Economcs 141 UCSC Professor Kletzer Sprng 2017 Homework 4 Answer Key 1. Use producton functon and MPK dagrams to examne Turkey and the EU. Assume that Turkey and the EU have dfferent producton functons q f(k) where q s output per worker and k s captal per worker. Let q Ak 1/3. Assume that the productvty level A n Turkey s lower than A n the EU. a. Draw a producton functon dagram (wth output per worker y as a functon of captal per worker k) and MPK dagram (MPK versus k) for the EU. (Hnt: Be sure to draw the two dagrams wth the producton functon drectly above the MPK dagram so that the level of captal per worker k s consstent on your two dagrams.) Answer: See the followng dagram. b. For now, assume captal cannot flow freely n and out of Turkey. On the same dagrams, plot Turksh producton functon and MPK curves, assumng that the productvty level A n Turkey s half the EU level and that Turksh MPK exceeds EU MPK. Label the EU poston n each chart EU and the label the Turksh poston T1. Answer: See the followng dagram. c. Assume captal can now flow freely between Turkey and the EU and the rest of the world and that EU s already at the pont where MPK r*. Label r* on the vertcal axs of the MPK dagram. Assume no rsk premum. What wll Turkey s captal per worker level k be? Label ths outcome pont T2 n each dagram. Wll Turkey converge to the EU level of q? Explan. Answer: See the followng dagram. Turkey s captal per worker wll rse once captal flows freely between the two regons but t wll stll reman below the captal per worker n the EU. Ths s because, ntally, Turkey s hgh MPK wll attract captal from abroad, ncreasng output per worker n Turkey. But a lower productvty level n Turkey requres a lower captal per worker n Turkey for the margnal productvty n the two regons to be equal. In equlbrum, Turkey's captal per worker and output per worker wll be lower than that n the EU. q q EU A MPK qt 2 q T T1 T2 Captal flows nto Turkey from EU, k T rses, and q T rses, but q T q EU. k T and q T rse, but q T q EU. MPK T T1 A r* MPK R T2 k T kt 2 k EU k k T kt 2 k EU k
2. Use the --FX graphs and words to answer each queston. The Mexcan peso floats aganst the US dollar. (a) In 2007-08, the US suffered a rapd fall n aggregate demand. Assumng no changes n polcy n ether the US or Mexco, how does ths shock affect the exchange rate of the peso aganst the dollar and Mexco s output, consumpton, nvestment and trade balance? Answer: The US contracton reduces US output and nterest rate gven the supply of money. The fall n the US nterest rate causes the dollar to deprecate gven the nterest rate for Mexco. The peso apprecates aganst the dollar. Ths s shown n the --FX dagram: DR, FR DR US - Y FX E FR The apprecaton of the peso reduces the trade balance for Mexco falls (because the peso apprecates n real terms wth stcky prces). As shown above, US output falls n recesson. The fall n US GDP reduces demand for Mexcan exports and reduces the trade balance for Mexco. Both the exchange rate effect (expendture swtchng) and the foregn demand effect reduce the trade balance for Mexco: TB = TB!!/$!!"!!!"#$%, Y T, Y T. As shown n the - dagram for Mexco below, the curve for Mexco shfts nward as aggregate demand for Mexcan output falls wth the trade balance. Mexco s GDP and nterest rate fall. Mexco - Y
The fall n Mexco s nterest rate partally offsets the deprecaton of the dollar aganst the peso as shown by the shft of the FR lne n the FX dagram. Consumpton n Mexco falls because GDP falls, and the fall n nterest rates rases nvestment for gven GDP. The trade balance (TB) falls. (b) In late 2015, the Fed rased US nterest rates. Imagne ths was a sgnfcant ncrease. How should ths change n monetary polcy affect current and expected exchange rates and Mexco s output, consumpton, nvestment and trade balance? Answer: The rse n US nterest rates shfts the curve up for the US and the DR lne up n the FX dagram for the exchange rate of the dollar aganst the peso. The dollar apprecates aganst the peso, and the peso deprecates aganst the dollar. US GDP falls as the US nterest rate rses. DR,FR DR FR US - Y FX E E s the exchange rate of dollars for pesos. For Mexco, the deprecaton of the peso aganst the dollar tends to ncrease Mexco s trade balance. The fall n US output tends to lower Mexco s trade balance. If the expendture swtchng s more mportant than the ncome effect on export demand, then Mexco s trade balance mproves; f t s less mportant, then Mexco s trade balance decreases. An mprovement n the trade balance for Mexco rases Mexcan GDP and rases the nterest rate a bt for Mexco. The FX dagram above shows the upward shft n the FX curve. Mexco - Y
3. Use the --FX model and words to answer each of these questons. The euro floats aganst the dollar. Both the US and EU are n recesson. (a) Suppose the US ncreases ts government defct, but the EU does not change polces. How does ths affect the US and EU economes? Be sure to nclude the effects on exchange rates and trade balances. Answer: A fscal expanson n the US rases output and nterest rates at home. The ncrease n the US nterest rate shfts up the DR lne for the US, leadng to an apprecaton of the dollar aganst the euro. If the fscal expanson s permanent, the US prce level wll rse to reduce real money balances to return output to the natural level of output n the medum run. The expected exchange rate of the dollar for the euro falls, although by less than the spot rate n the short run. Snce US output ncreases and the euro deprecates, the US trade balance falls and the EU trade balance mproves. The curve for the EU shfts outward and European output rses. European nterest rates rse, but not by as much as US nterest rates (n the short run). DR, FR DR FR US - Y FX E E s the exchange rate of dollars for euros. * EU - Y*
(b) Who benefts from the US fscal expanson n the EU? Do export and mport competng ndustres? Do consumers? How about n the US? Explan your answers. Answer: In the short run, European exporters and mportng competng producers realze hgher demand for ther outputs due to the deprecaton of the euro and rse n foregn (US) demand for mports. The EU nterest rate rses, so producers of nvestment goods experence a net fall n demand f nvestment demand only depends on nterest rates. However, f nvestment also depends on output, then the effect on captal goods producers s ambguous. EU consumers beneft as consumpton rses wth output, although ther expendtures swtch away from foregn goods towards home goods. In the US, consumers beneft from hgher ncome and swtch some expendture away from home goods toward mports. Exporters and mport competng producers face a decrease n demand. Exporter and mport competng producer revenues rse n Europe and fall n the US under normal condtons (that s, when the Marshall-Lerner condton holds as descrbed n the appendx to Chapter 7). (c) Suppose EU polcymakers care about export and mport competng ndustres. How should EU fscal authortes respond to the US fscal expanson? What happens to the exchange rate and to EU and US trade balances? Answer: EU polcy makers wll want the euro to deprecate. If the fscal expanson n the US rased EU output above the natural level, then the EU wll want to reduce the government budget defct (a fscal contracton n Europe). Ths would brng EU output back to the natural level of output and reduce European nterest rates. If EU output s below the natural level, then the EU wll want the ECB to loosen monetary polcy lowerng European nterest rates and deprecatng the euro. Deprecatng the euro further aganst the dollar rases demand for EU exports and mport competng goods further worsenng the US trade balance. (d) Explan why a cooperatve polcy n whch both the EU and US undertake fscal expansons can make everyone better off n recesson. Explan why unlateral polcy (only the US expands) can help some and hurt others, hence be poltcally costly. Answer: Suppose both the EU and US are n recesson. Unlateral fscal expanson n the US rases US and EU aggregate demand. The EU benefts from a postve externalty of the US expanson through the trade balance. The rse s demand for EU exports comes from both the rse n US dsposable ncome and expendture swtchng towards EU goods as the dollar apprecates aganst the euro. Therefore, the US only realzes part of the total beneft of a US fscal expanson. Ths should lead the US to underutlze fscal polcy n recovery from the recesson.
Cooperatve fscal polcy n a recesson mpactng both the US and EU would requre the US and EU to take fscal expansons at the same tme. Each would contrbute to a fscal expanson that benefts both. From the US perspectve, unlateral fscal expanson hurts traded goods ndustres. In a noncooperatve polcy, the EU beggars ts neghbor. Under a cooperatve polcy, both regons realze an expanson but wth less expendture swtchng. When the EU and US adopt cooperatve fscal expansons, the exchange rate does not change as much (wth symmetrc economes and recessons, t may not change at all). 4. Assume that ntally the curve s gven by 1 : Y 12 1.5T 30 2G and that the prce level P s 1, and the curve s gven by 1 : M Y(1 ) The home central bank uses the nterest rate as ts polcy nstrument. Intally, the home nterest rate equals the foregn nterest rate of 10% or 0.1. Taxes and government spendng both equal 2. Call ths case 1. a. Accordng to the 1 curve, what s the level of output Y? Assume ths s the desred full employment level of output. Answer: : Y 12 1.5(2) 30(0.1) 2(2) 10 b. Accordng to the 1 curve, at ths level of output, what s the level of the home money supply? Answer: : M 10(1 0.1) 9 c. Plot the 1 and 1 curves for case 1 on a chart. Label the axes, and the equlbrum values. Answer: See the followng dagram. 25% Problem 9 20% 15% 10% 5% 1 1 0% 8 9 Y d. Assume that forex market equlbrum s gven by ([1/E] 1) 0.10, where the two foregn return terms on the rght are expected deprecaton and the foregn nterest rate. The expected future exchange rate s 1. What s today s spot exchange rate? Answer: 10%: 0.10 ([1/E] 1) 0.10 E 1
e. There s now a foregn demand shock, such that the curve shfts left by 1.5 unts at all levels of the nterest rate, and the new curve s gven by 2 : Y 10.5 1.5T 30 2G The government asks the central bank to stablze the economy at full employment. To stablze and return output back to the desred level, accordng to ths new curve, by how much must the nterest rate be lowered from ts ntal level of 0.1? (Assume taxes and government spendng reman at 2.) Call ths case 2. Answer: Plug the desred value of output (Y 10) nto the new curve to fnd the mpled nterest rate, 2 : (10) 10.5 1.5(2) 30 2(2) 10 11.5 30 30 1.5 0.05 5% f. At the new lower nterest rate and at full employment, on the new curve ( 2 ), what s the new level of the money supply? Answer: Plug the output and nterest rate from (e) nto the curve to fnd M: M 10(1 0.05) 9.5 The money supply must ncrease from 9 to 9.5 to acheve the desred decrease n the nterest rate from 10% to 5%. g. Accordng to the forex market equlbrum, what s the new level of the spot exchange rate? How large s the deprecaton of the home currency? Answer: Plug the new nterest rate nto the UIP condton: 0.05 (1/E 1) 0.10 0.05 1/E 1 1/E 0.95 E 1.053 The nomnal exchange rate wll ncrease from 1 to 1.053 when the money supply ncreases. The currency deprecates by 5.3% ( [1.053 1]/1). h. Plot the new 2 and 2 curves for case 2 on a chart. Label the axes, and the equlbrum values. Answer: See the dagram below. 25% 20% 15% 10% 5% New 2 New 2 0% 8 9 Y
. Return to (e). Now assume that the central bank refuses to change the nterest rate from 10%. In ths case, what s the new level of output? What s the money supply? And f the government decdes to use fscal polcy nstead to stablze output, then accordng to the new curve, by how much must government spendng be ncreased to acheve ths goal? Call ths case 3. Answer: If the central bank wshes to keep 1 10%, then we can fnd the mpled level of output from the new curve: Y 10.5 1.5(2) 30(0.10) 2(2) 8.5 From the curve we can fnd the money supply n ths case: M 8.5(1 0.10) 7.65 The money supply must decrease from 9 to 7.65 to keep the nterest rate unchanged. If the government wants to stablze output by adjustng government spendng (at a fxed nterest rate of 10%), we can use the new curve to fnd the mpled value of G: 10 10.5 1.5(2) 30(0.10) 2G G 2.75 Therefore, G must ncrease from 2 to 2.75 to offset the effects of the foregn demand shock. j. Plot the new 3 and 3 curves for case 3 on a chart. Label the axes and the equlbrum values. Answer: See the fgure below. ' and ' ndcate the and curves when curve has the same shock as n part (e) and the central bank stll keeps the nterest rate at 10%. Ths s the case dscussed n part (). Notce that once the government ncreases spendng, the central bank wll ncrease the money supply from 7.65 to 9 as the nterest rate rses wth ncrease n government spendng. 3 and 3 are the same as 1 and 1 for part (c). 3 1 10% B A C 3 8.5 10 Y
5. Many countres experencng hgh and rsng nflaton, or even hypernflaton, wll adopt a fxed exchange rate regme. Dscuss the potental costs and benefts of a fxed exchange rate regme n ths case. Comment on fscal dscplne, segnorage, and expected future nflaton. Answer: Hypernflatons are the result of excessve prntng of money, usually because fscal polcy makers lack the resources or wll to rase taxes or ssue debt wthout monetzng the defct. For these countres, a fxed exchange rate regme may be desrable to serve as a nomnal anchor n the absence of monetary polcy ndependence/dscplne. The benefts of fxng may be greater n these countres as they can beneft from a reduced nflaton and fscal dscplne. In general, there s a poltcal/economc cost of abandonng a fxed exchange rate regme and therefore fxng exchange rates also commands fscal dscplne. If the country s decson to adopt a fxed exchange rate s vewed as credble by the rest of the world, t may reduce nflaton expectatons and nterest rates, and make the transton to lower nflaton somewhat less panful. 6. In the late 1970s, several countres n Latn Amerca, notably Mexco, Brazl, and Argentna, had accumulated large external debt burdens. A sgnfcant share of ths debt was denomnated n U.S. dollars. The Unted States pursued contractonary monetary polcy from 1979 to 1982, rasng dollar nterest rates. How would ths affect the value of the Latn Amercan currences relatve to the U.S. dollar? How would ths affect ther external debt n local currency terms? If these countres had wanted to prevent a change n ther external debt, what would have been the approprate polcy response, and what would have been the drawbacks? Answer: Contractonary monetary polcy n the Unted States would lead to an ncrease n the U.S. nterest rates and an apprecaton of the dollar relatve to other currences. The value of dollar-denomnated labltes (n local currency terms) wll ncrease, and therefore reduce external wealth n Latn Amerca (assumng a smaller porton of external assets are dollar-denomnated). The rse of U.S. nterest rates would also ncrease the sze of nterest payments for Latn Amercan countres. To prevent the decrease n external wealth, countres would have had to follow the Unted States and reduce ther money supples to boost domestc nterest rates and prevent the deprecaton n ther local currences aganst the dollar. The drawback of ths response s that t would requre a contracton n output, pushng output below ts desred level. 7. he effects of the global fnancal crss on Iceland and Ireland were smlar, but the polcy responses were very dfferent. To llustrate ths, consder two countres that have pegged ther currences to the euro. Both countres experence large captal nflows that fund real estate purchases. Ths results n a sharp rse n domestc household debt and a housng bubble for each country. For smplcty, assume that Iceland uses the krona, and Ireland uses the punt (fctonal, but helpful). (Dagrams wll be useful.) (a) Explan how a sudden collapse n the real prce of housng affect natonal wealth for ether country. How does ths wealth effect shft aggregate demand? Answer: The sudden collapse of the real prce of housng reduces real natonal wealth. You should thnk of ths as a sudden drop n the value of domestc captal. As natonal wealth decreases, we expect consumpton to decrease, reducng aggregate demand, and leadng to a decrease n GDP n the short run (under stcky prces). In an - dagram, the curve shfts nward.
(b) Suppose Ireland keeps the punt fxed to the euro. How does the collapse of the housng bubble affect Irsh GDP? Do Irsh nterest rates or nflaton change n the short run? Answer: If Ireland keeps ts currency, the punt, fxed to the euro, then the Irsh nterest rate s fxed equal to the Eurozone nterest rate. The fall n Irsh aggregate demand reduces Irsh GDP wthout as shown n the - (equvalently, -MP) dagram: DR, FR MP DR FR Ireland - Y FX E E s the exchange rate of Irsh punts for euro Irsh GDP falls much more than f Ireland fxed the supply of money nstead of peggng the punt to the euro. The Irsh nterest rate does not change; Irsh nflaton does not change n the short run (prces are stcky). c. Suppose Iceland lets the krona float followng the collapse of ts bubble. Explan the effects of the bubble on Iceland s GDP, exchange rate of the krona to the euro, and on Icelandc nterest rates and nflaton. Answer: When the housng bubble bursts, aggregate demand falls n Iceland, and the Icelandc curve shfts nward. If Iceland lets the krona float after the housng bubble bursts, then the Icelandc central bank can ncrease the supply of krona. The curve for Iceland shfts outward, lowerng nterest rates for Iceland, and shftng Iceland s DR curve n the FX dagram. The krona deprecates aganst the euro (as shown n the -- FX dagram below). Ths leads to a rse n GDP for Iceland relatve to what t was or would have been f Iceland remaned pegged to the euro.
DR,FR DR FR Iceland - Y FX E E s the exchange rate of Icelandc krona for euro. The krona deprecates as Iceland s nterest rates fall, and ts output rses. Inflaton does not change n the short run, and wll not change n the long run because Iceland only needs to ncrease ts money supply, not the growth rate of ts money supply. d. Over the long run, Ireland keeps the punt fxed to the euro. How must Irsh prces adjust n returnng to full employment? What could the Ireland do to ease ts adjustment back to the long run? Answer: If Ireland keeps the punt fxed the euro, Irsh output needs to rse towards full employment output n the long run. Wth the punt fxed to the euro, Ireland cannot use monetary polcy (and expanson) to lower nterest rates to rase GDP. The adjustment back to the long run requres the real exchange rate for Ireland to deprecate. As the real exchange rate deprecates, the curve wll shft outward, rasng output to full employment output at the gven Eurozone nterest rate. The real exchange rate s gven by q =!!/!!"#!!"#$%&'. Because E!/ s fxed and the prce level for the Eurozone s gven, the Irsh prce level must fall relatve to the Eurozone prce level to acheve a real deprecaton. Thus, n the adjustment back to full employment, Irsh nflaton must fall relatve to Eurozone nflaton.