理論経済学 I B: レオンチェフ・モデル投入・産出分析

理論経済学 I B: レオンチェフ・モデル
投入・産出分析
21st, 28th, Sept., 2005: TF:FKK
An Example of an economy: Two Commodities and two Industries
“Wheat”(小麦) and “Tractor”(トラクター)
 0.1 0.5   a11
 = 
A ≡ 
0
.
6
0
.
3

  a21
a12 

a 22 
aij : i commodity (商品); j industry (産業)
第 j 産業が第 j 財(商品)を１単位生産するのに必要な第 i 財の量。
material input coefficients (物質的投入係数)
l ≡ (l 1 , l 2 )
l j : 第 j 産業が第 j 財を１単位生産するのに必要な労働の量。
labour input coefficients (労働投入係数)
Leontief’s Fundamental Equations (基本方程式):
Quantity(数量):
x = (1 + g ) Ax + d ,
g: 均斉成長率
d: 最終需要ベクトル、 d = (d1 , d 2 )'
 x = a ⋅ x + a ⋅ x + d1
g=0 の場合、  1 11 1 12 2
 x2 = a 21 ⋅ x1 + a22 ⋅ x2 + d 2
Price(価格):
p = (1 + r ) pA + l ,
r: 均衡利潤率
 p = a ⋅ p + a 21 ⋅ p2 + l 1
r=0 の場合、  1 11 1
 p 2 = a12 ⋅ p1 + a22 ⋅ p 2 + d 2
*
２個の基本方程式の経済学的意味が重要
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政府関連の Home Pages:
http://www.stat.go.jp/data/io/
http://www.meti.go.jp/statistics/data/h2atop4j.html
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Wassily W. Leontief (1906-1999):
History:
Francois Quesnay (1694-1774)
Tableau Economique(1758): 「経済表」岩波文庫。
Karl Marx (1818-1883)
Das Kapital (1867): (「資本論」第一巻)。
1936: Wassily W. Leontieff (Nobel Laureate: 1973).
1940’s: Professor Seiichi Tohata: recommendation not to start the War.
1951: The “first” I-O table in Japan.
The Input-Output Tables are compiled every 5th year with the newest being
1995 tables.
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References:
W. Leontief, The structure of American economy, 1919-1939, New York:
Oxford Univ. Press, 1951. 264 pages
W. Leontief, Input Output Economics, 2nd ed., New York: Oxford
University Press, 1986. ISBN: 0195035275, $42.95.
T. Fujimoto, “Nonlinear Leontief Models in Abstract Spaces”, Journal of
Mathematical Economics, Vol.15(2), pp.151-156, 1986.
Wassily W. Leontief (1906-1999):
from: http://www.biograph.comstar.ru/bank/leontev.htm
Born - 5 august 1906 in Leningrad, USSR. Daughter - Eugenia Bekker. Son - Wassily Leontief.
Degrees - He received his M. A. degree from University of Leningrad in 1925. In 1928, he
earned a Ph. D. in economics from University of Berlin. Speciality - Input- Output
Analysis and Economics.
Professional activity NEW YORK UNIVERSITY - University Professor - Economics (1983-present);
Founder & Director, Institute for Economic Analysis (1978-85; Senior Member of
Research Staff (1986-present). HARVARD UNIVERSITY - Henry Lee Chair of
Political Economy (1953-1975); Professor of Economics (1946-1953); Associate
Professor (1939-1946); Assistant Professor (1933-1939); Instructor (1932-1933).
Director, Harvard Economic Research Project (1948-1972); Senior Fellow, Society
of Fellows, Harvard University (1956-1975; Chairperson 1965-1975). Research
Associate, Institute of World Economics, University of Kiel, Germany (1927-1928).
Economic Advisor, Chinese Government, Nanking (1928-1929); Research
Associate, National Bureau of Economic Research, New York (1931); Part-time
General Consultant, U. S. Department of Labor (1941-1947, 1961-1965); Part-time
Economic Consultant, Chief, Russian Economics Sub-Division, Office of Strategic
Services (1943-1945); Consultant, United Nations Secretary of General’s
Consultative Group of the Economic and Social Consequences of Disarmament
(1961-1962); Part-time General Consultant, U. S. Department of Commerce
(1966-1982); Member of Executive Board of the Science Advisory Council of the
Environmental Protection Agency (1975-1980); Part-time General Consultant,
Office of Technology Assessment (1980-present); Consultant, United Nations
Development Programme Transportation, Italian government (1984-present).
The most important creative works are Input-Output Economics, Essays in
Economics, The structure of the American Economy.
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The most significant publications –
The structure of the American Economy, 1919-1929 (1941, 1953);
Studies in the Structure of the American Economy (1953);
Input-Output Economics (1966), 2nd ed. (1986);
Essays in Economics (1966);
Essays in Economics, Vol. II (1977);
The Future of the World Economy (1977);
Military Spending: Facts and Figures, Worldwide Implications and Future Outlook,
with F. Duchin (1983);
The Future of Non-Fuel Minerals in the U. S. And World Economy, with J. Koo,
S. Nasar, and I. Sohn (1983);
The Future Impact of Automation on Workers, F. Dochin, co-author (1986).
Honorable titles and awards –
Order of the Cherubim, University of Pisa (1953); Doctor Honoris Causa,
University of Brussels (1962); Doctor of the University, University of York,
England (1967); Officer of the French Legion d’Honneur (1968); Bernard-Harms
Prize in Economics, West Germany (1970); Doctor Honoris Causa, University of
Louvain (1971); Doctor Honoris Causa, University of Paris (Sorbonne) (1972);
Nobel Prize in Economics (1973); Doctor Honoris Causa, University of
Pennsylvania (1976); Doctor Honoris Causa, University of Toulouse, France (1980)
Doctor Honoris Causa, University of Louisvile, Kentucky (1980); Doctor of Social
Sciences, University of Vermont (1980); Doctor of Laws, C. W. Post Center, Long
Island University (1980); Russian-American Hall of Fame (1980); Doctor Honoris
Causa, Karl Marx University, Budapest, Hungary (1981); Order of the Rising Sun,
Japan (1984); French Order of Arts and Letters, Commandeur (1985); Doctor
Honoris Causa, Adelphi College (1988); Foreign member, USSR Academy of
Sciences (1988); Society of the Optimate, Italian Cultural Institute, New York
(1989); Doctor Honoris Causa, University of Cordoba, Spain (1990); Takemi
Memorial Award, Institute of Seizon & Life Sciences, Japan (1991); Harry
Edmonds Award for Life Achievement, International House, New York (1995);
Doctor Honoris Causa, Humboldt University, Berlin, Germany (1995).
Hobbies - Trout Fishing.
Address: New York University, Institute for Economic Analysis 269 Mercer Street,
Room 203, New York, N. Y. 10003-6687
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Program:
Private Sub Command1_Click()
'*** TF: 31st, Oct., 2002 at Univ of Kagawa
'*** initialization
a11 = Text1.Text
a21 = Text2.Text
a12 = Text3.Text
a22 = Text4.Text
d1 = Text5.Text
d2 = Text6.Text
'*** rate of growth: Try 0.32
g = Text10.Text
g1 = 1 + g
a11 = g1 * a11: a21 = g1 * a21
a12 = g1 * a12: a22 = g1 * a22
'*** checking the productivity condition
HS = (1 - a11) * (1 - a22) - a12 * a21
If (HS < 0.001) Or (a11 >= 1) Or (a22 >= 1) Then
Form3.Show 1
Exit Sub
End If
'*** constants: tol=tolerance; sc=scale
tol = 0.001
sc = 500
'*** graphics: initialization
Form1.Picture1.Cls
xx0 = d1 / (1 - a11): yy0 = 0
If (a12 = 0) Then
xx1 = xx0: yy1 = 10
Else
xx1 = 10: yy1 = ((1 - a11) * xx1 - d1) / a12
End If
Form1.Picture1.Line (xx0 * sc, yy0 * sc)-(xx1 * sc, yy1 * sc), RGB(0, 128, 0)
yy0 = d2 / (1 - a22): xx0 = 0
If (a21 = 0) Then
yy1 = yy0: xx1 = 10
Else
yy1 = 10: xx1 = ((1 - a22) * yy1 - d2) / a21
End If
Form1.Picture1.Line (xx0 * sc, yy0 * sc)-(xx1 * sc, yy1 * sc), RGB(128, 0, 0)
'*** iteration: initialization: i% = the number of iteration
x10 = 0#
x20 = 0#
i% = 0
'*** iteration
Do
i% = i% + 1
x1t = a11 * x10 + a12 * x20 + d1
x2t = a21 * x10 + a22 * x20 + d2
Form1.Picture1.Line (x10 * sc, x20 * sc)-(x1t * sc, x2t * sc), RGB(0, 0, 128), B
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If ((Abs(x1t - x10) + Abs(x2t - x20)) < tol) Then
Exit Do
End If
x10 = x1t
x20 = x2t
Loop
Text7.Text = x1t
Text8.Text = x2t
Text9.Text = i%
Text10.SetFocus
End Sub
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