Part I. Labor- Leisure Decision (15 pts)

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1 Eon 509 Sping 204 Final Exam S. Paene Pa I. Labo- Leisue Deision (5 ps. Conside he following sai eonom given b he following equaions. Uili ln( H ln( l whee H sands fo he househ f f Poduion: Ah whee f sands fo he fim Time Endowmen of Househ l h H 00 Suppose he govenmen axes he oupu of he fim a ae, τ, and uses he ax evenues o bu a good ha povides no value o soie. a Show algebaiall ha his pe of poli has no effe on wok hous b solving fo he equilibium (0 poins.the budge onsain of he househ is wl 00w ( f 2. The govenmen budge onsain is g (2 3. Uili maximizing ondiions U / l 4. (3 U / l w 5. Goods Make Cleaing Condiion H g Ah (4 6. Pofi maximizing ondiion w ( A (5 7. Fom uili maximizaion ( Al (6 8. Subsiue ou fo onsumpion in Eq 6 ino househ budge onsain o aive a. 9. ( ( Al / 00( A (7 0. ( 00 h ( This is h 2. To ge onsumpion, jus plug h ino (4 b In wods explain, wh his poli has no effe on equilibium wok effo. (5 ps The inuiion is ha wih log uili, hee is no pie effe. The subsiuion effe offse he inome effe. The ax on fim s oupu onl affes he wage in he househ budge onsain. Wih he ax evenues being hown ino he oean, hee is no wealh effe assoiaed wih he poli. Hene he poli does no hange wok hous. Pa II. Savings and Govenmen Finane (50ps

2 All of he quesions in Pa II use he Ovelapping Geneaions model whee people live wo peiods. Eah geneaion has he same numbe of people. Pefeenes ae ln( ln(. Eah agen is endowed wih e unis of oupu when oung and e unis of oupu when.. Suppose hee is a lump-sum ax/ansfes when he agen is oung equal o Tx and a lump-sum ax/ansfe implemened when he agen is equal o Tx. The fis peiod budge onsain is s e Tx. The seond peiod budge onsain is e Tx ( s whee s is savings and is he eal inees ae. a. Deive he Ineempoal budge onsain (3 ps Take seond peiod budge onsain and solve fo s. ( e Tx s and subsiue in o he s peiod budge onsain o lg ( e Tx e Tx and wih some algeba we aive a he ineempoal budge onsain b. Deive he uili maximizaion ondiion (3 ps U / U / /(. Use (a and (b o deive he savings funion. Veif ha savings will no deease if he eal inees ae ineases. Assume e -Tx 0 (4 ps (b implies ha. Now subsiue ino he ineempoal budge onsain o ge e Tx ( e Tx and solve fo e Tx [ e Tx ] eolf Txolf Finall, s e e Tx s e Tx Take he deivaive wih espe i 0 2 ( 2. Solve ou he equilibium whee hee is no govenmen poli. Give he ondiion fo whih he ompeiive equilibium is no Paeo opimal. Povide some inuiion fo his esul. (0 ps When hee is no govenmen, e and e. The inees ae is deemine b he uili maximizing ondiion U / e i U / e /( i 2

3 The equilibium is Paeo Opimal if he inees ae is negaive, whih equies e e. When people ae bee endowed when oung, he despeael wan o save. Howeve, hee is no one o lend o. Thus he inees ae in equilibium mus be suffiienl unaaive (i.e. negaive so ha he oung will be happ wih saving zeo in equilibium. 3. Assume he ondiions exis in Quesion 2 above so ha he equilibium unde auak is no Paeo Opimal. Fuhe, assume he govenmen implemens a pa as ou go pension ssem ha allows eah geneaion o enjo he same level of onsumpion when oung and, i.e., =. Solve ou he equilibium fo his eonom (0 poins If hen =0. The govenmen budge onsain is Tx =T. Goods make leaing ondiion is e e. Sine =, i follows ha ( e e / 2. Now go o he househ budge onsains whee s=0. e Tx and e2 T,. Fom he fis peiod budge onsain and ou soluion fo, we know ha Tx e e e e [ e e ]. You an hek ha fom seond peiod househ onsain ha T e e e e [ e e ] Tx Wha is Riadian Equivalene? Use he esuls in quesions (2 and (3 o deemine whehe Riadian Equivalene hs in his eonom. Explain wh Riadian Equivalene eihe hs o fails o h in his eonom. (0 poins Riadian Equivalene is he esul wheeb a hange in lump sum axes has no affes on an eonom s inees ae and eal alloaions. A ompaison of he esuls shows ha Riadian Equivalene fails o h in his eonom. The eason is ha Riadian equivalene onl hs if he ineempoal budge onsain of eve geneaion is unhanged, bu i is leal hanged fo he alive a =. The ge a ansfe fom he oung alive in ha peiod. 5. Wha is a full funded pension ssem? Use he Ovelapping Geneaions model o explain wh i bee han a pa as ou go ssem in ems of equilibium ouomes. (Noe: You do no need o ompue equilibium in he OG model when a full funded and pa as ou go ssems ae implemened. Insead, ou ae being asked o epo and inepe he findings fom lass. (0 poins. A full funded ssems is one whee he onibuions of a oung agen equal he amoun he is paid ou as an peson plus a eun on hose savings. In he model wih leisue, we found ha i leads o wie as muh wok effo b oung agens and so wie as muh GDP. The eason fo his is ha he full founded does no diso oung people s wok effo. In he pa as ou go, he ge a gif fom he govenmen, funded b labo axes b he oung. Alhough hee is no pie effe fom he ax hange, he lump-sum gif

4 when geneaes a wealh effe making hem wan moe leisue and moe onsumpion IV. Business Cles (35 poins. Explain how Kdland and Peso (986 doumen he business le fas/egulaiies. Wh do he onlude, ha business les ae a monea mh? (8 poins Fis, he deend eah ime seies using he HP file. In his wa, he have deviaion, whih is log oupu less log of end. The hen ompue he sandad deviaion of he deviaion fo eah ime seies. The hen alulae he oelaion oeffiien beween deviaions in ohe ime seies wih he deviaions in oupu. The use he oelaion oeffiien o idenif polial, ounelial wih leads and lags. The onlude ha he business le is a monea mh based on he oelaion oeffiiens of he monea base and M2. Alhough M2 is polial wih a lean, he monea base, whih is unde he onol of he enal bank, shows ve lile oelaion and lead. 2. Wha ae some similaiies and diffeenes beween New Kenesian Eonomis and Real Business Cle Theo? In ou answe, be sue o ommen on wh monea poli is neual in he Real Business Cle wheeas i has eal effes in he New Kenesian model. (7 poins Similaiies ae he ae deived fom mio heo, uili maximizaion and pofi maximizaion. The ae diffeen in ha RBC assumes ha all pies ae fee o adjus in pefel ompeiive makes. In he New Kenesian model Calvo piing assumpion in a non-ompeiive seing. Speifiall, onl a faion of fims in an peiod an espond and adjus hei pies. All ohes anno. Those ha anno will see he demand fo hei podu inease as ohe pies in he eonom ise beause hei goods ae heape han he aveage pie. This means ha he AS uve is upwad sloping. In onas in RBC, he AS is veial. If he pie level is highe, he nominal wage will be highe, and so no hange in labo emploed o oupu. Wih a upwad sloping AS, an inease in AD hough a monea expansion will hange oupu. Fo RBC, i will have no effes sine he AS is veial. 3. Conside he Neolassial Gowh Model wihou leisue in he uili. The model is given b Pefeene ln( 0 Poduion: A Resoue onsain: ( ( k h k ( k a. Wha ae he uili maximizing ondiion(s fo he househ? (2 ps

5 U / U / /( b. Wha ae he pofi maximizing ondiions fo he fim? (2 ps w ( / h k / k. Wha is he elaion beween he enal pie of apial and he ine es ae fom he banking seo zeo pofi ondiion? ( ps k d. Solve fo he balaned gowh pah apial sok fo his eonom (5 ps BGP, implies gowh pah of onsumpion is onsan so ha is onsan fom hh uili maximizing ondiions. Fom banking zeo pofi, his implies ha k is also ( onsan. Wie ou / k as A k h. Sine h = is k k ( onsan, hen use his elaion o show ha he gowh ae of pe apia apial is equal o (+γ. We an show ha pe apia oupu and onsumpion mus also gow a his ae. Fom he hh uili maximizaion, we have ha ( and so ( ( k. Now o finish, we use his value fo k wih he Maginal Podu ondiion and have ( ( ( A( k whee we use he esul ha h=. Finall, we solve fo k /( A ( ( ( k e. Explain how ou would assign paamee values o β, δ, θ, γ and A in mahing he model s balaned gowh popeies o he long-un US gowh expeiene. (5 ps We ge γ b using he obsevaion fo US pe apia oupu gowh ogehe wih esul ha / We ge θ using he obsevaion fo he apial shae of inome wih he model esul ha kk / We se A= as we ae fee o hoose unis of measuemen. We ge δ b using K o GDP and X o GDP fo he US ogehe wih he law of moion fo he apial sok, ( k ( k x whee we exploi he BGP esul ha k ( k. Finall, we go bak o he pofi maximizing behavio k / k and solve fo he enal pie using he alibaed value of θ as well as he K o GDP aio fo he US. Given ou alibaed value of δ, and he zeo pofi ondiion fo he banks we impue he eal inees ae. Finall, we use he Househ MRSC wih he esul ha / o solve fo he value of β 4. Explain how Kdland and Peso deemine how muh of US business les ove he poswa peiod an be aouned fo b TFP shoks? (5 ps Fis he alibae all he paamees ohe han TFP shoks o he Long Run US expeiene. Nex, he impue US TFP using he imes seies fo GDP, Capial

6 and hous. Then he esimae an AR( poess given b z z The eo ems, i.e. he diffeene fom he aual TFP and pedied hen allow ou o deemine he mean and vaiane of he shoks. The hen feed hese shok poess ino he model and hen solve fo he ompeiive equilibium. The las pa is o ompae he model s pediions fo volaili and oelaions o he ones he doumen fo he daa.

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