An Explanation (Using th ISLM Modl) of How Volatilit in Expctations About th Profitabilit of Futur Invstmnt Projcts Can Mak Aggrgat Dmand Itslf Volatil. Th ISLM modl is a combination of two conomic modls; thos of intrst and savings (IS), and liquidit prfrnc and mon suppl (LM). To full undrstand th ffcts of changs in th various lmnts of th modl, it is ncssar to xamin th two major componnts in furthr dtail. Th IS curv is drivd initiall from th gnral quation for aggrgat dmand. It can b quit asil provn that, in a closd conom, th total dmand,, is givn b: = c + i + g, whr c, i and g ar dfind as dsird consumption, invstmnt and govrnmnt spnding rspctivl. It can also b drivd (but will not b hr, as onl th final rsults ar rlvant) that consumption is givn b th quation: c = a + b, as pr J M Kns thor of th consumption function 2 (th two othr variabls ar an autonomous lmnt and th marginal propnsit to consum rspctivl); and that invstmnt can b dfind in trms of th ral rat of intrst: m i = I + h( r P& 0 ), as dscribd b D W Jorgnsn 3 (I 0 is, again, an autonomous lmnt (th dprciation of xisting capital goods, whil h rprsnts th snsitivit of invstmnt to changs in th ral intrst rat). Th drivation of incom xpnditur is, obviousl, of highr importanc hr, and shall b xamind in gratr dpth latr. Finall, it can b assumd that g is an xognous constant, and is fixd b an indpndnt bod. Th ISLM modl was first dvlopd b Sir John Hicks, who also namd th IS and LM graphs. Th IS curv shows thos lvls of incom and intrst at which invstmnt quals savings; th LM curv shows thos lvls of incom and intrst at which mon dmand (which Kns calld liquidit prfrnc) quals mon suppl. Ths dfinitions ar xpandd on in th ssa. 2 S also Millr (996) 3 Jorgnsn (936) Pag
B combining th abov quations, and looking at th modl intuitivl, w can s that aggrgat dmand will b influncd b ral incom, intrst rats, xpctd inflation, and changing lvls of govrnmnt xpnditur. Howvr, b noting that w assum th actual xpnditur in th conom (which hr is rprsntd b th aggrgat dmand) is qual to both th actual incom and th actual output, w ma find that: a + I = m + g h( r P& b 0 ). This quation is said as dfining th IS curv; it shows how saving (which is dfind as incom minus consumption) varis, in a two-sctor conom, with invstmnt xpnditur. Th curv itslf tracs out lvls of incom and intrst rats at which th two factors mntiond ar qual; that is, whr injctions into th conom ar qual to withdrawals from th conom. This dfins quilibrium, as othrwis incom will ithr b rising or falling as housholds ar givn mor than th giv, or vic vrsa. From xamination of th abov quation, it can b sn that incom and intrst rats ar ngativl proportional; that is, th IS curv taks on a shap similar to th following: r m r m r m 2 2 Pag 2
This shap can b xplaind b considring how aggrgat dmand (and thus incom) is built up of invstmnt and consumption componnts. If w assum both govrnmnt xpnditur and th xpctd rat of intrst ar xognous (and so w labl th curv IS [ g, P& ]), w can xamin th ffcts of a chang in incom. Consumption is considrd as a stick variabl that is, it dos not altr instantanousl. Thrfor, an chang in intrst rats will, initiall, onl affct aggrgat dmand through th invstmnt function dscribd abov (and to b discussd blow). Changs in this aggrgat dmand (and thrfor also incom) will altr th consumption lmnt ovr tim, but b an amount lss than th initial incras in incom. Th dirction of influncs on th lvl of aggrgat dmand is obviousl important hr; it can b statd that a ris in intrst rats will mak saving mor attractiv than borrowing for invstmnt, and so aggrgat dmand (and thus incom) will fall. This can b addd to th abov paragraph to dtrmin th shap of th IS curv; it is known that invstmnt and consumption will altr in th sam dirction, and now it is known that a fall in intrst rats lads to a ris in incom. Th graph drawn abov follows. To look at th othr sid of th ISLM modl, that of suppl of and dmand for mon, it is first ncssar to dfin clarl som othrwis vagu trms. It is fundamntal, for xampl, to dfin mon as a form of financial asst that is radil xchangabl for goods and srvics; th dmand for mon would othrwis b infinit and th following analsis would b impossibl. Th dmand for mon, thrfor, is th amount of financial assts popl wish to hold in a form that dos not arn intrst but can b usd as pamnt for goods. This will, it is assumd, b a finit valu, as consumption dmands ar limitd ovr short priods of tim, and incom is anothr limiting factor. An othr assts will b hld as bonds, arning intrst and incrasing potntial consumption in th nxt tim Pag 3
priod. Tim Millr: Mon dmand will also b dfind to b a ral valu; that is, changs in montar valu du to inflation will b xcludd from this modl. Thr ar two major influncs on th dmand for mon thus dfind. Aggrgat ral incom is prhaps th most obvious, as it can quit asil b assumd that an incras in incom will lad to a gratr dmand for consumption, and thus a gratr nd for mon. Th rat of intrst on bonds is th othr main factor, as can b partiall sn from th dfinition of mon dmand; assts ar hld as ithr mon or bonds, and anthing that maks ithr of th options mor attractiv will bias th ratio in its favour. Mon dmand is thus ngativl proportional 4 to th rat of intrst. From this w can driv an quation for th nominal dmand for mon, m d,intrms of incom (), th gnral pric lvl (P), and th gnral intrst rat (r m ): m d m = P( k lr ), whr k and l ar positiv constants, rprsnting th snsitivit of mon dmand to changs in incom and intrst rats rspctivl. Th suppl of mon, convrsl, is vr asil (and obviousl) dfind; it is th amount of liquid assts manufacturd b th countr s govrnmnt and rlasd into circulation. As this is not influncd dirctl b an of th variabls in th ISLM modl, it shall b assumd to b xognous, and normall constant. It is ths dfinitions that lad to th drivation of an quation for th LM curv, and th corrsponding graph: 4 Not th us of th phras ngativl proportional rathr that invrsl proportional ; th lattr implis that on lmnt varis with th invrs of th othr (that is, on dividd b it), whil th formr implis that th two var dirctl, but with on of th lmnts mad ngativ. Pag 4
r m r m 2 r m 2 This graph is quit asil found from th quations for mon dmand and suppl in quilibrium, as alwas, suppl and dmand must b qual (and if th ar not, thr will b forcs acting to mak this so), and so th LM quation can b found b simpl substituting an xognous M (mon suppl) into th dmand for mon formula: m M lr = +. kp k Again, it is ncssar to assum that crtain factors ar constant to draw th graph from this quation, in this cas M and P. Th LM curv is thus writtn LM M, P ], [ and furthr analsis ma rval that variations in mon suppl and pric lvls hav th ffct of purl shifting th LM curv. Now that th IS and LM modls ar complt, it is possibl to combin th two to find a modl for aggrgat dmand in an conom. B dfinition, an conom in quilibrium will b on both th IS and LM curvs, as total withdrawals will qual total injctions, and mon dmand will qual mon suppl. Howvr, bcaus of th shaps of th functions, it can b sn that thr is onl on plac at which this is tru, and so quilibrium aggrgat dmand will b at a position whr th IS and LM curvs cross: Pag 5
r m LM M, P ] [ r m * IS [ g, P& ] * It can b sn that this lads to th conclusion that aggrgat dmand is influncd dirctl purl b th lvls of mon suppl, gnral prics, govrnmnt xpnditur, and xpctd inflation; and ths factors also dtrmin th intrst rat. This is, thrfor, obviousl a simplifid modl, but it can b shown that ths four factors ar th strongst influncs, and so th modl rmains approximatl valid. Th aggrgat dmand curv is thn found, from this modl, b varing th gnral pric lvl and thus shifting th LM curv (to th right for a fall in prics, to th lft for a ris). Th shift in LM curv will var according to th original pric, and it would b obsrvd that th aggrgat dmand curv volvd to b hprbolic in shap. In purl algbraic trms, it is possibl to quat th two formula for incom (or aggrgat dmand), and obtain th formula: d a + I + g + hp& 0 = b + hk l Mh +, P[( b) l + hk] which will hlp to look at how dmand will altr following changs in th individual lmnts, or, mor spcificall, in invstmnt. Bfor an conclusions can b drawn in this ara, howvr, it is first ncssar to xamin th invstmnt function, Pag 6
m i = I + h( r P& 0 ), in gratr dpth. It is first assumd that consumption is fixd, and so an xcss incom ma b spnt in on of two was; on bonds (with a fixd rat of intrst), or on invstmnt. B th law of diminishing rturns, th amount of gain from invstmnt will fall with ach xtra unit of mon invstd, whil th rat of rturn from bonds stas th sam. A rational consumr will thrfor invst up until th point at which bonds bcom a mor attractiv proposition, that is, whr th rat of rturn from invstmnt quals that of bonds. Th rat of rturn for bonds is simpl th intrst rat; th rat of rturn on invstmnt is found b adding th valu of srvics gaind (r ) to th xpctd inflation rat ( P & ), and taking awa th amount spnt on dprciation (d). Equating ths two statmnts, a gnral formula is obtaind: r m P & = r d ; and, from this, w can s that th optimum lvl of invstmnt is dtrmind b a function of th rat of intrst and th xpctd inflation rat. This is th point at which optimism is introducd, in that highr optimism lads to a highr xpctd rat of rturn and a lowr dprciation rat, and from th formula this must all b balancd b an altration in th xpctd inflation rat. Finall, it is assumd that invstmnt xpnditur is a linar function of th ral xpctd intrst rat (that is, th intrst rat minus xpctd inflation), and, knowing that dprciation must b includd in th formula and that it will b roughl constant du to th vr larg stock of capital in most conomis, th invstmnt function is rvald as that dscribd in th first part of this ssa. So, thn, it is now possibl to look at varing xpctations in th profitabilit of invstmnt projcts. As mntiond abov, th main (and possibl onl) indicator of varing optimism in th ISLM modl will b th xpctd rat of inflation, which in turn will var with th valus for th xpctd rats of rturn on invstmnt, and Pag 7
dprciation. It is th ffcts of changs in this variabl, thrfor, that must b xamind to dtrmin how volatilit in xpctations affcts aggrgat dmand. An volatilit in optimism, and thrfor in xpctd inflation, will lad to shifts in th lvl of invstmnt via th invstmnt function dscribd abov. A fall in xpctd inflation will incras futur valus of mon, and invstmnt will bcom lss attractiv compard to bonds; th ral rat of intrst will hav risn. From this, and b looking dirctl at th quation drivd for th IS curv, it is possibl to dduc that varing optimism will caus th IS curv to shift, to th right for incrass in xpctd inflation, and to th lft for dcrass. Transfrring this to th ISLM modl, w can s how shifts in th IS curv will affct th quilibrium lvl of aggrgat dmand for an givn pric lvl: r m LM M, P ] [ r m 2 r m IS [ g, P& ] IS [ g, P& 2 ] 2 ' A shift in th IS curv to th right (causd, as dtrmind, b an incras in xpctd inflation) will thrfor rsult in an incras in aggrgat dmand, but (as can b sn on th diagram abov, comparing th arrow 2 with th arrow ') th incras hr ( 2 ) will not b as larg as th original shift in th IS curv ( ' ). Th fraction of th original shift b which dmand will incras is dtrmind b th slop of th LM curv, which in turn rprsnts th rsponsivnss Pag 8
of incom and intrst rats to changs in th mon suppl (a stpr curv indicats largr rsponss). Th amount dmand (and incom) will ris is, howvr, th sam, rgardlss of th original position of th IS curv, for th sam shift in IS. It can b dducd from this that th ovrall ffct of th shift in IS will b to shift th ntir aggrgat dmand curv to th right b th amount rprsntd b th bold arrow in th last diagram: P P AD[ P,...] AD[ P 2,...] 2 It is, howvr, not th ffct of a spcific movmnt in optimism bing studid hr, it is th volatilit of this variabl. Th volatilit of th IS curv will b of a similar magnitud and varianc, and it can b gathrd from th spcific cas outlind abov that an changs in th IS curv will lad to a smallr but proportional shift in aggrgat dmand. B considring this cas in both dirctions it is possibl to s that volatilit in th IS curv (du to volatil xpctations) will lad to a smallr dgr of volatilit in aggrgat dmand, but th volatilit will still xist. Finall, this rsult can b considrd intuitivl; it is known that invstmnt is onl on part of aggrgat dmand, and th othr factors ar mor or lss (and assumd to b) indpndnt of optimism (and, spciall, as dfind in th titl, rfrring to rturns on invstmnt!). Invstmnt itslf contains an autonomous lmnt, and a multipling factor. Th xpctd inflation rat is, thrfor, a vr small proportion of Pag 9
th total dmand in th conom, and will hav lss of an ffct on it than on anthing dirctl xamining invstmnt. Riss in aggrgat dmand will, thrfor, not b as significant as riss in invstmnt functions. Pag 0
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