuchis$1milliontobedelivered20yearsinthefutureworthtodayiftherateis20就有100萬0.03310-1不同利率和到期時間下，12．當(dāng)利率提高時，跨時期的預(yù)算線是變得更陡峭還是變得更平Astheinterestraterises,doestheintertemporalbudgetconstraintsteeperorcwc(1r)cw1r)w，所以112 111的斜率為(1r)，當(dāng)利率提高時，預(yù)算線的斜率的絕對值增大，因此預(yù)算線會變得更加3．在研究跨期的食品購買時，商品完全替代的假設(shè)是否有WouldtheassumptionthatgoodsareperfectsubstitutesbevalidinastudyintertemporalfoodAconsumer,whoisinitiallyalender,remainsalenderevenafteradeclineininterestrates.Isthisconsumerbetterofforworseoffafterthechangeininterestrates?Iftheconsumerbecomesaborrowerafterthechangeishebetterofforworseoff?答：（1）假設(shè)在利率下降前，某消費者是一個貸款者，如果利率下降后，他仍然是一此時的最優(yōu)選擇變?yōu)锽由于B在原來的預(yù)算線之下，這就意味著：在利率變化前，消費者可以選擇B點的時候卻放棄了它，轉(zhuǎn)而選擇A那么由顯示偏好原理可知，消費者一定偏10－2好還是變壞。分析如圖10-3所示，假設(shè)利率降低后，消費者的最優(yōu)選擇點為C點，此時消10－55．如果利率是10%，一年后10－55．如果利率是10%，一年后100美元的現(xiàn)值是多少？如果利率為5%，它的現(xiàn)值又是thepresentvalueiftheinterestrateis5%?第11 資產(chǎn)市假定資產(chǎn)A在下個時期能賣11美元。如果與A相似的資產(chǎn)的報酬率是10%，請問資產(chǎn)A的現(xiàn)值是多少?SupposeassetAcanbesoldfor$11nextperiod.IfassetssimilartoAarepayingarateofreturnof10%,whatmustbeassetA’scurrentprice?答：資產(chǎn)Ap=11/1.1=10111萬美元的價格出售的住宅，現(xiàn)在可以賣到10萬美元。這幢房子的報酬率是多少？Ahouse,whichyoucouldrentfor$10,000ayearandsellfor$110,000ayearfromcanbepurchasedfor$100,000.Whatistherateofreturnonthis10%利率，人們面臨的邊際稅率是40%，不征稅債券的報酬率應(yīng)是多Thepaymentsofcertaintypesofbonds(e.g.municipalbonds)arenottaxable.Iftaxablebondsarepaying10%andeveryonefacesamarginaltaxrateof40%,whatratereturnmustthenontaxablebonds報酬率應(yīng)該等于征稅債券的稅收調(diào)整后的報酬率。在邊際稅率時40%10%的報酬率經(jīng)稅收調(diào)整后為10%(140%)＝6%，因此不征稅的債券的報酬率為6%410美元的價格才可得到，如果利率是10%，該稀缺資源今天的價格應(yīng)是多少Supposethatascarceresource,facingaconstantdemand,willbeexhaustedin10years.IfalternativeSupposethatascarceresource,facingaconstantdemand,willbeexhaustedin10years.Ifalternativeresourcewillbeavailableatapriceof$40andiftheinterestrateis10%,mustthepriceofthescarceresourcebe答：15.42美元。分析如下：10年后，稀缺資源的價格應(yīng)(1第12 不確定1．圖12－1是消費者在不確定的環(huán)境中購買保險時的預(yù)算線，請解釋預(yù)算線上初始稟HowcanonereachtheconsumptionpointstotheleftoftheendowmentinFigure12-12－1(1)u(c1c212a(1c12c2（a>0(2)u(c,c,,)cc 1 2(3)u(c1,c2,1,2)1lnc12lnc2Whichofthefollowingutilityfunctionshavetheexpectedutilityproperty?(a)21,π2)=a(π1c1+π2c2),π1c1+π2c2,=如果效用函數(shù)u(x如果效用函數(shù)u(x)滿足u(c1c21,2)a[1v(c12v(c2b，就說u(x)具（1（2，3．一個厭惡風(fēng)險的人要在以下兩種情形之間進(jìn)行選擇：他有25%的概率得到1000元，有75％的概率得到100美元；或者，他可以得325美元。他會怎樣選Arisk-averseindividualisofferedachoicebetweenagamblethatpays$1000withprobabilityof25%and$100withaprobabilityof75%;orapaymentof$325.Whichwouldhechoose?答：此人會選擇第二種情形。因為第一種選擇給消費者帶來的預(yù)期收入為12－2風(fēng)險厭惡者的效用函數(shù)4．如果消費者可以確定地得到320美元，他會怎樣選擇?Whatifthepaymentwas$320?答：3320Drawautilityfunctionthatexhibitsrisk-lovingbehaviorforsmallgamblesandrisk-aversebehaviorforlargergambles.6．為什么相對于火災(zāi)來說，在洪災(zāi)的情況下，6．為什么相對于火災(zāi)來說，在洪災(zāi)的情況下，相鄰而居的人們更難以相互提供Whymightaneighborhoodgrouphaveahardertimeselfinsuringforflooddamageversusfiredamage?第13 風(fēng)險資1．如果無風(fēng)險資產(chǎn)的報酬率是6%，某種風(fēng)險資產(chǎn)的報酬率為9%3%，那么，如果一個人愿意接受的標(biāo)準(zhǔn)差水平是2%，則他能夠?qū)崿F(xiàn)的最大報酬率是多少Iftherisk-freerateofreturnis6%,andifariskyassetisavailablewithareturnof9%andastandarddeviationof3%,whatisthemaximumrateofreturnyoucanachieveifyouarewillingtoacceptastandarddeviationof2%?Whatpercentageofyourwealthwouldhavetobeinvestedintheriskyasset?答：（1）此人能夠?qū)崿F(xiàn)的最大報8%。理由如下：假設(shè)此人的總投x比例3x2%x23rpxrs1x)rf39%368%，這里rsrf分別是風(fēng)險資產(chǎn)和無風(fēng)險資產(chǎn)的報酬率，rp是投資組合的報酬率。21題中的風(fēng)險價格是多少Whatisthepriceofriskintheabove21rp0.081Ifastockhasaβof1.5,thereturnonIfastockhasaβof1.5,thereturnonthemarketis10%,andtherisk-freerateofreturnis5%,whatexpectedrateofreturnshouldthisstockofferaccordingtotheCapitalAssetPricingModel?Iftheexpectedvalueofthestockis$100,whatpriceshouldthestockbesellingfor答：（1）該股票的預(yù)期收益率是12.5%。分析如下：根據(jù)資本資產(chǎn)定價模型rirfi(rmrf)rf5%rm10%rp5%1.510%512.5%（2）如果該股票的預(yù)期值為100美元，那么今天出售的價格應(yīng)該為： 1 14章消費者剩余1美元的從量稅，這種稅收的額外凈損失是多少？Agoodcanbeproducedinacompetitiveindustryatacostof$10perunit.Thereare100consumersareeachwillingtopay$12eachtoconsumeasingleunitofthegood(additionalunitshavenovaluetothem.)Whatistheequilibriumpriceandquantitysold?Thegovernmentimposesataxof$1onthegood.Whatisthedeadweightlossofthistax?以所有的消費者都會購買這種產(chǎn)品，即廠商的銷量為100。此時消費者剩余為（12-10）14-1供給等于需求時，市場均衡為11。此時消費者剩余為（12-11）×100=100，生產(chǎn)者剩余為（11-1-10）×100=01×100=100100＋100＝20014-214-2供給等于需求時，市場均衡2．假設(shè)需求曲線為Dp)10p。那么消費者消費614-2供給等于需求時，市場均衡2．假設(shè)需求曲線為Dp)10p。那么消費者消費6SupposethatthedemandcurveisgivenbyD(p)=10-p.Whatisthegrossbenefitfromconsuming6unitsofthegood?6的最高價格之和，也就是CS(10q)dq6018423246Intheaboveexample,ifthepricechangesfrom4to6,whatisthechangein464CSCS2CS1(10q)dq(10q)dq(10q)dq1000bSupposethataconsumerisconsuming10unitsofadiscretegoodandthepriceincreasesfrom$5perunitto$6.However,afterthepricechangetheconsumercontinuestoconsume10unitsofthediscretegood.Whatisthelossintheconsumer’ssurplusfromthispricechange?不影響結(jié)論），當(dāng)5元時，消費者消費10單位商品，消費者剩余SADG，當(dāng)格提高到6元后，消費者剩余為：SACBSCEG，這里之所以要減去三角形CEG是因為費者為多消費的商品愿意支付的價格低于實際購買價格6CSSCEGSCSSCEGSAGD10圖14- 第15 市場需IfthemarketdemandcurveisD(p)=100-0.5p,whatistheinversedemandAnaddict’sdemandfunctionforadrugmaybeveryinelastic,butthemarketfunctionmightbequiteelastic.Howcanthis圖 圖 吸毒者2的需求圖15－3吸毒者3的需圖 圖 )IfD(p)=12-2p,whatpricewillmaximizeRp124p0p3)SupposethatthedemandcurveforagoodisgivenbyD(p)=100/p.Whatpricewillmaximizerevenue?Trueorfalse?Inatwogoodmodelifonegoodisaninferiorgoodtheothergoodbealuxuryp1x1(p1,p2,m)p2x2(p1,p2,m)上式兩邊關(guān)于m求導(dǎo)，得到pp21s11s22s11s2222求收入彈性。所以如果一種商品是低檔品，不妨假設(shè)為商品1，那么必有11s1s21，所以必有212第16 均Whatistheeffectofasubsidyinamarketwithahorizontalsupplycurve?Withaverticalsupplycurve?t的補貼，所以補貼的好處全部由消費者得到圖16- 圖16- Supposethatthedemandcurveisverticalwhilethesupplycurveslopesupward.Iftaxisimposedinthismarketwhoendsuppaying圖16-圖16- 斜，令紅、藍(lán)鉛筆的價格分別為pr和pb。如果政府只對紅鉛筆征稅，會出現(xiàn)什么結(jié)果？Supposethatallconsumersviewredpencilsandbluepencilsasperfectsubstitutes.Supposethatthesupplycurveforredpencilsisupwardsloping.Letthepriceofredpencilsandbluepencilsbeprandpb.Whatwouldhappenifthegovernmentputataxonlyonred美國近一半的汽油是進(jìn)口的。假設(shè)石油生產(chǎn)者愿意以25oilproducersarewillingtosupplyasmuchoilastheUnitedStateswantsataconstantpriceof$25abarrel.Whatwouldhappentothepriceofdomesticoilifataxof$5abarrelwereplacedonforeignoil?00內(nèi)的石油與國外的石油對消費者而言是完全替代的，所以消費者會選擇價格便宜的石油消00圖16- Suppose圖16- Supposethatthesupplycurveisvertical.Whatisthedeadweightlossofataxinthis圖16- Considerthetaxtreatmentofborrowingandlendingdescribedinthetext.Howrevenuedoesthistaxsystemraiseifborrowersandlendersareinthesametax1題可知，對借款者和貸款者征稅，市場達(dá)到均衡的條件是：rb(q)rl1 1 者處于同一納稅等級，即tbtl，則由（1）07．當(dāng)tltb7．當(dāng)tltb1Doessuchataxsystemraiseapositiveornegativeamountofrevenuewhentl<第17 Consideranauctionofantiquequiltstocollectors.Isthisaprivate-valueorcommon-value如果競價增量是l美元。那么，在這個利潤最大化的英國式拍賣中，保留價格應(yīng)該是多少?（編者注：拍賣者并不清楚每個競價者的評價，只知道對某個特定的競價者而言，他是高）incrementof$1.Whatshouldthereservationpricebeinaprofit-maximizing答：在這個利潤最大化的英國式拍賣中，保留價格0（88（810（10，8）合出現(xiàn)的概率都是0.25。令r表示拍賣者的保留價格，那么：（8，9，9，100.2580.2590.2590.2510r9r（09，9，100.2500.2590.2590.25109792（0，10，10，100.2500.25100.25100.2510107.5102.50時，拍賣者可以獲得最大利潤。SupposethatwehavetwoCopiesofIntermediateMicroeconomicsSupposethatwehavetwoCopiesofIntermediateMicroeconomicstosellto(enthusiastic)students.Howcanweuseasealed-bidauctionthatwillguaranteethatthebidderswiththetwohighestvaluesgetthebooks?的期望收益是（其中“Prob”代表“概率”：Prob(b1min{b2,b3})[v1min{b2,1項是投標(biāo)人l2l勝出時，他所享有的消費者剩余。如果b1min{b2b31獲得的消費者剩余為零，從而也就沒有必要考慮包含Prob(b1min{b2b3})假定v1min{b2b3}，那么投標(biāo)人1就會使他勝出的概率盡可能大，他可以通過設(shè)實現(xiàn)這一點。另一方面，假定v1min{b2b3，那么投標(biāo)人1就會使他勝出的概4．考慮原書中Ucom公司的例子，這種拍賣設(shè)計是有效率的嗎?它使利潤實現(xiàn)了最大ConsidertheUcomexampleinthetext.Wastheauctiondesignefficient?Diditmaximize：（1）政府將經(jīng)營許可證授予對此項經(jīng)營評價最高的企業(yè)，從這層意義上講，這種（2）它沒有使拍賣者實現(xiàn)最大利潤，因為成交價格AgametheoristfillsajarwithpenniesandauctionsitoffonthefirstdayofclassusinganEnglishauction.Isthisaprivate-valueoracommon-valueauction?Doyouthinkthewinningbidderusuallymakesaprofit?答：（1）是一個共同價值拍賣，因為獎品的價值對所有競標(biāo)者都是相同的（2）第18 技1．假定生產(chǎn)函數(shù)為f(xxxx2 1Considertheproductionfunctionf(x1,x2)=x21x22.Doesthisexhibitconstant,ordecreasingreturnstof(tx,tx)Considertheproductionfunctionf(x1,x2)=x21x22.Doesthisexhibitconstant,ordecreasingreturnstof(tx,tx)t2x2t2x2tfx,xtfx,x4 12 12．假定一生產(chǎn)函數(shù)為f(xx)x2 1Considertheproductionordecreasingreturnsto.Doesthisexhibitconstant,111 f(tx,tx)4txt t6f(x1,x2)tf(x1,x2223 3．柯布一道格拉斯生產(chǎn)函數(shù)為f(x1x2)Axaxb。其規(guī)模報酬的情況取決于a+b1a+b值分別是多少TheCobb-Douglasproductionfunctionisgivenbyf(x1,x2)=Axa1xb2.Itturnsoutthetypeofreturnstoscaleofthisfunctionwilldependonthemagnitudeofa+b.Whichvaluesofa+bwillbeassociatedwiththedifferentkindsofreturnstoscale?答：利用2題的方法，給定t>1，可得f(tx,tx) axtabf(x1x2 13x2Thetechnicalrateofsubstitutionbetweenfactorsx2andx1is-4.Ifyoudesiretoproducethesameamountofoutputbutcutyouruseofx1by3units,howmanymoreofx2willyou答：12xMRSdx221Trueorfalse?Ifthelawofdiminishingmarginalproductdidnothold,theworld’ssupplycouldbegrowninaInaproductionprocessisitpossibletohavedecreasingmarginalproductinanandyetincreasingreturnstoInaproductionprocessisitpossibletohavedecreasingmarginalproductinanandyetincreasingreturnsto時規(guī)模報酬仍然可能出現(xiàn)遞增比如柯布—道格拉斯生產(chǎn)函數(shù)fx,x 1/22/ 22123/22/1/24/ 0 11xx4912出遞減，同時，對任意的t1f(txtx12x23)t7/6x1/2x2/ 第19 利潤最大Intheshortrun,ifthepriceofthefixedfactorisincreased,whatwillhappentomaxpf(x，zwxrzmaxpf(x，zwxrzrz中。所以r的提高會引起利潤的下降。Ifafirmhadeverywhereincreasingreturnstoscale,whatwouldhappentoitsprofitspricesremainedfixedandifitdoubleditsscaleoff(txtf(xx，其利潤為pf(xwx企業(yè)生產(chǎn)規(guī)模擴大一倍后，其利潤是pf(2x2wx2[pf(xwxIfafirmhaddecreasingreturnstoscaleatalllevelsofoutputanditdividedupintotwoequal-sizesmallerfirms,whatwouldhappentoitsoverallprofits？pwmaxpf(xwxpf(x*wx*pwmaxpf(xwxpf(x*wx*x*12[pf ) wx]pf(x)*** Agardenerexclaims:“Foronly$1inseedsI’vegrownover$20inproduce!”Besidesfactthatmostoftheproduceisintheformofzucchini,whatotherobservationswouldacynicaleconomistmakeaboutthissituation?Ismaximizingafirm’sprofitsalwaysidenticaltomaximizingthefirm’sstock（1）在一個具有完全確定性的環(huán)境中，企業(yè)的未來利潤流是已知的，那么這些利潤現(xiàn)值就是企業(yè)的價值，用公式表示，就是V(1r)6pMP1w11？IfpMP1>w1,thenshouldthefirmincreaseordecreasetheamountoffactor1inorderincreasemaxpf(x)pMPw 1果x2的價格下降，那么果x2的價格下降，那么x1的使用量會發(fā)生什么變化？該廠商的利潤水平會有什么變化？Supposeafirmismaximizingprofitsintheshortrunwithvariablefactorx1andfixedfactorx2.Ifthepriceofx2goesdown,whathappenstothefirm’suseofx1?Whathappenstothefirm’slevelofprofits?的表達(dá)式可知w2的下降不會影響x1的使用量，但會提高它的利潤Aprofit-maximizingcompetitivefirmthatismakingpositiveprofitsinlong-runequilibrium(may/maynot)haveatechnologywithconstantreturnstoscale.利潤pf(xLwxL0xL而言，會選擇t第20 成本最小Provethataprofit-maximizingfirmwillalwaysminimizecosts.maxpf(x)wxpf(x*)w對于給定的qf(x*)minws.t.f(x)pf(x')wx'pf(x*)wx*Ifafirmisproducingwherethesame2,whatcanitdotoreducecostsbutMP1/1MP2/MP1/1MP2/Supposethatacost-minimizingfirmusestwoinputsthatareperfectsubstitutes.Ifthetwoinputsarepricedthesame,whatdotheconditionalfactordemandslooklikefortheinputs?產(chǎn)量是q，那么該廠商的條件要素需求函數(shù)為：x10qx2qminx1x10,x2x1由于約束條件和目標(biāo)函數(shù)式相同，所以不論x1x2的取值如何，廠商都可以達(dá)到最小成x1=0到qx2qx1。Thepriceofpaperusedbyacost-minimizingfirmincreases.Thefirmrespondstothischangebychangingitsdemandforcertaininputs,butitkeepsitsoutputconstant.Whathappenstothefirm'suseofpaper?wx0，其中x(x1,......xn)，w(w1 wn)不等式wx0依然成立，從而企業(yè)的產(chǎn)量可以維持不變。如果除紙以外的其他某些要素需求不變，即xiwi0，i=2,3……n有x1w10，由于w10x10變化(i)和要素需求變化xi，顯示的成本最小化理論會導(dǎo)出什么不等式Ifafirmusesninputs(n>2),whatinequalitydoesthetheoryofrevealedIfafirmusesninputs(n>2),whatinequalitydoesthetheoryofrevealedcostminimizationimplyaboutchangesinfactorprices(△ωi)andthechangesinfactordemands(△xi)foragivenlevelofoutput?假設(shè)在q的產(chǎn)量，在q的產(chǎn)由（1）式-（2）式就得到21Whichofthefollowingaretrue?(1)Averagefixedcostsneverincreasewithoutput;averagetotalcostsarealwaysgreaterthanorequaltoaveragevariablecosts;(3)averagecostcanneverrisewhilemarginalcostsaredeclining.F ，所以AFC隨著Q的增加而減少Q(mào)ACAVCAFCQQ2當(dāng)02Q2TC(Q)3Q 2QQ2當(dāng)02Q2TC(Q)3Q 2 3Q6當(dāng)Q 121Q0Q1Q2QQ1 1 MC(Q)AC(Q)33Q3 Q36Q則當(dāng)2Q3時，MCACAfirmproducesidenticaloutputsattwodifferentplants.Ifthemargin