北大經(jīng)院微觀08作業(yè)題及答案08印過ans d

（班對。一般地，設(shè)線性齊次生產(chǎn)函數(shù)為Qf(K則QLf(KL,1)Lf(k，其中kKLMPLwf(kf(k)kw是關(guān)于k即K/L f(k 的一次齊次的C-D生產(chǎn)函數(shù)QKL1 Kw1。 按照定義，邊際技術(shù)替代率等于dx2

dx2MP1 根據(jù)替代彈性的定義可以算出CES的替代彈性為 1（這里CES為書上1標(biāo)準(zhǔn)形式QA[L1)K），對于不同的CES函數(shù)，各種CES函數(shù)中C-D生產(chǎn)函數(shù)的替代彈性為1（0）英文教科書Nicholson,Chapter11problem11.6page290Showthatfortheconstantreturns-to-scaleCESproductionfunctionq(KL)1/MPq1andMPq K

(LRTSL1Usethistoshowthat1/(1(KDeterminetheoutputelasticitIesforKandL.ShowthattheirsumequalsProve

1(KL)1/1K(KL)1/

q(q) =[ Kq=(K

1(KL)1/1L(KL)1/=[ Lq=(L

K

K)1 ( ln(L/K1∴=1-

dq Keq,KdKqKdqL eq,LdLqKL∴eq,Keq,L∵q(KL)(1)/Lq

∴∴

L)(1)/L=(KL)1/Lq(KL)1/ 或者直接用a問的結(jié)論MPq)1]11q q(q 英文教科書NicholsonChapter11problem11.7page292Consideraproductionfunctionoftheformq0 2KWhere0i1Ifthisfunctionistoexhibitconstantreturnstoscale,whatrestrictionsshouldbecedontheparameters0...3?Showthatintheconstantreturns-to-scalecasethisfunctionexhibitsdiminishingmarginalproductivitiesandthatthemarginalproductivityfunctionsarehomogeneousofdegreezero.Calculateinthiscase.Isq(tK,tL)tq(KL),0t<1 2tK3tLt(0 2K0t00當(dāng)00q1KL2KL2MPK 22 3

2

12L2K 1K2L2 1 1MP(tK,tL) (tK)2(tL)2

MP(K,L)

2

1 1

21K2L23 L

1K2L241 11 1K2L K/L2(K/1

1 11

21K2 22(K/d(K/d(KL)MRTSL,K K/英文教科書NicholsonChapter12problem12.3ProfessorSmithandProfessorJonesaregoingtoproduceanewintroductorytextbook.Astruescientists,theyhavelaidouttheproductionfunctionforthebookasqS1/2J1/Whereq=thenumberofpagesinthefinishedbook,S=thenumberofworkinghoursspentbySmith,andJ=thenumberofhoursspentworkingbyJones.Smithvalueshislaboras$3perworkinghour.Hehasspent900hourspreparingthefirstdraft.Jones,whoselaborisvaluedat$12perworkinghour,willreviseSmith’sdrafttocompletetheHowmanyhourswillJoneshavetospendtoproduceafinishedbookof150pagers?Of300pages?Of450pages?Whatisthemarginalcostofthe150thpageofthefinishedbook?Ofthe300thpage?Ofthe450th解：已知當(dāng)q=150時(shí)，根據(jù)qS1/2J1/2=>S=25；當(dāng)q-450時(shí)1 TC=12J=12q2/S

MC ∴當(dāng)q=150時(shí)，MC=4；當(dāng)q=300時(shí)，MC=8；當(dāng)q=450時(shí)，MC=12另法MC=12*((151/30)^2-25)Nicholson,Chapter12problem12.6Afirmproducinghockeystickshasaproductionfunctiongivenq2Intheshortrun,thefirm’samountofcapitalequipmentisfixedatK=100.TherentalrateforKv=$1,andthewagerateforLisCalculatethefirm’sshort-runtotalcostcurve.Calculatetheshort-runaveragecostWhatisthefirm’sshort-runmarginalcostfunction?WhataretheSTC,SATC,andSMCforthefirmifitproduces25hockeysticks?Fiftyhockeysticks?Onehundredhockeysticks?Twohundredhockeysticks?GraphtheSATCandtheSMCcurvesforthefirm.IndicatethepointsfoundinWheredoestheSMCcurveintersecttheSATCcurve?ExinwhytheSMC