an Faniso ae Univesi Mihael Ba ECON 30 Fall 04 Final Exam Tuesda, Deembe 6 hous, 30 minues Name: Insuions. This is losed book, losed noes exam.. No alulaos of an kind ae allowed. 3. how all he alulaions. 4. If ou need moe spae, use he bak of he page. 5. Full label all gaphs. Good Luk
. (5 poins). uppose a vaiable is gowing a onsan ae g. Pove ha he naual logaihm of ha vaiable is a linea funion of ime. Indiae he slope and he ineep of he linea funion. If a vaiable is gowing a onsan ae g, hen is value a ime is given b ( g) 0 Taking logs of he above: ln( ) ln( 0) ln( g) Whih is a linea funion of, wih slope ln( g), and ineep ln( 0 ).. (5 poins). Le x, be wo vaiables, and hei gowh aes ae denoed xˆ, ˆ. Pove ha he gowh ae of he podu x is appoximael equal o he sum of he gowh aes, fo small gowh aes. Tha is, pove ha x xˆ ˆ. Fom he definiion of he gowh ae of he podu x x x ( xˆ) ( ˆ) x x Taking logs: ln( x) ln( xˆ) ln( ˆ) Using he heoem ha ln( g) g fo small g, gives he equied esul: x xˆ ˆ
3. (5 poins). uppose ha in some eonom he nominal GDP gows a 8%, he pie level (GDP deflao) gows a 4%, and populaion gows a %. Wha is he appoximae gowh ae of Real GDP pe apia? You ae equied o wie he appoximaion fomula used, and plug in he numbes. We use he appoximaion fomula ha gowh ae of a podu is he appoximael he sum of gowh aes, and gowh ae of a aio is appoximael he diffeene of he gowh aes. GDP gowh gowh( GDP) gowh( P) gowh( POP) 8% 4% % % P POP 4. (5 poins). Conside he Classial model sudied in lass, and biefl desibed as follows. The onsume deives uili fom onsumpion C and leisue l aoding o U ( C, l) lnc ( ) lnl. He is endowed wih h hous whih he an alloae beween leisue and wok L. The eal wage is w. The onsume owns a fim and eeives dividend inome (pofi). The fim podues oupu Y using ehnolog Y AK L D, whee A is poduivi paamee (TFP), K is he apial owned b he fim, and L D is labo emploed b he fim. The govenmen axes labo inome a he ae of w and dividend inome a he ae of. a. Wie he onsume s uili maximizaion poblem. Consume s poblem max ln C ( )ln l C, l s.. C w( h l)( w ) ( )
b. Deive he onsume's demand fo onsumpion and leisue, and labo suppl, using he esuls fom Miofoundaions. Explain ou seps biefl. We ewie he budge onsain in he fom of pxx p I : C w( w) l wh( w) ( ) Explanaion: Fom Miofoundaions, we know ha onsumes wih hese Cobb-Douglas pefeenes, spend a faion of hei inome on C and a faion a of hei inome on l. Thus, he demand is: Demand fo onsumpion: C wh( w) ( ) Demand fo leisue: l wh( w) ( ) w w ( ) h w ( w). uppose ha iniiall w 30%, and equilibium emplomen and equilibium oupu wee L 4, Y 00. The govenmen wans o simulae he eonom b loweing he ax ae o 0%. Find he new equilibium emplomen and equilibium oupu. Explain ou answe biefl. L 4, Y 00 In a model wih he same ax ae on boh pes of inome, he govenmen anno affe he equilibium emplomen o oupu b hanging he ommon ax ae. The onl effe of hanges in axes is on he division of oupu beween pivae and govenmen onsumpion. 3
5. (0 poins). Conside he apial make in a losed eonom, wih suppl of apial (pivae saving) given b p and pivae demand fo invesmen I 0 0. 5, boh ae funions of he eal inees ae (in peen). a. uppose ha govenmen budge is balaned. olve fo equilibium in he apial make (find equilibium eal inees ae, pivae saving, govenmen saving, and invesmen). In a losed eonom, he saving and invesmen equaion is: I 0 0 0.5.5 0 I p p G 4 4 8 0 G (given) 0 0.5 4 8 b. uppose ha he govenmen uns a budge defii a he size of.5, in an aemp o simulae he eonom. olve fo equilibium in he apial make (find equilibium eal inees ae, pivae saving, govenmen saving, and invesmen)..5 0 0.5.5.5 I p p G 5 G I 5 0.5 (given) 0 0.55 7.5 4
. The las seion illusaes a mehanism of owding ou. Tue/false, ile he oe answe and explain biefl, based on ou esuls in he las seion. Indeed, highe defii means ha he govenmen needs o boow moe in he apial make, and his ineases he eal inees ae (fom 4% o 5%). This lowes pivae invesmen (fom 8 o 7.5), whih is owding ou of pivae invesmen. Moeove, he ise in pivae saving means deline in pivae onsumpion, eeis paibus, whih is owding ou of pivae onsumpion. d. Daw a full labeled gaph of he apial make, demonsaing he iniial equilibium in pa a, and he even desibed in pa b. ( ) p G () p 5 4 I (), I I 7.5 p I 8 p 0 5
6. (0 poins). Conside he wo-peiod model of onsumpion and saving disussed in lass. Thee ae N idenial onsumes ha live fo wo peiods ( and ) and deive uili fom onsumpion and in he wo peiods: U (, ). Consumes eeive inome and in he wo peiods and pa a lump sum ax and o he govenmen. The onsumes deide how muh o onsume in eah peiod and how muh o save in he fis peiod. We denoe he saving in he fis peiod b s. Consumes an boow and lend a eal inees ae, whih is assumed exogenousl given. Thus he budge onsains in he wo peiods ae BC : s BC : ( ) s The govenmen olles ax evenues T N and T N, and spends G and G in he wo peiods. The govenmen an boow and lend a eal inees ae wih he onsain ha he pesen value of spending = pesen value of axes G T G T a. uppose ha he eal inees ae is 0% and he govenmen lowes he axes b 00. In he seond peiod, he govenmen will have o inease/deease axes (ile he oe answe) b 0 (alulae he neessa inease o deease). Plugging he uen hange in axes ino he govenmen budge onsain, and solving fo he neessa fuue ax hange: T T T T 00 T T 00 0 T 00( ) 00. 0 6
7 b. uppose ha he onsume s uili is ) ln( ) ln( ), ( U. Wie he onsume s demand fo onsumpion in boh peiods and his suppl of saving. Wiing he onsume s poblem wih he lifeime budge onsain helps fo his seion. s.. ) ln( ) max ln(, Now we an see ha sine he pefeenes ae of he Cobb-Douglas fom, he onsume will spend a fixed faion of his lifeime inome on and : The saving, fom he fis budge onsain s
. Consumes wih highe ae moe likel o be boowes. Tue/false, ile he oe answe and povide a poof and eonomi inuiion fo ou answe. Fom he opimal saving, deived above, we have: s we 0 ( ) whee we. Thus, opimal saving is ineasing in, so onsumes wih highe will save moe, eeis paibus, and ae moe likel o be lendes, no boowes. Inuiivel, is he weigh on uili fom fuue onsumpion. Highe means ha fuue onsumpion is moe impoan, and onsumes will end o save moe. d. uppose ha inome in he fis peiod ineases b $000. Find he esuling hange in onsumpion of boh peiods, and he hange in saving, if he eal inees ae is 7% and. s o s? ( ) 500 000 000 500 0.5 000.07 535 0.5 000 500 8
7. (5 poins). Conside he quani heo of mone equaion: MV PY. a. Wie his equaion in appoximae gowh aes. Mˆ Vˆ Pˆ Yˆ b. uppose ha veloi is onsan, he gowh ae of eal GDP is 5% and he enal bank wans o ahieve inflaion of %. Wha is he equied gowh of he mone suppl? Mˆ Vˆ? 0% Pˆ Yˆ % Mˆ 7% 5%. Now suppose ha veloi gowh is deeasing in he gowh ae of mone: Vˆ 0.3Mˆ, ohe hings being he same as in he pevious seion. How would ou answe he pa b hange? Mˆ? Vˆ 0.3Mˆ Pˆ Yˆ % Mˆ 0.3Mˆ 7% 0.7Mˆ 7% Mˆ 0% 5% 9
8. (0 poins). uppose ha he publi wans o hold uen/deposi aio of d 0., and he equied eseve/deposi aio is d 0. 4. The iniial onsolidaed balane shee of ommeial banks is: Asses Liabiliies R? D 00 B G 5 L??? a. Find he monea base, he mone suppl and he mone muliplie in his eonom, and omplee he missing values in he above balane shee. CU d D 0. 00 0 R d D 0.4 00 40 MB CU R 0 40 60 M CU D 0 00 0 ( o M mm MB) d 0. mm d d 0. 0.4 ine oal asses ae 00, and R 40, B 5, hen loans ae G L 00 R B 45 G 0
b. uppose ha he enal bank pefoms an open make opeaion and bus govenmen bonds fom he ommeial banks a he amoun of 6. Find he new monea base, he mone suppl and show he new balane shee of he ommeial banks. MB 66 M mm MB 66 3 D MB 66 0 d d 0.4 0. d 0.4 R MB 66 44 d d 0.4 0. d 0. CU MB 66 d d 0.4 0. Asses Liabiliies R 44 D 0 B G 9 L 57 0 0