r, this equation is graphed in figure 1.

Transcription

1 Washigto Uivesity i St Louis Spig 8 Depatmet of Ecoomics Pof James Moley Ecoomics 4 Homewok # 3 Suggested Solutio Note: This is a suggested solutio i the sese that it outlies oe of the may possible aswes to the questios i the homewok Chapte Questio 3 a Pluggig i the cosumptio ad ivestmet fuctios ad the values fo G ad T give i the questio, the cuve is give by: ( 75) + 75( ) Fo {,}, this equatio is gaphed i figue Figue b The cuve is detemied by equatig demad fo ad supply of eal moey balaces The supply of eal balaces is /5 Thus, settig this equal to moey demad: 5 5 +

2 The cuve is gaphed, fo {,}, i figue above c Fom the ad equatios, it follows that Pluggig this back i eithe equatio, the This equilibium poit is depicted i figue above d If Govemet puchases icease fom to 5, the the cuve becomes 9 Figue depicts this chage The cuve shifts to the ight by Figue By equatig the ew cuve with the oigial cuve, it follows that Ad hece, equilibium output is give by Theefoe, a icease i govemet puchases causes the equilibium iteest ate to ise fom 6 pecet to 7 pecet, while output iceases fom to, as depicted i figue e If moey supply iceases fom to, the the supply of eal balace is ow /6, ad so the equatio becomes: 6 +

3 Figue 3 depicts this chage The cuve shift to the ight by because of the icease i eal moey balaces Figue By equatig the ew cuve with the oigial equatio, it follows that Substitutig this ito eithe equatio, equilibium output is give by 5 Theefoe, the icease i moey supply causes the iteest ate to fall fom 6 pecet to 55 pecet, while output iceases fom to 5 This is depicted i figue 3 f If the pice level ises fom to 4, the eal moey balaces fall fom 5 to /45 The equatio the becomes: 5 + To detemie the ew equilibium iteest ate, this ew cuve is equated to the oigial equatio to yield: Substitutig this ito eithe the o the equatio, the equilibium output is give by 975 Theefoe, the ew equilibium iteest ate is 75 ad the ew equilib ium level of output is 975, as depicted i figue 4 below Fom the figue, it is also see that the cuve shift to the left by 5 because the icease i the pice level educes eal moey balaces 3

4 Figue g To deive the AD cuve, the ad equatios ae solved fo as a fuctio of P To do so, both equatios ae solved fo, give that M: Combiig both equatios, it follows that: 7 ( / P) ( / P) This AD cuve is gaphed i figue 5: / P P Figue

5 If fiscal policy iceases as i pat (d), the ew AD cuve would be give by the cuve i pat (d) ad the oigial cuve 9 ( / P) Solvig fo : ( / P) / P By compaig this ew AD cuve to the oe peviously deived, it ca be see that the icease i govemet puchases by 5 shifts the aggegate cuve to the ight by If moey supply iceases as i pat (e), a simila deivatio shows that the ew AD cuve is give by: / By compaig this ew AD cuve to the oe oigially deived, it is see that the icease i moey supply shifts the AD cuve to the ight P Chapte Questio 7 a If all shocks to the ecoomy aise fom exogeous chages i the demad fo goods ad sevices, the all shocks ae to the cuve Suppose a shock causes the cuve to shift fom to Figue 6 shows what effect this has o output ude the two policies Figue 6: shock Holdig the Moey Supply Costat Holdig the Iteest Rate Costat 5

6 Output fluctuates less if the FED follows a policy of keepig the moey supply costat Thus, if all shocks ae to the cuve, the the FED should follow a policy of keepig the moey supply costat b If all shocks i the ecoomy aise fom exogeous chages i the demad fo moey, this meas that all shocks ae to the cuve If the FED allows a policy of adjustig the moey supply to keep the iteest ate costat, the the cuve does ot shift i espose to these shocks the FED immediately adjusts the moey supply to keep the moey maket i equilibium Figue 7 shows the effects of the two policies Figue 7: Shock Holdig the Moey Supply Costat Holdig the Iteest Rate Costat Output fluctuates less if the FED holds the iteest ate costat I this case, the FED offsets shocks to moey demad by chagig the moey supply so that all vaiability i output is elimiated Hece, if all shocks ae to the cuve, the the FED should adjust the moey supply to hold the iteest ate costat, theeby stabilizig output 3 Chapte Questio 7 Sice people demad moey balaces i ode to buy good ad sevices, it makes sese to thik that the pice level that is elevat is that of the goods ad sevices they buy This icludes both domestic ad foeig goods But the dolla pice of foeig goods depeds o the exchage ate Fo istace, if the dolla ises fom ye/dolla to 5 ye/dolla, the a Japaese good that costs 3 ye falls i pice fom $3 to $ This povides some ituitio fo the pice equatio a A highe exchage ate makes foeig goods cheape To the extet that people cosume foeig goods (a factio λ ), this lowes the pice level P that is elevat fo the moey maket This lowe pice level iceases the supply of eal balaces M/P To keep the moey maket i equilibium, icome must ise to icease moey demad as well Hece, a highe exchage ate equies a highe level of icome, ad so the cuve is upwad slopig 6

7 b I the stadad Mudell-Flemmig model, expasioay fiscal policy has o effect o output ude floatig exchage ates As show i figue 8, this is o loge tue i this cotext A cut i taxes (o a icease i govemet spedig) shifts the cuve to the ight, fom to Sice the cuve is upwad slopig, the esult is a icease i output Figue 7 e e e c I the stadad Mudell-Flemmig model, a icease i iteest ates educes ivestmet ad thus shifts the cuve to the left Similaly, a highe iteest ate leads to a eductio i the quatity demaded fo eal balaces Sice the supply of moey is fixed, icome must ise to clea the moey maket Cosequetly, the cuve shifts to the ight Thus, the exchage ate depeciates, icome iceases ad the pice level emais costat I this vesio of the Mudell-Flemmig model, the chage i the cuve is the same as i the stadad model To udestad how the cuve shifts, ecall that it is a set of poits (e,) that satisfies: λp d S M + ( λ) P f / e L D (, ) Hece, if iceases, the ight-had side becomes smalle To clea the maket fo eal balaces, the exchage ate falls popotioally Thus, the cuve shifts to the ight, fom to Figue 8 below depicts oe of the possible esults Uambiguously, the exchage ate depeciates ad the pice level iceases Howeve, the fial effect o output is idetemiate Figue 8 shows the case i which the icease i the cuve exactly offsets the decease i the cuve, so that output is uchaged But the esultat level of output will deped o the magitudes by which the ad cuves shift Note that i the stadad Mudell-Flemmig model, output 7

8 iceased uambiguously because the cuve was vetical, so that a eductio i did ot have ay effects o Figue 8 e e e 4 Chapte 3 Questio 6 a The atual ate of uemploymet might deped o ecet uemploymet fo, at least, two easos, suggested by theoies of hysteesis Fist, ecet uemploymet ates might affect the level of fictioal uemploymet Uemployed wokes lose job skills ad fid it hade to get jobs; also, uemployed wokes might lose some of thei desie to wok, ad hece seach less had fo a job Secod, ecet uemploymet ates might affect the level of wait uemploymet If labo egotiatios give a geate voice to isides tha outsides, the isides might push fo high wages at the expese of jobs This will be especially tue i idusties i which egotiatios take place betwee fims ad uios (eg costuctio, ca idusty) b The, i the fist peiod, the Phillips cuve equatio implies that: π π 5( u u ) ( u u ) That is, the uemploymet ate must be pecetage poits above the oigial atual ate u Next peiod, howeve, the atual ate will ise as a esult of cyclical uemploymet, as assumed i the questio Thus: u 5( u + u ) 5[( u + ) + u ] u + 8

9 Hece, the atual ate of uemploymet ises by pecetage poit If the FED wats to keep iflatio at its ew level (ie, π π), uemploymet i peiod must equal the ew atual ate u (as implied by the Phillips cuve) Hece, it follows that u u + I evey subsequet peiod, it is tue that the uemploymet ate must equal the atual ate Thus, this atual ate eve etus to its oigial level Ifomally, this ca be show by deivig the sequece of uemploymet ates: u 3 ( / ) u + (/ ) u u + 3 / u / ) u + (/ ) u u 5 / 4 4 ( 3 + u 5 ( / ) u4 + (/ ) u3 u + / 8 Uemploymet always emais above the oigial atual ate I fact, it ca be show that it is always at least pecetage poit above the oigial atual ate Thus, to educe iflatio by pecetage poit, uemploymet ises above the o igial level by pecetage poits i the fist yea, ad by o moe pecetage poits evey yea afte that c Because uemploymet is always highe tha it stated, output is always lowe tha it would have bee As a cosequece, the sacifice atio is ifiite d Without hysteesis, thee was a shot-u tadeoff but o log-u tadeoff betwee iflatio ad uemploymet With hysteesis, thee is a log-u tadeoff betwee iflatio ad uemploymet: to educe iflatio, uemploymet must ise pemaetly 5 Chapte 3 Questio 9 Table below shows the oveall level of iflatio ad the coe iflatio fo the yeas Table σ Oveall Iflatio Coe Iflatio

10 The CPI data was obtaied fom the Fedeal Reseve Ecoomic Database (FRED) The key featue to otice fom table is that the oveall level of iflatio is moe volatile tha coe iflatio (ie, iflatio excludig food ad eegy pices) I fact, the stadad deviatio fo the oveall level of iflatio is 67 wheeas that fo coe iflatio is oly 36 This diffeece eflects shocks to the pice of food ad eegy - especially eegy pices, which ae highly volatile Whe eegy pices, say, go dow, total iflatio will ise less tha coe iflatio This epesets a supply shock, which shifts the aggegate supply cuve ad the Phillips cuve dowwads