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Intermed Macro Theory

by: Madie Schinner

Intermed Macro Theory ECN 101

Madie Schinner
GPA 3.57


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This 9 page Class Notes was uploaded by Madie Schinner on Tuesday September 8, 2015. The Class Notes belongs to ECN 101 at University of California - Davis taught by Staff in Fall. Since its upload, it has received 70 views. For similar materials see /class/191894/ecn-101-university-of-california-davis in Economcs at University of California - Davis.


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Date Created: 09/08/15
University of CalifomiaDavis TA Larry Hu ECN lOlIntermediate Macro Email ucdhuucdavisedu Handout 2 1 Key Concept Review 2 Problems 1 Consider an economy that only produces and consumes bathing suits durable good suntanlotion nondurable good and ights to Cancun service Use the data below Using 2005 as the base year compute the following statistics for 2006 2005 2006 bathing suits price 30 40 cplantity l 00 l 50 suntan lotion price 635 7 5 quantity 200 300 ights to Cancun price 200 600 quantity 30 0 a nominal GDP b real GDP c GDP de ator d CPI Why do the CPI and GDP de ator give different characterizations of how much prices have risen from 2004 to 2005 Discuss which you would recommend as the more accurate re ection of the cost of living in this particular case and explain your reasoning Arguments exist for both choices 2 Consider the following production function Y 9KAl3LA23 where the level of capital in the economy is 100 and the level of labor in the economy is 100 3 Compute the equilibrium real wage and real rental rate on capital b Compute the total payments to labor and that to owners of capital UmvelsllynfcallfnmlarDavls TA lasmLee ECN lOlrSummHZOOX Emmi lawle ucdavlsedu I Revlew ofSolow Model A Sugply Slde Technnlngyls de ned as nut wnmcummunnv mu whchwe assumemn have 1151 umsm scale En zY 4mm lrwe wantedtn cxpressdnngsmperwmkenems we setz 1L a YL FKLl Nmahm kKL may YL we guy rm The musesmepmmmmrumunn x mng 7413 13 Flguxe l shwws a gaph an hnldlngK cmnstanl Igunl FWD Slde Recall fmm Ch 2 manhe dcmandfm nds and semcesls bmkm dwinan 4 smegma Y 0 1 6 NX mm s nlww Mndel we make me fullnwmg slmpllrymg assumpnnns ItlsadnsedrecmnmyanX0 We ellmlmle me mle wr gnvemmem than 15m G at 1 1e s m an afmnpmsaved Ths as a hehwse hhawh as he smngs ha e h v Thnsme unnmxmsmqempexvmxkzxs Nme ha he meshhem rhhehah wl have he same shape as he antpm rhhenahhm wm necessmlybe lavex hah v sahee n 5 s 51 See Figure 2 rah haw he meshhem ruhenah laaks hhe Figul 2 v MM FKL sFkL K 4 waging c Accumulauon of Caplml As we hawe seen he amanm afcapml peh kazns he ae eh he he 1m armnpa maehvanahxe ha wm m peh 5a he nex q es mn we mhs ask kaznccaxdmg a he Sainme 1 as wha ae enhahes he eve af eapuax ah ah eeahamyr We laak a he aeeumhsanah afcapnnl Accnm mmnafcapml s aeraheaas he amaum arhew eapnax ehea ea ah a gaveh yzar mahhs he amaum afcapnnl as an he same yzu eah eapua he hasw Each yzar a eenaah fm an afcapnnl aepzeemes ah wears am ahaas has Ta qnmhfy39hls we have mmnhmg and he dzpnziz nnntz wheh as smplythe mash afcapnnl ha wears am an a gaveh yzar Far example mhe ayeregemeehme lasts 20 years Lhm apprmnmalely 120 hr 5 hr Lhe manhmes wm wear am 5 wm be Lhe depreuaunnrate thm Depreclahnnrale a Thus Lhe amnunt hr eapuex mm m a year due in depreclahnn ax Fxgure 3 graphs depreuaunn Figure 3 Utwuakw m K Na we have a mm m placetn examme hnthe Snlnwmndel predt s whatLhe 1eye nfcapxtahsm meemmy LetAK anme aunn hr capxta m a gven year ew capxta created 7 emuhg capxta my my men ew capxtal created mmng eepua 1m xhyeeuhehz e Depreuaunn ye ax Depreclahnn AK AK ems aeshe may sme lzvel nfczpiml as Lhe 1eye nfcapxta where Lhe 1eye hr mvesmet depreuaunn nrwhae AK a mans Evil Lhasxs rm ehehge m Lhe 1eye hr eepua IN THE lHNG 1am ACCHRDING m THE SHLHWMHDEL ANEcuNuMY WILL ALWAYS FIND ITSELFAT m5 STEADYSTATE lEVEl HF CAHTAL FxgurEA shew why Lhatwnuld be Lhe case 11ng d all AK Jill T WSY 3 I 47gt k X K Nale um K teadysulz level afcapnnl Al hls pamllmeslmem deprecm an llws me level afcapnnl wl xemam the sum smee AK n Lel39s Junk m wlm umldd happn lull ecammyms Manymhexlevel afcapnal Scemln m Snppuse llle ecammy ms m K lm was the level afcapml the mam armveslmem umlddbe gleam than me ammlm afdepzecunan AK gt D New cap al wl be genenleamllle eeammy and the capital smckwl Increase Thus we wdlmvve amyfmm K Thls pmcess wdlcammvz um we nach lz studystnlz level a cap al K Scemln on Snppuse llle ecammy ms m K1 lm was the level afcapml the mam afdzpzecutlnn umlddbe gleam than me ammlm anmeslmem AK lt n Mme cap al wl be lnsl ale m dzptecutmn than xeplemshzdvu lnvesfmenL thus the capllnl slackpewmlm umlddfa ms pmcess wnld mm mm we reach the steadysme up ll Thu me umme duly me Inward me atbth level u ume D NumzriczlExample Snppuse anecanamycmbe clumtenudbythe mam mm Y F Kl Km Snppuse um ll depreclanannte ls lEI39 and the savmg ml ls 2w Mel assume mule mammymmeleml l anddu abaxls xedf mu a Find the steadystate level of capital Step 1 Use the fact AK sY 7 dK We know that at steadystate AK 0 thus it must be that sY dK Step 2 Substitute Y AK13L23 Thus we get sAK13Lz3 dK Step 3 Rearrange the equation so that you get K on one side of the equation 23 23 SA which we can simplify to SA K 3 Solving for K we get 23 32 21 Step 4 Plug in the given values of s A L and d 32 W 0201100 3 010 K 28284 b Solve for the steadystate level of output Since Y AKmLm Plug in the given values of A and L and the derived value of K Y 1282841310023 14142 c Solve for the steadystate level of consumption Use fact that C 1sY C 17 02 14142 11314 11 Economic Growth in the Solow Model What does the Solow model have to say about longrun economic growth Let s start by using our usual production function Y AK13Lz3 What we are interested in is the growth of output over time That is we want to nd gy Using our growth rates properties from Chapter 3 we can easily derive this as gy gAlBgZBg Ifwe cssumc mm the Snlww mndel mum mdL cu cum cunsumuun cu 0 cud a 0 Leavmgusthh gy 15 But m nu lnngd39un capml stuck mu be u suudysuu when AK 0 At 01mm 3 0 Thus xtmustbe Lhatm39he 1mgcuu gy 0 Thus uuuu sucfucc xtwwuld appezrthatthe Snlnw mndel xsnntveryuseful m explmuglmgmm ecnnnmxc gwwth ekmw Lhatnverthe nngmnmnstcnumnes such usuu UmtedSmes have emnyed gqu rates nf nuwul nf apprnxxmalelylnn pu year The Snlnw mndel wnuldbe unable cu explmnwhythsxs nbsewed Impnrlanl Cnnclun39nn Then is In Incng ecnnnmic gmwll wwtl ufY under llle Soan Mum D1 Gmghlcal Analysls Whmhuppcns m mlpul cud cupcm xfwe adgust same nf39he mucus m nu Snlww mndd7 In pzrumlzr whatwnuld nccur xf39he suvmgsmc M 0m depreuaunnmle were m change Scenariu 01 Change in the wings nle Suppnse cu ccmumywus u may suu mmzlly Suppnse further thale mugs cm were in snmehnw mums FxgmeS shnws such u scemnn F39gun 5 lmh ythz ecnmmywas m Kr The mamas m the mug mt swam msmm curve m snm up At Kr msmemxsmwgma enhanthz capitahhatdepxecxams AK gt o and the capital slack wm gmw The capital stack wm canhmlz a gmwunh me ecnmmymachzs a new smadysme m K2 Smriz 2 Cling ind mumMme Agamsuppwg we smnatasma yslam lzvelnfcapml xrmecmmysawaaemm m the me nfdepxecxahnn what effect mum n have an the smadysm Figure 5 mp lsanalyu m smatmn F39gul 5 q A decrease m the deprecxatmn mt causes the deprecxahnn m a get mm tl39ns 15 me because we slap nf hz deprecxahnnlmz xs mwsmallzr Thusthe deprecxahnncum snms all Ann nngma smadysta e level K1 msmmsgmmn n deprecxatmn and Ms AK gt a As a dam quotsum the capital slack mum mamas mm we with a new sleadystace lzvel m K2 IV Convergence and Transmon Dynamms Cnnvexgence deals mm m qnemn whether pm cannmzs can each up a ricth cannmzs m m 1mg nm Ecummlss mg m umvugutecanuccur 1fwm ecnmmxzs have the same museum cams thz am swings rate pupnlahnn mw h me techmlngwal progress production function etc but start with different initial levels of capital stock then in the long run they will enjoy the same steadystate level of capital per worker and hence the same level of output per worker One good example of this idea of convergence occurred in the aftermath of the American Civil War It s not unreasonable to assume that the economies of the Southern states and the Northern states had the same underlying economic features both before the Civil War However after the Civil War the war devastated the capital stock in the southern states with crops buildings railroads and livestock destroyed while the capital stock in the northern states were relatively unaffected The result was that the southern states saw a drop in its level of capital per worker The figure below shows that in 1865 the North was at or near its steady state level of capital while the South was significantly below the steady state At the lower level of capital per worker Ak gt 0 for the South thus we would expect growth of capital per worker and income per worker Since we have assumed that the North was at its steadystate the Northern states would experience no growth Ak 0 Eventually the South would catch up to the North in terms of output per worker In the long run poorer countries with similar economic features will catch up to richer counties If however countries have different economic features then convergence will not occur Conditional convergence argues that different counties have different steady states Counties converge to a steady state determined by different underlying variables In the figure below suppose that there are two countries the United States and Ghana that have the same underlying economic features except that Ghana has a higher population growth rate As a result the United States and Ghana will have different steady states Ghana can achieve economic growth in the short run because it has a low level of capital per worker but once it reaches its steady state it will stop growing Ghana will never reach the income level of the United States


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