1) According to the article, what is the main reason investors in US government bonds grow less optimistic?

Transcription

1 4.02 Quz 3 Soluon Fall 2004 Mulple-Choce Queon Accordng o he arcle, wha he man reaon nveor n US governmen bond grow le opmc? A They are concerned abou he declne (deprecaon of he dollar, whch, n he long run, lead o an ncreae n he prce level. B They are expecng hgh nflaon due o rng ol prce, whch would lead o a fall n real nere rae n he fuure, depe he Fed ghenng. C Becaue he Fed n ghenng mode, due o repor of hgher job creaon and evdence of low nflaon, and hu hey expec he prce of bond o decreae. D Becaue he Fed n ghenng mode, due o repor of hgher job creaon and evdence of low nflaon, and hu hey expec he prce of bond o ncreae. E Boh A and D. Anwer: C. The nveor are growng more bearh becaue he Fed lely o eep rang nere rae depe he declne of he dollar. The fac ha job creaon ha pced up and ha nflaon no a problem a he momen pon o he renghenng of he economy. So, here no reaon for he Fed o op ghenng. Wha happen f nere rae re? We now from he exboo chaper on valuaon of ecure ha bond prce are nverely relaed o nere rae. A nere rae ncreae, reaure loe her value (her prce decreae. Th mgh eem good from a perpecve of a buyer of a bond. Bu remember ha he reaure nveor n he arcle are already holdng he ecure! Obvouly, hey are no happy abou he decreae n he value of her holdng. 2 The repor ay ha A Bloomberg ew urvey la wee howed ha mo exper expeced he Fed o rae he arge level for overngh loan beween ban o 2.25 percen from 2 percen on Dec. 4. A monh ago, only a few foreca an ncreae n he federal fund rae. Th nformaon mple he valuaon of any ae (hn: ue he formula for EPDV dcued n cla and aume nohng ele change n reacon o wha he Fed doe: A Wll decreae on Dec. 4 f he Fed ncreae he arge level o 2.25 percen. B Wll decreae on Dec. 4 f he Fed rae he arge level o 2.50 percen. C Have decreaed from la monh o oday. D Boh A and C. E Boh B and C. Anwer: E. V a negave funcon of e (+. The repor ugge ha e ha ncreaed durng he la monh and expeced o ncreae on Dec. 4, herefore V ha decreaed durng he la monh (hu, opon C correc, f he Fed ncreae he nere rae a expeced nohng ele wll change (herefore A no correc.

2 And f he Fed ncreae he nere rae by more han expeced, ae prce wll decreae agan (hu B alo correc. Then, he correc anwer E. 3 The arcle repor ha he dollar weaened 3.9% agan he euro over he la monh. If he dollar connue o weaen, we hould expec (aume ha he Marhall-Lerner condon hold A Expor from he US o Europe o ncreae. B US mpor from Europe o ncreae. C The US rade balance wh Europe o deerorae. D Boh A and C. E Boh B and C. Anwer: A. The deprecang dollar wll weaen he purchang power of US conumer v-à-v European good, whch wll lead o a declne n mpor. The US rade balance wll mprove under Marhall-Lerner condon a a reul of hgher expor and lower mpor. 4 The arcle menon he Chna Scare, ang ha US governmen bond fell on ov. 26 afer Chna Bune ew repored Yu Yongdng, a Chnee cenral ban offcal, ad Chna had cu holdng of U.S. deb. Why dd he prce of US governmen bond fall a a reacon o he new from Chna? A The demand for dollar declned whch ha o lead o an ncreae n curren US nere rae. B The demand for dollar declned whch ha o lead o an ncreae n curren and fuure US nere rae. C US nere rae are expeced o re o preven he US from runnng no problem wh fnancng rade defc. D The Fed wll have o rae nere rae o preven he US governmen from ellng bond. E Baner n ew Yor were worred ha he repor wa acually dored whch lead o uncerany abou he rue demand for dollar. Anwer: C. When a counry ha a rade defc, need o borrow fund from abroad o fnance h defc. The fac ha Chna hold U.S. governmen bond help o fnance he U.S. rade defc. For example, he U.S. buy more good from Chna han Chna buy from he U.S. and hu ranfer more dollar o Chna han he Chnee need o buy U.S. good. Chna accep hee addonal dollar nce hey ue hem o buy U.S. governmen bond (ha he U.S. borrow h money from Chna nce bond are ju IOU. If Chna uddenly decde ha wan o buy fewer U.S. governmen bond, he U.S. won be able o borrow a much from Chna, unle he U.S. ncreae he nere rae on governmen bond. Increang he nere rae would mae U.S. governmen bond more aracve a an nvemen nce hey would pay a hgher reurn.

3 Y Long Queon I (35/00 pon Open Economy AS-AD and Growh Aume ha he economy decrbed by he followng e of equaon. Exchange rae: E = E Prce Seng: W P = (+ µ A Wage Seng: W = P e A e F(u,z AD: Y= C(Y, T + I (Y, + G + X (Y, Y*, ε Aume ha he Marhall-Learner Condon afed.. Suppoe he economy a a place where u < u (pon Q. Aume ha A and A e are conan. Whou fcal polcy and moneary polcy nervenon, wha happen over me? Show graphcally. Label all curve. Label he medum-run equlbrum a pon M clearly. LM MR 0 M Q IS 0 P P P 0 Y M IS MR Y 0 Q Y AS MR AS 0 AD 0 E A pon Q, Y 0 > Y, o u 0 < u. Th mean ha he economy a a level ha beyond capacy. So, people expec he prce level o ncreae n he near fuure. When P e ncreae, W ncreae nce he wage eng relaon ell u ha W = P e A e F(u,z. An ncreae n W ncreae P nce he prce eng relaon ell u ha P = (+ µ (W/A. A P ncreae, he AS curve hf o he lef and up. A he ame me, LM hf up, becaue an ncreae n P decreae he real money E Y Y 0 Y

4 Y upply even hough he Fed no decreang nomnal money upply. Th proce connue unl he economy reache pon M whch he medum-/long-run equlbrum where Y=Y and u=u. 2. If he cenral ban announce a one-me revaluaon of currency ha credble, wha happen over me? Sll, aume ha A and A e are conan. Show graphcally. Label all curve. Label he medum-run equlbrum a pon M clearly. LM LM MR LM 0 0 M Q IS 0 UIP 0 IS MR UIP Y Y 0 Y E E 0 E If a counry ha a credble fxed P exchange rae yem, hen announcemen of a one-me revaluaon alo credble. So, f he AS = 0 AS MR cenral ban announce a one-me revaluaon of currency, beleved by he nveor. Credbly P 0 P M mean ha nveor expec he exchange rae of h counry o Q decreae and be fxed a new level. AD 0 So, E e decreae by he amoun of he announcemen. Th hf he AD MR nere-rae pary condon curve o Y he lef/down. Snce he cenral ban 0 Y ha no changed he nomnal money upply, oday exchange rae ncreae o E and =*. When he exchange rae decreae, ne expor (X decreae due o he Marhall- Lerner condon. Th mean ha he IS curve wll hf o he lef. Th alo hf he AD curve o he lef, and P ar o fall. In a fxed exchange rae regme, moneary polcy mu accommodae. The cenral ban now mu decreae he money upply o ha he exchange rae doe no devae from E. oce ha he cenral ban acually decreae he money upply, o ha he LM curve hf o LM, bu he

5 becaue of a decreae n P, he LM curve LM MR n he medum-/long-run. Pon M he medum-/long-run equlbrum. 3. Wha he advanage of governmen nervenon, namely one-me revaluaon of he domec currency n queon 2, f he peed of adjumen from pon Q o he medum-run equlbrum wa he ame a n queon? Lm your anwer o a few enence. The man dfference beween he medum-run equlbrum of queon and 2 he equlbrum prce. Even f he peed of adjumen he ame (uually he adjumen n queon 2 faer, he medum-run equlbrum prce hgher f he governmen (and he cenral ban doe no nervene. Th mean ha nflaon hgher under he cenaro n queon. Th problem of nflaon doe no ex wh one-me revaluaon. 4. ow, he economy a he medum/long-run equlbrum (pon M bu experence an ncreae n producvy. Wha happen o naural rae of unemploymen f people expecaon abou prce and producvy are correc? Why? Show graphcally. Label all curve. W P A + µ A 0 + µ M u M PS WS PS 0 When h economy experence an ncreae n producvy, nohng happen o naural rae of unemploymen. Th becaue boh he PS chedule and he WS chedule hf up by he ame amoun. Why by he ame amoun? I becaue people expecaon of producvy are equal o he acual producvy mprovemen. The WS curve hf up becaue an ncreae n A e ncreae W and h ncreae he real wage (W/P. The PS curve hf up becaue an ncreae n A mean ha P decreae nce le labor requred for producon. The decreae n P ncreae he real wage. WS 0 u

6 Y 5. A n queon 4, he economy a he medum-run equlbrum (pon M, bu experence an ncreae n producvy whch doe no affec AD. If people expecaon abou producvy are alway correc, wha happen n he hor- and medum-run? Show graphcally. Label all curve. Label hor- and medum-run equlbra clearly. ( pon (hn: u = Y/AL LM 0 LM SR LM MR 0 M M M IS MR IS IS 0 Y Y Y 2 Y E E P AS 0 AS SR P 0 M AS MR M M AD 0 Y Y Y 2 Y

7 In he hor-run: When producvy ncreae (an ncreae n A, he AS curve hf down and o he rgh. Th lower P whch ha 2 effec. Fr, he real money upply ncreae even hough he nomnal money upply ha no changed. Th hf he LM curve down. A he ame me, a decreae n P lead o a real deprecaon of he domec currency. Th ncreae ne expor due o he Marhall-Lerner condon. So, he IS curve hf o he rgh alo. The nerecon of IS-LM mu be a pon M. Why? A fxed exchange regme mean ha = * and E = E. (oe: If he decreae n P no enough (or oo much o ncreae real money upply whch would correpond o LM SR, hen he cenral ban mu eher ncreae (or decreae nomnal money upply o ha =* mananed, nce ha wha mean o be n a fxed exchange regme. Anoher mporan pon here ha wh a hgher A (producvy, doe no change he naural rae of unemploymen nce people expecaon were correc. However, u=- (Y/AL. So, even hough u conan, Y ncreae. Shor-run o medum-run: A pon M, he economy performng a a level below ha of he naural level of oupu. So, people expecaon of prce ar o decreae. A P e decreae, he AS curve ar o hf o he rgh/down unl reache pon M. A he AS curve move oward pon M, he acual prce level alo drop. Th ncreae real money upply (he LM curve hf down and he real exchange rae (IS hf rgh. Agan, nce =* a all me, we now ha a pon M, he IS and he LM curve mu nerec, and he AS and he AD curve mu alo nerec.

8 Long Queon II (45/00 pon Growh The Republc of Solowaa ha he followng producon funcon: α α Y = F( K, = A K, where α<. Aume for now ha A conan over me (here no echnologcal progre n h economy, o A =A, g he growh rae of, δ he rae of deprecaon n h economy, and he avng rae.. Verfy ha he above producon funcon ha he propery of conan reurn o cale and rewre he producon funcon n erm of only capal per worer. (Defne K Y = and y =. Fr, we mu verfy ha f(λk, λ = λf(k,, ha, f you mulply all npu by a calar, you wll end up mulplyng oupu by he ame amoun. f(λk, λ =A(λK α (λ α =λ α+ α AK α α =λak α α = λf(k,. To wre he producon funcon n nenve form, le λ=/. α α α K K F( K = =, A A Defne f o ha f ( F(,. Then, y = f( =A α. (Recall ha A ju a conan n h model! 2. Solve for he eady ae value of capal per worer (*, oupu per worer (y*, and conumpon per worer (c*. Draw a dagram ha how all hree eady ae value you calculaed. Recall ha he eady ae gven by he crong of he nvemen and he requred nvemen chedule. Tha, f(*=(g +δ*. (See page 225. * = f ( *( * = A( * ( * * α α = A( ( g g g α α = A ( g Pluggng h * no he producon funcon, we ge y*:

9 y* = A( * α α α α α α = A ( A ( = A ( g g c =y (- α α = α c* A ( g ( α y y* c* Requred Invemen ( δ + g Producon funcon A α Invemen A α * 3. Fnd he avng rae a whch eady-ae conumpon maxmzed (.e. we are a he Golden Rule eady ae. There are a few way of dong h, bu here we wll maxmze eady-ae c * conumpon by eng equal o zero. * oe ha c*=y* -- y*= y* -- (δ + g * c * y * = ( δ + g * * y * = ( δ + g * y * α = Aα( * * α α α A α( A ( = δ + g g g α ( = δ + g =α. Th ay ha he opmal level of avng equal o he hare of capal n he producon funcon, α. The nuon ha dmnhng reurn reduce he uefulne of addonal un of capal, o nveng more no alway opmal.

10 4. Suppoe ha a me here a one-me nflow of foregn worer no he counry, o ha jump from 0 o. (Aume ha h doe no affec g. Draw wo dagram: one howng wha happen o he nvemen and requred nvemen chedule, ncludng dynamc, and one depcng he effec of h nflow on capal per worer over me. An nflow of foregn worer equvalen o an ncreae n. Therefore, K/ decreae ( decreae. So, n h cae, capal per worer would (mmedaely jump down o a level uch a n he hor-run. However, n he long run, he dynamc wll brng he economy bac o he orgnal eady-ae level of capal per effecve worer, *. Why? When here an ncreae n, we end up a pon E, where nvemen per worer equal he vercal dance E. The amoun of nvemen requred o manan ha level of capal per worer clearly maller han he amoun E (dance D. Becaue acual nvemen exceed nvemen ha requred o manan he exng level of capal per worer a E, ncreae. Hence, arng from, he economy move o he rgh, wh he level of capal per worer ncreang over me. Th connue unl nvemen per worer ju uffcen o manan he exng level of capal per worer, ha unl we reurn o he nal eady-ae, E. (See page 248. So, he effec of mmgraon wll only be emporary (becaue nohng happened o nvemen or requred nvemen. y E E Requred Invemen ( δ + g Invemen A α D E D * The fgure on he lef depc he evoluon of capal per worer over me. Pror o me, capal per worer a he level *. A me, when here an nflow of worer no Solowaa, capal per worer mmedaely drop o. Then, over me, capal per worer ncreae bac o he orgnal eady-ae level, *. Tme

11 5. Suppoe Solowaa (S and Macronea (M have dencal producon funcon and ame δ, g, and. However, A S >A M. Whch counry wll have a hgher eady-ae capal per worer? Prove your anwer mahemacally and wh a dagram. * α α = A ( g α * α α = A ( A α g, where ={S,M} >0 (Becaue α< and all he oher parameer are pove Therefore, a A ncreae, * ncreae. So, he counry wh a hgher echnologcal parameer, A, wll have a hgher eady-ae level of capal per worer (whch, n h cae, Solowaa. Inuvely, h follow from he fac ha h echnologcal change ncreae he margnal produc of capal a every level of per worer capal oc. y ( δ + g E F A S α A M α M * S *

12 6. Aume ha all counre are headng oward he ame eady ae (ha, n he long run, all counre have acce o he ame echnology and have he ame preference a manfeed n he ame avng rae and populaon growh rae. Doe he model predc growh for poorer counre hould be faer, lower, or he ame a rcher counre? Show mahemacally. (Hn: Defne he growh rae of capal a g K =. In h model, a poor counry poor becaue capal per worer ( furher below he eady-ae value han he capal per worer of a rch counry (.e. he margnal produc of capal greaer n he poor counry. Th alo mean ha ncome per worer (y furher below he eady-ae ncome per worer. Counre ha are approachng he eady ae from below (whch rue for poor counre grow accordng o he exce of acual nvemen over nvemen ha requred o manan exng level of capal. The greaer he dfference, he faer growh. Tha, counre ha ar ou wh lower ( poor counre grow faer han counre wh cloer o he eady ae ( rcher counre. Mahemacally: K K + = + = = y ( + g δ (See page 223, equaon.2. Dvdng boh de by : y = g K = ( δ + g Recall ha n par we found ha y = f( =A α. α α g K = A ( δ + g = A ( δ + g g K α We ee ha nce 0<α<, g K decreang n (.e. = A( α 2 < Suppoe ha α=0.5 n he gven producon funcon. Aume ha he level of echnology n he counry depend on capal per worer, n parcular A= β. Dcu convergence and growh n an economy wh β=0.5 and compare o an economy wh β<0.5. Ue dagram and word. For h economy, y = β Convergence herefore wll depend on he value of β. If he nvemen funcon, ha β + 0.5, concave n capal per worer, hen here ex a eady ae oward whch econome wh mlar avng rae, echnology growh rae, and deprecaon rae wll evenually converge. If convex, we wll no converge o he eady ae (he eady ae wll be unable. For wha value of β wll he funcon be concave/convex? We can loo a he econd paral wh repec o capal per worer, a we dd on he problem e:

13 y 2 y 2 = ( β β 0.5 = ( β + 0.5( β 0.5 β.5 Th la expreon negave (and hu he funcon concave f and only f β<0.5. For β>0.5, convex. When β=0.5, he funcon a lne. In parcular, he followng dagram decrbe he economy when β=0.5. y Invemen Requred Invemen If he counry ar ou a he level of capal per worer uch a 0, wll grow forever. Th rue for any arng level of capal per worer. In h ene, he economy wll never converge o a eady ae. The reaon ha he producon funcon lnear n capal, and herefore doe no exhb dmnhng reurn o capal. Wha abou growh n h economy? We can ue he ame logc a n par 7 o anwer h queon. = = y ( g + δ + = A ( δ + g Dvdng boh de by : = g K = A δ g, whch a conan. Th how ha grow a a conan rae. So, h a model of endogenou growh, becaue generae eady growh even whou echnologcal progre. In conra o he Solow model, growh depend, even n he long run, on he avng rae. For β<0.5, here ex a eady ae o whch econome wll evenually converge. To fnd we agan e f(*=(g +δ*. β ( * * = g 0

14 ( * 0.5 β * = ( g = g 0.5 β 0.5+ β 0.5 β β y * = ( * = ( g We have he andard dagram. (See oluon o par 4. In h model, ju a n he andard Solow model, here convergence o he eadyae. The re of he oluon ju F.Y.I. Wha abou when β>0.5? Then he dagram become: y Requred Invemen C Invemen 0 ** 0 The eady ae C locally unable. Tha, f we ar a any level of capal per worer below **, he economy wll hrn o nohng (lluraed by he move from 0 o zero. So, h le a povery rap he counry ha ar ou very poor no only ay poor, bu grow poorer over me. Why? Becaue a 0, he amoun of nvemen requred o manan ha level of capal per worer exceed acual nvemen. Therefore, decreae, and he economy move o he lef, wh he level of capal per worer decreang over me. However, f he economy ar a a level of capal per worer above **, hen he economy wll grow forever. Th becaue a 0, acual nvemen exceed he amoun of nvemen requred o manan ha level of capal per worer. Therefore, ncreae, and he economy eep movng o he rgh, wh he level of capal per worer ncreang over me. In h ene, here no convergence for an economy wh β 0. 5.