A re-examination of Solow's growth model with applications to capital movements

A RE-EXAMINATION OF SOLa'l' S GRCWl'H MODEL WI'.rH APPLICA'llIONS TO CAPITAL MOVEl".ENTS

Neantro Saavedra Rivano

-ｎ･ｾｮｴｲｯ＠ ｓｾｒｶ･､ｲ｡Ｍｒｩｶ｡ｮｯＪ＠

1. Introductlon nnd _{｣ｵｾｾ｡ｲｷ＠}

Thc maln purpose of ｴｨｬｾ＠ ｐｾｐｅｲ＠ ls to re-examlne thc

ｮｾｯＭ｣ｬｾｳｳｬ｣｡ｬ＠ Solow's ｾｲｯｷｴｨ＠ ｭｯ､ｾｬＮ＠

A

veru ｾｬｭｰｬ･＠ ｦｯｲｾ｡ｬｬｳｭ＠

unde:rluing this model ｉｾ＠ developcd (sectlon 2> ｾｮ､＠ shown to

have sevcral ubes. Flrst, lt allow& · ｾｮ＠ casy 9e:nerallzatlon

of Solow's modpl to the ca5e of ､ｬｦｦｾｲ･ｮｴｩ｡ｴ･､＠ savlng

propcnslties (sectlon 3). Second, two-country models ｣｡ｾ＠ be

tre;ücd r1ort.· slmply <section 4>. And flnally, some:- generally

a c ｣Ｍｾ＠ p te d ｮＺｾ＠ s u 1 t s o n t h e 1 o n 9 -r u n b e n e f I t 6 o f f r e e c a p I t a 1

mobll lty can be properly lnterpretcd and understood. In

p a r t I c IJ 1 i! r , i t i s 6 h o vm t h ct t u n d e r r e as o n a b 1 e a 55 um p t i o n s r

In the: conte:xt of a two- country model, and starting from an

｡ｵｴ｡ｲｾｬ｣＠ long-run equllibrlum, free:ing the: move:ments of

physical capital may diminish in the long run the we:lfare of

one of the countrles and e:ve:n ｾｨｲｬｮｫ＠ the per-capita world

capital stock.

2. ｔｨｾ＠ ｳｩｾｰｬ･＠ ｾｯ､･ｬ＠

Let U$ recall, for convenlcnce, the conventlonal

neo-classical (Sol ov ian> settin g of a one-se: ctor growing

･｣ｯｮｯｾｹＮ＠ A single good i s produced using capital K and labor

L In a ｾ｡ｹ＠ descrlbed by a linear homogene:ous productlon

function FCK,L >. Lctting k = K/L and

the usual <Inada) conditlons on the production ｦｵｮ｣ｴｩｦＧ ｾ＠. ... an

be: stated as follows:

f(0) = 0 f'Od

>

0 fO<>- l<f'C!<:

>e

lirn f'(l<) c 0 lim f'Ü) =m f''(l{) ( 0

k +co k+ 0

It is further ｡ｳｳｵ ｭｾ､＠ that a ｣ｯｮｳｴｾｮｴ＠ fract ion 5 of

income:-<ide:ntical to lhe product, up to this point) is saved, and that labor grows at a constant rate: n • The accumulation

ｾｱｵ｡ｴｬｯｮＬ＠ exp,.-essed In pc,.--capita te:rms, is e:aslly found to

ic Professo r. Escol.J de PÓs-Graduacão em Economia , Fundacão Cc tÚlio ｖ＼Ｚｾｲﾭ

gas,· Hio de·Janl:!iro,RJ 22 . 250 . 1\.n ･｡ｲｬｩ｣Ｑｾ＠ and prcliminary vendon of tlüs paper \vas prc t.cnLed at thc 7th Brazilian Mect1ng of. Economct1·ics. T \o.' :Jn t

be

•

k • $f( k) - nk ( 1 )

lhlG 15 & rnthcr ￧ｬｭｰｬｾ＠ ､ｬｦｦｾｲ･ｮｴｬ｡ｬ＠ equntlon In thc

ｳｴｾｴｾ＠ v«rtablc k. It ｨ｡ｾ＠ n ｵｮｬｱｵｾ＠ cqutllbrlum $olutlon

k,

whlch I\:. C?r.. i lu Ç,hOl'JO to be 910b •. lly stable. lhe

ｾｴｲ｡ｬＹｨｦｯｲｷ｡ｲ､＠ mcthod of flndlng thc ｾｴ･｡､ｙＭｇｴ｡ｴｾ＠ ｶｾｬｵ｣＠ Df

the ｣｡ｰｩｴ｡ｬＭｬｾ｢ｯｲ＠ ratlo 15 ｾｉｭｰｬｾ＠ to equatc to zero thc

rlght-hund sldc of (1)

sf<k) Ir: nk

lhls cnn be also done graphlcnlly by flndlng the

intcrscctlon (othcr than the orlgln) of the graph of the

concave functlon 6f(k) wlth the ｳｴｲｾｩＹｨｴ＠ llne nk.

ｔｨｾ＠ Mcthod of ｳｯｬｵｴｬｾ＠ n we will adopt Instead 16 lC5S

dlrect, but it will ｾ｣ｲｶｾ＠ us well in what follows. It

consists Df two stcps. lhe flrst may be intcrpreted as

solvlrig a version of thls model for a smal1 ｯｰｾｮ＠ economy.

The second is the ｾｳｰ｣｣ｩ｡ｬｬｺ｡ｴｩｯｮ＠ from this enlarged case to

the original closed economy case. It turns out that this procedurc uncovcrs some Interest ing features of the Solow Model and allows also for easler generalizations.

Let us rewrlte "the accumulation equation (1) as

ｾ＠ r:: sy - nk

where per-caplta Income y substltuted per-caplta output

f(k), and dEcompose now income according to factor payruEnts:

y ::: rk +

w

(2 )

where r is thc profit ratet w thE wagE rate. ａｓｾＧｬｭ･＠ no;,.;

that the proflt rate is exogenously givEn, while the ｾｾｾ･＠ !s

rElatcd to it through the factor-price frontier. The

resulting accumulution equation is •

k c sw - (n-sr)k (3)

and it should be interpreted as that of a small open econoruy

faclng a glvem world proflt rate. Notice that capital k,

ownEd by nationals, which Is fixed in the short run, differs

in general from capital cmploYFd domestlcally and entcring the production function, so that there wil1 be Imports or

exports of physical capital according to whether the formEr

is largEr or ｾｍ｡ｬｬ･ｲ＠ than the latter. The latter, dcnoted by

the Inverse ｲｵｮ｣ｴｬｯｮｾｬ＠ ｲ･ｬｾｴｬｯｮ＠ wlll be dcnoted K(r). Of COUrbC, flxing r ｉｾ＠ cqulvalEnt to flxlng K ｾｮ､＠ ＮＱｾｯ＠

to flxlng thc wagc ｲｾｴ｣＠

w,

note In nddltlon the followlng

u&cful thou9h wcll-knoun ｲｅｬｾｴｬｯｮ＠

__ d_w_ = -IC (r)

dr· ₍₄₎

lhe growth model dC5cribed by (3) 15 linear .nd haç In

particular the Intcrcstlng fcaturc that Its stcady-stRtc

equlllbrlum solution can be determlned expllcltly as a

functlon of the given parumeters, especially among them the world proflt rate rI

k (r) - _ｾｷ＠ (r

1

- n-sr (5)

Of course, a necessary and sufficient conditlon for thc existence of an economical1y meaninsful long-run equilibrium Is that denominator of the preceding expression bc positiv€

r ( n/s (6)

lhe equilibrlum solution is then unique and globally

stablc. From now on it wlll alwê\Ys be assuMed that the

proflt rate is in the range defined by thls inequality. Of even .sreater interest are the properties of the function k(r) that gives the steady-state value of the capital-labor ratlo as depcndlng pn the world profit rate and which can be summarized in the following proposition

Propos;t ioo 1. a) lhe function ｫｾｲＩ＠ is U-shaped, attainin9

Its rninin1um value at

ro

charactf--; ized by

b) At Its rniniMum re

c) k(r) is larser (resp. smaller) than lC(r)

Ir and ｯｮｬｾ＠ If r is largcr (resp. smaller) than

ro-In addition, the derlvativE of k(r) can be computed

k I ( r ) c [k( r) - te (r» s ...

n -sr

(7)

For a praof ｾ｣･＠ tne Appcndlx. lhe ￧ｬｴｵｾｴｬ｡ｮ＠ ls plctured In

ｾｬｧｵｲｅ＠ 1. The rc&ults af ｴｨｅＦｾ＠ proposltion roay bc $CEn from

ｾ＠ dlfcrent pcrspcctlvE if Dne rcc«lls ｴｨｾｴ＠ the datum af r Is

･ｱｵｩｶｾｬ｣ｮｴ＠ to ｴｨｾｴ＠ of capital ､ｯｾ･ｳｴｬ｣｡ｬｬｾ＠ ｾｭｰｬｯｹ｣､＠ K , ｾｯ＠

that thc ｳｴ｣ｾ､ｹＭｳｴｾｴ･＠ ｶｾｬｵ･＠ of k con be ｾｬｴ｣ｲｮ｡ｴｩｶ･ｬｹ＠ seen

as a funct lon of te , denotcd ｾｬｳｯ＠ k ( te ) _ ｏｮｾ＠ ｾ･･ｳ＠ then

IromEdiatcly, from the precEdlng proposltlon, that, as a

ｾｵｮ｣ｴｩｯｮ＠ of K C a) k Is also a U-shaPEd functlon, that

attains its minimum at !Co E IC (ro); b) af Its min/muro,

k :: K: and c) k (te) Is larger (resp. smaller) than te If and

only If te Is sn,allE.'r (resp. largEr) than !Co- Figurc 2

illustratcs these results.

2.2. The ｣ｬｯｳ･､Ｍ･｣ｯｮｯｾｹ＠ solutlon

It às clear ｴｨｾｴ＠ thE lang-run equilibrium solution ｾ＠ to

Solow's original mode} (1) corresponds to ｴｨｾ＠ autarkic

particular solution af (3), obtained when there are no

E'xports oor imports af physical capital or, in other tcrms,

""hen

k ( !C)

=

!C

Thls Is equlvalent to

k (r) i:: lC(r)

where, as befol'c, !C(r) is the !:" .. ersc function of' r

=

f'(d.

Fron, t hc abovc prapos i t i _;... or·, and ｓｕ｢ｓｃｱｬＬｾｰｴ＠ comment s, i t

ｾｯｬｬｯｷｳ＠ that K == !COr tl·c Doint at whi"'-:l k( te) attains its

minimum. As in the loi'f' run pf'l'-capita incomE is

proportianal to the ｣｡ｰｬｴ｡ｬＭＱｾｾｯｲ＠ ｾ｡ｴｩｄＮ＠ ｴｾｅ＠ praposition can

be ｩｮｾ･ｲｰｲ･ｴ｣､＠ ｾｳ＠ stating that any ､･ｶｩｾｾＺｑｮ＠ from autarky

(bc it by importing or exporting capital) wiil improvc thE

welfare of thE ･｣ｯｮｯｭｾ＠ and r IndEedr that the larger the

deviation from autarky the largcr the gains in thE capital-labor ratio, and thus in welfare. In short, a country will

benefit from opening itsclf to intErnational capital

ｾｯｶ｣ｾ･ｮｴｳ＠ in the 10n9 run as wel1 as In the short run.

That thc long-run part of this last statement Is not as

safely ｣ｳｴｾ｢ｬｩｳｨ｣､＠ as the short-run part (seE

HacDougall(1C;'60) for the lattcr) wll1 bc secn in the nE'>:t

section. At this point, .hoVlcver, it is Interestlng to note

thc following asymmEtry in thE preceding rcsult. WhilE

inpor-ts of c",pltal in any amount wil1. IncreasE: nccessarilu

the steadu-slatc capital-labor ratio, thcre ｾｲ｣＠ limlts to

ｔｨｬｾ＠ ｉｾ＠ ｢￧｣ｾｵＤ｣＠ ｉｾｰｯｲｴｾ＠ of ｣ｾｰｬｴ｡ｬ＠ ｣ｯｲｲ･ｾｰｯｮ､＠ to • lowtrlng

Df rwhllp cxport& cf ｣ｾｰｬｴ｡ｬ＠ nmount to ｉｮ｣ｲｾ｡ｳｬｮｧ＠ r, whlch

ｉｾ＠ ｣ｯｮＶｴｲｾｬｮ｣､＠ bu ｉｮ｣ｱｵｾｬｬｴｾ＠ (6).

3.A

Kaldorinn ｰ｣ｮｾｲ｡ｬｩｺｮｴｩｯｮ＠

Folloulng KBldor (1957) ｗｾ＠ wlll consldcr now the ｃｾＶｃ＠

cf ､ｬｦｦｾｲ｣ｮｴｬｯｴ｣､＠ ｾ｡ｶｬｮｧ＠ ｰｲｯｰ｣ｮｾｬｴｬ｣ｳＮ＠ It wlll be ｾｳｳｵｭ･､＠

ｴｨｾｴ＠ ｾ＠ ｣ｯｮｾｴｾｮｴ＠ proportion ｾｌ＠ of wage Income ｴｯｧ｣ｴｨｾｲ＠ with ｾ＠ ｣ｯｮｳｴｾｮｴ＠ proportlon sK of proflt Income IG saved. It Is

cxpccted thnt the ｾ｡ｶｬｮｧ＠ propcnslty out of wa9ES Is sMaller

than that out af proflts, allhough thls 15 not a necessaru

restrlct lon In whRt follows. lhe accumulatlon ｾｱｵ｡ｴｬｯｮ＠ Is

･｡ｳｩｬｾ＠ SEcn to ｢｣｣ｯｭｅｾ＠

•

k ｾ＠ SLW + ÇKrk - nk (8)

whcrE, as before, the proflt rate Is cxogcnous and the wage rate Is relatcd to it through the factor-prlcE frontler.

3.1. Thc gencric ｣ｮｾ･＠

We ｾｩｬｬ＠ considcr in the first plnce the generlc caSE when lhe snving propensity out of wages Is positive. lhe ｳｴ｣ｾ､ｹＭｳｴ｡ｴ｣＠ valuE af the ｣｡ｰｩｴ｡ｬＭｬｾ｢ｯｲ＠ ratio, as a functiun

af the ｾｑｲｬ､＠ proflt rate r, is agaln explicltly obtained

from thE linear differential equation (8)

k (r)

=

(9)

n - sKr

lhe ｮ･｣ｅｳｳｾｲｹ＠ and sufficient condition for existence of this

long-run equilibrium, which ensures its ｵｮｩｱｵ･ｮ･ｾｳ＠ and

9lobal stability, is

(10)

Propos!u...o.n. 2. ai The funct ion k(r) is U-shaped, attalnlng

Its rninirnuM valuE at ｴｾ＠ charactcrized by

sK f (t::: (r o) ) = nK o

b) At its ｾｩｮｩｭｵｭ＠

1 Wc are not ｵｮｒｷｾｲｅ＠ of the controvcrsy sparkcd by this

"I( ?, 1 d o r- i ｩＢｾ＠ n n h y p o t ti c s i s o n S a v i n 9 5 ( f o r a n a c c ou n t o f t h i 5 ,

ｳ｣ｾ＠ for ｩｮｳｴｾｮ｣｣Ｎ＠ Hahn and Matthews 1964». NEvErthclEs5. WE

will cdopt it ｾｳ＠ ct convEnient way of FEflEctlng the ｩｾｰｾ｣ｴ＠

c) k(r) I,. la.rgc.r ( rR'&p. smal1tr ) than

I;L':<r)/".: If ".n ｯｮＱｾ＠ If r Is l",..g[.'r (rcr.p. r.hlii\11er) thl\n

r ••

In ｾ､､ｬｴｬｯｮＬ＠ the derlvatlvc of k(r) can computtd

expllcltlY"-6

k '(1"):= sKk(r) - Ep: (r) ,

n - sKr (11)

For ｾ＠ proof ｾｃ＠ lhe Appendlx. The sltuatlon 15 plctured

In figures 3 and 4, for thE caSE when the ｾ｡ｶｬｮｧ＠ ｰｲｯｰ･ｮＶｬｴｾ＠

out of ｾｾｧ･ｳ＠ lú çmallcr than ｴｨｾｴ＠ out of proflts (the other

case bclng ｳｬｭｩｬｾｲＩＮ＠ Notice that figure 4 ＱＱＱｵｳｴｲｾｴ･ｳ＠ the

reGults tnklng capltnl domestlcully emploYEd K , whose datuhl

IG equlva1cnt to that of r, as the dEPcndEnt varlablc. As It

is plc:turcdC 9.) k (.:) is a U-shuped functlon, ｡ｴｴｾｩｮｬｮＹ＠ its

m I n I r.1 u 111 a t K e- i.:: .: (r ｾＩ［＠ b) ｾ＠ t i t s m I n I m um, s K k

=

5 L':; a n de)

k( r.) 16 lv,f'gCIP (resp. sm<:l.11cr) thÇ\n ｾｌｋ＠ 16

K If ano ｯｮｬｾ＠ if'

K 16 sma11cr ＨｲｾｳｰＮ＠ ＱｾｲＹｅｲＩ＠ than ｲＮｾＮ＠ ,

As propositlon 2 shows and figures 3,4 Illustrate, thE

steady-statc va1uE of the capital-labor ratlo attains Its

minimum in autarky only in the very sPE'cial case of equal

saving proPEnsitics. Otherwise, the rnlnlrnurn Is rcached

･ｬｳ･ｾｨｅｲｅＮ＠ For InstancE'r If sL< sK' a ruovernent ｡ｾ｡ｹ＠ frorn

autarky wi11 IncreasE the ｰ｣ｲＭ｣ｾｰｩｴ｡＠ capital stock In the

case of lending but wi11 decrea5e It In the case of

borrowing. The Intult ive rcason for the decrease In the

latter caSE is c1ear: an Influx of capital will depress the

rate of profit, thus a1tering the distributlon of Income to

thc benefit af labor; ｳ｡ｹｩｮＹｾ＠ arising in ｾ＠ larger proportion

out of proflts, as assurncd. thE ec:onomy wil1 ｬ･｡ｙｾ＠ its

steady-state .path for ｡ｮｾ＠ where the per-caplta capital 5tock

de:cn?iH:,es.

A similar bchavlor is observcd for per-capita income.

At 'the steady state, per-capita incoMe Is

so r.hat

At the samc posit ive rnlnimurn point

we havE.· t hat

lending lE'ads minit.lum valuE' lE'nding than

I s.

y(r) = w(r) + rk(r) (12)

!::.i ＢＧＬｾＩ＠

=

k(r) - lC(r) + rk '(1") (13)

autad<ic r->oint k:= IC , bot:h y' and k' have thE'

sign (WF assume always 5 _L

<

sK ); but: at thE'

dEfincd by ｾｫ＠

=

sf'lC r whErE k' c: 0 and k <Ie r

y' is ncg?,tlve. his mE'ans that, a1though

a150 to a dEcrease in per-capita income, thE

of InCOME' is rEachEd at a lowcr leveI of

the minimum vaIue of the capital-labor ratio

3.2. Thc Ｂ｡ｲｸｩｾｮ＠ ｾｩｮｧｵｬ｡ｲ＠ tasc.

Ir

thF ｳＨＧＮＮｶｬｮｾＧ＠ ｰｲｯｰ･ｮｳｬｴｾ＠ out of -wages is zero, the

ｬｨ｣ｲｾ＠ li'> no functlon k(r) Ira thl", ＬＮｉｮｧｵｬｾｲ＠ case, ｉｮＬＮｴ･ｾ､＠ the

ｶｾｬｵｾ＠ of ｴｨｾ＠ proflt ｲｾｴｾ＠ IG ｦｬｸｾ､ｺ＠

(15)

whlch ｮ｣｣｣ｾＬＮ｡ｲｬｬｾ＠

productlon ｾｳ＠ ｾ｣ｬｬ＠

fixe,. the:- cap I ta 1-1 ｾ｢ｯｲ＠ ratlo _In

In

the uutarklc ｣｡ｳｾＬ＠ k = ｾｷｐ＠ ｾｨｬｬｲ＠ In the 6mall

economy ｣ｾｳ｣Ｌ＠ k becomeG arbitrary. A movement ｾｷｾｹ＠

autarklc long-run cqulllbrluru ｉｮ｣ｲ･ｾｳ･ｳ＠ income if

opcn-from

ｴｨｾ＠

country is a lender, decreases It If lhe country

borrower. ｉｮ､ｾ･､Ｌ＠ y c kr + w, so that, wlth r, w

Income is ü linear function of k and the ｣ｯｵｮｴｲｾ＠ I,. a

(resp.'borrower) whcnevcr k 15 largcr ＨｲｾｳｰＮ＠ smaller)

4. ｔｾｯＭ｣ｯｵｮｴｲｹ＠ models

4.1. lhe setting.

i s a

fixed, lender than

We shall dcal ｳｩｭｵｬｴｾｮ･ｯｵｳｬｹ＠ wlth two ･｣ｯｮｯｭｩｾｳ＠

(labelled by the

similRr to thosc In wlll be given by

•

numbcrs l p2), obeylng ｾｰ･｣ｬｦｩ｣｡ｴｩｯｮｳ＠

sEctlon 3 abovc. lhe accumulation ruIe

k c sr.i wi + iici ri k_i -nk_i i c 1,2 (16)

as In ($). lhe same rate n of population growth Is assumed

･ｶｾｲＢｾＬｭ｣ｲ･Ｌ＠ but ｮｾＢｬｮ･ｲ＠ the saving propensit ｩｾｳ＠ nor ｴｨｾ＠

ｰｲ｣ｾｾ］ｾＡ｣ｮ＠ funrtiC"r ｮｾｾｾ＠ be the samc across countrics.

ｾｩＺＱ､｣ｲ＠ capi·",J immobil ity (autarl<y), the two ｾ｣ｯｮｯｭｩ･ｳ＠

are tot.-, ly ｩｮ､｣ｰ｜ＮＮｲ､ｾｮｴＬ＠ the equê,t ions in (16) being solved

separatcly in the:- ｭｃＢＮｾｲ＠ indicatcd bcfore. On the other

hand, under perfect capital mobility capital fIows

ｩｮｳｴ｡ｮｴｾｮ･ｯｵｳｬｹ＠ across borders 50 as to equalize:- the:- rate af

profit at alI ｴｩｭｾｳＮ＠ BccausE af the interdependence iruplie:-d

bH a comrnon rate of profit, thE Equat ions in (16) constitute

a system that must be solve:-d simuItancously.

We:- are:- intErcsted in the comparlson af the long-run

Equilibria corrEsponding to these two capital ｭｯ｢ｩｬｩｴｾ＠

r e gim e s. S p e:-c i f i c ?,1 1 H • t h e e:->: p c r i m C' n t t o b e:- c a r r i e dou tis

the followlng. Starting from the:- long-run autarkic

equilibrium, allow capital to flow ｵｮｩｾｰ･ＺＭ､ｃＧ､＠ acr05S

｣ｯｵｮｴｾｩ｣ｳ＠ ｾｯ＠ ｴｨｾｴＮ＠ undcr the:- ncw accumulation rule:-, a new long-run cquiIibriurn wlll be:- attaincd. 'lhE qUE"stion thcn Is

run ｦｲｯｾ＠ ｴｨｬｾ＠ ｴｲｾｮｾｬｴｬｯｮＬ＠ ｾｾ＠ ｍｾＮｇｵｲｾ､＠ In ｴｾｲｍｾ＠ of ｰｾｲＭ｣Ｎｰｬｴｾ＠

capital ｯｷｮｾ､＠ Qnd ｉｮ｣ｯｭｾＮ＠

Equntlng to zero thc rlght-hand ｾｉ､･＠ cf (16), the

ｦｯｬｬｯｾｩｮｧ｣ｯｮ､ｬｴｬｯｮｳ＠ on thc ｾｴ｣ｾ､ｹ＠ ｾｴｾｴ･ｳ＠ of ｴｨｬｾ＠ ｴｷｯＭ｣ｯｵｮｴｲｾ＠ world are obtnlncd (recall(9»

s

1.i ""i _{li: 1,2 (17)}

In the autarkic case each of ｴｨ･ｾ･＠ two ･ｸｰｲ･ｳｾｬｯｮｾｲ＠

togcther wlth the ｲｅｾｐｅＧ｣ｴ＠ Iv€' condit lons .ri z: f{(ki)' ylelds

the long-run values ki of the per-caplta capital ｾｴｯ｣ｫＮ＠ In

thc case of pcrf€'ct capital mobility; we need specify the depEndence of the common rate of profit r on the per-capita

cap ital stocks of both countr ics. If k" _k2 are the two

countries' ｲ･ｬｾｴｩｶ･＠ factor endowments at a given moment, let

k be total world capital normallzed by the population of

country 1:

(18)

where A

-=

L2/L1 1st he const ant 1 abor force rat i o. Under a

regime cf ｰｾｲｦ･｣ｴ＠ capitalrnobility, capital Is allocated in

production across countries ｾｵ｣ｨ＠ that

k 1:':1 + A':₂

f_{1' (':1)} I:

fi

(K

2)

lhe common profit rate r thus established at each ｾｯｭ･ｮｴ＠

ＭＺＺｾｰ･ｮ､ｳ＠ uniquely on the world factor ratio k and not on ｴＺＡｅｾＧ＠

distribution of Its ownership R. It turns out ｴｨ｡ｾ＠ the

inverse functional relation is easier to describe=

(19)

whcre ICi(r) is the inverse function of fi (K_{i )}

2.2. and Kw(r) denotes the world factor ｲｾｴｬｯ＠

wlth a given inteínational profit rate r.

defined In associated

While Kw(r) should be interprcted as

world stock demand for capital associated profit ratc r. we a1so have the normalized

stock ｾｵｰｰｬｹ＠ for capital associated with r

the norlllalized with a glven long-run wor1d

(20)

2 Thls rclles crucially, of course, on thc onc-good

whcrc ki(r) ｷｾｳ＠ dcflncd In (17). lhe $teadY-5tate value

r

of

thc world proflt rDte, from wlch the values of alI othcr

ｶｾＢｬ｡｢ｬ｣ｦＮＬ＠ Ci'\n bc dctcrmlncd, 1& then obti'inE'd f"ol'lI the

CQUé'.t i 011

(21)

ｾ＠ It is worth rccalllng ｴｨｾｴ＠ the autarklc long-run value

ｾ＠ Df the profit rate In each country is obtalned from

ki(r) ｾ＠ lI:i(r)

as was shown In scction 3 abov€.

As for the solutlon of (21), we have the followlng

ProPDsJtloo 3. For r< min (n/5 K" ｮｾＵｋＲｾＧ＠ equation (21) has

a solutlon, and Rny such solutlon ll€s In the interval

｢ｴｷｾ･ｮ＠ f, and F

2 •

Sce the Appcndix for a proof. We will always SUPPOSE

that the solution is unique, the sltuation is then pictured

in figurE' 5.

A variety of situations appear that wil1 depend on the

values of the saving propensitics in the two countrles and on the valucs of the autarkic profit rates. Some of thC5C wlll bc dcscribcd now.

4.3. Ruffin'ç case

In an elegant paper, Ruffin (1979) shows that, Ir each

country saves a constant proportioo of its incomcr the

transition from loog-ruo autarkic eQuilibrium to a rcgime of

perrect capital mobility will bc mutually ｡､ｶ｡ｮｴ｡ｾｾｾｵｳ＠ in

the 10ng ruo. We 'can establish Ruffin's result ｾｾ［ｹ＠ caslly

within our framcwork. Indced, it ｷｾｳ＠ provco In ｾ･ｾｾｩｷｾ＠ 2

(under thc assumption of a uoiform saviog ｰｲｯｰ｣ｮｳｬｾｾＩ＠ that

any ooo-autarkic long-run equilibrium results, for cach country, lo a welfarc Improvemcnt (as rucasured by per-capita

income or capital stock) OVEr thc autarkic steady-statc.

4.4. 'North-South' case.

Supposc, as In Fiodlay (1980), that couotry 1 (thE

'North') has a unlform saviog propcnsity s1' whllc In

country 2 (thc 'South') thc propcnslty to saVE out of ｷｾｧ｣ｓ＠

Is ZEro 50 that only a ft"act 100 _ｾ＠ out of proflt locomc Is

si-w€d for accurllu1ation purposcs. W€ shal1 i:\ssume, In

addilion, that the autnrkic long-run proflt ratE Is hlgher

lo thc South than in the North, so that after a regime of

｣ｾｰｩｴ｡ｬ＠ ｭｯ｢ｩｬｩｴｾ＠ is Estnblished, capital will ｦｬｯｾ＠ from thE

North to thc Soulh. As io the precendiog caSE, thc North

wi11 bcncfit from this traoslt ion, in thc seos€ that both

the ｮｾｷ＠ long-run ｾｱｵｬｬｬ｢ｲｬｵｲｮＮ＠ On the ｯｴｨｾｲ＠ hand, ｾｉｮ｣･＠ ｴｨｾ＠

South "bccomc6 i\ ｢ｯｲｲｯｾＢｉｃＧｲＬ＠ ｉｴｾ＠ pcr-cl\pltl\ Incorne and ｣｡Ｎｰｬｴｾｬ＠

owncd Ｌｾｉｬｬ＠ ､･｣ｲｾｾｾｾＬ＠ ｾｾ＠ ｷ｡ｾ＠ ￧｣ｾｮ＠ In ｾ･｣ｴｬｯｮ＠ 3.2. above. More

ｲｬＺｲｮｾｲｫｴ｜｢ｬ｣＠ 11> the fi\ct thl\t lhE' Ｌｦｾｬｬ＠ In k2 muçt ｾｬｷｾ｜ｬ￧Ｌ＠

excccd the rlç;e: In k, , ç;o that In effect ｴｨｾ＠ world cconorny,

.5

rne:t\r.ured bH k IC k, + ｾｫＲ＠ ,contrnctl;. To prove thlf>

aSiicrtlon,obr.c,-vc In the ｦｬｲｾｴ＠ ｰｬｾ｣･＠ th"t th€ long-run

""alue of lhe Southern r?te of proflt 16 the ç;amE" under both

｣｡ｰｬｴｾｬ＠ boblllty rculmcii ($ce(15» and thus capital-labor

ratl06 ｾｕＤｴ＠ ｾｬｳｯ＠ coincide

(22)

On the other hand, the Northern rale of proflt Increases

ｾｦｴ｣ｲ＠ the ｴｲｃ｜ｾｩｴ＠ lon to a regime of capital moblllty, and thE"

capital labor-ratlo dlminlshes ｡｣｣ｯｲ､ｬｮｧｬｹｾ＠

Slncc,· In but l€"?vcs decline:

the 10ng K2 and

K

1

<

k,

run, capital mobillty thus reducesK1'

). unchanged, K w ｾ＠ K 1 + ｾ＠ JC 2

=

k must

,.

k

<

1< (23)

4.5. A DQre general ｡ｳｹｾｾ･ｴｲｹＮ＠

We propose to show thal some of the preceding results

can be malntained even if the propensity to save out of

wages s' In the South 16 nonzero, albelt smaller than the

propcnsity to saVE aut of profits s. To simplify matters, let us assume that both countries share the same production function f, that).::: 1, and that the Northern unlform savlng propensity equals the Southern propensity to save out of profit.

The analysis of the steady states outllned in ｳｾｾｩｯｮ＠

4.2. becomes partlcularly slmpleand can b€ ｩｬｬｵｳｴｾｾｩ･､＠ in

t-19ure 6. Given the assurnpt ions just madc, in part Ｚ［ＺｬＢＺｾＺＭＮＡＢＬ＠

s'

<

s, ｾＲ＠ (r) is mult iple of k1 (r) and 1 ies belL" it.

Whilc _{r 1 is determlncd by the intersect ion af} f

:<1")

a,t.t1

k_{1 {r),whlch occurs at its minimum,}

ri)

is neccssarily larger.

In addition, as it follows from proposition 3, the long-run

world profit rate

r,

1 ies in between

r

and 1--_{2 • It follows}

then that while the North bcnefits in the 10ng run from thc

transitian to perfcct capital mobility, the South will ｾ･＠

Its per-capita capital stock dimlnish a.nd in general also

Its per-caplta income.

Of €ven more interest Is the fact that in some cases

the world capital stock will shrink r l.e.

kw ( r ) ( k,

(F, )

+ k2

(-r

2 )

ｔｨｩｾ＠ happcns, for ｩｮｾｴ｡ｮ｣･Ｌ＠ if the production function is af

the Cobb-Douglas type

FUNDAÇÃO GETÚLIO VARGAS

wlth a c ｾＮＲ＠ .nd the ｶｾｬｵ･ｾ＠ for the othcr ｰ｡ｲ｡ｍｾｴｴｲＵ＠ areC

s ｾ＠ 0.4, L' c 0.1,

n

c 0.02_l In ｴｨｬｾ＠ ｃｑｾｾ＠ kw(F> ｾ＠

54.2

,

k,(r,>

ｾ＠

42.3

and _{k 2 (r2) ｾ＠}

'3.5

•

It could nol bc dctcrrnincd, ｨｯｾ｣ｶ･ｲＬ＠ whether ｴｨｾ＠ world

｡ｶ･ｲｾＹ｣＠ per-caplta Incotroc mlght ｾＱｾｯ＠ decreaçe In thc

transition to perfcct capital moblllty In thls ｣ｾｳ･Ｎ＠

5. Concludlng ｲｾ･ｲｫ＠ ••

Thls artlcle has rc-cxamlned 5010w's one-sector growth ｾｯ､･ｬ＠ with the obJcctlve of ｾｰｰｬｾｩｮｧ＠ It to the dlscussion of

Gome ｣ｯ｣ｾｯｮｬｹ＠ &cccpted proposltions on the bcnefits of

perfect ｣ｾｰｬｴ｡ｬ＠ rnobillty in the ｣ｯｮｴｾｸｴ＠ of a ｴｾｯＭ｣ｯｵｮｴｲｹ＠

9rowln9 world. Adoptlng the conventlona1 assuruption of constünt savlng propensities, It was found that a situation Df ｭｵｴｵｾｬ＠ per-caplta Income gains for both countries 15

rather cxceptional. Not only may borrowing countries easily lose but, globê.11y, the world fllay, In some instances, become worse off as a consequence of frec capital movements. lhese

results a1so hclp to understand ｳｯｾ･＠ previous results of

Burgstal1cr and Rivano (1984> and of Saavedra-Rivano (1982>.

C\ppendix.

Ai. prpof Qf prQEPsjtlpns 1 and 2.

Proposition 1

proposition 2, we

dlffercntiation with (9), giVES easily

belng clearly a ｰ｡ｲｴｩ｣ｵＱｾｲ＠ case of

wi11 only prove the 1atter. Sitlple

rcspect to r of k(r>, as Expressed ｩｾ＠

k '(r>

=

which is the 1ast assertion in proposition 2. Next, from the exprcssion (9) for k(r) onc immediate1y finds that

A2. proa! ｾｲｾ｣ｾｬｴｬｯｄ＠ 3.

ｌｾｴ＠ us ｾＶＶｵｭ･Ｎ＠ wlthout 1065 of ｧ｣ｮ･ｲｾｬｬｴｹＮ＠ ｴｨｾｴ＠ ; , ; •

Observe

ｾｬｳｯ＠

tht\t the rC6trictlon on the vi'lluCG of r 1n

ｴｾ｣＠

body of ｰｲｯｰｯｾｬｴｬｯｮ＠ 3. whlch Ic nothlng More than _

r e s l ｩｾ＠ l c n; e: n l o f t h c r e r. t r I c t i o n ｾＮ＠ t. ｾ＠ U m t:: d I m rn e d I a t E' 1 Y il f t e r

ｉｮ｣ｱｵｾｬｬｴｹ＠ (6), serves to en6ure thnt k1 (r) ｾｮ､＠ k2 (r) ｾｲｅＧ＠ _lwayó posltlvc. In order to prove the proposltlon, let us

note ｴｨｾｴ＠ ｾｳ＠ ｾ＠ ｣ｯｮｳ･ｾｵ･ｮ｣･＠ of proposltlon 2, ｫＱＨｾＩ＠ - Kt (r)

16 ncsativE for r Ｈｾ＠ and ｰｯｳｬｴｬｶｾ＠ for ｾｲＩ＠ r , whllc

ｳｬｭｩｬ｡ｲｬｾ＠ .... k2(r) - K2(r) it> nE'Si\tive for r (r2 .. nd 1 posltlvE'

for ,-

>

r2. ｾｊ･＠ thU5 conclude that thelr sum k(r) - K(r) 11:t

ne;Btlvc for r ( ｾ＠ and positive for r ) ｾＬ＠ whence the

proposition follows irumediately by ｣ｯｮｴｬｮｾｬｴｹＮ＠

Reference-s

Burssta11cr, A. and N. Saavedra-Rivano, Capital moblllty and

growth in a North-South model, Journnl of

Developcent ｅ｣ｯｮ｡ｾｩ｣ｳＬ＠ 15, Scptember 1984.

Flndlay, R., lhe terms af ·tradc and equillbrluru growth in

the world economy, ａｾ･ｲｬ｣ｾｮ＠ Economic Reviewr 70,

June 1980. _{. ,.}

Hahn, F. and R. Hatthcws, The thcory of economlc growth& a

5urvey, Econo3ic Journal , 70, Occcmber 1964.

Kaldor, N., A model of cconomic growth, Economlc Journal ,

67, Oeccmber 1957.

MacOougal1, G. O. A., The bcncfits and costs of private

invcstmcnt from abroad: a theoretical ｡ｰｰｲｯｾｾｨＬ＠

ｅ｣ｯｮｯｾｩ｣＠ Record , 37, Harch 1960.

Ruffin, R. r Growth and the lons-run theory of internat!onal

capital movcments, Acerican Econo"ic ｒ･ｶｩ･ｾＬ＠ 19,

Decernber 1979.

Solow, R., A c0ntribution to the theory of economic growth,

Quartcrly Journal of ｅ｣ｯｮｯｾｩ｣ｳｲ＠ 70, Fcbruary 1956.

Saavedra-Rivano, N., North-South rodcls of ｣ｾｰｩｴ｡ｬ＠ ｾｯ｢ｩｬｩｴｹＬ＠

k k

=

11:

Figure 1

k

11: (r)

k(r)

r

k k I: IC

,

ｾＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭＭ

K

k

K (r)

k(r)

,

L-__________________________ ｾＭＭＭＭ r

.-k

k

(r)

Figure 5

t: (r}

k, (r) _--,,/"2(Tl

Figure 6

r

(a partir do nº 100)

100. JUROS, PREÇOS E DíVIDA PÚBLICA VOLUME I: ASPECTOS TEÓRICOS - Marco AntGnio C. Martins e Clovis.de Faro - 1987 (esgotado)

101. JUROS, PREÇOS E DíVIDA PÚBLICA ｖｏｌｕｾＧｩｅ＠ 11: A ECONOMIA BRASILEIRA - 1971/85

- An to n i o Sal a z a r P. 8 r a n dã o, Clóvis cE Faro e Marm A. C. i""8I'tim - 1987 (esg::rta:b) 102. MACROECONOMIA KALECKIANA - Rubens Penha Cysne - 1987

103. O ｐｒｾｍｉｏ＠ DO DÓLAR NO MERCADO PARALELO, O SUBFATURAMENTO DE

EXPORTAÇnES E O SUPERFATURAMENTO DE ｉｍｐｏｒｔａￇｾｅｓ＠ - Fernando de Holanda

Barbosa - Rubens Penha Cysne e Marcos Costa Holanda - 1987 (esgotado)

104. BRAZILIAN EXPERIENCE WITH EXTERNAL DEBT AND PROSPECTS FOR GROWTH-Fernando de Holanda Barbosa and f'1anuel Sanchez de La Cal - 1987 (esgotado) 105. KEVNES NA SEDIÇÃO DA ESCOLHA PÚBLICA - Antonio M.da Silveira-1987(esgotado) 106. O TEOREMA DE FRoBENIUS-PERRON - Carlos Ivan Simonsen Leal - 1987

107. POPULAÇÃO BRASILEIRA .. Jessé Montello-l987 (esgotado)

108. MACRoECO N Ofv'!I A - CAP í TU LO V I: "D EMAND A POR MO EDA E A CU RVA U1 li

- Mario Henrique Simonsen e Rubens Penha Cysne-1987 (esgotado) 10 9. fv'! A C R O E C O N O M I A - C A P í T U L O V I I: " bEM A N D A A G R E G A D A E A C U R V A I S "

- Mario Henrique Simonsen e Rubens Penha Cysne - 1987 - (esgotado) 110. MACRoECONOMIA - MODELOS DE EQUILíBRIO AGREGATIVO A CURTO PRAZO

- Mario Henrique Simonsen e Rubens Penha Cysne-1987 (esgotado) 111. THE BAVESIAN FoUNDATIONS DF SoLUTIoN CoNCEPTS DF GAMES - Sérgio

Ribeiro da Costa Wer1ang e Tommy Chin-Chiu Tan - 1987 (esgotado)

112. PREÇOS LíqUIDOS (PREÇOS DE VALOR ADICIONADO) E SEUS DETERMINANTES;

DE PRODUTOS SELECIONADOS, NO PERíODO 1980/1Q _{Seme3tre/1986}

- Raul Ekerman - 1987

113. EMPRtSTIMoS BANCARIoS E SALDo-MtDIo: O.CASo DE PRESTAÇÕES - Clovis de Faro - 198B (esgotado)

114. A DINAMICA DA INFLAÇÃO - Mario Henrique Simonsen - 1988 (esgotado) 115. UNCERTAINTV AVERSION AND THE oPTIMAL CHoISE DF PORTFOLIo

-James - Dow e Sérgio Ribeiro da Costa Werlang-1988 (esgotadc) 116. O CICLO ECONÔMICO - Mario Henrique Simonsen - 1988 (esgotado) 117. FoREIGN CAPITAL AND ECoNoMIC GROWTH - THE BRAZILIAN CASE

STUDV-Mario Henrique Simonsen - 1988

118. CoMMoN KNOWLEDGE - Sérgio Ribeiro da Costa Werlang - 1988(Esg:Jt.:riJ)

119. OS FUNDAMENTOS DA ANALISE MACROECONÔMICA-Prof.Mario Henrique Simonsen e Prof. Rubens Penha Cysne - 1988 (esgotado)

120. CAPíTULO XII - EXPECTATIVASS RACIONAIS - Mario Henrique Simonsen - 1988 (esgotado)

121. A OFERTA AGREGADA E O MERCADO DE TRABALHO - Prof. Mario Henrique Simonsen e Prof. Rubens Penha Cysne - 1988 (esgotado)

122. INtRCIA INFLACLONARIA E INFLAÇÃO INERCIAL - Prof. Mario Henrique Simonen - 1988 (esgotado)

123. MODELOS DO HOMEM: ECONOMIA E ADMINISTRAÇÃO - Antonio Maria da Silveira - 1988

124. UNDERINVDICING DF EXPORTS, OVERINVUICING DF IMPoRTS, AND THE

1 2 (,. P L A!W C R LJ Z fI D D: C O r ｾｾＮ＠ [ P

ç

1\ U E O E R li [l D [

r o

L

1

T ] C A rIS C A L - R u b (' n 5

Penhn Cysnp - 1988

127. TAXA OE ｊｕｒｏｾ＠ ｲｌｕｔｕａｾｬｅ＠ VERSUS ｃ｛ｉｒｒｅￇｾｕ＠ ｍｏｾ｛ｬｾｒ｝ａ＠ DAS ｐｒｅｓｔａￇｾｅｓＺ＠

UI-iA COr'íP{IF\f,ÇkO IW CASO DO SAC E ｬｴｊｆｌａￇＷｾＰ＠ COr\SThNTE - Clovis de

raro - 198G

128. CAP1TUlO JJ - tI.OrnlARV COr:REClIO!\ AIW REAL IN1EREST ａｃｃｏｕｉｊｔｉｲｾｇ＠

Ｍｒｵ｢ｾｮｳ＠ Prnha Cysne - 1988

129. CAPiTULO J11 - ＱＱｾ｣ｯｲﾷｾ｛＠ ArWDU'IAIW POLICIES lfJ BRAZIL - Rubens Penh2 Cysne - 19GB

130.

131.

132.

133.

131.; •

CAPíTULO

IV -

ｂｒａｚｉｌｉａｾ＠ ｅｃｏｾｏｋｙ＠ ｉｉｾ＠ lHE EIGHTIES ANO lHE D[8T CRISlS - RuberE ｐｾｮｨ｡＠ Cy5ne - 1908

1 f! [ b E ｾＬｚ＠ J L I {l. r ｾ＠ f:. G R 1 C U L 1 U R P. L P o L I C V E X P E R I E U C [: R A 1 I O 1\ A L E A I W

FUlUR[ ｄＡｒｅｃｔｉｏｾｓ＠ - Antonio ｓ｡ｬｾｺ｡ｲ＠ Pessoa ｂｲ｡ｮ､ｾｯ＠ - 198B

l-i O F\(\ í

é

F: J (l, 1

rn

E R 1\ A I D

1

V I D r:, P Ú B L I C A E J U R O S R E AIS - M a r i a Si 1 v i 2

ｂ｡Ｕｴｯｾ＠ ｍＲｲｱｵｾＵ＠ e ｓｾｲｧｩｯ＠ RibEiro da Costa Werlang - 1988

CAPiTULO IX - TEORIA DO CRESCH'IErJTO ｅｃｯｴｾￔｲＧＮｉｃｏ＠ - Mario HenriquE'

S i Tr. o n s e n - 1 9 8 8

C O ｉｾ＠ G E L [\I!. E In o C 01-'1 1\ i3 o:W S A L A R I A L G E R MW o E>: c E S S O o E o E 1'1 A N D A

-- J08quir.. Vielra Ferrei!'ê Levy e SÉrgio Ribeiro da Costa Werlang - 19C5

135. AS ｏｒｉｇｅｾｓ＠ E CoNSEqUtNCIAS DA INFLAÇAo NA AMERICA LATINA - • Fernando dE Holanda 8arbosa - 1988

136. A CONTA-CORRENTE DO GOVERNO - 1970-1988 - Mario Henrique Simonsen - 1989

137. A REVIEW oN lHE THEORY DF CoMMoN KNoWLEQGE - Sérgio Ribeiro da Costa Werlang - 1989 138. ｾｾｐＬｃｒｏｅｃｏｩ｜ｯｲＭｩｬａ＠

- Fernando dE Holanda Barbosa - 1989 (esgotadu)

139. T E O R I A D O E A L A ｉｾ＠

ç

O DE P A G A!-'I E: N lOS: U ｾＱ＠ A A B O R D A G ｈｾ＠ S I til P L I F I C A D A -- JOBD Luiz Tenreiro Barroso -- 1989

11; O. C O

tn

A 6 I L I D ｲｾ＠ D E C O M J U R O S R E A I S - R U B ｅｴｾ＠ S P E ｉｾ＠ H li C Y S H E - 1 989

11;1. "CF:EOlT ｒｲｾＱＱＰｴｾｬｲｾｇ＠ ａｲｾｄ＠ THE ｐｅｒｴｾａｴＺ｛ｴｮ＠ INCOrll HYPOTHESISfI

- Vicente ｾＧＮ｡､ｲｩ￧｡ｬＮ＠

Tommy Tan, Daniel Vicent, ｓｾｲｧｩｯ＠ Ribeiro da Costa Werlang - 1989

11;2. fiA ａｍａｚｏｾｉａ＠ BRASILEIRA" - Ney Coe de Oliveira - 1989 143. ｄＺｓｾｇｉｏ＠ DAS LFTs E A PROBABILIDADE IMPLICITA DE MORA1CkIA

ｬＧｾＲＮｲｩ｡＠ Silvia Bastos Karques e Sérgio Ribeiro da Costa v.!eI"lanf - ＱＹＸｾ＠

144. THE LDC DEBT PROBLEM: A GAME-THEORETICAL ANALYSIS

Mario Henrique Simoflsen e Sérgio Ribeiro da Costa Werlang - 1989

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145. ANALISE CONVEXA NO Rn - Mario Henrique Simonsen - 1989 146. A CONTROVtRSrA MONETARISTA NO HEMISFtRIO NORTE

Fernando de Holanda Barbosa - 1989

147 _ FISCAL REFORM ANO STABILIZATION: THE BRAZILrAN EXPERIENCE - Fernando de Holanda

149. PREFERENCES, COMMON KNOWLEDGE, AND SPECULATIVE TRADE - James Dow, Vicente Madrigal, Sérgio Ribeiro da Costa Werlang - 1990

150. EDUCAÇÃO E DISTRIBUIÇÃO DE RENDA

Carlos Ivan Simonsen Leal e Sérgio Ribeiro da Costa - 1990

151. OBSERVAÇOES

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MARGEN DO TRABALHO "A AMAZONIA BRASILEIRA" - - Ney Coe de Oliveira - 1990

152. PLANO COLLOR: UM GOLPE DE MESTRE CONTRA A INFLAÇÃO? - Fernando de Holanda Barbosa - 1990

153. O EFEITO DA TAXA DE JUROS E DA INCERTEZD SOBRE A CURVA DE PHILLIPS DA ECONOHIA BRASILEIRA - Ricardo de Oliveira Cavalcanti - 1990 154. PLANO COLLOR: CONTRA FACTUALIDADE E SUGESTOES SOBRE

A

CONDUÇÃO

DA POLíTICA MONETÁRIA-FISCAL - Rubens Penha ｃｹｾｮ･＠ - 1990

155. ｄｅｐￓｓｉｾｏｓ＠ DO TESOURO: NO BANCO CENTRAL OU NOS BANCOS COMERCIAIS? Rubens Penha Cysne - 1990

156. SISTEMA FINANCEIRO DE HABITAÇÃO: A QUESTÃO DO DESEQUILíBRIO DO FCVS - Clovis de Faro - 1990

157. COMPLEMENTO DO FAScíCULO f'1!;' 151 DOS "ENSAIOS ECONOMICOS" (A

AMA-ZONIA BRASILEIRA) - Ney Coe de Oliveira - 1990 158. POLíTICA MONETÁRIA ÓTIMA NO COMBATE

A

INFLAÇÃO

- Fernando de Holanda Barbosa - 1990

159. TEORIA DOS JOGOS CONCEITOS BÁSICOS Mario Henrique Simonsen -- 1990

160. O MERCADO ABERTO BRASILEIRO: ANÁLISE DOS PROCEDIMENTOS OPERACIO-NAIS - Fernando de Holanda Barbosa - 1990

161. A RELAÇÃO ARBITRAGEM ENTRE A ORTN CAMBIAL E A ORTN MONETÁRIA -- Luiz Guilherme Schymura de Oliveira -- 1990

162. SUBADDITIVE PROBABILITIES ANO PORTFOLIO INERTIA - Mario Henrique Simonsen e Sérgio Ribeiro da Costa Werlang - 1990

163. MACROECONOMIA COM M4 - Carlos Ivan Simonsen Leal e sérgio Ribeiro da Costa Werlang - 1990

164. A RE-EXAMINATION OF SOLOW'S GROWTH MODEL WITH APPLICATIONS TO CAPITAL MOVEMENTS - Neantro Saavedra Rivano - 1990

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