Fall 2014 Final Exam (250 pts)

Transcription

1 Eon 509 Fall 04 Final Exam (50 ps S. Paene Pa I. Answe ONLY ONE of he quesions below. (45 poins. Explain he onep of Riadian Equivalene. Wha ae he ondiions ha mus be saisfied fo i o h? Riadian Equivalene- a hange in lump-sum axes has no eal effes on he eonom, eihe in ems of poduion and onsumpion alloaions o eal pies. Thee ae 3 ondiions ha ae needed: ( axes ae lump-sum ( hee ae no edi onsains on househs and (3 he same peson ha eeives oda s ax inease o deease is he same one who will eeive he fuue ax inease o deease.. Wha is he heo of Raional Expeaions? Use a mahemaial example o illusae he onep. Raional expeaions is an assumpion ha people use all available infomaion ino aoun when foming an expeaion and a in a wa ha is onsisen wih hose beliefs. Mahemaiall, i oesponds o he ondiional expeaion of aa vaiable. As an example onside he following AR( z. 95z. Sine he expeaions opeao is linea, we have (CE E z }.95z E{ }. { Assuming ha he mean of ε is zeo, he ondiional expeaion of z + is jus.95 z. This is he aional expeaion of z. The aional expeaion (i.e., he ondiional expeaion is ve diffeen fom he unondiional expeaion. To alulae he unondiional expeaion we ieae bakwads on he em A on he lef hand side of (CE. Given ha (AR mus appl in all peiods, we an ewie he equaion as z 95. If we oninue his bakwad ieaion foeve, we aive a [.95z ].95 z. 3 z Now if we appl he expeaions opeao o boh sides, and mainain ou assumpion ha he mean of he eo em is zeo eah peiod, hen we find he unondiional expeaion of z + =0. Tha is o sa ha if ou did no have an infomaion a ime, (i.e., he value of z, hen ou bes guess fo z + is zeo. 3. Explain how maoeonomiss make welfae ompaisons assoiaed wih alenaive poliies. Illusae wih an example. To ompae welfae aoss alenaive poliies, maoeonomis ompue he equilibium alloaions and pies unde he alenaive poliies, and hen ompue how muh onsumpion in one of he equilibium mus be saled up (o down o give he househ ha same uili aoss he wo equilibium. Fo example, in a sai model in Pa II below: Conside as an example a poli expeimen wheeb he ax ae on labo inome would be aised fom.40 o.60. Househ welfae will be lowe unde he highe ax ae. Thus, we would like o know b how muh we would have o inease he onsume s onsumpion so ha his uili is equal o he uili ha he ealizes wih he lowe ax ae of.40. Mahemaiall, we ae ineesed in finding he value of he saling fao, +, suh ha

2 log( ( 0.40 log(00 h( 0.40 log(( ( 0.60 log(00 h( 0.60 (3 Theefoe, (+ is he fao ha onsumpion mus be saled if hee is a hange in he ax ae fom 40% o 60% o leave people indiffeen o he hange. The welfae loss in onsumpion equivalens is. Pa II. Labo- Leisue Deision (30 ps Conside he following sai eonom given b he following equaions. Uili: ln( H f f ln( l whee H sands fo he househ. Poduion: Ah whee f sands fo he fim. Time Endowmen of Househ: l h H 00. Suppose he govenmen axes he wage inome of househs a ae, τ, and uses he ax evenues o bu a good ha povides no value o soie. Show algebaiall ha his pe of poli has no effe on wok hous b solving fo he equilibium (0 ps.the budge onsain of he househ is ( wl 00( w (. The govenmen budge onsain is 3. Uili maximizing ondiions U / l 4. (3 U / l ( w H g wh ( 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. To ge onsumpion, jus plug h ino (4 In wods explain wh his poli has no effe on equilibium wok effo. (0 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. 3 Wha is he Laffe uve? Wha would i look like in his eonom? (0 poins

3 The laffe uve depis he elaion beween he ax ae, whih anges fom 0 o, and he amoun of govenmen evenues. In his ase, he laffe uve is a sil ineasing uve. Pa III. Ovelapping Geneaions (80ps. Conside he following Ovelapping Geneaions model whee people live wo peiods. Geneaion is imes lage han geneaion -, i.e. N(=N(-. Pefeenes ae ln( ln(. Eah agen is endowed wih e =8 unis of oupu when oung and e =4 unis of oupu when. a. Wie down he househ s budge onsains in he peiod when he is oung and he peiod when he is. (0 ps The fis peiod budge onsain is s e. The seond peiod budge onsain is ae. 3 e ( s whee s is savings and is he eal inees b. Deive he Ineempoal budge onsain. (0 ps Take seond peiod budge onsain and solve fo s. e s and subsiue in o he s peiod budge onsain e e and wih some algeba we aive a he ineempoal budge onsain. Deive he uili maximizaion ondiions. (0 ps U / U / /( d. Use (a- ( o deive he savings funion. Veif ha savings will no deease if he eal inees ae ineases. (0 ps ( implies ha. Now subsiue ino he ineempoal budge onsain o ge e e and solve fo e [ e ] e Finall, s e e s e Take he deivaive wih espe o i 0 ( e. Find he Equilibium onsumpions and he eal inees ae. (0 ps

4 . When hee is no govenmen, e and deemine b he uili maximizing ondiion So =-.50 e. The inees ae is U / U / Now onside he same model bu whee hee is a wa fo he househ o soe some if is oupu when oung. Speifiall, assume ha he househ has aess o a efigeaion ehnolog b whih if i soes uni of oupu when oung, i has (-ρ unis of oupu when, whee 0. a. Wie down he househ s budge onsains in he peiod when he is oung and he peiod when he is. (0 poins The fis peiod budge onsain is s k e. The seond peiod budge onsain is e ( k ( s whee s is savings and is he eal inees ae. b. Wha ae he make leaing ondiions fo his eonom? (0 ps Goods make is e e ( k as alive have soed k and so i is pa of suppl in peiod. Savings make is jus N ( s 0. Find he Equilibium onsumpions and he eal inees ae. (0 ps The ke o solving he equilibium is o ague ha ρ=. This is a no abiage agumen. The ineempoal budge onsain would be 4 he same and given ha =ρ, i follows ha [8 ] and so ( 4( Pa IV. Govenmen Finane (30 poins. Conside a govenmen ha has he abili o pin mone. Wie down he govenmen s budge onsain in peiod. (0 M M ps G B Tx ( B P. Conside a govenmen ha does no have he abili o pin mone. Suppose ha he w las wo peiods. Show ha if he govenmen has a defii in one peiod i mus have a suplus in anohe. (0 ps Peiod g B Tx. Peiod G Tx ( B. 4

5 G Tx Ineempoal G Tx 0. Thus if G -Tx >0, hen G -Tx mus be negaive. 3. Again onside he ase of a govenmen wihou he abili o pin mone. This ime suppose he w neve ends. On aoun of a pas defii, he govenmen enes oda wih some ousanding deb, B 0 =B and inees pamens on ha deb B. Is i possible fo he govenmen o oll ove his quani of deb, B, eve peiod? Demonsae ou answe. (0 ps Yes, i is possible. Esseniall, he govenmen has o un a suplus eve peiod ha will exal equal he inees pamen. Take he budge onsain B ( B ( Tx G Se B Tx G. Then B + =B. ( IV. Business Cles (65 poins. Explain how o use he H-P file in Exel. In paiula, suppose ou have inpued quael US eal GDP daa in olumns A hu A50 in ou exel spead shee. Lis he seps o appl he file o his daa and obain he deviaions. (0 ps Sep : onve Real GDP seies ino log Sep : Highligh enie new olumn B-B50. Sep 3: In olumn pe in =HP(B:B50; 600. This euns end in C- C50. Sep 4. In olumn d, d=b= o obain deviaion.. Now ha ou have he end and deviaion omponens fom he end, explain how o alulae he volaili measue of a maoeonomi vaiable x and he omovemen of x wih eal GDP. (0 poins Comovemen is he oelaion oeffiien so he deviaion of vaiable fom is end. The fomulas fo he oelaion oeffiien is ( d x, d ( d ( d x x d d x( d x d ( d d 3. Aoding o Kdland and Peso (986, he omovemens of he maoeonomi vaiables wih eal GDP fo he US eonom in he peiod sugges ha he Kenesian view ha he business les is pimail diven b aggegae demand shoks is wong. Wha is he basis fo hei agumen? (0 poins Comovemen of pies wih oupu is negaive in he daa. Comovemen wih eal (aveage wage in posiive in he daa. Demand diven so pedis opposie oelaions. Also, hee is volaili in eal wage. Kenesians have sik wage. 5

6 4. Explain he alibaion poedue sep b sep in Kdland and Peso s Real Business Cle model. Noe ha in Sep, ou mus desibe he suue of he model, and in sep 4 ou mus explain how he paamees ae assigned. Finall, in Sep 5, idenif he model s suesses and failues being aeful o povide inuiion. (5 ps Sep : How muh of he volaili in US oupu in poswa peiod an be aouned fo b poduivi shoks Sep : Neolassial gowh model wih leisue in uili, and poduivi shoks o TFP Sep 3: Define onsisen measues. Govenmen onsumpion ges pu ino onsumpion, govenmen invesmen ges pu ino invesmnen as wella s ne expos. On inome side, Taxes on poduion and popieos inome ae spli beween labo inome and apial inome. All laims ohe han wages, sala go ino apial inome. Sep 4: Laz paamee in uili is alibaed o hous woked using househ uili FONC beween and leisue. Exogenous ae of ehnologial hange is alibaed o peen pe ea gowh ae. Exogenous ae of Capial shae paamee is alibaed o /3, Depeiaion ae is alibaed o K/Y and X/Y using apial sok equaion. Subjeive ime disoun ae is se o he value implied b ineempoal FONC and implied inees ae AR fo ehnolog shoks is esimaed using impued Solow esiduals fom gowh aouning exeises. Sep 5. Feed AR esimaed equaion ino RBC model and solve fo equilibium pah. Geneae 500 o so suh simulaions, and hen ompae aveage volaili and oelaions fo hese 500 simulaion wih oesponding saisis being sue he model daa is HP fileed. Suess is ha /3 d of volaili in oupu an be aouned fo b TFP shoks. Model ges volailil of onsumpion and invesmen abou igh. Whee i messes up is ha i pedis no enough volaili in hous. Also, i pedis a oelaion beween wages o aveage oupu pe wok hou and hous lose o one wheeas in he daa i is lose o zeo. The inuiion fo hese failues is ha in he labo make he alibaed labo suppl is ahe seep so a poduivi shok, whih is a shif in labo demand does no bing abou a lage inease in wok hous. Also, i pedis ha he wage and hous move one o one wih eah ohe. Wha one eall needs is some pe of shok ha auses he labo suppl o inease when labo demand ineases. 5. Some eonomiss have iiized he Real Business Cle heo fo is lak of ealism. In paiula, alhough he have no poblem wih he onep ha a posiive Tehnolog shok oesponds o he disove of a new idea, he do have a poblem wih he onep of a negaive ehnolog shok, as i suggess an undisoveing of an idea. Explain wh his iiism is no valid. (0 poins Thee is no poblem if we hink of TFP being deemined b poli. A negaive ehnolog shok ould be a hange in poli of he pe we sudied in he gowh and developmen poion of he book. Fo example, a 6

7 empoa inease in seui, bad weahe, empoa egulaion all would lowe TFP. 7