Minimum wage regulation and economic growth

Minimum Wage Regulation and Economic Growths John 2. Drabicki and Akira Takayama

Of~Wth,dhttbrmtrim~w~ll0or,Iitis !3ufmemuy lllgb,alosesthe awnoalytod+cey8utheway toward he origin. The effcets of a **wage-mark-up*’ pdky,svariationofMWR,areatsoexamhed.

Ah i> well known. minimum wage regulation (MWR)

MWR.

has rtvently

a great deal of the

should properly

artention of both economists and noneconomists. AI

along the curve

rhc empirical

been altracting

level. there has been an impressive

such as the employment displacement et&t. incorporate ml

both the movement

the shift of the curve.

In fact, the shift of the labor demand curve due IO

r0d point

amount nfstudics showing the employment displace-

an increase in capital will become a

ment effcyr of MWR.’

economy in which a positive amount of saving exists;

At

the rheoretical

level.

in an

Johnson (1969) prohahly offers the first study that

such saving provides funds for investment that con-

in\estipates

the problem

tinuously shifts the labor demand. The present study

equilibrium

fr’ramework where he. like many later

rigorously

in a general

intends to investigate the long-run consequences of

works on this topic. assumes that the minimum wap

the MWR.

floor ib \ct in real terms and that the given minimum

real terms and which is enforced on a national level.’

n-age law i< enforced nationally.

which fixes the minimum wage floor in

In this study.

upon economic growth via the continuous shift of the

Johnson (1969. p. 599) describes the then current

labor demand curve resulting from capital accumu-

status of t:rc theory on this lopic as”an application of

lation. Although recently there have been a number of

lhc clement.lry theor! of demand and supply as to the

interesting

cll2~rs of price-support policies.” Although Johnson

equilibrium framework that does not involve errors of

theoretical

advances using a general

dots not cxplicitl:; reveal the weakness involved in

glossing over the shift of the labor demand curve,

huch a partial equilibrium analysis. many studies on

these studies somehow are mostly concerned with the

M WR fall into the error

ofconfusing

a shift of a curve

u ith ;I movement along a curve. Namely. it is argued

problems of international

trade (e.g.. Lefeber 1971,

Rrecher I974a. 1974h Hazari 1978). and few rigorous

rhat M WR raises rhe wage rate above the equilibrium

investigations have been made with regard to the

rate and creates unemployment. which is explained in

consequences and implications of MWR

terms of the movement along the downward-sloping

nomic growth.

labor demand curve. The pitfall of this :?rgurnent. though

it is

wide spread. is quite simple. The mi-

nimum wage floor. if it is effective.

upon eco-

Among other results. we shall show in this paper that if the minimum wage rate is set suficiently

high.

will make labor

relatively more expensive compared to capital, caus* Minimum

ing the substitution of capital for labor. Such a

wages ~YT usually legislated

term5 of money.

in turn. causes an upward shift

Hence. while they may have been orgmally mtendcd IO musethe real

of the marginal producl of labor curve (i.e.. the labor

wage above Ihe market level. the intention may have been flusmucd

demand

(!

suhstiturion off&iors.

curve). Hence, analysis of the :lTecrs of

and Ihe mimmum wage may have become meffecuve.

Johnson

69). havmg noted dub. explicitly lgnorrd this complication by

assuming that the minimum wage IS effective in raising the real wage ’ See Welch (1974)

for a 5ummary and empuical work XI

mmimum wage laws. Fur more recent studies. see Mincer Welch and Cunnmgham John 2. Arizona. Texas

( 1476) and

I 197%). for eaample.

Dmbicki is from dte University of Arizona. Tucson.

AJdm Takayama is from le

Depattment of

Econom1c5,

Address reprint requests lo Prof. John Drabicki. Department of

Journal of Economics and Business 34.231-240 @ IV82 Temple University

t 1982)

MOSI

theonical

works after Johnson also impose the same

Inte& to Investigate the gmti consequences of a minimum wage. this assumption may be more natural here than in oIber studies cast in a static context. Incidentally. we may also mcnlion lhatthe investigation of the consequences of a f.ned money wage rate obviously requires the explicit introduction of money into die model.l%e imfxxtance of the

A & M University. College StaGon. Texas.

Economics. University of Arizona. Tucson. Arizona 8572

TN.

assumption tha%we follow in the present analysis. Since our study

I.

disklion

between nationaJ (or federal) and lucal minimum wage

laws is pointed out by Hicks

( 1932).

J. 2. Crabicki and A. Takayama

232 the economy wiil decay in the sensethat the capitallabor endowment ratio and both per capita output and consumption

will decrease exponentially

over

employment. Suppose that MWR

is enacted at time

zero and is effective, but the minimum wage floor is sulliciently low so that the economy grows. We shall that per capita income and per

time toward the origin. We shall obtain the necessary

ccnclude

and suficient conditions for this to happen. This

consumption will be smaller at each instant of time

result

UIII

be

shown to be crucially dependent on the

relative magnitudes of the marginal productivity

of

capital and the rate of population growth as well as

than it would have been had the MWR

capita

not been

enacted (and had the economy thus followed the full employment path). As is well known, M WR i> very popular legislation.

the propensity to save. Rough!y speaking, the above rather striking cancluslon oi a possible decay can be explained

as

The implication may then be that the general populace is unaware of these growth effects.’ In this case,

follows. Thesubstitution ofcapital for labor by MWR

the merit of the present study would be a clarification

lowers the marginal productivity of capital. If it is

of these eflecas.

lowered

suficiently,

the reproduction

of capital

would not be hlgb enough to keep up with the growth tn

population,

capital-labor

which in turn causes a fall in the

endowment

ratio and a decay of the

economy In other words. “overcapitalization.*’ in the

Suppose ;Q~Wthat the government is fully aware c’ the adverse growth effects of setting the minimum wage floor high, including that of a possible econom;. annihilation.

On the other hand, due to the popu-

larity of MWR. the government may wish to pursue ;

cQnsethat the capital-labor ~rnpk~_~rnr~r ruriogets “too

different sort of minimum

hrgh.- is the source of possible decay.

certain

One may argue that MWR is an important form of

socio-political

wage policy, e.g., due to

pressures that

claim

the

equilibrium wage rate (H*) is “too low,” suppose that

“friction” imposed on the b!onomy, and hence it

the government

would mt lx surprising That such a friction can cause

certain markup, i.e., C = 13.

decay. However. the beha\ ior of the economy would

as the economy grows, the markup wage rate also

depend on the type of friction imposed. and it would

increases. We shall conclude that under such a policy,

IO

legislates the wage rate rS, with a do> 1. Since K* increases

argue that un_~form of friction would cause

there exists a unique steady state that is asymptoti-

the same type ofeconomic decay. A notable feature of rhe above conclusion is that this form of frtction.

cally glcbally stable, and that per capita consumption

%4WR. can cause the economy to decay cili rllr KIJ

under full employment.

be hard

ir~~~ll~/~~ rl.~,IU,~IU. instead of. for example. bringing the economy caphi

IO

the steady state with a lower level of per

income cornparcd to a frichonless economy,

One ma) also (quite ndtlirall!,) argue that it is hard

along such a steady state is always lower than that We now point out one important shortcoming of the present study. Many empirical studies of MWR are directed towards the employment effects of MWR

displacement

on minorities and teenagers; the

IL! cc)mprehenJ w hl the grqvernment would insist on

distinction betwcen skilled labor (“human capital”)

XIWR if Ii would cause the economy IO decay to such

and unskilled labor is considered an important one.

a degree. Hbwe\,er. there is one important lmplicatron mmlmum

frum tI!e

atwve

policy

While we are fully aware of the importance of this

conclusion. i.e.. if the

distinction, we heroically assu;me that all labor is

wage floor is h!gh and if the economy is

homogeneous.

This will enable us to focus our

dccaymg. this should give a reaso;l for the poky

attention ;m the growth effects of MWR

authoritk:s to suspect that therr may be a causal

going into the complication of the complementarity-

rrlatron between the iwo. 3-1~s. one merit of the

substitutability relationships of three or more factors

without

prestrnt study IS to ~lar~fj the logical connecti,on

involving skilled and unskilled labor and physical

bctuccn MWR

capital. Such a complication would naturally be quite

and possible economic dtiay.

Another cnncluwon HC i&in

In this paper is that

complex and would blur the focus of the growth

V WR. rf rt IS effective. always lowers the growth rate

r&cts of MWR

of the economy even when the economy expands,

of raising the capital-labor employment ratio caused

rather than decays. Thrs implies for example, that,

by the substitution

t)ther thine

via “overcapitaliiation” of capital

in the sense

for labor

through

being equal. it takes longl:r for an

monomy with it higher mmimum wage to reach full employment equilibrium than for an economy with a Another conclusion can be obtained by comparing hc pro\cth

path under

MWR

3 Although dtese growth effects ate not known in the liteta~m.

employmentdisplacement

lorrer mmimum wage to do so. with that of full

effect of MWR

tk

is well known in Ihc

literature. To explain the populari~ of MWR in spite of this, we may need other noneconomic. scrio-political perspectives. See Steindie

t 1974)

and Cox and Oaxaca

( 1980).

for exatnple.

Minimum Wage Regulation

MWR.

233

We wish therefore. to postpone a full-fledged

three (or more) factor analysis to a future study.4 Incidently. all ofthe theoretical studies on MWR

that

we cited earlier impose the same simplifying assump

From this. z is determined umquely as a function of 1%. i.e.. I = :( H.).

where z’ > 0.

(3)

The labor demand schedule is then obtained from (3)

tion of homogeneous labor. In this paper, we shall use the basic framework exemplified by the neoclassical growth model 1 la

Solow (1956) and Swan (1956).’ We find it useful to exposit the problem posited in terms of such a familiar growth process. There is. however. opt: crucial distinction between this familiar growth process and oursrhe usual model presupposes rull employment

of

labor. while our study presupposes that the M WR is

and z=K!N

as

(4)

li)~K,:(w’,.

N=N(w.

so that we clearly have iN,‘&cO. Let A signify the supply of labor. If the real wage rate is flexible. then the equilibrium real wage I ate (H*) is obtained as. N(#*.

K)=fi

K!:(n*)=N.

or

(51

effective in raising the real wage rate above the market level and thus(as shown later) is elTectivein producing

at which the full employment

labor unemplcyment.

Suppose now that \v is lixed at G by the MWR, and

In the section following immediately hereafter. WC

of labc>r is achieved.

assume that it is “effective” m the sense that C> H*.

develop the basic model in which the employment

This then creates unemployment.

displacement effect of MWR

since z’ > 0. In Figure I. the N(\v. K)-curve illustrates

is shown. We are then

concerned with the long-run growth effects of MWR.

i.e.. K;z(c)<

N.

the labor demand curve. which is downward sloping

in which WCshow the possibility ofexponential decay.

for a fixed value of K. The volume of unemployment,

and relating the dynamic process under MWR

when the minimum wage rate is set at ,T: is illustrated

to the

familiar fuil employment path li la Soiow and Swan.

by YIB in Figure 1, which is equal to N - K;:(k).

Since

Finally. we analyze the growth effect oi‘a variation of

an increase in K shifts the N(\\: K) curve to the right.

MWR

as is also illustrated in Figure 1. capital accumulation

in the form of a wage markup policy.

reduces unemployment.

MINIMUI\’ WAGE REGULATION AND UNEMPi2YMENT We consider an economy

provided

t/m

W stays con-

stant. If ii’ also increases. then the volume of unemployment may increase or decrease. depending on the relative magnitudes of the shifts of the N(\v. K)

that produces a single

curve and the N-line. Let k denote the capital-labor rrdo~~~r~~~rrnb. i.e..

consumption, investment good(Y) with the useof two factors. labor (h’) and capital (K). under the usual

bK

neoclassical technology of constant returns to scale

-_I K N. the capital-labor rmpb.~ne,tf r&o. The11we

and diminishing returns. i.e..

may rewrite (5) as

Y=F(,%‘.

A = :( ,I*).

or

(1)

where drP/dk

= 1;:’ ~0. This shows that the equilib-

the

FIGURE I.

K)=Nj(z).

where z~k’;N.j’>O and /“co.

N,

which

should

be

distinguished

\P = ,\“(li).

from

(6)

which also satisfies the usual lnada conditions. Assume that the real wage rate (1~) is equal marginal physical prhduct of labor: i.e..

to

Unemployment

of

labor

under

a minimum

wage.

\\ =,j(:)-~~‘(~).

(2)

w

---

_.-- _..-

’ For a &velopment of such a general model mvolvtng mulnple tdcr~~rs.see Takayama ( IQ8I b. ’ As a matter of fat& the tmphcation of ftxmg ~hcreal wage rate on the level of employment tn the contex1 of an ag;egate growth model wa

already sketched briefly m Solow’s well known work

( 19%).

although he drd no1 sperlfy the fintng of the reel wage r&e as a consequence of the MWR. nordid he indicate the possibility of decay. In any caSe. it IS unfonunate rhat his analysis on t!tis point has been more

or

less tgnored.

although his investigauon for the full

employmerrt case has auracted a gear deal of attention. Our present study thus tntends. in pan. 10 expand tus brief discusston ICI a fullfledged anersis and place It in a proper perspective in Ihe context of the MWR

V/e hope that the current strong mtere% on MWR justdies

such a @udy

0

-N

J . 2. Drabickiand A. Takayama

234

FIGURE 2. Determinationofztw) and unemployment.

rlum real wage rate (\?I is determined for a given

Note that II= Y K; i.e.. /I signifies output per unit of

ialue of /,. ztd that \\* increases as k increases.

capital. Assume further that the labor supply (ff) grows at a constant rate II. Then recalling k I k: N. we

To illustrate the concept of ~(6) further. we ma) utlilte

Figure

2. where the point of intersection of the

tangent hne to the,/(z) curve with the vertical axis. as is

obtain from (8). (%I)

I; = i( r\)l;.

well known. determines the marginal product of labor [cf. (:)]. Thus. given the minimum wage lloor legislated. z(\j ) ISdetermined by the condition in which the

where i(C) rr/r[,-(E)]

-II.

with i.’
(9b)

line passing through the vertical axis at k is tangent to the f(:tcur\e. Let i,, denote the initial value of the endowment ratio I, before the MWR is enacted. The

(exponentially over time) depending on whether i. > 0

wage rate that ensures full

at k,, is

or i c 0. and /. decreases as ti increases. When i. < 0. k

in Figure 2. which is determined bb

decreases all the way to the origin. To illustrate the

rlluctrated

I-I!, P

employment

the “tangcnc! condition.” Note that the MWR

is

Thus the endowment ratio A increases or decreases

case of i. > 0. suppose that the initi,:i endowment ratio

“cffectlvc” (I.c.. \r > I\*) if and onI> if z(G)> k,,. If the

!J,.;! is less than ~(69 so that the MWR

cct~norn! entoy full employment initially at k,,. then

initially. If i > 0. the endowment ratio h increases over time. while the capital-labor t~nplo,t~nt~~tratio re-

I hc MU’R

&es

from X,, to :(I\ I\ ahsorhed

the c~pird-ltrhrw

wqdow~~~r

I Thi\ tncrt’:ic in the cmplqmcnt

h> a kill In labor employment.

,rctio ratw

is effective

mains constant at z(G). Thus unemployment

de-

.I’. for a

creases. and I; eventual11 becomes equal to z($) acd

gnen vahie of AI;.namely. bj creating unemployment oflabor. That :tM.)Increases as 6, increases is also clear

full employment is achieved (see Figure 3). The time

from Flgurc 2. Kate that as 11increases. the marginal

cornputt\

product ~dcap~tal (I+ hich is measured b! the slop OT the taryent

hnr)

Jl?W_?ilSt3.

requtred to reach the full employment stage may be as

I’ =( I i.1 log [z(k) A,,].

(10)

For t > P. the economy simply follows the familiar full employment path ;i la Solow and Swan. Note that P depends on rl. i.e., P(\i ). We may easily conclude [II* [lfi, > 0 b> rccallinp i.’ c 0; namely. an increase in the minimum wage rate Gclays the economy’s attainment of full employment. We may’ give a different perspective to this result by interpreting it in terms of the relative performance of difierent economies. The :*ame result. therefore. (*an a1so be stated as Collows: other things being equal, it takes longer for an economy with a higher minimum wage to reach full employment equilibrium than for an economy with a lower minimum wage to do so. Let !‘E 1’ 1%’(per capita outptit) and csC!N

(per

capita consumption). so that c=( 1 -.s)~‘. Then we may casilq observe: j’= It(z

Hence if i ~0. both 1’

Minimum Wage Regulation

FIQJJRE 3. Growth or decay under a minimum wage.

time

and c. as well as k, decrease exponentionally

over

time. Define f. &(P)]

Note thatj’[=(@)]

signifies the marginal productivity

of capital implied by the given minimum wage rate, by E.(P) =O. i.e.,

and

= n/s.

(I’)

that (1 -0)

Condition

signifies capital’s reiative share.

(14) indicates that in order for j.>O, the

marginal productivity of capital, ceteris paribus, must Recalling h’ < 0 and z’ > 0. we may conclude from ( 15) i(ti)hO

according to whether kg%**.

(12)

Thus 12’ signifies the criticat level oft he real wagerate:

be sufficiently high. Equation (14) reveals that the sign of 1 crucially depends on the marginal productivity of capital, especially when I) is constant as observed in various countries.

the level that determineswhether the economy grows

We now summarize some of the above conclusions.

or decays. The relation between the critical minimum wage rate (rV)and

s/n may be illustrated in Figure 4

Proposition 1. The necessary and sufficient condition

where we may recall h’ ~0 and z’ >O. Note that the

for the economy to grow is j.(%)>O. where j.(G)

critical rate (G+) tends to be smaller, the smaller the

decreases as I? increases. In particular,

value of(s/n). This Indicates that an economy with a

minimum wage rate (G) is set sufficiently high, then

small propensity to save (such as that of the United

A becomes negative and the economy decays in the

States) cannot afford to have a very high level of the

sense that the capital-labor

minimum wage rate (unless n is small enough).

per capita output (r), and per capita consumption

To futher illustrate our discussion let 8 be labor’s relative share, so that O=cf-zf’)/f:

endowment ratio (k),

(c) all decrease exponentially

Then we obtain

critical minimum wage rate (P)

for any w.’

if the

over time. The that causes the

economy to decay is lower. the lower the proand

w=Uf(r)

h(z) =/‘(z)/(

I - @.

pensity to save (s) is and the higher the rate of

(13)

population growth (n).

Recalling i = sh - n. we may then conclude #)=sf’[:(P)]/(l

-0)-n.

Intuitively,

(14)

the above conclusion of a (possible)

economic decay may be explained as follows. The MWR.

FxlXJRE 4. The cntical minimum wage rate and s/n.

if effective, fixes the marginal productivity of

labor (and, consequently, also of capital). An increase

;*

in the minimum wage rate from one fixed level to another thus causes the substitution of capital for labor by making labor relatively more expensive compared to capital, so that the capital-labor employment ratio increases. The resultant Increase in the capital intensity will then lower the marginal productivity of capital. If it is lowered sufficiently, the

,/

’ 8 = cf t 0

if’.

s/n

rf’ )/f

= wfyields

we get L = w( I - W(~‘).

w = e/. Combining this wlrh w = f -

Thuswe have the following: h = f/z=

(w/e)(8f')/w(l - 6)=f'/!l - 8).

J. Z. Drabicki and A. ‘Drkayama

236

j-___--+::___i_N -_-,__-_ ?----+_______

FIGURE 5. Determination of various parameters under a minimum wage.

A-’

I

Y

ii

v*

0

n

reproduction of capital would not be high enough to

value k,) as time extends without limit, where ks is

keep up with population growth, which in turn causes

defined by.

a fall in the capital-labor endowment ratio (and also a Cdllin per capita output and

over time.”

COtWUnptiOII)

(16)

sJ’(k& = n/is. On the other hand, if the MWR

In short. a fall in the marginal productivity of capital

is enacted and if it

due to “overt-apitalization.” in the !;enseof an increase

is effective. so that k,
in the capital-labor employment ratio. is at the heart

is given by (9). We may readily observe.

of the abov,e proposition. In comparing two different economies in which

/.z.\j(z),-_--

II =

[sj(:)

-

II:].

:.

where : = l(G).

;. ~0. we obtain: Ropasitkrn 2 It takes longer for an economy with a higher minumum wage. other things being equal. to reach full employment

equilibrium

than

Then, in view of (16). we may conclude i. $0

according to whether z(k);

k,.

This conclusion may be illustrated in Figure 6. As can be seen easily from the diagram, if:(%)=:,

IJsing y(.=fl/(:l which

and (I41 we may rllustrate the

of z(M+. ;(w,) and ti* in Figure 5, in

: IS measured

on the vertical

(18)

an

economy with a lower minimum wage.

de(ermination

(I 7)

axis (lo save


s.f(z,)-K, >O (so that A>O). while if ~(w)=:~>k~. then s./‘(:,1-r1:,<0 (so that ;.
wage rate (6) defhted in (14) is

space). and 11is assumed (for simplicity) to be constant.

precisely the same as the one obtained by setting E,=0

Given

,C, the left panel diagram

in (18).

Gncn

such a -_(nl. we k.an determine the value of

We now investigate the dynamic process under the

using the right panel dia-

MWR by examining three cases that depend on the relative magnitudes of z(C) and !iP

.\\‘(z) (1 -0)wlhen

:=z(wi

determines ~(6,).

gram. T’he value of j.(til is given by the difference between

this value and

II. Note

that

Figure

S

illustrates the case in which i.(rVl
CUSP I. :(*I
(i.e.. ;. >O). In this case, the dynamic

process is subject to the following rule:

mter!section of the >/‘(:I (! -rllcurve and the n-line in I;=j.k.

the right panel.

for R,,$k
L =SJ‘(kl-fik.

FULL EMPLOYMENT PATH AND THE P4TH UNDER .4 %lINIML~M WAGE

THE

fo; I(i?)6k

(l9a) SAs.

(l9bl

where we assume k, < z(C), i.e.. the MWR

is elTectivc

initially. Thus the rrvlowme~r ratio k grows exponentially over time at the rate of i.. reaches z(k). the point

We now wish to compare the above dynamic process

at which full employment

mder

follows the familiar full employment path a la Solow

the MWR

to the familiar neoclassical growth

process with full employment. As is well known, the full

employment

path

follows

the

is achieved. and then

and EC&an.Yore that.

differential

cquat1on.

x’=.\/fkl-

The

value

ISolow-Swan)

rrA.

w

of k that :teadt

satisfies

(15) converges

state L, (regardless

ofrhe

to the initial

-

-* A similar conchon

extended to a “two-good”

can be obtaiued when the aulysis is economy that invnlvesaconsumpttongood

and a capital good. See Sgtu wd Takayarna

( 198 1).

Minimum Wage Regulation

FIGURE 6. The characterization of thesign of A byk,.

237

=2 1

0 5

kS

k

\I

sf(k)

-

nk

FIGURE 7. illustration of (22). k

sf(k)

by 417). Hence, using Figure 7. we may easily determine the i.k-ray. Also. from Figure 7. we may easily observe j,k < sj’(k) - Nk.

O
for k,sAC:(*).

nk

signifiesthe path in the absenceof the MWR. i.e., the full employment path.

(21)

Cuse 2. k,
(22)

&=i.k,

We may conclude I;,‘k=E.~[sJ‘(k)-nk],k.

-

The rate of growth (k/k) under the MWR (2) is less compared to that of the full employment path R la Solow and Swan for each k, k,S k
i
for all 1. when k,cz(ti).

(23)

The economy decaysexponentially over time, when k,<,lG). If k,>z(G), the MWR is not effectivein the beginning but k still decreasesover time accordingto the full employment path. The endowment ratio k eventually reachesz(k) and then decreasesexponentially over time at a fixedrate (i. 1toward zero,passing through k,. The value of & in this caseis illustrated in Figure 9 where k, can be anywhere. Cuse 3. k,=z(G)(i.e.. i.=O). If k,z(t+), the MWR is not effective.and k decreasesover time accordingto the full employment path ( 16). converging to k, as time extends without limit.

J.

Z. Drabicki and A. Takayama

FIGURE 8. Comparison of two phs.

/

--1

\

J

\

‘.

‘\

k

s

z(W)

FIGURE 9. Decayunder a mimmum wage.

0

se(k)

-

nk

A WAGE

MARK-UP

POLICY

In the above, we observed that the economy will decay completely if the minimum wage rate is set sufficiently high so that i.(C) < 0. Furthermore. the economy

grows, the growth

under the MWR

with unemployment

one under full employment.

I I-en

government I. /_$O

according to whather -_(k)sks,

2. II b,,
popular

legislation

reflecting

possible socio-political

inlluence. We may r\ow investigate,

pmt

ferent sort of minimum

follows the usual full employment to I,, as time extends without

path. converging

limit. If the MWR

the equilibrium IS

the! uould heavebeen had the MY ‘R 001 br-t-n

government

enacted.

becomes the growth

tctu,ards the origin regardless of the value of k,.

a dif-

real wage rate that ensures fuilemploy-

certain so&political

3. If b , < ~6 1.then A decays over t:me all the way

therefore,

wage policy: that is to say, given

ment at the existing value of k, suppose that there exist

then I 1;; values oi k, L. :Ind (’ will be smaller at each instar:: of time r!!an

enacted at I = 0 and is e&&e.

of the

hand, if .< M WR may remain

cnponentlally at the rate i. and reaches ~(6,) the at which full employment is achieved. It then

is less than the

Suppose then that the

is now aware of 3~ ,-h implications

M WR. On the otha

V the endowment ratio k grows

even if j,(K) > 0 and rate of the economy

pressures to raise the real wage

rate above the equilibrium

More

wage rate, and that the

conforms to such pressures. The question

specilically,

consequences of such a policy. letting

h*(k) be the equilibrium

real wage rate for a given value of k. we may ask what

Minimum Wage Regulation

239

would be the growth consequencesof setting the minimum wage rate 3 such that k = a@(k),

a>l.

k/k

(24)

For simplicity, we assumethat the markup ratio zxis a constant. We call such a policy a wvzge-@up policy (WMp). To analyze the effect of WMP, we may first note n@(k)can be detumined by w =J(& &f(k), so that n* = w+(k)with dw*/dk = -kf’(k)>O. Then substituting (24) into z(S), we may observe z =;(k)zz[z@(k)],

where ; >O.

k

(25)

Also from the strict concavity of I; we may easily conclude

FIGURE 10 The growth consequences of WMP.

k
From this it is clear that k dependson s, II. n, in such a way that

(26)

Diagrammatically, this can be seeneasily by replacing k,. z(s) and * in Figure 2, respectively by k. c(k) and SW*. From (261 we may also observe that the W M P always createsunemployment. Next,substituting(25)into(S)and recalling that the labor supply grows at a constant rate n we may obtain

k=k(n;s, a),

with c’k/?(n:s)
(30)

PropositioIl4. Under the WMP, thereexistsa uniquesteady statd value of the endowment ratio. k , which is asymptotically globally stable. 2. The value of k is lessthat k s, and for each k the rate ofgrowth(k/k)underthe WMPisalwayslessthan the one under full employment. 3. An increasein the rate of population gowth (n), a fall in the propensty to save (s).or an increasein the wagemarkup ratio (cx)all lower the steadyrtate value of the endowment ratio under MWP [h 1. 1.

k =,c(k)k.

where ~~(k)=sh[;(k)] -11 and 11’~0.

That 11’< 0 follows from /r’ < o and <’ > 0. Let k be the value of k for which ~r(lrf) -0.

(27)

i.e.,

.X&(C)] = )?.

(28)

The existenceof a unique value of k that satisfies(28) will be ensuredunder the usual assumptionsonji Note that k definesthe steadystate value tif the endowment ratio under the WMP. Since 11’~0. k’ is glo%lly asymptotically stable. Tocompare the valueofk with thesteadystate value of k under the usual full employment path g la Solow and Swan (i.e.. k,) we may rewrite (15) as k/k=sh(k)-,I.

(15’)

f%utby (26) and It’ ~0, we may easily ob.serve Sly-,l>Sh[j(k)]-n.

(29)

From this we may conclude that k s> k , and that. for ecrchk the growth rate (k/k) un.ier full employment is larger than the one under the WMP. This may be illustrated in Figure 10. Under the WMP, k increases (&creasesrespectwely)over time if the initial value. k,, is less (respectivelygreater) than k . Recalling (25). we may rewrite (28) as .Sk[Z(X#“(k)]= 11.

h’ 0.

The authors are indebted to the anonymous referees for their useful comments.

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m Johnson. H. G. Nov. 1969. Minimum wage laws: a general equilibrium approach. Cursmfiun Jorrrnol qf Economics and Political Science I I99-604. Johnson, H. G. 1973. The Theoty of Income Distribution. London: Gray-Mills. esp. pp. 104-109. Lefeber, L. 197 I. Pqmems.

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and Welfoe

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growth effects of a minimum wage for a two-sector economy. Economic Record 57: I BQ-185 Solow. R. M. Feb. 1956. A contribution to the theory of economr growth. Quartedy /our& of Economics LXX:65-94. Stemdl. F. G. Wmter

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Accepted 2 I May IV8

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