1. Explain why the theory of purchasing power parity is often referred to as the law of one price.


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1 Chaper Review Quesions. xplain why he heory of purchasing power pariy is ofen referred o as he law of one price. urchasing ower ariy () is referred o as he law of one price because he deerminaion of he exchange rae implies ha similar radable goods cos he same regardless of where hey are purchased. If he price of domesic and foreign radable goods were and * respecively, hen he cos of foreign goods in domesic currency erms would be * where is he nominal exchange rae. The law of one price hus saes ha exchange raes are deermined so ha = *. is upheld by arbirage in he goods marke which acs o close any inernaional price differences (arbirage is he simulaneous ac of selling he good where i is expensive and buying i where i is cheap making a riskless rading profi hese rades hough enac price changes ha close he arbirage opporuniy). Therefore deviaions from he law of one price can only exis emporarily. a b = d c A poin a: >, so domesic goods are cheaper han foreign goods. There are hree possible pahs ha can resore he law of one price. a o b: increased demand for domesic goods raises prices o (price adjusmen), = *. a o c: increased relaive demand for serling o purchase cheaper domesic goods sees an exchange rae appreciaion o (exchange rae adjusmen) so ha = *. a o d: a mixure of boh price and exchange rae adjusmens.
2 = b d c a Alernaively, consider he case where a poin a, < domesic prices are higher han hose overseas in erms of he same currency. There are again hree pahs ha can resore he law of one price. a o c: falling demand for domesic goods reduces prices o (price adjusmen), so ha = *. a o b: Falling demand for serling o purchase domesic goods sees a depreciaion of he domesic currency o depreciaion (exchange rae adjusmen), = *. a o d: a mixure of boh price and exchange rae adjusmens xchange rae adjusmen is normally considered o be sronger han price adjusmen. This is primarily because inernaional currency markes are more compeiive han domesic goods markes, so prices respond much faser o changes in demand. The law of one price also esablishes ha he real exchange rae (R) is consan in he long run. I.e. if = *, hen R = * / =.. According o wha would happen o he exchange rae under he following circumsances. a. An increase in he overseas money supply If he quaniy heory of money holds rue hen changes in he money supply have a direcly proporional impac on he price level. % Δ M = % Δ
3 According o he heory of he exchange rae is deermined so ha =. * Hence: % Δ % Δ % Δ, his is he relaive condiion. The domesic exchange will appreciae in roughly he same proporion as he overseas increase in he money supply. % ΔM = % Δ = % Δ b. A reducion in he margins on domesic goods prices If domesic prices are se as a mark up over domesic marginal coss, = ( + μ)mc hen changes in his margin will have a direc impac on he domesic price level. Given ha he exchange rae is defined by he raio of domesic and overseas price levels = hen % Δ = % Δ. The domesic exchange rae will again appreciae. c. Wha would happen o he real exchange rae in each insance? The real exchange rae is defined as he raio of foreign o domesic prices when boh are expressed in he same currency: R = Therefore, he change in he real exchange rae can be approximaed as follows: ΔR Δ Δ Δ + R In par a. he increase in foreign prices is offse by an appreciaion in he exchange rae leaving he real exchange rae unchanged. Δ Δ = Δ Δ + = 0 ΔR hence = 0, R
4 In par b, he fall in domesic prices is offse by a nominal appreciaion, again leaving he exchange rae unchanged. Δ Δ = Δ Δ = 0 ΔR hence = 0 R This confirms ha heory predics a consan long run real exchange rae. 3. The domesic ineres rae falls, so ha i sands 3% below he overseas ineres rae. This ineres differenial is expeced o remain for one year. According o he heory of uncovered ineres pariy, wha would be he effec on he domesic exchange rae? The effec of a emporary 3% ineres differenial ( r r 3% ) = on he pah of he exchange rae can be shown using demand and supply analysis. Iniially foreign bonds offer higher ineres raes. Therefore, domesic consumers swich o foreign bonds and foreign invesors repariae funds. As a resul he demand for foreign currency rises and he supply of foreign currency falls. S S D D Q The domesic currency hen depreciaes ( ) relaive o domesic currency rises.  i.e. he price of foreign currency
5 In one year s ime he ineres differenial disappears. The rise in domesic ineres raes reverses he demand and supply shifs seen before and as a resul he exchange rae reurns o is original posiion. How much is he iniial depreciaion? The answer is 3% due o uncovered ineres pariy (UI). The reurns from holding foreign asses consis of he ineres hey pay plus he capial gains or losses made when convering hese gains back ino domesic currency. The capial gains/losses arise from a depreciaion/appreciaion in he domesic currency whils he invesor held foreign asses. If he depreciaion is greaer han 3%, say 4%, hen he reurn on foreign bonds relaive o domesic bonds is 3%  4% = %. In his case i pays o swich back ino he domesic currency so i appreciaes. If depreciaion is less han 3%, say %, hen excess reurn on foreign bonds are 3% % =%. As a resul he domesic currency depreciaes furher because invesors sill face a posiive incenive o swich from domesic o foreign asses. Only if here is a depreciaion of 3% is here no pressure for he exchange rae o change furher. The movemen in he exchange rae acs o equalise he reurns on financial asses regardless of which currency hey are expressed in. Because financial markes are considered o be large and compeiive, arbirage ensures ha UI holds in he shor run. Oherwise unexploied arbirage opporuniies will exis. e Δ Therefore, = r r, he expeced change in he ineres rae is equal o he difference beween domesic and foreign ineres raes. r r ime
6 Wha if? a) If he ineres differenial was 6% Quie simply he iniial depreciaion of he domesic currency would be 6%. From UI, he expeced change in he exchange rae would be a 6% appreciaion. Δ e * = r r, hence for a 6% appreciaion o exis here mus be an iniial 6% depreciaion. r r ime b) he 3% ineres differenial lased for years This would also produce an iniial depreciaion of approximaely 6%. This is because UI holds in each period. Therefore, for he firs year a 3% ineres differenial creaes an expecaion of a 3% appreciaion. The same will siuaion will occur in he second period. Therefore, over he cause of wo years foreign bonds will pay roughly 6% more in ineres, bu he 6% appreciaion in he domesic exchange rae over he same period creaes capial losses equal o his ineres rae premium. If he iniial exchange rae depreciaion was less han 6%, hen he expeced appreciaion would be less han 6% and hence he capial losses from holding foreign bonds would no offse he ineres rae premium. Consequenly i would be profiable o swich from domesic o foreign bonds which would lead o an exchange rae depreciaion. If he iniial depreciaion were greaer han 7%, hen capial losses from holding foreign bonds exceed he ineres rae gain. There is a movemen ino domesic bonds
7 and he exchange rae appreciaes. Only a an iniial depreciaion of 6% does he currency marke remain in equilibrium. r r 3 ime c) There was a 5% risk premium aached o domesic bonds * From UI you migh deduce ha r r = 5%, hence he domesic exchange rae will appreciae by 5%. However, he 5% premium on domesic bonds simply represens he compensaion for holding riskier asses perhaps because he risk of defaul is greaer. Therefore, in riskadjused erms ineres raes remain he same as he overseas rae, so here would be no movemen in he exchange rae. Δ % Δ = = r μ r = 0 if r * r = 5% bu he risk premium 5% μ =. 4. In he Financial Times, you noice ha ineres raes in he UK are 6 percen, whereas in he US hey are currenly only 3 percen. A friend has proposed a ge rich quick scheme where you borrow from he US banks and reinves in UK banks, and make a profi on he difference in ineres raes. Is his plan likely o work? According o he predicions of uncovered ineres pariy (UI) his won work. In order o exercise his plan i is necessary o borrow from he US bank in US dollars and conver he funds ino Briish pounds in order o deposi hem in UK banks. This ransacion will lead o a change in he exchange rae ha will offse he ineres differenial. * According o UI, over he period in which r r = 3% he US dollar will appreciae by 3% relaive o he Briish pound. Therefore, paying back he US dollar loan will require 3% more Briish pounds compleely offseing he ineres premium. As soon
8 as he ineres differenial arises he Briish pound will appreciae by 3% agains he US dollar, creaing he expecaion of a subsequen 3% depreciaion. rofis can only be made if you are excepionally quick o spo he differenial and can ac on i before i is arbiraged away. I is assumed ha financial markes are very compeiive and highly liquid, so compeing invesors can reac vigorously o profi from any arbirage opporuniy. However, heir acions ac o close he profis by moving prices owards equilibrium. Therefore, he exchange rae would be expeced o jump almos insanly bu for he very early movers here is a chance ha hese ransacions can be underaken before he exchange rae has moved sufficienly. In his case here are profis o be made. 5. Under wha condiions will devaluaion in he exchange rae improve he curren accoun? The necessary condiion is ha he MarshallLerner condiion is saisfied. Tha is he sum of he price elasiciies of expors and impors sum o greaer han uniy. An exchange rae depreciaion raises he coss of impors in domesic currency erms as ( ). I also lowers he cos of domesic goods in erms of foreign /. In erms of he balance of rade his has wo effecs: currency ( ) Subsiuion: as domesic goods become cheaper relaive o foreign goods in world markes, impors will fall and expors rise. This will improve he balance of rade. Terms of rade: The rise in he price of impored goods raises lowers he erms of rade so each impored good now coss more. This effec deerioraes he balance of rade. For devaluaion o improve he balance of rade, i mus be he case ha he subsiuion effec ouweighs he erms of rade effec. Therefore, changes in he erms of rade mus elici sufficien subsiuion from foreign o domesic goods. This is mos likely o happen when impored and expored goods are price elasic, so demand is relaively sensiive o price changes. This is he essenial principal behind he MarshallLerner condiion. The MarshallLerner condiion is mos likely o be saisfied in he long run, raher han he shor run. Due o he ime involved in underaking search, price elasiciies of demand are likely o be larger in he longer run. This gives rise o a Jcurve ype effec in he rade balance following a depreciaion. In he shor run impors and expors are relaively price inelasic, so a devaluaion sees he erms of rade effec dominae and he rade balance deerioraes. However, over ime he price elasiciies rise and he devaluaion sars o creae sufficien subsiuion o improve he rade balance. The MarshallLerner condiion is considered a necessary bu no sufficien condiion. Sufficien condiions would also ake ino effec he following:
9  Absorpion effecs: a rise in ne expors raises domesic income, some of which is hen spen on impors.  ricing o marke: firms may aler he mark up on heir producs o preven exchange raes from alering heir prices in inernaional markes.  Real wage resisance: an increase in impor prices raises he overall price level in he economy and reduces he real wage of households. If workers push for higher nominal wages o mainain he value of he real wage, hen his will feed hrough ino he prices of domesic goods alering he inernaional erms of rade. More advanced problems 6. urchasing power pariy () is a long run heory of he exchange rae Discuss. There are various poins o make: The law of one price is driven by arbirage in he good marke his however is relian on households successfully searching for he cheapes goods prices. Because his search akes ime i is likely ha deviaions from he law of one price migh be persisen. The evidence ends o sugges ha in he shor run exchange raes are more volaile han prices whereas heory argues ha hey should share a common variance. I herefore appears o be he case ha shor run exchange raes reac o more han jus relaive prices. The Dornbusch model of overshooing is one possible explanaion (see he response o quesion 7 below). This model is consisen wih holding in he long run, bu in he shor run exchange raes are driven by uncovered ineres pariy (UI). Given ha financial markes are likely o be larger, more liquid and more compeiive, i is easy o jusify ha UI will have more validiy as a model of exchange rae deerminaion in he shor run. 7. Wha facors accoun for high exchange rae volailiy in he shor run? mpirical evidence suggess ha in he shor run exchange raes are more volaile han prices. One explanaion, according o he Dornbusch overshooing model, is ha exchange raes overreac o changes in he money supply when prices are rigid. The Dornbusch model works by exploring he ineracion beween he UI and heories of exchange rae deerminaion. If here is an increase in he money supply hen from he Quaniy Theory of Money here is a proporional change in he price level. % Δ M = % Δ. In his case here is no change in he real money supply and ineres raes remain consan:
10 M M =, 0 Δr = r ( M ) M s ( M ) M s r r M D, ( r Y ) M d, M s Then according o, % Δ = % Δ, hence prices and exchange raes exhibi he same degree of volailiy. However, suppose ha in he shor run prices adjus slowly so ha he Quaniy Theory of Money does no hold. % Δ M > % Δ As a resul a nominal expansion in he money supply also leads o a real expansion, puing downward pressure on equilibrium ineres raes in he money marke. M M <, Δ r = r r < 0 From UI, here is now an expecaion of exchange rae appreciaion % Δ e = r r. In he long run hough prices are assumed o fully adjus, so he real money supply will fall, ineres raes rise, and he exchange rae will depreciae in view of he higher price level and he predicions of. When prices adjus slowly, he ineracion of UI and hough creaes a siuaion where an expansion in he money supply leads o a shor run expecaion of appreciaion, bu a long run depreciaion. The only way hese wo faces can be
11 reconciled is if he exchange rae over depreciaes is long run level in he shor run. Therefore, % Δ < % Δ as he empirical evidence indicaes. M r M r M r (A) (C) 0 0 O (B) (D) 0 0 Anoher reason why exchange raes over shor horizons may be volaile is because of he linkage beween currency markes and equiy markes. Ineres bearing bonds are no he only financial asses ha invesors can purchase. However, because equiy prices are far more volaile han bond yields, some of he observed volailiy in financial markes may be ransmied ino exchange raes.
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