International migration, non-traded goods and economic welfare in the source country

Jaurttal of Development Economics 16 (NH)

321424. North-Holland

INTERNATIUNAL MIGRATION, NON-TRADED GOODS AND ECONOA3IC W&X,YAREIN THE !!3OURCECOUNTRY

Received March 1983, final version received June 1983 Labor migration redistributes income in a two factor, two good economy where one good is intemstianally non-traded. Labor’s nominal wage rise9 as nominal capital payments fall. Recent nxarch has shown that the prices of non-traded goods rise, causing society’3 welfare to decline. Hcrc the induced change in the real income of each factor is considered stmarateiy. There is an ambiguity with regard to the xal income of non-emigrating i&or. If labo; spends a relatively small diction al income on the non-traded good, its real intorne may rise, even though society sufks the loss of welfare.

Recent research by Rivera-Batiz (1982a) examines the welfare effects of emigrating labor in a two factor, two good trade model, where one of the goods is non-traded. Labor emigration leads to a rise in the price of the nontraded good, due in part to a rising labor wage, when the non-traded sector is labor intensive. It is shown that the emigration causes the economy as a whole to suffer a welfare loss. Labor, considered separately, however, faces ticher prices with a higher nominal wage. This creates what has been called the neoclassical ambiguity, uncertainty regarding the net effect upon labor’s real income. There is no such uncertainty for the owners of capital, whose payment falls. We examine here the conditions which determine the fate of labor’s real income. 2, The model The solution of this general equilibrium model is well-known and sketched in the appendix of Rivera-Batiz (1982a). Two resources, labor (L) and capital (K), produce two types of go&p, non-traded (N) and traded (T), in constant returns to scale production. The amount of a factor used to produce one unit of a good depends upom the ratio of wages (w) to rental rates (r), i.e., where i = .L, K, anu j= N, 7: The economy is small in that it clj = Cij(W[r), KW--3878/84/%3.00 $j !984, Elscviet Science Publishtxs B.V. (North-Holland)

H. Tbmps& ;fntermtlorral ?n&wion,. . . : CtrrMrertt

322 km

no d&t

upon the world market for tradeables. We also assume full employment and competitive pricing: CtnrXN+CITXT= v,, and

( 1

WC&J W&J = P&

(21

The term xj represents the output, and Pj the price, of the jth good, while the endowment of the ith factor is represented by I$. The price of non-tradeables is determined endogenously in the markets for the two goods. Supply must equal demand in each market. Where P= PN/PI’ and Y=XT+PXlh x, = D,(P, Y).

(31

The non-traded seetor ‘is assumed to use !abor intensively, i.c,, Cix/CLr > Let Ali represent the percentage of factor i used in industry j G&T. (A,iisCijXjfI$), and 8,j the share of factor i from industry 5 (@iiSW,C~~/P~). For notati.&ml eonvenienee, A4 lLNAgT -- ALTAKNI and 6 zz8,,BKT- &TC)IN. It follows from the factor intensity condition that A> i) and 8 > 0. Cost minimizing behavior of firms insures that 8,,C& + 8KjC~j=O. (For any variable x, x* ESdx/x.) The substitution term bj, defined as (C& - Clj)/( W*- r*)v is positive. We see that Cfj =

-°Kjoj(w*

-P)

and

C& =OLjoj(w*-P).

(41

It follows from (1) and (4) that - &w* + &r* + &X;F + A,,X*, = Vt,

and

(5) &W* - pd[r*+ n,,xa + A&.,.X*, = Vg, where pL SER,O,,o, + ALTUK1’~T, and PKE A,,&,a, minimization, from (2), one can show that

+ AK@,_ra,. Given ~osf

~LjM’*+ ~,j’* = Pi.

(6)

Positive demand elasticities in !he economy are tfpN= -- (dD,/dP)( P/D,), GT -ta&l~P3(P/&), (3), that

and tlvj = (SD,/8 Y)( r;lDj)* We find from differentiating

and The

X*,- %A

- ‘luTY* = VP&$. (7)

complete model is gic,en by eqs. (5), (6), and 17). Thz comparative

statics

Ii. T

32.3 Table 1

to a change ii the cconomy*s labor force ate presented in table I The negative detorminant D of the system equals - qI.Nj3Y - qFr -fir -- 8iLq.where q E ~vs~Pr + plvT.ylPtl p, = The expressions in the table would fit&+ + B&, and BT= &,& + &&. be divided by D to obtain the actual elasticities. Other notation< used ir, the table are: qrr z &,p rN+ dgr’tYr, and QP = LVPN - hTtfP~. effects on each cndagenous variable

with

regard

3. Results The productkon of non-traded goods falls as non-traded prices rise with labor emigration. The fall in supply must outweigh the fall in demand. The economy as a whole suffers, as Rivera-Batiz (1982a) points out. Owners of capital see their payment falling, suffering a real income loss. The direction of change in labor’s real income depends upon its consumption share of non-tradeables, as shown by Rufin and Jones (19771. The elasticity of labor’s wage with respect to changes in P, is denoted by pLN, i.e., B = w*/PE We see that with changing endowments, pLN=8,,/6, which is &itive; far capitalists, /lKN=P/P;t, and equals --8&I, which is negative. Let ON represent the percentage of the income of factor i which is spent on the non-traded good. The r:al income of a factor is altered by .--#:VP$ as P, changes. The net effect on that factor’s real income can then be !,tated

The real income of capilalists always moves in the opposite dircxtion to the induced change in PN, fr:liing with labor emigration. When O’;.::FJI,,~, u’c st’c that J!: ~0,

i.e.. labor’s real inctir.le falls. But labor’s real incorrc

would

rise

with labor ;pendirlg a relatively small fraction oi its income @c j?,,, on the non-traded good. These results depend directly upon the factor intensity condition. as stressed by Pivera-Batiz ( 198 ?b). There are also circumstances where capital owners could benefit from the in case

emigrating

labor.

If the model

~xre expanded

to include

b<,th skilled and