pays no interest per $ r LT r ST per $

Transcription

1 IS-LM analysis assumes thee is only one inteest Standad. his is vey unealistic. In the eal wold thee ate many inteest ates, depending on the how long you lend ae money and at what isk of default. o undestand M. you theoy of the speculative demand fo money (idle Keynes's we at least need to distinguish the inteest ate on alances), and the inteest ate on long-tem lend- lending S shot-tem ing focused on. mainly we now assume an economy with thee financial as- Hence in addition to demand deposits D paying no inteest and sets: deposits paying S, thee ae also long-tem onds time Let P value of its futue payments. Fo pepetuities, the discounted discounted value fomula is especially simple: pesent C is the coupon on the ond, that is, C is the amount whee the ond pomises to pay each yea foeve. 1 his fo- that eflects the invese elation etween the pice of onds mula the long-tem inteest ate. and lending involves inteest-ate isk: when you lock Long-tem a long ate this yea, you ae not sue what the long ate into e next yea. Pehaps you have locked into lending at too will a ate? he lende's expected ate of capital gains low long-tem lending this yea is the amount he expects fom onds to appeciate in value this yea, pe dolla put into his whee P e P e to pevail next yea (that is, his est guess aout expects value of the long ate next yea). His expected ate the etun fom long tem lending equals his cuent inteest of pe dolla in onds plus his expected ate of capital income hold the ond this yea and then esell it next yea, you will get C only inteest this yea, ut next yea the C dollas of inteest will go dollas PORFOLIO CHOICE AND MR. KEYNES'S SPECULAIVE DEMAND C P ; FOR MONEY Intoduction: 3 assets and 2 inteest 1. ates onds: e P e P g ; P ecause M. Keynes unlike textook Keynesians the pice of onds the lende expects will pevail is next yea. In othe wods, using the invese picing fomula, C e, whee e is the long tem inteest ate the lende which fo simplicity we take to e pepetuities paying. pays no inteest S pe $ pe $ gains: R e + g e : D 1 is paid to the cuent owne. So if you uy the ond this yea and C it foeve, you will get a check fo C dollas each yea. But if you keep e the cuent pice of a ond, that is, the pesent to the new owne. 1

2 simplicity, we will assume that individuals ae isk neutal. Fo hat is, they choose etween financial assets to ty to thei expected ate of etun. Unlike isk-avese individuals, maximize isk-neutal individuals only hold the financial as- with the highest expected ate of etun; they do not set(s) divesify. at the micoeconomic level, conside an individual with Now dollas to lend. hink of W as his total Wealth excluding W amount of money he needs to hold in his checking account the tansaction puposes. he individual's potfolio choice fo is to detemine what mix of financial assets to hold polem Wealth. In ou case, thee ae only 3 financial assets, his his potfolio choice polem educes to how much of his hence dollas to put into D, how much to put into, and how W choice polem even futhe y assuming S > 0. potfolio he will not put any of his Wealth into D: offes a hen etun. hus, fo now we can just focus on his choice highe shot-tem lending and long-tem lending. etween Define min as the lowest value of such that the individ- would still e willing to lend long-tem this yea. Recall, ual he lends long-tem, his expected ate of etun will e if R S S shot-tem lending involves no inteest ate isk (at the since of the yea he will get ack his oiginal pincipal plus his end thee is no chance of a capital loss, that is, his oiginal inteest; shinking in size). Consequently, min is given y the pincipal value of even a little elow min, the individual will put all of falls into ecause R S > R e, so he would do no long-tem W On the othe hand, if > min, he will put all lending. W into since onds offe a highe expected etun. Only of when lending since oth and yield the same expected long-tem Summaizing: etun. will e Micoeconomics: An Individual's 2. Choice Polem Potfolio that satisfies the fomula R S R e ; o equivalently, when min : S + g e (1) S pe $ pe $ he idea is illustated elow. much to put into. Potfolio choice when S > susection 2.3 elow, we will simplify the individual's Until When min : -g e pe $ o see why Equation (1) chaacteizes min, oseve that if min will he e indiffeent etween shot-tem and R e + g e : On the othe hand, if he lends shot-tem, his ate of etun 2

3 individual's optimal potfolio choice An if S > 0: ule min, the individual is indiffeent etween the of his Wealth he puts into onds and time amount 1: Wealth put into athe than as a function Figue of the cuent long ate, assuming S > 0 he aove ang-ang (that is, all-o-nothing) featue Note: of the individual's optimal potfolio choice unless happens to equal the individual's min follows fom ou just of isk neutality. A isk avese individual would assumption put some of his Wealth in even if R S < R e against the inteest ate isk involved in long-tem lending. hedge hat is, he would hold a divesified potfolio athe than potfolio concentated on the one financial asset with the a expected etun. highest 2.2 How to calculate min little calculation will give us a neat fomula fo the individual's A min : Notice his min e 1+ e (1 + S ) : is a function of oth his expectations e the cuent shot ate S, hence we can wite min and min ( e ; S): In paticula, the individual's min goes up (+) min ( e (+) ; S ): min the deivation of the fomula. Recall when Hee's min : P 1: e in ode to > min, the individual just puts all his Wealth W onds this yea. into deposits this yea. < min, the individual just puts all his Wealth W time deposits this yea. into min he ule is illustated in Figue 1. in this segment >, min so the individual only lends long-tem min in this segment, so he is indiffeent min etween shot-tem and long-tem lending in this segment <, min so he only lends shot-tem when eithe e o S goes up, so 0 W deposits in if S > 0 S + g e : (1) It is useful to have a little fomula fo g e. Recall e (P e P ) g P P e he picing fomula fo pepetuities implies: P C and P e C : 3

4 into the fomula fo g e, the C's cancel yielding: Plugging ou little fomula fo g e, (1) ecomes: Using S +( e 1): (1 + S ): 1 (Speculative alances need not e idle): Example an individual with Wealth W $10; 000 to lend. Conside ß 9:2%. hat is, if the cuent long ate wee elow (1:01) the individual would not e willing to lend long-tem 9.2%, yea, pefeing to put all his Wealth W into a time deposit this in spite of the fact that his time deposit only pays 1% inteest. he seeming paadox is explained y the him that he expects the long ate to ise to 10% next yea; fact so if speculating on the long ate inceasing. In this sense his in in might e called speculative alances" even deposits they ae not eing held idle (that is, in D) ecause though S > 0. So fa we have assumed S of demand fo idle speculative alances, wenow need to theoy this assumption. In this susection we assume S 0, elax holding one's wealth in eithe checking D o savings does so matte to the individual: eithe way he'll have a zeo ate not individual's optimal potfolio choice An if S 0: ule > min, the individual just puts all his Wealth W onds this yea since they have a positive ex- in pected ate of etun, while oth D and min, the individual is indiffeent etween the of his Wealth he holds in onds, time de- amount, o demand deposits D this yea since they posits have zeo expected ate of etun. all < min, the individual is indiffeent etween the ofhiswealth W he puts into time-deposits amount o demand deposits D this yea, ut he does no lending this yea ecause its expected ate long-tem M. Keynes's micoeconomic theoy of 2.3 M d P ) spec: Potfolio choice when S 0 ( g e e 1: > 0. o aive at M. Keynes's etun on his Wealth. he fomula fo the individual's min of unchanged. But now his optimal potfolio choice may emains Solving fo we find that when min : include some idle alances if» min : e e 1+ So we have aived at ou fomula fo min! S 1% and the individual expects e 10%. Suppose plugging into the fomula we find his min :1 1:1 hen have a zeo etun. < 9:2%, the individual will want to hold his money etun is negative (the ate of capital losses g e of lage). is 4

5 ule is illustated in Figue 2 elow, dawn assuming he individual holds all his Wealth in his checking account the Figue 2: S 2 (Speculative alances may e idle when Example S 0): Conside again the individual in Example 1 with W $10; 000 and expectations e Wealth S now 0% athe than 1%. hen plugging into the fomula fo min we find that now his min :1 if the cuent long ate wee elow 9.1%, the individual is, not e willing to lend long-tem this yea, pefeing to would all his $10,000 of Wealth idle in spite of the fact that hold alances pay him no inteest. he seeming paadox is idle y the fact that he expects the long ate to ise to explained next yea. So if < 9:1%, he pefes holding his money 10% this yea as Keynesian idle speculative alances," speculating idle on the long ate inceasing next yea. Since S 0%, is no lost inteest in holding his cash idle in D, athe thee putting it into whee the ank may e-lend it. hat than in tems of potfolio choice, he's indiffeent etween D and is,, ut pefes eithe to. Indeed, even if he puts some of his Wealth into, since S will lend all the money in out even on a shot-tem ank Just like the individual, the ank has nothing to lose asis. let's move to the maco level. In geneal, diffeent people Now have diffeent eliefs aout the futue long ate. One may may e vey optimistic and expect the long ate to peson a lot next yea, so fo him e is much lage than ; ise peson may e pessimistic and expect the long ate anothe fall next yea, so fom him e <. he optimistic to will have a high min and, hence, may cuently e individual lots of speculative alances gamling on the long ate holding By contast, the pessimistic individual will have inceasing. low min and e glad to lock into the cuent long ate y a in Example 1, even the optimistic individual will not e like any idle speculative alances if S > 0: As long as holding S a savings account which pays no inteest; the ank will e-lend his savings D so his speculative alances will not sit idle. deposits, equiliium values y S and. We will us denote these eveyone is isk neutal. Futhemoe, fo assume to continue min hee <, so the individual min may e holding some idle alances in his potfolio y holding some of the deposits in as idle eseves. when < min hence as idle speculative alances. 0 thee is no paticula eason the Macoeconomics: M. Keynes's 3. fom CQ escape 0 W M spec d 0, some people may hold idle speculative alances. 10%. Suppose 1:1 lending long-tem today efoe ates go any lowe. ß 9:1%. hat Notice, > 0, he will want to put his speculative alances into athe than into his checking account now want to detemine the equiliium values of S We, given people's expectations aout the futue. Let and 5

6 we will also estict ou attention to the special simplicity, in which case eveyone has the same expectations e, a given fixed ffl nume. e is fixed, if the cuent long ate goes elow Since e, lendes elieve it will evet to e next yea. hus this follows M. Keynes. Recall he thought lendes assumption a elief aout a nomal" level fo the long tem inteest have ate. Wheneve lendes see the cuent long ate nomal ate, they elieve it will soon etun to nomal; in this jagon, Keynes elieved individuals have inelastic inteest the expectations. We identify lendes eliefs aout what is the ate level of the long ate with thei fixed expectations nomal" next yea's long ate, e. aout ticky thing is that we need to detemine 2 inteest he not just one. Othewise we could just look at the inteest ates, at an IS-LM cossing. We will poceed in 3 steps. he step take of this ticky polem: it will show fist will cae a simple elation etween S and. So exists thee that Step 1: he elation etween S and claim is that, in equiliium, the expected ates of etun My shot-tem and long-tem lending must e equal, given fom lendes' expectations. hat is, R S Why? Suppose R S > R e. hen no one would lend long- (ecall eveyone is isk neutal and has the same expectations)tem Hence fims could not get any long-tem loans to thei investments. hey would offe to sell thei copoate finance onds fo less, to attact lendes. But y the invese P #) ". So the long ate would ise until equality elation, is eached etween the two ates of etun. On the othe hand suppose R S anks would get no deposits in savings accounts shot-tem; since onds ae moe attactive. But then anks would e to attact deposits since they see they could take the eage paying only S and then lend the money out long- deposits making an expected pofit. o attact depositos, they tem, aise S until again thee was equality. Summaizing, would the ates of etun fom lending long-tem and shottem unless ae equal, eithe S o will adjust. So, as asseted, S + g e. in equiliium S, ecall min ( e ; S ) is pecisely the given any Fo ate that equalizes the expected ates of etun fom longtem long and shot-tem lending. So, anothe way to expess ou S * pe $ * pe $ In equiliium : -g e pe $ fall elow < R e. hen no one would want to lend if we know one equiliium ate, we will know them oth! R e,ogaphically: that in equiliium min ( e ; S ). hat conclusion is eveyone has the same e, the fomula fo an indi- when is, vidual's min is also the fomula fo the equiliium value of 6

7 e 1+ e e 1+ e that is, the long ate that, pevail if the shot ate wee zeo. he gaph of (2) would is shown in Figue 3 elow. Notice fom the gaph that 0 min ate ecause people expect capital gains. hese conclusions long can e e-expessed in tem of the tem stuctue of ates, that is, the gaph in which the tem to matuity inteest of loans is put on the hoizontal axis and the inteest sloping e < when upwad e >. when We will use an IS-LM diagam with to detemine. hen we will e done, since eithe axis o Figue 3 gives us the coesponding equili- (2) Equation value fo the shot ate. ium the LM descies all cominations of and Y Recall the money maket fo a given eal money supply. equiliate we have to know what detemines money demand in ode So divide up total money demand into tansaction demand, we demand, and speculative demand. pecautionay know that (3) leads to a vetical LM if people hold no You alances. asset Keynes focused on speculative athe than pecautionay Since alances, we will follow him and also assume in the couse we will look at pecautionay demand.) (Late let's conside the speculative demand fo money. Finally, M. Keynes we have aleady assumed that people Following fixed expectations e. So when they see fall e- have e this yea, they expect it will evet to e next yea. low you know, this may give ise to a speculative demand fo As money. 2 Step 2: he shape of the LM cuve given S! In paticula: on the vetical (1 + S ) : (2) o gaph (2), define 0 min that * to detemine the shape of the LM. Following M. e Keynes, min o e S * conside tansaction demand. Recall that M. Keynes Fist with CQ that tansaction alances ae not vey in- ageed sensitive (unlike textook Keynesians). So, following teest and M. Keynes, assume that tansaction demand is CQ given y: M d P ) t ky: (3) ( Figue 3: he gaph of equation (2) intecept, and that S only when equals the vetical e. e <, the shot ate is elow equal ates oth long ecause expect capital losses fom longtem the ate people if e >, the shot ate is aove the while lending; M d P ) pecautionay 0: ( he tem stuctue is on loans is put on the vetical axis. and it is downwad sloping 7

8 paticula, analysis of individuals' potfolio choice In ou that as long as S > 0, no one will hold any money shown has as 0 > min (ecall Equation (2)). his implies the long analysis individuals' potfolio choice also showed that ou of S 0, no one will e willing to lend long-tem elow when speculative Hence total money demand equals as alances. as long as S > 0 o, equivalently, as demand tansaction LM cuve is vetical until 0 min just as in CQ. But 0 min speculating instead on the long ate ising next yea. unlike CQ, the LM has a floo at 0 min. Comining these So, shows that (3) plus ou assumption that eveyone osevations the same fixed e yields an LM that looks like the one has ae now essentially done. Comining ou Keynesian LM We an IS will tell us the equiliium long ate, and hence with (2) o Figue 3 will tell us the coesponding equiliium Equation shot ate. Suppose the economy has een at full em- equiliium a time at point A 1 in the figue ployment fo long S 10%. Since this has gone on fo a with elow, time, lendes have gown accustomed to getting 10% on long loans, hence e 10% also. Oseve that this long-un thei with Figue 3: S e. equiliium is consistent is a small eal shock and the IS shifts down a thee now 2 : will go down enough to completely offset the point A and, (2) tells us that the shot ate S will also shock; eal S will go down moe than ecause go down. Indeed losses fom long-tem lending; and in capital expect people the expected ates of etun fom shot-tem and equiliium, lending must e equal. long-tem instead thee is a lage eal shock and the IS shifts down IS 3, the economy will go into a liquidity tap ecession at to : will go down to 0 min ß 9:1%, which is not enough to A 3 eal shock; and, (2) tells us that the shot ate S the offset go down even moe, indeed all the way to zeo. will that afte each of the aove eal shocks the shot Notice IS 3 IS 2 IS 1 IS 0 M LM( P ) 0 * A 0 1 * 10% 2 * 0 min 9.1% A 3 A 2 A 1 Y 3 Y FE Y in Figue 4 elow. Step 3: Comining Keynes's LM with an IS Figue 4: M. Keynes's escape fom CQ Example 3: little to IS 2, the economy will emain at full employment at By money" we mean M1 (naow money, hence D) athe than 2 (oad money, including oth D and ). he naowe definition of M2 money is moe appopiate fo IS-LM analysis. ate fell elow the long ate, so the tem stuctue of inte- 8

9 ates was upwad sloping (which empiically is its usual est Conside instead a tempoay incease in the IS shape). is, an incease in attactive investment oppotunities to that 0. hen the economy will move toa 0 with the long ate go- IS up to 0. his ise in the long ate is needed to discouage ing demand given that the existing eal money supply investment finance moe tansactions. Futhe, (2) tells cannot any eal S will go up even moe than, so thee will that us an invesion of the tem stuctue: people can get moe e lending shot-tem than y lending long-tem. How toex- y it? e >, people expect capital gains fom Since plain lending. So... (you should e ale to fill in the long-tem est). 9