Add the transfer payments and subtract the total taxes from (1): Using these definitions, the above becomes: The Saving and Investment Equation:

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San Fanio Sae Univei Mihael Ba ECON 30 Fall 06 Poblem e 5 Conumpion-Saving Deiion and Riadian Equivalene. (0 poin. Saving and Invemen equaion. a. Deive he aving and invemen equaion. The fomula fo GDP uing he expendiue appoah i: GDP C I G NX ( Defining dipoable inome: YD GDP TR T, whee TR i anfe pamen and T i oal axe ne of ubidie. Defining pivae aving: S P YD C, ha i he dipoable inome ha i no pen on onumpion. Defining govenmen aving: S G T TR G, ha i he govenmen inome fom axe ha i no pen on onumpion and anfe pamen. Add he anfe pamen and uba he oal axe fom (: GDP TR T C I G TR T NX Uing hee definiion, he above beome: YD C I SG NX YD C SG I NX The Saving and Invemen Equaion: SP SG I NX b. Suppoe ha in ome eonom he pivae aving i 5, he domei invemen i 0, and he govenmen un a defii of 3. Wha mu be he uen aoun defii in ha oun? Uing he aving and invemen equaion: S S P G I 5 3 0 Thu, he balane on uen aoun i NX 8, and he uen aoun defii i heefoe 8.. (35 poin. In hi queion ou need o ue Exel and daa fo HW5 poed on he oue web page. The queion ha we adde hee ae how big i he govenmen deb, and wha i he deb buden, i.e. how muh inee doe govenmen pa beaue of he deb. a. Plo he gaph of he govenmen deb a a faion of GDP fo all he ea fo whih he daa i available. NX?

Fedeal govenmen deb a a faion of GDP 0% 00% Peenage 80% 60% 40% 0% 0% 935 945 955 965 975 985 995 005 05 Yea b. Wh doe i make ene o look a he deb a a faion of GDP, and no a he deb ielf? The deb elaive o GDP ell u how big he deb i elaive o he oal inome in he eonom, and how diffiul i i fo ha eonom o pa i deb. Thi i he onl enible wa o ompae deb ao ime and beween ounie. Suppoe ha U.S. ha 0 illion dolla deb, and Geee ha illion dolla deb, bu he U.S. eonom i 0 ime lage han he eonom of Geee. In hi ae, alhough U.S. ha lage deb in dolla amoun, he deb o GDP aio in Geee i wie a lage a he U.S. The following gaph demonae hi poin. Publi Deb o GDP Raio 0 50 00 50 00 50 JAPAN GREECE ITALY PORTUGAL BELGIUM SINGAPORE IRELAND SPAIN CANADA FRANCE UNITED KINGDOM EUROPEAN UNION UNITED STATES VIETNAM MEXICO HONG KONG SWITZERLAND CHINA 5.3 54.3 46.5 37 34.4 06. 04.7 0. 99. 98.6 96. 89 86.8 73.6 3.8 9 77.4 30

. Wha wa he deb o GDP aio duing he la ea of he daa? The deb in 05 wa abou 73.7% of he GDP. d. In wha ea wa he ize of he deb he lage, and in wha ea wa he deb buden (deb/gdp aio he lage? The lage deb wa in 05, of abou 36.69 billion ( 3. illion The lage deb buden wa in 946, of abou 06% of GDP. e. Plo he gaph of he inee pamen a a faion of govenmen inome (o of deb fo all he ea fo whih he daa i available. Inee pamen a a faion of govenmen Inome Peenage 0% 8% 6% 4% % 0% 8% 6% 4% % 0% 935 945 955 965 975 985 995 005 05 Yea f. Wh doe i make ene o look a he govenmen inee pamen a a peenage of i inome? Wha mae i he inee pamen elaive o he govenmen inome. The dolla value of an of he govenmen expendiue i oall uninfomaive. If we wan o lean anhing abou govenmen pending, we mu look a ha pending a a faion of govenmen inome. Fo example, pending on naional defene, eduaion, inee pamen, all need o be peened a a faion of govenmen inome. g. In wha ea wa he inee pamen he lage, and in wha ea wa he o of deb (inee a a faion of govenmen eeip he lage? The lage inee pamen wa in 008, of abou 5.757 billion. The lage inee a a faion of govenmen eeip wa in 99, of abou 8.43% of GDP. 3

3. (40 poin. Conide he wo-peiod model of onumpion and aving. a. Wie he onume poblem of uili maximizaion ubje o he budge onain in wo peiod. max U (,,,.. BC : BC : ( b. Deive he lifeime budge onain fom he budge onain in eah peiod. Show ou deivaion. Subiue fom he eond peiod budge onain ino he fi peiod budge onain. I i ea o do when ou divide boh ide of BC b o ge BC : Now add he wo budge onain and ge he lifeime budge onain: PV of lifeime onumpion we lifeime wealh. Give he eonomi inepeaion of he lef hand ide and he igh hand ide of he lifeime budge onain. The lef hand ide i he peen value of lifeime onumpion, and he igh hand ide i he peen value of lifeime ne-of-axe inome, whih we all he lifeime wealh (we. d. Daw a full labeled gaph of he lifeime budge onain wih a angen indiffeene uve indiaing he opimal hoie fo a lende, and label he aving a well. In ode o eeive all he poin ou gaph hould be lea and he line ae aefull dawn wih a ule. 4

The nex figue how he opimal hoie fo a onume who i a lende. The opimal hoie (opimal onumpion bundle i a poin A. we ( A E >0 ( we e. Daw a full labeled gaph of he lifeime budge onain wih a angen indiffeene uve indiaing he opimal hoie fo a boowe, and label he aving a well. In ode o eeive all he poin ou gaph hould be lea and he line ae aefull dawn wih a ule. 5

The nex figue how he opimal hoie fo a onume who i a boowe. The opimal hoie (opimal onumpion bundle i a poin A. we ( E A <0 ( we f. An ineae in uen inome will ineae he uen onumpion b he ame amoun (i.e.. Tue/fale, ile he oe anwe, and povide a poof. We ee fom he lifeime budge onain ha an ineae in will hif he budge onain o he igh. Given ha boh good (uen onumpion and fuue onumpion ae nomal, he onume will ineae he onumpion in boh peiod. In ode o ineae he onumpion in he eond peiod he onume mu ineae hi aving. Thu, an ineae in he uen inome will ineae he uen onumpion b le han he hange in he uen inome. We all hi eul onumpion moohing. To ummaize:,,, < g. Conide he govenmen budge onain and uppoe ha he eal inee ae i 6%. If he govenmen give a ax u of 30 in he fi peiod (i.e. T 30, find he neea hange in he eond peiod axe ( T? ha would keep he peen value of axe unhanged. 6

7 3.8.06 30 30( 0 30 30 T T T T h. Sae he Riadian equivalene heoem. If he peen value of govenmen pending emain unhanged, hen hange in he axe do no affe he houehold opimal onumpion hoie (,. 4. (0 poin. Suppoe ha inead of a lump-um axe, he axe ae popoional o inome (, 0 < <, o ha he budge onain ae now BC BC ( ( : ( : Pove ha he Riadian Equivalene heoem ill hold. The onume lifeime BC i:. Fom he govenmen lifeime BC we ee ha N G G, hu, he lifeime ax liabili of he onume i ill fixed when he peen value of govenmen pending i fixed. 5. (5 poin. Conide he wo-peiod model of onumpion and aving. Suppoe ha he onume uili i ln( ln(, ( U. a. Wie he onume poblem BC BC ( : :.. ln( max ln(,, b. Wie he onume demand fo onumpion in boh peiod and hi uppl of aving. Wiing he onume poblem wih he lifeime budge onain help fo hi eion... ln( max ln(,

8 Now we an ee ha ine he pefeene ae of he Cobb-Dougla fom, he onume will pend a fixed faion of hi lifeime inome on and : ( ( ( ( The aving, fom he fi budge onain. Pove ha aving fo hi onume i ineaing in eal inee ae. Noie ha i deeaing in (ee eion b, and. Thu, i ineaing in. Anohe wa o how ha i ineaing in i o ake he deivaive ( 0 > (Obvioul, he axe ae no geae han inome, o he em 0 >, and he above deivaive i alwa poiive. d. Suppoe ha inome in he fi peiod ineae b $00. Find he hange in he fi peiod onumpion. 00 00 Thu, he hange in i 00 e. How doe he hange in he hange in in he la eion depend on he paamee? Povide eonomi inuiion fo hi eul. We an ee ha highe implie malle hange in uen onumpion. Reall ha epeen he weigh on fuue uili, and highe mean ha eond peiod onumpion beome moe impoan. Theefoe, wih highe, he onume will onume a malle faion of he addiional uen inome. We an hink of he em a epeening he maginal popeni o onume (MPC ha we enouneed in he Keneian model.

Invemen 6. (30 poin. Conide he model of opimal invemen diued in la. a. Wie he fim maximizaion poblem. θ θ θ θ A K L ( δ K wl max V A K L w L I L, L, I, K.. K ( δ K I b. Explain in wod wha he fim wan o maximize. The fim wan o maximize he peen value of he eam of dividend: π V π. Aoding o hi model, wha hould be ok pie of he fim? The ok pie hould be he maximized value of V. d. Deive he opimal invemen ondiion and povide eonomi inepeaion of i. Subiuing he onain ino he objeive give θ θ θ θ A K L ( δ K wl max V A K L w L K ( δ K L, L, I, K F.O.C. fo K : θ θ V θa K L δ 0 K A he opimum, he o of ineaing fuue apial b uni mu be equal o he benefi fom ha exa uni of apial. The benefi in he nex peiod oni of he maginal podu of apial and he non-depeiaed value of he exa uni of apial. Dividing he nex peiod benefi b give he peen value of he benefi. θ θ We an eaange he above o obain θa K L δ. The lef hand ide i he ne eun on invemen in phial apial and he igh hand ide i he ne eun on invemen in he finanial make. e. Illuae gaphiall he impa of an ineae in eal inee ae on he demand fo invemen. 9

A eal inee ae goe up, he opimal apial in he nex peiod goe down, a hown in he figue above (fom K o K '. A a eul, he opimal invemen alo goe down, ine I K ( δ K. f. Illuae gaphiall he impa of fuue ehnologial impovemen on he demand fo invemen. Noie ha he maginal podu uve hif upwad, o ha fo an given level of K i maginal podu ineae. The opimal level of K (and alo of invemen will heefoe ineae. 0

Capial Make 7. (5 poin. Daw a full labeled diagam of he apial make fo an open eonom wih ade defii. 8. (5 poin. Suppoe he govenmen ineae i defii. Illuae gaphiall he impa of hi even on he apial make. Show wha happen o he equilibium aving, invemen, and ade defii.

9. (5 poin. Suppoe ha fuue poduivi in he eonom i expeed o ineae. Illuae gaphiall he impa of hi even on he apial make. Show wha happen o he equilibium aving, invemen, and ade defii.

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