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Trade-off between aggregate efficiency and interregional equity
TRADE-OFF BETWEEN AGGREGATE EFFIUENCY AlVD INTKRREGIONAL EQIITY A Comment Komci SASAKJ 7 tddtt
l’titt vrd
I.
Jctpirtt
Mera (1973) analyzes empirically the trade-off between interregional equity and aggregate efficiency when the government tries to eliminate or improle the interregional inequity by controlling the distribution pattern of social capital among regions. In his analysis. two different experiments concerning the case of Japanese economy are performed. First. the short-run effects of redistribution of social capital which aims to achieve the interregional equality are estimated under the condition that the distribution of labor and private capital among regions is in status quo. The second experiment is to estimate the long-run c‘ffects of redistribution of social cilpital \vhich nims IO achicvc IhC inter-regional t2qUillit~. itSSUlllillp llliil 1101 only SO&l Cilpital hut Ao
labor
and
pribatc capital ;Lrc r~diatrlbuti~bk.
In that USC.
it is supposed
that the distribution patterns of labor and private capital iIre prescribed by that of social capital although the economic implication of this statement is 1101 CICU. In other words. tllC SOCiitl Cilpltktl is itI1 ‘itllr~c;~t<~r’ of labor and pri\-;ltc capitul. Then hc t_~~v~ludcs th;lt eliminating or irnpro\~in~ the iW~lli~lil!, illllOH~ rqiwb Rhtlllh in il IOSS in lli1liWli~l inconic fcJr both c:f tu’c~ cxpcrinicntk
In the first experiment, the value which sh~~uld hc comp;lred \vith the Ic~el of national income without redistribution of social capital is the level of national income to be attained when the social capital is redistributed to equalize the marginal (not the average) products of labor among regions d sectors. In such a case, we cannot judge a priori whether it will result in a loss in national income or not. In the second experiment, it is obvious that the national income will be maximized when the marginal productivities of labor, private capital and social capital are respect;vely equalized among all regions. Therefore, since the reward per worker will be equalized in this case, the elimination of the interregional inequity does not contradict maximizing the cfl7ciency. On the contrary, two policies are complementary. If the competitive force Morkf in both of labor and capital markets and the mobility of these factors among regions is perfect or close to perfect, it is well expected that the marginal productivity of each of them will be equalized in all regions in the long run.’ In brief, there is no rational for the assertion that there is the trade-off between aggrc;-lte efficiency and interregional equity,, as long as the marginal productivity of labor is taken as the criterion of int :rregional equity. Mew’s analysis is not only unreasonable but also misleading as ~1guide lint to the regional economic policy.3
i = I. 21. The problem of this ccnnomy X =X,
is to musnnirc
t x,,
III
subject to L = L, +L,
and
K = Ic, +h’:.
(2)
where X, L, K are, respectively. output, labor and capital stock. If WC assumC that ~hcrc ib no corner solution IX, = 0 or X2 = 0). the abo\fe problem is 10 solve the simuir;lncous equation of (3).
0,x,
+fIJ2
= 1, and
h,X,
+ /),X2 = K.
131
In this case. the levels of produced income per workor ol’ ~wa rcgionh do not coincitlc CXCC~I for the special case (0, = (1; ‘, and so inhxrcpional incquiry ih urc\ir;thlc [ hcc Mcra (lW7)l. However. in the above problem the reward of input ih nt~ ~rca~cd cxphcitl!. WC C~II~CI IIW value of reward of each input which is considcrcd to bc C'OIINI~~~I~ IO IWO rcpicms by aal\ wg IIIC dual equation of (3). ~r,tIJ+
h*p = I
and
f12t'J-I-I':/' .= 1 1
I"Jl
where w and I) arc real wage and real rcnlal, rcbpcctl\ cl). Therefore, we can say that interregional inequity as for the reward per worker as long as the perfect competition prevails in both of labor and capital markets. 2See Sakashita
and Kamoike
3Mera (1967) should
(1974) for a dynamic
be criticized
for this paint loo.
formulation
of this prnhlcm
tlors
not
occur.
References Mcra, K.. 1967. Trade-off hrtwcn rtggregatc cllicisncy and interregional equity: A static analy% Quarlcrly Jlsurnai of Economics 81.658 694. Metn. K.. 1’(173. Trade-all between aggregate efiiciency and intcrrspinnai cyuity : The case of Japan. Regional and Urban Ecnnomia 3_ 172 300. Sakash~a, N.. 1971 Chiiki kztihatw no kewn hunwk~ IAn cconrrmio analy& of regional dewlopmcnt), m: M fa!emnto and T. Wstan;ltw Shimhunsha. Tok>111 m Japanete.
eds.. Gendai no Kci/agaku
3 (Nihonhcizai
l’titt vrd
I.
Jctpirtt
Mera (1973) analyzes empirically the trade-off between interregional equity and aggregate efficiency when the government tries to eliminate or improle the interregional inequity by controlling the distribution pattern of social capital among regions. In his analysis. two different experiments concerning the case of Japanese economy are performed. First. the short-run effects of redistribution of social capital which aims to achieve the interregional equality are estimated under the condition that the distribution of labor and private capital among regions is in status quo. The second experiment is to estimate the long-run c‘ffects of redistribution of social cilpital \vhich nims IO achicvc IhC inter-regional t2qUillit~. itSSUlllillp llliil 1101 only SO&l Cilpital hut Ao
labor
and
pribatc capital ;Lrc r~diatrlbuti~bk.
In that USC.
it is supposed
that the distribution patterns of labor and private capital iIre prescribed by that of social capital although the economic implication of this statement is 1101 CICU. In other words. tllC SOCiitl Cilpltktl is itI1 ‘itllr~c;~t<~r’ of labor and pri\-;ltc capitul. Then hc t_~~v~ludcs th;lt eliminating or irnpro\~in~ the iW~lli~lil!, illllOH~ rqiwb Rhtlllh in il IOSS in lli1liWli~l inconic fcJr both c:f tu’c~ cxpcrinicntk
In the first experiment, the value which sh~~uld hc comp;lred \vith the Ic~el of national income without redistribution of social capital is the level of national income to be attained when the social capital is redistributed to equalize the marginal (not the average) products of labor among regions d sectors. In such a case, we cannot judge a priori whether it will result in a loss in national income or not. In the second experiment, it is obvious that the national income will be maximized when the marginal productivities of labor, private capital and social capital are respect;vely equalized among all regions. Therefore, since the reward per worker will be equalized in this case, the elimination of the interregional inequity does not contradict maximizing the cfl7ciency. On the contrary, two policies are complementary. If the competitive force Morkf in both of labor and capital markets and the mobility of these factors among regions is perfect or close to perfect, it is well expected that the marginal productivity of each of them will be equalized in all regions in the long run.’ In brief, there is no rational for the assertion that there is the trade-off between aggrc;-lte efficiency and interregional equity,, as long as the marginal productivity of labor is taken as the criterion of int :rregional equity. Mew’s analysis is not only unreasonable but also misleading as ~1guide lint to the regional economic policy.3
i = I. 21. The problem of this ccnnomy X =X,
is to musnnirc
t x,,
III
subject to L = L, +L,
and
K = Ic, +h’:.
(2)
where X, L, K are, respectively. output, labor and capital stock. If WC assumC that ~hcrc ib no corner solution IX, = 0 or X2 = 0). the abo\fe problem is 10 solve the simuir;lncous equation of (3).
0,x,
+fIJ2
= 1, and
h,X,
+ /),X2 = K.
131
In this case. the levels of produced income per workor ol’ ~wa rcgionh do not coincitlc CXCC~I for the special case (0, = (1; ‘, and so inhxrcpional incquiry ih urc\ir;thlc [ hcc Mcra (lW7)l. However. in the above problem the reward of input ih nt~ ~rca~cd cxphcitl!. WC C~II~CI IIW value of reward of each input which is considcrcd to bc C'OIINI~~~I~ IO IWO rcpicms by aal\ wg IIIC dual equation of (3). ~r,tIJ+
h*p = I
and
f12t'J-I-I':/' .= 1 1
I"Jl
where w and I) arc real wage and real rcnlal, rcbpcctl\ cl). Therefore, we can say that interregional inequity as for the reward per worker as long as the perfect competition prevails in both of labor and capital markets. 2See Sakashita
and Kamoike
3Mera (1967) should
(1974) for a dynamic
be criticized
for this paint loo.
formulation
of this prnhlcm
tlors
not
occur.
References Mcra, K.. 1967. Trade-off hrtwcn rtggregatc cllicisncy and interregional equity: A static analy% Quarlcrly Jlsurnai of Economics 81.658 694. Metn. K.. 1’(173. Trade-all between aggregate efiiciency and intcrrspinnai cyuity : The case of Japan. Regional and Urban Ecnnomia 3_ 172 300. Sakash~a, N.. 1971 Chiiki kztihatw no kewn hunwk~ IAn cconrrmio analy& of regional dewlopmcnt), m: M fa!emnto and T. Wstan;ltw Shimhunsha. Tok>111 m Japanete.
eds.. Gendai no Kci/agaku
3 (Nihonhcizai