Optimum and Equilibrium for Regional Economies: Collected Papers of Noboru Sakashita

216 Pages·1996·11.235 MB·English

by  Prof. Dr. Noboru Sakashita (auth.), Prof. Dr. Komei Sasaki (eds.)

Optimum and Equilibrium for Regional Economies
Collected Papers of Noboru Sakashita
Springer
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Komei Sasaki (Ed.)
Optimum and Equilibrium
for Regional Economies
Collected Papers
of Noboru Sakashita
i
Springer
Editor
Prof. Dr. Komei Sasaki
Tohoku University
Graduate School of Information Sciences
Katahira 2, Aoba-ku
Sendai 980, Japan
Author
Prof. Dr. Noboru Sakashita
University of Tsukuba
Institute of Socio-Economic Planning
Tsukuba, Ibaraki 305, Japan
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Sakashita, N6bOru:
Optimum and equilibrium for regional economies: collected
papers of Noboru Sakashita I Komei Sasaki (ed.). - Berlin;
Heidelberg; New York; Barcelona; Budapest; Hong Kong;
London; Milan; Paris; Santa Clara; Singapore; Tokyo:
Springer, 1996
NE: Sasaki, Komei [Hl'Sg.J; Sakashita, Noooru: [Sammlung <engl.»
ISBN-13: 978-3-642-80137-2 e-ISBN-13: 978-3-642-80135-8
DOl: 10.1007/ 978-3-642-80135-8
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Introduction
This volume reproduces some important contributions to regional
and urban economics made by Noboru Sakashita - one of the lead
ing scholars in this field. Since graduation from the University of
Tokyo, Noboru Sakashita has been teaching and advancing the re
search at Hokkaido University, Tohoku University, Osaka University
and the' University of Tsukuba.
The career of Noboru Sakashita as a regional and urban econo
mist started in 1965 when he visited the University of Pennsylvania's
Regional Science Department as a Fulbright scholar. While staying
there, he concentrated on research on regional science in a stimula
tive atmosphere surrounded by Walter Isard, the founder of Region
al Science, and Isard's young colleagues, all of who were full of pas
sion for this newborn research field. The first two papers in this vo
lume were written during his stay at the University of Pennsylvania.
Since returning to Japan, he has been carrying out his own research
activities as well as fostering many promising disciplines in the field
of regional and urban economics. Of course, Noboru Sakashita is a
world renowned famous scholar, presenting many influential papers
at World Congress, North American and European Meetings of the
Regional Science Association, and other conferences, and publishing
many articles in respected journals. He was elected president of the
Regional Science Association International for 1987-88, and served
as the first president of the Applied Regional Science Conference
from 1987 to 1989.
The academic contribution of Noboru Sakashita is characterized
by the following three distinguished features:
1. demonstrating rigorous theoretical analysis
2. modeling practical subjects
3. providing methodology for policy evaluation.
These are all important and indispensable features to regional
science which intends to solve various real world regional problems
scientifically. Noboru Sakashita is not a pure theorist, although he is
an excellent theorist. His research has been strongly motivated by
real problems of regional and urban economy. We are impressed to
see that in his many papers, theoretical analysis is complemented by
V
empirical or numerical simulation analysis so that the meaning of
theoretical models can be fully understood.
We will introduce several articles which seem to reflect clearly Sa
kashita's characteristics. The paper - Production Function, Demand
Function and Location Theory of the Firm - generalized the pre
vious location-choice model by allowing the simultaneous choice of
production technology and location under the substitutability
among inputs. As one of the basic works in location theory, this pa
per still attracts many readers even though it was written twenty seven
years ago. Two papers on National Growth and Regional Income In
equality are also types of rigorous theoretical analysis of regional eco
nomics: they showed that there is no trade-off relation between
national economic growth and regional income equality under a
proper measure of regional disparity. As for models of practical sub
jects, two papers can be cited: Economics of Multi-habitation and
Optimal Utilization of the Central Business District with Economy
and Disecon011o/ of Agglomeration. The former article was intended
to explore the rationale of multi-habitation policy in Japan as a
measure of population dispersion from the viewpoint of regional
economic theory. Readers might be surprised that this topic is
tackled from the standpoint of optimizing allocation of living time.
The latter article is concerned with agglomeration economy and dis
economy of a CBn in a city, arguing the measure for utilizing the
function of a CBn efficiently. Both Distributional Biases in the Wel
fare Pricing of Public Transport Service and Evaluation of Regional
Development Policy are policy-oriented papers although they are the
oretical analyses. In the first paper, public transport pricing is treat
ed in an attempt to integrate welfare pricing theory and public in
vestment decision theory. The second paper compares alternative re
gional development policies to attain a desired regional population
distribution from the point of view of social costs as well as the
amount of subsi4y needed. The only empirical study in this volume,
Urban Growth Analysis in Postwar Japan is an excerpt from the
comprehensive analysis of urban dynamics in postwar Japan under
taken by Sakashita and his research group at Japan's Economic
Planning Agency. In this paper, Hoover indices for Japanese cities
for 1955-1975 are used intensively to show the tendency of popula
tion to concentrate in a few metropolitan areas despite the U-turn
or J-turn population phenomenon during the period considered.
In 1996, Noboru Sakashita will retire from the University of Tsu
kuba. The publication of these collected papers was planned by his
colleagues, students, and friends to commemorate his retirement.
Even after retirement from the University of Tsukuba, Noboru Saka
shita will continue research and education of regional and urban
economics. We hope these collected papers will stimulate young
scholars particularly so that they will further evolve regional and ur
ban economics study.
Komei Sasaki
VI
Contents
[1] Regional Allocation of Public Investment. . . . . . . . . . . . . . 1
[2] Production Function, Demand Function and Location
Theory of the Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
[3] On a Simple Model of Dynamic Fiscal Policy. . . . . . . . . .. 37
[4] (with o. Kamoike t) National Growth and Regional
Income Inequality: A Consistent Model . . . . . . . . . . . . . .. 61
[5] (with o. Kamoike t) National Growth and Regional
Income Inequality: Further Results. . . . . . . . . . . . . . . . . .. 73
[6] Distributional Bias in the Welfare Pricing
of Public Transport Service . . . . . . . . . . . . . . . . . . . . . . .. 81
[7] Urban Growth Analysis in Postwar Japan: Fact Findings
on the Distribution of Urban Population . . . . . . . . . . . . .. 103
[8] Resolution of Mutual Loss Conflict Induced by the
Embargo Threat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 113
[9] Evaluation of Regional Development Policy
- An Alternative Approach. . . . . . . . . . . . . . . . . . . . . . . .. 121
[10] Location Quotients, Export Industries
and Shift-Share Analysis. . . . . . . . . . . . . . . . . . . . . . . . .. 131
[11] Optimum Location of Public Facilities
Under the Influence of the Land Market ............... 149
[12] Presidential Address:
Spatial Interdependence and Externalities. . . . . . . . . . . . .. 161
[13] Optimal Utilization of the Central Business District
with Economy and Diseconomy of Agglomeration . . . . . .. 173
[14] Economics of Multi-Habitation. . . . . . . . . . . . . . . . . . . . .. 193
[15] An Economic Theory of Urban Growth Control ......... 209
Permissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 217
VII
[1]
Papers of the Regional Science Association, Arizona, Vol. 19 (1967) 161-182
REGIONAL ALLOCATION OF PUBLIC INVESTMENT
NOBORU SAKASHITA, Tohoku University, Japan
In many countries, the allocation of public funds among regions to promote
the social capital formation in each regional unit is becoming one of the most
important decisions by the central government. In spite of the significance of
this problem, however, there is scarcely any definite guiding principle for the
efficient regional allocation of public investment even in a theoretical sense.
The causes of this may be explained as follows.
On the one hand, those regions which have almost the same set of industries
in each territory lack the complementarity to each other existing in a related
system of many industries. So some simple optimizing criterion like the
maximization of total national income may easily lead to a very extreme and
unpractical (if not unrealistic) conclusion. We can observe this phenomenon in
some of the Rahman-type models of investment allocation.!
On the other hand, the regional allocation of public funds may be typically
a political rather than economic problem, especially in the presence of conflicting
provincialism among the regions. In these cases, an efficiency criterion of the
allocation will be powerless (if not useless) in persuading the interested partici
pants to reach a rational conclusion.
Granting that these difficulties are extremely hard to overcome, we still
need some guidepost capable of examining the desirability of particular
regional allocation policies taken by the central government. Without such an
efficiency guidepost, every decision on such matters will be made on the ad hoc
basis and, in the long run, may bring a tremendous waste of resources.
In the present paper, a pair of models will be proposed to evaluate the
effect of regional allocation of public investment on the growth pattern of a
multi region economy. 2 The difference between the two models comes from
different presumptions on the productivity of the public investment.
In the first model, it is assumed that the public investment has no direct
productivity, but it contributes to raising the productivity of the private capital
The author is a postdoctoral fellow with the University of Pennsylvania. The present
paper is a product of his research on the basic theory of regional growth which has been
supported by a grant from the Ford Foundation. This support is gratefully acknowledged.
He is indebted to Professors W. Isard, B. H. Stevens, and J. Kissin for their valuable
comments on the earlier draft of this paper. Of course, the author alone is responsible
for any remaining errors.
! Rahman, Md. Anisur, "Regional Allocation of Investment," Quarterly Journal of
Economics, LXXVII, No.1, February, 1963, pp. 26-39.
---, "Regional Allocation of Investment: The Continuous Version," Quarterly
Journal of Economics, LXXX, No.1, February, 1966, pp. 159-60.
2 Our analysis, however, will be concentrated on the cases of two-region economy for
the sake of simplicity. The results obtained in a two-region model can be generalized into
those of three or more regions without essential difficulty. 1
161
162 PAPERS OF THE REGIONAL SCIENCE ASSOCIATION
through its externality effect. We call this type the social overhead investment
or the Hirschman-type public investment.3
In the second model, the public investment is assumed to possess a direct
productivity effect as does the private investment, and we call this category
the investment by public enterprises or the Musgrave-type public investment!
Of course, we cannot suppose any clear-cut borderline between those two
categories of public investment. But this distinction is useful, at least, for the
analysis of the perturbation effect of public investment on the process of
economic growth, because each presumption requires a different technique of
analysis.
THE CASE OF SOCIAL OVERHEAD INVESTMENT
Growth Pattern in a Two-Region Economy
If we neglec~ the activity of the public sector in a two-region economy for
a while, the supply of funds for investment in the economy will be limited to
the sum of private savings in each r~gion. In addition, if we take a .neoclas
sical point of view, this sum will be divided into the realized investments in
respective regions. The shares of the realized investment in each region, A
and 1 - A, will be determined by some market mechanism that is far from being
easily identified.
In theory, there is no reason to assume A to be a constant over time. But,
in practice, we may consider it as a relatively stable parameter for a certain
length of time compared to other fluctuating economic variables. In other
words, it will be permitted to apply a technique of piece-wise linearization as
to the intertemporal change of the value of A, and we wish to take advantage
of this convenience.
The realized investment in each region will have an incremental produc
tivity effect on the same region's aggregate income, and this effect will be
measured by a certain output-capital ratio of the region. The increased income
of the region will, in turn, determine the amount of the region's saving in the
next period.
The preceding discussion may result in a following system of differential
equations as a descriptive model of the two-region economy.
Parameters
= =
Si the saving ratio in region i(i 1, 2),
= the incremental output-capital ratio in region iCi = 1, 2), and
(Ji
A = the proportion of private investment shared to the first region
(0 ~ A ~ 1).
Variables
a Hirschman. Albert 0., The Strategy of Economic Development (New Haven: Yale
University Press. 1958). chap. 5.
4 Musgrave. Richard A .• The Theory of Public Finance: A Study in Public Economy
2 (New York: McGraw-Hili. 1959). chap. 20. C.
SAKASHITAI REGIONAL ALLOCATION OF PUBLIC INVESTMENT 163
x, y = the regional incomes of the first and the second regions,
z = x + y = the national income, and
W = x - y = the regional income disparity.
ddxt = O'lA ( 51X + 52Y ) (1)
dy
dt = 0'2(1 - A)(5IX + 52Y) • (2)
The above two equations are not independent of each other, so some special
treatment is needed for the solution, see Mathematical Appendix A. The fin'll
solutions are
+
x = O'IA(5Ixo 52YO) eY!;- 52{O'IAYo - 0'2(1 - A)Xo} (3)
g g
+
y= 0'2(1 - A)(5IXo 52YO) e y! + 5dO'IAYo - O'll - A)Xo} (4)
g g
where Xo and Yo are the initial values of x and y, and
g = 51tTIA + 520'2(1 - A) • (5)
The growth path of the aggregate income in this two-region economy will
be expressed as
z = x + y = al'(ePt - 1) + (xo + Yo) (6)
where
= +
a (51Xo 52YO)
I' = O'IA + 0'2(1 - A)
+
51O'IA 520'2(1 - A)
On the other hand, the time behavior of the discrepancy between two
regions' incomes will be given as
W = x - y = ar(eg! - 1) + (xo - Yo) (7)
where
O'IA - 0'2(1 - A)
r=
+
SIO'IA 520'2(1 - A)
If we assume that the labor force is immobile among regions, W can be taken
as an approximation of the discrepancy in the regions' per capita incomes.
Disaggregation of 01 and .i!
There may be little vagueness about the implications of such parameters
as 51 and 52 in the formulation of the preceding model. But f.urther explanation
will be needed as to the composition of tTi and A in the same model.
Suppose there are R industries in this two-region economy; each of which
has incremental output-capital ratios of 0'1; and 0'2; i~ region 1 and 2 respectively,
(j = 1, ... , R). In addition, let r; be the share of j-industry in the nationwide, 3