I. Answer each as True, False, or Uncertain, providing some explanation

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1 PROBLEM SET 6 Solutions Principls of Macroconomics April 20, 2005 Du April 27, 2005 I. Answr ach as Tru, Fals, or Uncrtain, providing som xplanation for your choic. 1. If consumrs and invstors ar forward-looking, a on-tim incras in th lvl of th nominal mony stock only shifts th LM curv. Fals. By mony nutrality, output will b back to th natural lvl of output. Sinc it taks tim for output to b back to th mdium-run lvl, th transition from th short run to th mdium run implis highr-than-original output for awhil. If agnts ar forward-looking, thy will tak priods of xpctd highr output into account and incras consumption and invstmnt today. As a rsult, IS shifts. Notic that in th txt, if w assum that th scond priod to b th mdium-run priod, of cours it will hav no impact on today s IS. But in gnral, th scond priod can b any tim btwn today and th mdium-run priod. 2. Incrass in currnt and xpctd futur nominal intrst rats do not lad to an incras in nancial walth, if currnt and xpctd ral intrst rats ar unchangd. Fals. Rcall that bonds ar claims to dollars, rathr than goods in th futur. If consumrs hold bonds, incrass in currnt and xpctd futur nominal intrst rats imply lowr bond prics, and lowr nancial walth. 3. A country can hav xports largr than its GDP. Tru. Suppos that th only valu addd in a country is its labor input. If it imports intrmdiat goods and transforms thm into nal goods using only labor, it is possibl that th valu of xports is highr than th valu addd to th nal goods (which also quals labor incom hr). S th Focus box "Can Exports Excd GDP?" P.376 for an xampl. 4. If in ation in th U.S. is highr than that in Japan, th nominal xchang rat (masurd as th pric of dollars in trms of yns) dcrass. Fals/ Uncrtain. At rst sight, it sms that th nominal xchang rat is indpndnt of th chang in rlativ prics of th two countris, i. thir in ation rats. (if you mntion this part only, you still gt full crdit.) Howvr, for a givn nominal intrst rat in Japan and a givn xpctd nominal xchang rat, th intrst parity condition rquirs th nominal xchang rat to b positivly corrlatd with th U.S. nominal intrst rat (an upward sloping UIP curv in a (E,i) plan). Sinc a highr in ation in th U.S. can b du to a scal or a montary policy shock, th nominal intrst rat can incras or dcras. Thus, th nominal xchang can also incras or dcras. (Th scond part of th answr is from Chaptr 20) 1

2 5. A country s GNP is qual to its GDP if its trad balanc is 0. Fals. Rcall that GNP corrsponds to th valu addd by domstically ownd factors of production. By d nition, GNP is qual to GDP plus nt factor paymnts from th rst of th world. Evn though trad balanc is qual to 0 (i. import=xport), a country can hav positiv or ngativ nt factor paymnts. For xampl, if a country has a lot of rms ownd by forign invstors but dos not hav much ownrship of rms abroad, its GNP is smallr than GDP bcaus factor paymnts to forignrs ar highr than th factor paymnts rcivd from th rst of th world. 6. In thory, a capital account d cit implis a currnt account d cit. Fals. By d nition, th capital account is qual to th ngativ currnt account. Thus, a capital account d cit implis a currnt account surplus. II. Th Budgt D cit in Dnmark Considr th following statistics for Dnmark in th 1980s. (Sourc: "Can Svr Fiscal Contractions B Expansionary? Tals of Two Small Europan Countris," NBER Macroconomics Annual, 1990, , by F. Giavazzi and M. Pagano.) Avrag growth rat of public consumption 4.0% 0.9% Public dbt as % of GDP 10.2% 0.0% Avrag growth rat of disposabl incom 2.6% -0.3% Avrag growth rat of privat consumption -0.8% 3.7% Avrag growth rat of businss invstmnt -2.9% 12.7% 1. Th Danish govrnmnt mad som scal policy changs at th nd of 1982 and at th bginning of From th numbrs abov, what do you think thy did? Th Danish govrnmnt cut govrnmnt consumption (spnding) at th nd of 1982 and at th bginning of 1983, as illustratd by a dcras in th avrag growth rat of public consumption from 4.0% to 0.9%. Thy succdd in rducing th public dbt by mor than 10% in a fw yars. (Public dbt as % of GDP dcrasd dramatically from 10.2% to 0%) Also, a dcras in th avrag growth rat of disposabl incom (from 2.6% to -0.3%) coupld with an incras in output growth implis that tax rats wr raisd around that priod. Notic that with an incras in tax rats, a highr growth rat of GDP from 1983 to 1986 incrasd tax rvnu and shrank th budgt d cit furthr. 2. If w mploy th standard IS-LM modl (without xpctations), i. with C = C(Y T ) and I = I(Y; r), th impact of a dcras in govrnmnt consumption on businss invstmnt is ambiguous. Explain. 2

3 If w impos th rstriction that invstmnt can only ract to th contmporanous output and ral intrst rat, a dcras in govrnmnt consumption/ spnding dcrass aggrgat dmand and thus th quilibrium output. Th ral intrst rat nds to drop to clar th mony markt. On on hand, a lowr ral intrst rat is associatd with a highr lvl of invstmnt. On th othr hand, a lowr lvl of output implis lowr invstmnt. Th nt ct on invstmnt is ambiguous. 3. Instad, w obsrv a drastic incras in businss invstmnt (its growth rat incrasd from -2.9% to 12.7%). How can an inclusion of xpctations in th standard IS-LM modl hlp in xplaining such an unambiguous incras in invstmnt? W know that output in th mdium run will b back to its natural lvl. A dcras in govrnmnt spnding and a lowr natural rat of intrst implis an incras in invstmnt in th mdium run. If invstors form xpctations on vnts during th transition from th short run to th mdium run, thy will tak futur incrass in output and invstmnt into account and ract to th contmporanous dcras in output lss. Also, in th long run, a highr capital to output ratio lads to a highr long-run output. If invstors look forward to th long-run, thy ract vn lssr to th contmporanous dcras in output. 4. If w mploy th standard IS-LM modl (without xpctations), i. C = c 0 + c 1 (Y T ), a dcras (both growth rats and lvls) in disposabl incom triggrs a dcras in privat consumption. How can an inclusion of xpctations in th standard IS-LM modl hlp in xplaining th obsrvd incras in privat consumption growth (from -0.8% to 3.7%)? In th mdium run, w know that output will b back to th natural lvl of output. A dcras in govrnmnt spnding implis a lowr short-run output, but also a gradual incras in output back to th natural lvl. If consumrs tak th futur incras in output into account (btwn now and th mdiumrun), thy will ract lss to th contmporanous dcras in output. If th impact of xpctations dominat, thy may vn incras privat consumption in th short run. Now you ar told that th long-trm ral intrst rats for that priod ar th following Ral intrst rat 6.7% 3.3% 5. What happnd to th prsnt valu of an avrag consumr s xpctd nancial walth by 1986? Can this chang in nancial walth hlp xplain th incras in privat consumption, vn though th avrag growth rat of disposabl incom dcrass (from 2.6% to -0.3%)? If so, why? 3

4 Ys. Th prsnt valu of an avrag consumr s xpctd nancial walth incrasd as a rsult of a dcras in th ral intrst rat, bcaus sh discountd hr xpctd futur walth lss. According to th lif cycl thory of consumption, an incras in prmannt walth implis an incras in prsnt consumption. Evn though th growth rat of disposabl incom dcrass this priod, th growth rat of privat consumption can incras in rspons to a prcivd incras in futur walth. From 1983 to 1986, th Danish consumrs bcam mor optimistic and might vn choos to borrow against th futur to nanc thir prsnt consumption. III. Th Yn and th Dollar 1. You will go to Japan tomorrow. Bfor dpartur, you go to th bank, cash out all your saving of $3000 and xchang that for U306,000. What is th nominal xchang rat E (th pric of dollars in trms of yns)? 306; 000 E = = Onc you arriv at th airport in Tokyo, you raliz you miss hamburgrs alrady (and it is too arly for sushi.) You go to your favorit fast-food chain and buy a hamburgr. Th hamburgr costs U306. How much is it in dollars? P = = 3 3. What is th ral xchang rat (masurd as th pric of hamburgrs in th Unitd Stats in trms of hamburgrs in Japan) if th pric of a hamburgr (xactly th sam kind) in th U.S. is $2. = E P P = = 2 3 i. A hamburgr in th U.S. can only buy you 2/3 hamburgrs in Japan. 4. Aftr th trip, you hav U100,000 lft, and th nominal xchang has dcrasd to 100. Did th dollar dprciat rlativ to th yn? Ys. Bcaus ach yn is worth mor than bfor, or quivalntly, ach dollar buys you lss yn. 5. You ar now considring whthr you should invst th mony lft ithr in Japans on-yar bonds or U.S. on-yar bonds. Th U.S. on-yar nominal intrst rat is i t (not in prcntag), whil that for Japan is i t (not in prcntag). Writ down th condition so that you choos to buy U.S. bonds instad of Japans bonds. Explain intuitivly why you nd this condition. (1 + i t ) (1 + i Et t ) Et+1 4

5 If I spnd on dollar to buy U.S. bonds, I will gt 1 + i t in on yar. If instad, I spnd 1 dollar to buy Japans bonds, i. E t yns, I willgt (1 + i t ) E t yns in a yar. In xpctd trms, (1 + i t ) E t yns qual (1 + i t ) Et E dollars t+1 in a yar. A yar from now, if 1 + i t is largr than (1 + i t ) Et E, I should t+1 prfr to buy U.S. bonds. If th abov condition holds as an quality, I am indi rnt btwn buying ithr of thm. Th quality condition is calld th uncovrd intrst parity condition (UIP). 6. A minut bfor you mak th dcision, you har from th nws that th Japans conomy will do grat this yar and th yn will bcom "strongr." How dos this a ct your dcision in (5)? If th yn is xpctd to b strongr rlativ to th dollar, Et+1 dcrass. A highr E t E t+1 maks th condition in (5) lss likly to hold. I am mor likly to buy Japans bonds today. If th condition was hld as an quality bfor, Japans bonds ar xpctd to b mor pro tabl and I buy thm instad. 7. In thory, arbitrag rquirs that th condition you hav in (5) holds as an quality. Giv a rason why it may not hold as an quality in rality. It ignors transaction costs. For xampl, buying Japans bonds rquirs an xchang of U.S. dollars to Japans yns. Whn th bond maturs, an xchang from yn back to dollars is also ndd. It ignors risks. Th xchang rat a yar from now is uncrtain. If th xchang rat is xpctd to b volatil in th coming yar, holding Japans bonds is risky and risk-avrs invstors dmand a highr rturn than what is promisd by th UIP. 5