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Unemployment, tariffs and the theory of international trade
Journal of International Economics 7 (1977) 295-306. North-Holland Publishing Company
UNEMPLOYMENT, TARIFFS AND THE THEORY OF INTERNATIOMiL TRADE
Raveendra N. BATRA* Southern Methodist Universit>, Lbllas, TX 75275, U.&‘.A.
Avinash C. SETH Oflce Systems Division, Xerox C:-qxration, Dallas, TX., U.S.A.
Received August 1975, revised WIGon received July 1976 In this paper, we introduce diminishing returns to scale in Brecher’s model of international trade with unemployment and then investigate some issues embodied in the theory of international trade. Our principal results are that tariffs need not improve a country’s terms of trade and that capital accumulation also need not result in a predictable change in the terms of trade.
1. Introduction
Haberler’s (1950) pioneering contribution has recently inspired many economists to introduce unemployment in the standard two-sector trade model where full employment is general& assumed. The contributions by Johnson (1965), Bhagwati (1968), Lefeber (1.969),Batra and Pattanaik (1971), Findlay (1973) and Brecher (1974a,b) explore the impact of rigid factor prices for a small country’s gains from trade. Brecher (1971) also investigates some positive aspects of trade theory, such as the implications of tariffs, in the presence of unemployment. In addition, these studies deal with the possibility of generalized unemployment which is somewhat different from the sector-specificunemglsp= ment resulting from the rigidity of the sector-specificreal wage. The normative aspects of this latter type of unemployment have been analyzed by Harris and Todaro (1970) and BhaLgwatiand Srinivasan (1974, 1975). In the present paper, we utilize Brecher’s model (1974a,b) of generalized unemployment where the assumption of constant returns to scale along with rigidity of the real wage results in the Ricardian type of production indeterminacy (at one product--priceratio) or in complete specialization (in the presence of international trade at any other product-price ratio). By making the assumption of diminishing returns to scale, we show that Brecher’s model retains some *We are grateful to Professor J.N. Bhagwati and a referee for their stimulating comments, Batra’s research was supported by a faculty fellowship from Southern Methodist University.
2%
R.N. Batm ad A.&: Seth, ZRe theory of internationaltrade
properties of the standard Heckscher-Ohlin model, and thus becomes useful in exploring those normative and positive aspects of trade theory where the Heckscher-Ohlin model has been explicitly used. Applying this model to the traditional theory of tariffs, we show that tariffs still normally result in an improvement in the terms of trade, although the formula for the optimum tariff is different. We also apply our model to the analysis of economic growth and the terms of trade and get many new results. 2. Assumptionsand the model As noted in the aforementioned articles, underutilization of a resource may occur if the real reward of that factor is rigid. Accordingly, we assume here that the real wage rate is rigid and that this rigidity results in unemployment of labor. Otherwise our assumptions are the same as those of the standard twosector model, except that we no longer assume that the production functions are linearly homogeneous and concave. Concavity is all that we need for our analysis. Thus our assumptions include two sectors, X and Y, two factors, K and L, profit maximization on the part of producers, perfect competition in all markets except the labor market, perfect factor mobility, concave production functions, full employment of capital (K) and, finally, a rigid real wage rate with all nominal variables expressablein terms of any product price. The two production functions are:
where Ki and Li are the capital and labor inputs utilized in the ith sector (i = X, Y). We assume tiat all marginal products are positive but diminishing. For example, XL> 0, X& c 0, and XKt > 0, and so on. Furthermore, concavity of X(&, &) implies that XLLXKK-X& > 0. With competitive producers maximizing profits, w = PXLKX, Lx),
(3)
w = YL(ILIy,LY),
0
r = Pm&,
(5)
&I,
wherey is the price of X relative to Y and w and r are respectively the real wage rate and rental of capital. In the presence of full employment of capital,
where Kis assumed to be inelastically supplied.
R.N. Batra and A.C. Seth, The theory of international trclde
297
3. Some properties of our model
The eqs. (3)-(7) contain five variables, &, L,, KY,Ly and Y, and three parameters, W,p and K. Once Ki and Liare obtained, X and Y can be determined. Hence the system is determinate. Let us &St examine the effect of a change in the product-price ratio, p, on the two outputs. For this, substitute for KYfrom (7) in (4) and (6), keep Kconslcint and differentiate eqs. (3)-(6) to obtain PXL,
0 P&L
I
0
0
0
dLx
yL15
O
dKx
P&L
-YKL PxKK
o
- YKK
yK.L
-l
dLy
-l
dr
-&dP
II 1 0
-XKdp
=
’
(8)
0
The denominator of the system (8) is given by
which is negative because XLLand YLLare negative and ( YLLYKR-Y&) and XiL)are positive from the concavity of production functions which MLLXKKare assumed not to be linearly homogeneous. The solution of this system yields:
dL, -=
-x,[pxKK~,L+~y~,yK,-y~~~~+~xKxKLyLL
D
dP dKx -s-m
dP aY
dp=
dK, =
-I;'yLL(xKxLL-xLxKL)
D
dP PyKL(xLxKL--xKxLL) D
.
9
w
9 (12)
From our assumptions about the production functions, dL,/dp and dK,/dp are positive, whereas d&/dp and dL,/dp are negative. From this we conclude that dX/dp > 0 and d Y/dp c 0. In adddition, we can write
with
298
R.N. ipatm and A.C. Seth, The theory of internationaltrade
In other words, a tiansformation curve type of relationship exists in our model i.n spite of unemployment of labor, although the equilibrium vtrluc of J/’ does not equal -p, as is the case in the full~employmentmodel. This can be seen most easily by differentiating (1) and (2) to obtain dY -= dX I.&
Y&dLr+YKd#y XLdLx+XgdKx
l
d&+d.Ly = dL. Then, in view of eqs. (3)-Q), we get
Note that since d Y/dX < 0, XLdL/dX < 1. Note further that if labor were fully employed and inelastically supplied then dL ==0 and d YjldX== -p, which is what we obtain in the full-employment model. What is the sign of dL/dX? Since dX/dp > 0, the sign of dL/dX depends on the sign of dL/clp, which in view of (10) and (12) is given by dL SC.- dLx dLy dp +dp dP
Here all the terms except the last are positive. However, if we assume that the production functions are homogeneous of degree ai, where ai c 1, and if we let ki = KilLi, we can show that1
‘If production functions are homogeneous of degree CQ,(i = X, Y), then marginal product is homogeneous of degree (aI- 1). Then, from Euler’s theorem, the following holds:
(ax- WL,
Lx&L+Kx&L
=
LX%dKXxEK
= @X-l)&
Ly YL,+ Ky Y, = (aY- 1)YL, LYKcL+KY&Jc
=
(au-l)Yg.
Substituting_ for YLL,YKg,etc. from above , we get (15).
R.N. Batra and A.C. Seth, 17rethem-yof internatima!
dL
-=dp
-1 lJ [
:rade
299
(aX-l)(aY-a)&yL
XL(YLLbr
yi3+
yL JKXLY
1
X,,(#,-l)YL P,-k, Ly -+(+KLyn,j+y+*-kX)y,Lx,
I
(aY-l)yL+
I I
LY
+xx(aX LK
1)y -
1
kX_kY KL( \
kx
h
(15)
l
It may now be observed from (15) that dL/dp r 0 if ky 2 kx. In other words, if X is labor intensive (or not capital intensive) relative to Y,a rise in the relative price of X will raise total employment in the economy. All this enables us to conclude that dL x2=-p
dL/dP > 0 ’
if X is not the capital-intensive sector. Otherwise dL/dX is indeterminate. Before proceeding further, let us compare our model with Brecher’s model, which differs from ours in that Brecher, as with much of trade theor!{, assumes linearly homogeneous and concave production functions, whereas we, make the assumption of concavity only. Brecher’s model functions like the Ricardian model where, for a small country, production is indeterminate in the case of incomplete specialization [possible only at one product-price ratio) and where international trade leads ts complete specialization (at any other product-price ratio). For example, in the presence of linearly homogeneous production functions, D equals zero so that the Jacobian determinant of the system vanishes and the production side either becomes indeterminate (at one product-price ratio) or requires complete specialization (at any other product--price ratio). If, however, we assume conctivity only, then the Jacobian is nonzero and our production system retains some of the properties of the IIeckscher-Ohlin model. This is the basic difference between Brecher’s model and our mode!.. Actually, our model is more general than the Heckscher-Ohlin model because the full-employment case turns out to be a special case of our model. 4. Tariffs and the terms of tmde We are now in a position to utilize the model developed above in analyzing some standard propositions of trade theory which have been traditionally derived from the full-employment model. One of the basic results in trade theory is that if a country possesses monopoly power in trade, it can move the world terms of trade in its favor by imposing a tariff on its imports. This result, which
300
R.N. Batra and AC. Seth, l%e theory of internationaltrade
continues to hold in Brecher’smodel, is valid as long as the foreign trade market is istableeven when exportables are inferior and importables are luxury items in social consumption. We will now show that even in the presence of unemployment, a tariff causes an improvement in the terms of trade of the tariff imptising country as long as exportablesare noninferiorgoods. In developing this result, we follow the procedure outlined by Jones (1969) and more recently by Batra (l9?3). Let us assume that there are two countries, home country H and a foreign country F, which produce the two tradeable goods X and Y. Home country imposes the tar8 on its imports of X. Let & be the home import demand for X. Then *
where pwdenotes the world relative price of X and T = (1 + t), with f being the tar8 rate. Eq. (16) merely suggests that the home import demand is a function of the terms of trade and the rate of tariK Differentiating (16) totally and letting an asterisk denote proportional change, we obtain
(17) where ah =
and
The signs of ah and A, will be established later in this section. By definition,
E, =
cxcP9 I)- x(p),
(‘8)
where Ci denotes the consumption of the ith got\& I denotes real income aad. p equals the domestic, tariff-inclussve price ratio in the home country, i.e. P = Tp,. Ipowever, the change in I can be approximated by a change in social
utility given by
u=
_f U(Cx, Cy).
R.N. Batra and A.C. Seth, The theory of international trade
301
If the government returns the tariff revenue to its citizens, then the budget constraint in terms of domestic prices is given by = pX+
pcx+cy
(20)
r+Ip,&.
Differentiating (19), we obtain dU - = dI = pdCx+dCY. WY
Differentiating (20), remembering that p = p,(l + t), assuming that there is no initial tariff and utilizing (21) and (14), we get
Differentiating (18) and utilizing (22), we obtain dL, dX
1
p2X, -* - p" - Exdpw - s,p” 3 dX dp
E; =
(23)
.where eh =
-ma-
acxP aP
Ex’
and sh
dX =---* dP
P
Ex
Here eh captures the substitution effect of a price change and is nonnegative, mh is marginal propensity to consume X and 8, captures the price effect on output and is positive. Since p = Tp, and p* = T* +p$ aUi with initially T = 1, (23) reduces to E; = -
Ieh + m,
+ sh(l
-
m,xLdL/dX)b: -
[t?h+$,(l- m,&dL/dX)]T*.
(24)
m
RN. Btztra and A.C. Seth, 2%ethewy of internationaltrade
A comparison of (17’)with (24) reveals that
and Al, = eh+sh(l -m,&di/da.
(26)
The signs of ah and Aa can now be easily established. It has already been argued in (14) that X,dLldX < 1. Therefore if ?+, < 1, ah and Ahare both positive. In other words, if the home marginal propensity to consume importables is less than Unity, both ai, and & are positive. k&hng that
and
we conclude that for any tarif; rate, an increase in the world relative price of home importables causes a decline in the home demand for imports, and for any terms of trade, the introduction of the tariff also leads to the same result. Both of these are standard results and they continue to hold in our model. However, if mh > 1, that is, if importables are luxury items, both ah and Ah may be negative or zero, or ai, may be positive, but Ahmay be negative or zero. These results, of course, are not available in the full-employment model where dL = 0. ?‘here are two necessary conditions for these perverse results. First mh > 1 and second dL/dX > 0, which, of course, requires X or importables to be labor intensive. Thus we conclude that if importabtes are luxury items and relative& labor ifltensive, a country’s elasticity of import demand may be positive and a tariff at constant terms of trade may tead to a rise in the demandfor imports. The ewnomic explanation for this paradox is very simple. In the conventional
full-employ~ent model, a rise in t&e relative price of importables causes a fall in import demand for Mary reasons. First, real income fans and if mh > 0, Cx Talk Secor:d,th e rise in p causes a fall in Cx owing to the substitution effect, and fmally the output of X risei. However, in the presence of unemployment, a rise in p may raise real income if the total employment rises, that is, when X is labor intensive. NOWsince X rises and Y fatis, the rise in real income will always be less than the rise in X, which means that ifk+, 5 1, the rise in C&from this reason will be less than the rise in X, so that the import demand will definitely decline.
R.N. Batra and AC. Seth, The fheor.v of international trade
303
That is why the necessary conditions for paradoxical results require not only X to be labor intensive, but also & to be greater than one. A similar explication, applies to the effects of the tariff on & at constant terms of trade. With so many results already available, it is now a simple matter ta find the effects of a tariff on the terms of trade. Under balanced trade, PwE,hv9
n = EY(Pwh
where Eu = home exports or :foreign imports. Differentiating (27) totally and utilizing (17), we obtain p; = -
where af =
AhT” af+&-1
(28)
’
is the foreign elasticity of demand for imports. As is well known, stability requires that af + ah ;, 1. We have already shown that if mh a 1, Ah > 0. Thus, E$‘p$
or a tariff leads to an improvement in the terms of trade. If mh > 1, apossibihly, however remote, exists that the terms of trade willdeteriorate or remain unchanged. Furthermore, since in the presence of unemployment the magnitudes of Ah and ah are different, the extent of the change in pW will differ from the fullemployment case. 5.
Optimum
tariff
In this section we derive the formula for the optimum tariff in the presence of unemployment, assuming that the country is interested in maximizing
subject to the trade-balance constraint expressed in foreign prices and the 1+4(x) function given by (13). Since CX = X+ E’ and Cu = 9(X) - Er, and since PIVEX=
EY9
The two first-order conditions for the maximization of U are: where Us =
au - , aci
(29)
304
R.N. Batra and AC. Seth, TAethemy of internationaltrad”
and
Utilizing (14) and (29) in (30), we obtain
[pb)(l :,$I== whem b = &dL/dX < 1. Since p
‘t* =
(1 -b)+ba/ (a/- I)(1 4)
0, = (I+
t)pw,
the optimum tariff is given by
l
If b = 0, we get the conventional optimum tariff formula, 1 4, =‘:m aI-1
-
.
In the traditional case, the optimum tariff is characterized by the condition aI > 1. ‘This,however, does not guarantee to to be positive in the presence of unemployment, because b, although less than one, may be negative or positive. However, if we assume that af > 1, then to > 0 if b > 0, so that importables are labor intensive. Furthermore, if b > 0, to :b f,. This follows from the fact that to-t,
=
baf
(a/- I)(1 -b)
’
On the other hand, if b < 0, which requires importables to be capital intensive, then to < tc. In fact, if b < 0, the optimum tariff may be zero or even negative. It is not difkult to see that .if importables are highly capital intensive, tarifk may cause such a loss in employment and income that overall welfare may decline even if terms of trade improve. In this case, an export subsidy may be desirable. 6. Economic growth and the terms of trade
In this section we explore the implications of an increase in the supply of capital for the growing county’s terms of trade. It is well known from the usual fulkmployme@ model that at constant prices, an increase in the supply of
R.N. Batra and A.C. Seth. The theory of ijzternationaltrade
305
capital raises the output ofthe capital-intensive good and causes a decline in the output of the labor-intensive good. In the well-lknown trade theory jargon, capital growth is ultra-biased. If goods are noninferior, this is bound to create an excess demand (or supply) for the country’s importable good, which in turn in the new equilibrium is corrected by a predictable adjustment in the world price ratio. We will now derive an eminently plausible result, showing that in the presence of unemployment an increase in the supply of capital at given prices will raise the output of both goods and increase total employment in the economy. Capital growth is no longer ultra-biased. Since the output of both goods rises, the noninferiority of the goods is not sufficient to reveal the sign of the excess demand (or supply) of the importable good. Thus, the implications for the terms of trade are indeterminate. Differentiating (3~(7) with respect to K, and remembering that w and p are constant, we obtain dX Vu-dK dY -=I
(XLXKL- XKXLL)(YLLy&L- GL) I-. 3
D
(YLYKL-
YK YLL)WLL&r
dK
D
I- 9
A;3
and dL -=dK
xKL(yLL
YKK -
GLI
+
D
YKLWLL&ur
XiL)
9
which are all positive. 7. Conchsions Using a model where unemployment of labor is present in the economy, we have shown that tarif% normally improve the terms of trade of the tariffimposing country. Thus the conventional assumption of full employment turns out to be unnecessary for this result. However, if exportablcs are inferior in social consumption, terms of trade may actually deteriorate. Also, the optimum tariff formula needs to be modified. Interestingly enough, if importables are labor intensive, the optimum tariff is higher than that needed in the full-employment economy. Otherwise, the optimum tari!? mary be zero or negative. Additionally, if the tariff results in a rise in the domestic relative price of the importable good, total employment in the economy -will rise if the latter is relatively labor intensive. Finally, an increase in the supply of capital, at constant
306
JW. Bkatracad AC. Seth, 7Iie theory of internationaltra&
terms of trade, raises employment as well as the output of both goods, so that its implications for the terms of trade are indeterminate if no specifications about demand conditions are made. References Batra, RX, 1973, W&es in the pure theory of international trade, chapLers 5 and 10 (Macmillan, London). Batra, RN, and PK. Pattanaik, 1971, Factor market imperfections and gains from trade, mord Economic Papers, 182-188. Bhagwati, J., 1968, The theory and practice of commercial policy, Frank Graham Memorial Lecture (1967),Special Papers in International Economics. Bhagwati, J.N. and T.N Srinivasan, 1974, On reanalyzing the Harris-Todaro model: Policy rankings in the case of sector-specificsticky wages, American Economic Review, 502-508. Brecher, R.A., 1971, Minimum wage rates and the theory of international trade, unpublished doctoral dissertation, Harvard University. Brecher, RA., 1974a, Minimum wage rates and the pure theory of international trade, Quarterly Journal of Economics, 98-l 16. Brecher, R.A., 1974b,Optimum comlmercialpolicy for a minimum wage economy, Journal of International Economics 4, no. 2,140-148. Findlay, R.E., 1973, Xnternational trade and development theory, chapter 5 (Columbia University Press, New York). Haberier, G., 1950, Some problems in the pure theory of international trade, Economic Journal, 223-240. Harris, J. and M. Todaro, 1970, Migration, unemployment and development: A two sector anaiysis, American Econnmic Review, 126-142. Johnson+ H.G., 1965, Optimal trade intervention in the presence of domestic distortions; in: Trade, ,gr*owth and balance of paymeats (Rand-McNally, Chicago). Jones, R.W., 1969,Tariffs and trade in general equilibrium: Comment, American Economic Review, 418-424. Lefeber, L., 1971, Trade and minimum wage rates; in: J.N. Bhagwati et al., eds., Trade, balance of payments and growth (North-Holland, Amsterdam) 91-l 14. Magee, S.P., 1973, Factor market distortions, production and trade: A Survey, Oxford Economic Papers. Srinivasan, R.N. and J.N. Bhagwati, 1975, Alternative policy rankings in a large, open economy with sector-specific, minimum wages, Journal of Economic Theory, 356-371.
UNEMPLOYMENT, TARIFFS AND THE THEORY OF INTERNATIOMiL TRADE
Raveendra N. BATRA* Southern Methodist Universit>, Lbllas, TX 75275, U.&‘.A.
Avinash C. SETH Oflce Systems Division, Xerox C:-qxration, Dallas, TX., U.S.A.
Received August 1975, revised WIGon received July 1976 In this paper, we introduce diminishing returns to scale in Brecher’s model of international trade with unemployment and then investigate some issues embodied in the theory of international trade. Our principal results are that tariffs need not improve a country’s terms of trade and that capital accumulation also need not result in a predictable change in the terms of trade.
1. Introduction
Haberler’s (1950) pioneering contribution has recently inspired many economists to introduce unemployment in the standard two-sector trade model where full employment is general& assumed. The contributions by Johnson (1965), Bhagwati (1968), Lefeber (1.969),Batra and Pattanaik (1971), Findlay (1973) and Brecher (1974a,b) explore the impact of rigid factor prices for a small country’s gains from trade. Brecher (1971) also investigates some positive aspects of trade theory, such as the implications of tariffs, in the presence of unemployment. In addition, these studies deal with the possibility of generalized unemployment which is somewhat different from the sector-specificunemglsp= ment resulting from the rigidity of the sector-specificreal wage. The normative aspects of this latter type of unemployment have been analyzed by Harris and Todaro (1970) and BhaLgwatiand Srinivasan (1974, 1975). In the present paper, we utilize Brecher’s model (1974a,b) of generalized unemployment where the assumption of constant returns to scale along with rigidity of the real wage results in the Ricardian type of production indeterminacy (at one product--priceratio) or in complete specialization (in the presence of international trade at any other product-price ratio). By making the assumption of diminishing returns to scale, we show that Brecher’s model retains some *We are grateful to Professor J.N. Bhagwati and a referee for their stimulating comments, Batra’s research was supported by a faculty fellowship from Southern Methodist University.
2%
R.N. Batm ad A.&: Seth, ZRe theory of internationaltrade
properties of the standard Heckscher-Ohlin model, and thus becomes useful in exploring those normative and positive aspects of trade theory where the Heckscher-Ohlin model has been explicitly used. Applying this model to the traditional theory of tariffs, we show that tariffs still normally result in an improvement in the terms of trade, although the formula for the optimum tariff is different. We also apply our model to the analysis of economic growth and the terms of trade and get many new results. 2. Assumptionsand the model As noted in the aforementioned articles, underutilization of a resource may occur if the real reward of that factor is rigid. Accordingly, we assume here that the real wage rate is rigid and that this rigidity results in unemployment of labor. Otherwise our assumptions are the same as those of the standard twosector model, except that we no longer assume that the production functions are linearly homogeneous and concave. Concavity is all that we need for our analysis. Thus our assumptions include two sectors, X and Y, two factors, K and L, profit maximization on the part of producers, perfect competition in all markets except the labor market, perfect factor mobility, concave production functions, full employment of capital (K) and, finally, a rigid real wage rate with all nominal variables expressablein terms of any product price. The two production functions are:
where Ki and Li are the capital and labor inputs utilized in the ith sector (i = X, Y). We assume tiat all marginal products are positive but diminishing. For example, XL> 0, X& c 0, and XKt > 0, and so on. Furthermore, concavity of X(&, &) implies that XLLXKK-X& > 0. With competitive producers maximizing profits, w = PXLKX, Lx),
(3)
w = YL(ILIy,LY),
0
r = Pm&,
(5)
&I,
wherey is the price of X relative to Y and w and r are respectively the real wage rate and rental of capital. In the presence of full employment of capital,
where Kis assumed to be inelastically supplied.
R.N. Batra and A.C. Seth, The theory of international trclde
297
3. Some properties of our model
The eqs. (3)-(7) contain five variables, &, L,, KY,Ly and Y, and three parameters, W,p and K. Once Ki and Liare obtained, X and Y can be determined. Hence the system is determinate. Let us &St examine the effect of a change in the product-price ratio, p, on the two outputs. For this, substitute for KYfrom (7) in (4) and (6), keep Kconslcint and differentiate eqs. (3)-(6) to obtain PXL,
0 P&L
I
0
0
0
dLx
yL15
O
dKx
P&L
-YKL PxKK
o
- YKK
yK.L
-l
dLy
-l
dr
-&dP
II 1 0
-XKdp
=
’
(8)
0
The denominator of the system (8) is given by
which is negative because XLLand YLLare negative and ( YLLYKR-Y&) and XiL)are positive from the concavity of production functions which MLLXKKare assumed not to be linearly homogeneous. The solution of this system yields:
dL, -=
-x,[pxKK~,L+~y~,yK,-y~~~~+~xKxKLyLL
D
dP dKx -s-m
dP aY
dp=
dK, =
-I;'yLL(xKxLL-xLxKL)
D
dP PyKL(xLxKL--xKxLL) D
.
9
w
9 (12)
From our assumptions about the production functions, dL,/dp and dK,/dp are positive, whereas d&/dp and dL,/dp are negative. From this we conclude that dX/dp > 0 and d Y/dp c 0. In adddition, we can write
with
298
R.N. ipatm and A.C. Seth, The theory of internationaltrade
In other words, a tiansformation curve type of relationship exists in our model i.n spite of unemployment of labor, although the equilibrium vtrluc of J/’ does not equal -p, as is the case in the full~employmentmodel. This can be seen most easily by differentiating (1) and (2) to obtain dY -= dX I.&
Y&dLr+YKd#y XLdLx+XgdKx
l
d&+d.Ly = dL. Then, in view of eqs. (3)-Q), we get
Note that since d Y/dX < 0, XLdL/dX < 1. Note further that if labor were fully employed and inelastically supplied then dL ==0 and d YjldX== -p, which is what we obtain in the full-employment model. What is the sign of dL/dX? Since dX/dp > 0, the sign of dL/dX depends on the sign of dL/clp, which in view of (10) and (12) is given by dL SC.- dLx dLy dp +dp dP
Here all the terms except the last are positive. However, if we assume that the production functions are homogeneous of degree ai, where ai c 1, and if we let ki = KilLi, we can show that1
‘If production functions are homogeneous of degree CQ,(i = X, Y), then marginal product is homogeneous of degree (aI- 1). Then, from Euler’s theorem, the following holds:
(ax- WL,
Lx&L+Kx&L
=
LX%dKXxEK
= @X-l)&
Ly YL,+ Ky Y, = (aY- 1)YL, LYKcL+KY&Jc
=
(au-l)Yg.
Substituting_ for YLL,YKg,etc. from above , we get (15).
R.N. Batra and A.C. Seth, 17rethem-yof internatima!
dL
-=dp
-1 lJ [
:rade
299
(aX-l)(aY-a)&yL
XL(YLLbr
yi3+
yL JKXLY
1
X,,(#,-l)YL P,-k, Ly -+(+KLyn,j+y+*-kX)y,Lx,
I
(aY-l)yL+
I I
LY
+xx(aX LK
1)y -
1
kX_kY KL( \
kx
h
(15)
l
It may now be observed from (15) that dL/dp r 0 if ky 2 kx. In other words, if X is labor intensive (or not capital intensive) relative to Y,a rise in the relative price of X will raise total employment in the economy. All this enables us to conclude that dL x2=-p
dL/dP > 0 ’
if X is not the capital-intensive sector. Otherwise dL/dX is indeterminate. Before proceeding further, let us compare our model with Brecher’s model, which differs from ours in that Brecher, as with much of trade theor!{, assumes linearly homogeneous and concave production functions, whereas we, make the assumption of concavity only. Brecher’s model functions like the Ricardian model where, for a small country, production is indeterminate in the case of incomplete specialization [possible only at one product-price ratio) and where international trade leads ts complete specialization (at any other product-price ratio). For example, in the presence of linearly homogeneous production functions, D equals zero so that the Jacobian determinant of the system vanishes and the production side either becomes indeterminate (at one product-price ratio) or requires complete specialization (at any other product--price ratio). If, however, we assume conctivity only, then the Jacobian is nonzero and our production system retains some of the properties of the IIeckscher-Ohlin model. This is the basic difference between Brecher’s model and our mode!.. Actually, our model is more general than the Heckscher-Ohlin model because the full-employment case turns out to be a special case of our model. 4. Tariffs and the terms of tmde We are now in a position to utilize the model developed above in analyzing some standard propositions of trade theory which have been traditionally derived from the full-employment model. One of the basic results in trade theory is that if a country possesses monopoly power in trade, it can move the world terms of trade in its favor by imposing a tariff on its imports. This result, which
300
R.N. Batra and AC. Seth, l%e theory of internationaltrade
continues to hold in Brecher’smodel, is valid as long as the foreign trade market is istableeven when exportables are inferior and importables are luxury items in social consumption. We will now show that even in the presence of unemployment, a tariff causes an improvement in the terms of trade of the tariff imptising country as long as exportablesare noninferiorgoods. In developing this result, we follow the procedure outlined by Jones (1969) and more recently by Batra (l9?3). Let us assume that there are two countries, home country H and a foreign country F, which produce the two tradeable goods X and Y. Home country imposes the tar8 on its imports of X. Let & be the home import demand for X. Then *
where pwdenotes the world relative price of X and T = (1 + t), with f being the tar8 rate. Eq. (16) merely suggests that the home import demand is a function of the terms of trade and the rate of tariK Differentiating (16) totally and letting an asterisk denote proportional change, we obtain
(17) where ah =
and
The signs of ah and A, will be established later in this section. By definition,
E, =
cxcP9 I)- x(p),
(‘8)
where Ci denotes the consumption of the ith got\& I denotes real income aad. p equals the domestic, tariff-inclussve price ratio in the home country, i.e. P = Tp,. Ipowever, the change in I can be approximated by a change in social
utility given by
u=
_f U(Cx, Cy).
R.N. Batra and A.C. Seth, The theory of international trade
301
If the government returns the tariff revenue to its citizens, then the budget constraint in terms of domestic prices is given by = pX+
pcx+cy
(20)
r+Ip,&.
Differentiating (19), we obtain dU - = dI = pdCx+dCY. WY
Differentiating (20), remembering that p = p,(l + t), assuming that there is no initial tariff and utilizing (21) and (14), we get
Differentiating (18) and utilizing (22), we obtain dL, dX
1
p2X, -* - p" - Exdpw - s,p” 3 dX dp
E; =
(23)
.where eh =
-ma-
acxP aP
Ex’
and sh
dX =---* dP
P
Ex
Here eh captures the substitution effect of a price change and is nonnegative, mh is marginal propensity to consume X and 8, captures the price effect on output and is positive. Since p = Tp, and p* = T* +p$ aUi with initially T = 1, (23) reduces to E; = -
Ieh + m,
+ sh(l
-
m,xLdL/dX)b: -
[t?h+$,(l- m,&dL/dX)]T*.
(24)
m
RN. Btztra and A.C. Seth, 2%ethewy of internationaltrade
A comparison of (17’)with (24) reveals that
and Al, = eh+sh(l -m,&di/da.
(26)
The signs of ah and Aa can now be easily established. It has already been argued in (14) that X,dLldX < 1. Therefore if ?+, < 1, ah and Ahare both positive. In other words, if the home marginal propensity to consume importables is less than Unity, both ai, and & are positive. k&hng that
and
we conclude that for any tarif; rate, an increase in the world relative price of home importables causes a decline in the home demand for imports, and for any terms of trade, the introduction of the tariff also leads to the same result. Both of these are standard results and they continue to hold in our model. However, if mh > 1, that is, if importables are luxury items, both ah and Ah may be negative or zero, or ai, may be positive, but Ahmay be negative or zero. These results, of course, are not available in the full-employment model where dL = 0. ?‘here are two necessary conditions for these perverse results. First mh > 1 and second dL/dX > 0, which, of course, requires X or importables to be labor intensive. Thus we conclude that if importabtes are luxury items and relative& labor ifltensive, a country’s elasticity of import demand may be positive and a tariff at constant terms of trade may tead to a rise in the demandfor imports. The ewnomic explanation for this paradox is very simple. In the conventional
full-employ~ent model, a rise in t&e relative price of importables causes a fall in import demand for Mary reasons. First, real income fans and if mh > 0, Cx Talk Secor:d,th e rise in p causes a fall in Cx owing to the substitution effect, and fmally the output of X risei. However, in the presence of unemployment, a rise in p may raise real income if the total employment rises, that is, when X is labor intensive. NOWsince X rises and Y fatis, the rise in real income will always be less than the rise in X, which means that ifk+, 5 1, the rise in C&from this reason will be less than the rise in X, so that the import demand will definitely decline.
R.N. Batra and AC. Seth, The fheor.v of international trade
303
That is why the necessary conditions for paradoxical results require not only X to be labor intensive, but also & to be greater than one. A similar explication, applies to the effects of the tariff on & at constant terms of trade. With so many results already available, it is now a simple matter ta find the effects of a tariff on the terms of trade. Under balanced trade, PwE,hv9
n = EY(Pwh
where Eu = home exports or :foreign imports. Differentiating (27) totally and utilizing (17), we obtain p; = -
where af =
AhT” af+&-1
(28)
’
is the foreign elasticity of demand for imports. As is well known, stability requires that af + ah ;, 1. We have already shown that if mh a 1, Ah > 0. Thus, E$‘p$
or a tariff leads to an improvement in the terms of trade. If mh > 1, apossibihly, however remote, exists that the terms of trade willdeteriorate or remain unchanged. Furthermore, since in the presence of unemployment the magnitudes of Ah and ah are different, the extent of the change in pW will differ from the fullemployment case. 5.
Optimum
tariff
In this section we derive the formula for the optimum tariff in the presence of unemployment, assuming that the country is interested in maximizing
subject to the trade-balance constraint expressed in foreign prices and the 1+4(x) function given by (13). Since CX = X+ E’ and Cu = 9(X) - Er, and since PIVEX=
EY9
The two first-order conditions for the maximization of U are: where Us =
au - , aci
(29)
304
R.N. Batra and AC. Seth, TAethemy of internationaltrad”
and
Utilizing (14) and (29) in (30), we obtain
[pb)(l :,$I== whem b = &dL/dX < 1. Since p
‘t* =
(1 -b)+ba/ (a/- I)(1 4)
0, = (I+
t)pw,
the optimum tariff is given by
l
If b = 0, we get the conventional optimum tariff formula, 1 4, =‘:m aI-1
-
.
In the traditional case, the optimum tariff is characterized by the condition aI > 1. ‘This,however, does not guarantee to to be positive in the presence of unemployment, because b, although less than one, may be negative or positive. However, if we assume that af > 1, then to > 0 if b > 0, so that importables are labor intensive. Furthermore, if b > 0, to :b f,. This follows from the fact that to-t,
=
baf
(a/- I)(1 -b)
’
On the other hand, if b < 0, which requires importables to be capital intensive, then to < tc. In fact, if b < 0, the optimum tariff may be zero or even negative. It is not difkult to see that .if importables are highly capital intensive, tarifk may cause such a loss in employment and income that overall welfare may decline even if terms of trade improve. In this case, an export subsidy may be desirable. 6. Economic growth and the terms of trade
In this section we explore the implications of an increase in the supply of capital for the growing county’s terms of trade. It is well known from the usual fulkmployme@ model that at constant prices, an increase in the supply of
R.N. Batra and A.C. Seth. The theory of ijzternationaltrade
305
capital raises the output ofthe capital-intensive good and causes a decline in the output of the labor-intensive good. In the well-lknown trade theory jargon, capital growth is ultra-biased. If goods are noninferior, this is bound to create an excess demand (or supply) for the country’s importable good, which in turn in the new equilibrium is corrected by a predictable adjustment in the world price ratio. We will now derive an eminently plausible result, showing that in the presence of unemployment an increase in the supply of capital at given prices will raise the output of both goods and increase total employment in the economy. Capital growth is no longer ultra-biased. Since the output of both goods rises, the noninferiority of the goods is not sufficient to reveal the sign of the excess demand (or supply) of the importable good. Thus, the implications for the terms of trade are indeterminate. Differentiating (3~(7) with respect to K, and remembering that w and p are constant, we obtain dX Vu-dK dY -=I
(XLXKL- XKXLL)(YLLy&L- GL) I-. 3
D
(YLYKL-
YK YLL)WLL&r
dK
D
I- 9
A;3
and dL -=dK
xKL(yLL
YKK -
GLI
+
D
YKLWLL&ur
XiL)
9
which are all positive. 7. Conchsions Using a model where unemployment of labor is present in the economy, we have shown that tarif% normally improve the terms of trade of the tariffimposing country. Thus the conventional assumption of full employment turns out to be unnecessary for this result. However, if exportablcs are inferior in social consumption, terms of trade may actually deteriorate. Also, the optimum tariff formula needs to be modified. Interestingly enough, if importables are labor intensive, the optimum tariff is higher than that needed in the full-employment economy. Otherwise, the optimum tari!? mary be zero or negative. Additionally, if the tariff results in a rise in the domestic relative price of the importable good, total employment in the economy -will rise if the latter is relatively labor intensive. Finally, an increase in the supply of capital, at constant
306
JW. Bkatracad AC. Seth, 7Iie theory of internationaltra&
terms of trade, raises employment as well as the output of both goods, so that its implications for the terms of trade are indeterminate if no specifications about demand conditions are made. References Batra, RX, 1973, W&es in the pure theory of international trade, chapLers 5 and 10 (Macmillan, London). Batra, RN, and PK. Pattanaik, 1971, Factor market imperfections and gains from trade, mord Economic Papers, 182-188. Bhagwati, J., 1968, The theory and practice of commercial policy, Frank Graham Memorial Lecture (1967),Special Papers in International Economics. Bhagwati, J.N. and T.N Srinivasan, 1974, On reanalyzing the Harris-Todaro model: Policy rankings in the case of sector-specificsticky wages, American Economic Review, 502-508. Brecher, R.A., 1971, Minimum wage rates and the theory of international trade, unpublished doctoral dissertation, Harvard University. Brecher, RA., 1974a, Minimum wage rates and the pure theory of international trade, Quarterly Journal of Economics, 98-l 16. Brecher, R.A., 1974b,Optimum comlmercialpolicy for a minimum wage economy, Journal of International Economics 4, no. 2,140-148. Findlay, R.E., 1973, Xnternational trade and development theory, chapter 5 (Columbia University Press, New York). Haberier, G., 1950, Some problems in the pure theory of international trade, Economic Journal, 223-240. Harris, J. and M. Todaro, 1970, Migration, unemployment and development: A two sector anaiysis, American Econnmic Review, 126-142. Johnson+ H.G., 1965, Optimal trade intervention in the presence of domestic distortions; in: Trade, ,gr*owth and balance of paymeats (Rand-McNally, Chicago). Jones, R.W., 1969,Tariffs and trade in general equilibrium: Comment, American Economic Review, 418-424. Lefeber, L., 1971, Trade and minimum wage rates; in: J.N. Bhagwati et al., eds., Trade, balance of payments and growth (North-Holland, Amsterdam) 91-l 14. Magee, S.P., 1973, Factor market distortions, production and trade: A Survey, Oxford Economic Papers. Srinivasan, R.N. and J.N. Bhagwati, 1975, Alternative policy rankings in a large, open economy with sector-specific, minimum wages, Journal of Economic Theory, 356-371.