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

Transcription

1 14.02 Quiz 3 Soluion Fall 2004 Muliple-Choice Queion 1) According o he aricle, wha i he main reaon inveor in US governmen bond grow le opimiic? A) They are concerned abou he decline (depreciaion) of he dollar, which, in he long run, lead o an increae in he price level. B) They are expecing high inflaion due o riing oil price, which would lead o a fall in real inere rae in he fuure, depie he Fed ighening. C) Becaue he Fed i in ighening mode, due o repor of higher job creaion and evidence of low inflaion, and hu hey expec he price of bond o decreae. D) Becaue he Fed i in ighening mode, due o repor of higher job creaion and evidence of low inflaion, and hu hey expec he price of bond o increae. E) Boh A) and D). Anwer: C). The inveor are growing more bearih becaue he Fed i liely o eep raiing inere rae depie he decline of he dollar. The fac ha job creaion ha piced up and ha inflaion i no a problem a he momen poin o he renghening of he economy. So, here i no reaon for he Fed o op ighening. Wha happen if inere rae rie? We now from he exboo chaper on valuaion of ecuriie ha bond price are inverely relaed o inere rae. A inere rae increae, reaurie loe heir value (heir price decreae). Thi migh eem good from a perpecive of a buyer of a bond. Bu remember ha he reaurie inveor in he aricle are already holding he ecuriie! Obviouly, hey are no happy abou he decreae in he value of heir holding. 2) The repor ay ha A Bloomberg ew urvey la wee howed ha mo exper expeced he Fed o raie he arge level for overnigh loan beween ban o 2.25 percen from 2 percen on Dec. 14. A monh ago, only a few foreca an increae in he federal fund rae. Thi informaion implie he valuaion of any ae (hin: ue he formula for EPDV dicued in cla and aume nohing ele change in reacion o wha he Fed doe): A) Will decreae on Dec. 14 if he Fed increae he arge level o 2.25 percen. B) Will decreae on Dec. 14 if he Fed raie 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 i a negaive funcion of i e (+). The repor ugge ha i e ha increaed during he la monh and i expeced o increae on Dec. 14, herefore V ha decreaed during he la monh (hu, opion C) i correc), if he Fed increae he inere rae a expeced nohing ele will change (herefore A) i no correc).

2 And if he Fed increae he inere rae by more han expeced, ae price will decreae again (hu B) i alo correc). Then, he correc anwer i E). 3) The aricle repor ha he dollar weaened 3.9% again he euro over he la monh. If he dollar coninue o weaen, we hould expec (aume ha he Marhall-Lerner condiion hold) A) Expor from he US o Europe o increae. B) US impor from Europe o increae. C) The US rade balance wih Europe o deeriorae. D) Boh A) and C). E) Boh B) and C). Anwer: A). The depreciaing dollar will weaen he purchaing power of US conumer vi-à-vi European good, which will lead o a decline in impor. The US rade balance will improve under Marhall-Lerner condiion a a reul of higher expor and lower impor. 4) The aricle menion he China Scare, aing ha US governmen bond fell on ov. 26 afer China Buine ew repored Yu Yongding, a Chinee cenral ban official, aid China had cu i holding of U.S. deb. Why did he price of US governmen bond fall a a reacion o he new from China? A) The demand for dollar declined which ha o lead o an increae in curren US inere rae. B) The demand for dollar declined which ha o lead o an increae in curren and fuure US inere rae. C) US inere rae are expeced o rie o preven he US from running ino problem wih financing i rade defici. D) The Fed will have o raie inere rae o preven he US governmen from elling i bond. E) Baner in ew Yor were worried ha he repor wa acually diored which lead o uncerainy abou he rue demand for dollar. Anwer: C). When a counry ha a rade defici, i need o borrow fund from abroad o finance hi defici. The fac ha China hold U.S. governmen bond help o finance he U.S. rade defici. For example, he U.S. buy more good from China han China buy from he U.S. and hu ranfer more dollar o China han he Chinee need o buy U.S. good. China accep hee addiional dollar ince hey ue hem o buy U.S. governmen bond (ha i he U.S. borrow hi money from China ince bond are ju IOU). If China uddenly decide ha i wan o buy fewer U.S. governmen bond, he U.S. won be able o borrow a much from China, unle he U.S. increae he inere rae on governmen bond. Increaing he inere rae would mae U.S. governmen bond more aracive a an invemen ince hey would pay a higher reurn.

3 Y Long Queion I (35/100 poin) Open Economy AS-AD and Growh Aume ha he economy i decribed by he following e of equaion. Exchange rae: Price Seing: Wage Seing: E = E P = (1+ µ) W A W = P e A e F(u,z) AD: Y= C(Y, T) + I (Y,i) + G + X (Y, Y*, ε ) Aume ha he Marhall-Learner Condiion i aified. 1. Suppoe he economy i a a place where u < u (poin Q). Aume ha A and A e are conan. Wihou fical policy and moneary policy inervenion, wha happen over ime? Show graphically. Label all curve. Label he medium-run equilibrium a poin M clearly. i i LM MR i 0 M Q IS 0 P IS MR Y Y 0 M AS 0 P 1 P 0 Q Y AS MR AD 0 E A poin Q, Y 0 > Y, o u 0 < u. Thi mean ha he economy i a a level ha i beyond i capaciy. So, people expec he price level o increae in he near fuure. When P e increae, W increae ince he wage eing relaion ell u ha W = P e A e F(u,z). An increae in W increae P ince he price eing relaion ell u ha P = (1+ µ ) (W/A). A P increae, he AS curve hif o he lef and up. A he ame ime, LM hif up, becaue an increae in P decreae he real money E Y Y 0 Y

4 Y upply even hough he Fed i no decreaing nominal money upply. Thi proce coninue unil he economy reache poin M which i he medium-/long-run equilibrium where Y=Y and u=u. 2. If he cenral ban announce a one-ime revaluaion of i currency ha i credible, wha happen over ime? Sill, aume ha A and A e are conan. Show graphically. Label all curve. Label he medium-run equilibrium a poin M clearly. i LM 1 LM MR i LM 0 i 0 M Q IS 0 UIP 0 IS MR UIP 1 Y Y 0 Y E 1 E 0 E If a counry ha a credible fixed P exchange rae yem, hen i announcemen of a one-ime revaluaion i alo credible. So, if he AS = 0 AS MR cenral ban announce a one-ime revaluaion of i currency, i i believed by he inveor. Credibiliy P 0 mean ha inveor expec he exchange rae of hi counry o P 1 M Q decreae and be fixed a i new level. AD 0 So, E e decreae by he amoun of he announcemen. Thi hif he AD MR inere-rae pariy condiion curve o Y he lef/down. Since he cenral ban 0 Y ha no changed he nominal money upply, oday exchange rae increae o E 1 and i=i*. When he exchange rae decreae, ne expor (X) decreae due o he Marhall- Lerner condiion. Thi mean ha he IS curve will hif o he lef. Thi alo hif he AD curve o he lef, and P ar o fall. In a fixed exchange rae regime, moneary policy mu accommodae. The cenral ban now mu decreae he money upply o ha he exchange rae doe no deviae from E 1. oice ha he cenral ban acually decreae he money upply, o ha he LM curve hif o LM 1, bu he

5 becaue of a decreae in P, he LM curve i LM MR in he medium-/long-run. Poin M i he medium-/long-run equilibrium. 3. Wha i he advanage of governmen inervenion, namely one-ime revaluaion of he domeic currency in queion 2, if he peed of adjumen from poin Q o he medium-run equilibrium wa he ame a in queion 1? Limi your anwer o a few enence. The main difference beween he medium-run equilibrium of queion 1 and 2 i he equilibrium price. Even if he peed of adjumen i he ame (uually he adjumen in queion 2 i faer), he medium-run equilibrium price i higher if he governmen (and he cenral ban) doe no inervene. Thi mean ha inflaion i higher under he cenario in queion 1. Thi problem of inflaion doe no exi wih one-ime revaluaion. 4. ow, he economy i a he medium/long-run equilibrium (poin M) bu i experience an increae in produciviy. Wha happen o i naural rae of unemploymen if people expecaion abou price and produciviy are correc? Why? Show graphically. Label all curve. W P A µ A µ M M PS 1 WS 1 PS 0 WS 0 When hi economy experience an increae in produciviy, nohing happen o i naural rae of unemploymen. Thi i becaue boh he PS chedule and he WS chedule hif up by he ame amoun. Why by he ame amoun? I i becaue people expecaion of produciviy are equal o he acual produciviy improvemen. The WS curve hif up becaue an increae in A e increae W and hi increae he u 1 real wage (W/P). The PS curve u hif up becaue an increae in A mean ha P decreae ince le labor i required for producion. The decreae in P increae he real wage.

6 Y 5. A in queion 4, he economy i a he medium-run equilibrium (poin M), bu i experience an increae in produciviy which doe no affec AD. If people expecaion abou produciviy are alway correc, wha happen in he hor- and medium-run? Show graphically. Label all curve. Label hor- and medium-run equilibria clearly. (11 poin) (hin: u = 1 Y/AL) i LM 0 i LM SR LM MR i 0 M M M IS MR IS 1 IS 0 Y 1 Y 1 Y 2 Y E E P AS 0 AS SR P 0 M AS MR M M AD 0 Y 1 Y 1 Y 2 Y

7 In he hor-run: When produciviy increae (an increae in A), he AS curve hif down and o he righ. Thi lower P which ha 2 effec. Fir, he real money upply increae even hough he nominal money upply ha no changed. Thi hif he LM curve down. A he ame ime, a decreae in P lead o a real depreciaion of he domeic currency. Thi increae ne expor due o he Marhall-Lerner condiion. So, he IS curve hif o he righ alo. The inerecion of IS-LM mu be a poin M. Why? A fixed exchange regime mean ha i = i* and E = E. (oe: If he decreae in P i no enough (or oo much) o increae real money upply which would correpond o LM SR, hen he cenral ban mu eiher increae (or decreae) nominal money upply o ha i=i* i mainained, ince ha wha i mean o be in a fixed exchange regime. ) Anoher imporan poin here i ha wih a higher A (produciviy), doe no change he naural rae of unemploymen ince people expecaion were correc. However, u=1- (Y/AL). So, even hough u i conan, Y increae. Shor-run o medium-run: A poin M, he economy i performing a a level below ha of he naural level of oupu. So, people expecaion of price ar o decreae. A P e decreae, he AS curve ar o hif o he righ/down unil i reache poin M. A he AS curve move oward poin M, he acual price level alo drop. Thi increae real money upply (he LM curve hif down) and he real exchange rae (IS hif righ). Again, ince i=i* a all ime, we now ha a poin M, he IS and he LM curve mu inerec, and he AS and he AD curve mu alo inerec.

8 Long Queion II (45/100 poin) Growh The Republic of Solowaia ha he following producion funcion: α 1 α Y = F ( K, ) = A K, where α <1. Aume for now ha A i conan over ime (here i no echnological progre in hi economy, o A =A), g i he growh rae of, δ i he rae of depreciaion in hi economy, and i he aving rae. 1. Verify ha he above producion funcion ha he propery of conan reurn o cale and rewrie he producion funcion in erm of only capial per worer. (Define K = and y = Y.) Fir, we mu verify ha f(λ K, λ ) = λ f(k, ), ha i, if you muliply all inpu by a calar, you will end up muliplying oupu by he ame amoun. (λ ) 1 α =λ α+ 1 α 1 α f(λ K, λ ) =A(λ K ) α AK α =λ AK α 1 α = λf(k, ). To wrie he producion funcion in inenive form, le λ =1/. α 1 α α A K K A F ( K, 1) = = Define f o ha f ( ) F (, 1). Then, y = f( ) =A α. (Recall ha A i ju a conan in hi model!) 2. Solve for he eady ae value of capial per worer (*), oupu per worer (y*), and conumpion per worer (c*). Draw a diagram ha how all hree eady ae value you calculaed. Recall ha he eady ae i given by he croing of he invemen and he required invemen chedule. Tha i, f(*)=(g +δ)*. (See page 225.) * = f ( *)( ) g α * = A ( *) ( ) g 1 α ( *) = A( ) g α * = A 1 α ( ) g Plugging hi * ino he producion funcion, we ge y*:

9 1 1 1 α 1 α y* = A( *) α 1 α = A ( A ( ) 1 α ) α = A 1 α ( ) g g c =y (1-) 1 α c* = A 1 α ( ) 1 α ( 1 ) g y y* c* Required Invemen ( δ + g ) Producion funcion A α Invemen A α * 3. Find he aving rae a which eady-ae conumpion i maximized (i.e. we are a he Golden Rule eady ae). There are a few way of doing hi, bu here we will maximize eady-ae c * conumpion by eing equal o zero. * oe ha c*=y* -- y*= y* -- (δ + g )* c * y * = (δ + g ) * * y * = (δ + g ) * y * α 1 = Aα ( *) * 1 1 Aα ( A 1 α ( g )1 α ) α 1 = δ + g α ( g ) = δ + g =α. Thi ay ha he opimal level of aving i equal o he hare of capial in he producion funcion, α. The inuiion i ha diminihing reurn reduce he uefulne of addiional uni of capial, o inveing more i no alway opimal.

10 4. Suppoe ha a ime here i a one-ime inflow of foreign worer ino he counry, o ha jump from 0 o 1. (Aume ha hi doe no affec g.) Draw wo diagram: one howing wha happen o he invemen and required invemen chedule, including dynamic, and one depicing he effec of hi inflow on capial per worer over ime. An inflow of foreign worer i equivalen o an increae in. Therefore, K/ decreae ( decreae). So, in hi cae, capial per worer would (immediaely) jump down o a level uch a in he hor-run. However, in he long run, he dynamic will bring he economy bac o he original eady-ae level of capial per effecive worer, 1 *. Why? When here i an increae in, we end up a poin E, where invemen per worer equal he verical diance E. The amoun of invemen required o mainain ha level of capial per worer i clearly maller han he amoun E (diance D ). Becaue acual invemen exceed invemen ha i required o mainain he exiing level of capial per worer a E, increae. Hence, aring from, he economy move o he righ, wih he level of capial per worer increaing over ime. Thi coninue unil invemen per worer i ju ufficien o mainain he exiing level of capial per worer, ha i unil we reurn o he iniial eady-ae, E. (See page 248.) So, he effec of immigraion will only be emporary (becaue nohing happened o invemen or required invemen). y E E Required Invemen ( δ + g ) Invemen A α D E D * The figure on he lef depic he evoluion of capial per worer over ime. Prior o ime, capial per worer i a he level *. A ime, when here i an inflow of worer ino Solowaia, capial per worer immediaely drop o. Then, over ime, capial per worer increae bac o he original eady-ae level, *. Time

11 5. Suppoe Solowaia (S) and Macroneia (M) have idenical producion funcion and ame δ, g, and. However, A S >A M. Which counry will have a higher eady-ae capial per worer? Prove your anwer mahemaically and wih a diagram. 1 1 * = A 1 α i ( ) 1 α, where i={s,m} g α 1 * 1 1 α >0 A i = 1 α A i 1 α ( g ) (Becaue α <1 and all he oher parameer are poiive) Therefore, a A increae, * increae. So, he counry wih a higher echnological parameer, A, will have a higher eady-ae level of capial per worer (which, in hi cae, i Solowaia). Inuiively, hi follow from he fac ha hi echnological change increae he marginal produc of capial a every level of per worer capial oc. y ( δ + g ) E F A S α A M α M * S *

12 6. Aume ha all counrie are heading oward he ame eady ae (ha i, in he long run, all counrie have acce o he ame echnology and have he ame preference a manifeed in he ame aving rae and populaion growh rae). Doe he model predic growh for poorer counrie hould be faer, lower, or he ame a richer counrie? Show mahemaically. (Hin: Define he growh rae of capial a g = K.) In hi model, a poor counry i poor becaue i capial per worer () i furher below he eady-ae value han i he capial per worer of a rich counry (i.e. he marginal produc of capial i greaer in he poor counry). Thi alo mean ha i income per worer (y) i furher below he eady-ae income per worer. Counrie ha are approaching he eady ae from below (which i rue for poor counrie) grow according o he exce of acual invemen over invemen ha i required o mainain exiing level of capial. The greaer he difference, he faer i growh. Tha i, counrie ha ar ou wih lower ( poor counrie ) grow faer han counrie wih cloer o he eady ae ( richer counrie ). Mahemaically: K + 1 K = + 1 = = y (δ + g ) (See page 223, equaion 11.2.) Dividing boh ide by : y = g K = (δ + g ) Recall ha in par 1 we found ha y = f() =A α. α g = A α 1 K (δ + g ) = A (δ + g ) K α 2 We ee ha ince 0<α <1, g K i decreaing in (i.e. g = A(α 1 ) < 0 ). 7. Suppoe ha α =0.5 in he given producion funcion. Aume ha he level of echnology in he counry depend on capial per worer, in paricular A= β. Dicu convergence and growh in an economy wih β =0.5 and compare i o an economy wih β <0.5. Ue diagram and word. β For hi economy, y = Convergence herefore will depend on he value of β. If he invemen funcion, ha i β, i concave in capial per worer, hen here exi a eady ae oward which economie wih imilar aving rae, echnology growh rae, and depreciaion rae will evenually converge. If i i convex, we will no converge o he eady ae (he eady ae will be unable). For wha value of β will he funcion be concave/convex? We can loo a he econd parial wih repec o capial per worer, a we did on he problem e:

13 y = ( β + 0.5) β y β 1. 5 = ( β )(β 0.5) 2 Thi la expreion i negaive (and hu he funcion i concave) if and only if β <0.5. For β >0.5, i i convex. When β =0.5, he funcion i a line. In paricular, he following diagram decribe he economy when β =0.5. y Invemen Required Invemen 0 If he counry ar ou a he level of capial per worer uch a 0, i will grow forever. Thi i rue for any aring level of capial per worer. In hi ene, he economy will never converge o a eady ae. The reaon i ha he producion funcion i linear in capial, and herefore i doe no exhibi diminihing reurn o capial. Wha abou growh in hi economy? We can ue he ame logic a in par 7 o anwer hi queion. + 1 = = y ( δ + g ) = A ( δ + g ) Dividing boh ide by : = g K = A δ g, which i a conan. Thi how ha grow a a conan rae. So, hi i a model of endogenou growh, becaue i generae eady growh even wihou echnological progre. In conra o he Solow model, growh depend, even in he long run, on he aving rae. For β <0.5, here exi a eady ae o which economie will evenually converge. To find i we again e f(*)=(g +δ )*. ( *) β * = g

14 ( *) 0. 5 β = g * = ( g 1 ) 0. 5 β 0.5+β 0.5 β y* = ( *) β = ( ) g We have he andard diagram. (See oluion o par 4.) In hi model, ju a in he andard Solow model, here i convergence o he eadyae. The re of he oluion i ju F.Y.I. Wha abou when β >0.5? Then he diagram become: y Required Invemen C Invemen 0 ** 0 The eady ae C i locally unable. Tha i, if we ar a any level of capial per worer below **, he economy will hrin o nohing (illuraed by he move from 0 o zero). So, hi i lie a povery rap he counry ha ar ou very poor no only ay poor, bu grow poorer over ime. Why? Becaue a 0, he amoun of invemen required o mainain ha level of capial per worer exceed acual invemen. Therefore, decreae, and he economy move o he lef, wih he level of capial per worer decreaing over ime. However, if he economy ar a a level of capial per worer above **, hen he economy will grow forever. Thi i becaue a 0, acual invemen exceed he amoun of invemen required o mainain ha level of capial per worer. Therefore, increae, and he economy eep moving o he righ, wih he level of capial per worer increaing over ime. In hi ene, here i no convergence for an economy wih β 0. 5.