経済学提要パレートManuale d’economia politica (1906)Vilfredo-Pareto

経済学提要パレートManuale d’economia politica (1906)Vilfredo-Pareto
https://nam-students.blogspot.com/2020/02/blog-post_11.html

Manual of Political Economy: A Critical and Variorum Edition (English Edition) 1st Edition, Kindle版

Vilfredo Pareto  (著), Aldo Montesano (編集), Alberto Zanni(編集), Luigino Bruni (編集), John S. Chipman (編集), Michael McLure (編集)

Index of Chapters (Numbers indicate paragraphs) 

CHAPTER I, PP. 1–19 General Principles 

CHAPTER I I, PP. 20–71 Introduction to Social Science 

CHAPTER I I I, PP. 72–124 The General Concept of Economic Equilibrium 

CHAPTER IV, PP. 125–44 Tastes 

CHAPTER V, PP. 145–72 Obstacles 

CHAPTER VI, PP. 179–91 Economic Equilibrium 

CHAPTER VI I, PP. 192–219 Population 

CHAPTER VI I I, PP. 220–31 Landed Capital and Capital Goods Proper 

CHAPTER IX, PP. 232–72 The Concrete Economic Phenomenon 

APPENDIX (1906), PP. 279–308 

APPENDIX (1909), PP. 309–97

Chapter章の索引（数字は段落を示します）
第I章、PP。 1–19一般原則
第I章I、PP。 20–71社会科学入門
第I章I、PP。 72–124経済均衡の一般概念
第IV章PP。 125–44味
第V章、PP。 145–72障害
第VI章PP。 179–91経済均衡
第VI章I、PP。 192–219人口
第VI章I、PP。 220–31上陸資本と資本財の適切な
第IX章、PP。 232–72具体的な経済現象
付録（1906）、PP。 279–308
付録（1909）、PP。 309–97‬

CHAP TER I I I、PP。 –経済均衡の一般概念§、。政治経済の対象。 –。経済的問題の難しさ、およびこれらの困難のいくつかを取り除くために数学を使用する価値がある方法。 -、、。経済問題がどのように単純化されるか。純粋な経済。 –。純粋な経済の3つの部分–、、。経済統計連続的な現象を研究します。 -、。 2つのクラスの理論。最初の目的は男性の感覚を比較することであり、2番目の目的は異なる男性の感覚を比較することです。政治経済は前者だけを扱っています。 –。この研究で従う方法。 -、。私たちは、味、障害、そしてそれらの対照から経済的均衡がどのように生まれるかを研究します。 -、、。経済財とそれらが提供する感覚。 –。組み合わせなければならない要素は、好みと障害です。 -、。経済財の定性的および定量的な組み合わせ。 –。経済均衡の定義;実際の動きと仮想的な動き。 –、、、。平衡問題に関するデータ。 –。一般に、均衡はどのように決定されるか。 -、。男性の好み;経済学者の使用価値という概念を通じて、かつて持っていた不完全な概念。 -、。誤った概念を修正することにより、純粋経済の理論がどのように生まれたのか。 – to[およびbis]。 Ophelimity。 –。経済現象の条件の間に存在する制約。 –。代数的シンボルを使用せずに、純粋経済の理論を説明するよう努めます。 –。味の直接的および間接的な影響。 –から。味から派生した現象の種類。自由競争;独占。 –。社会主義システムのタイプ。 -、。タイプがどのように混在し、どのように考慮する必要があるか。 –から。好みの無関心なライン。 -、。 ophelimityのインデックス。 -、、。個人の嗜好がどのように表されるか。喜びの丘。 -、。さまざまな量の経済財を連続して持っている男性の状態をパスで説明することができます。 -、、。パスに関する考慮事項。終点と無関心線との接点。 -、、。連続的および不連続的なバリエーション。 –。障害物。 –。最初の種類の障害。 -、、。経済財の変容。 -、。第二の種類の障害。 –。客観的な変換における障害の無関心線。 –。プロデューサーの無関心線。 –から。好みの無関心線と障害物の無関心線の類似点。 –。利益の丘。 –。コンペ。 –。交換の場合の競争。 –。生産の場合の競争。 –。 1つは、他のコミュニティから分離されたコミュニティを調べることから始まります。 –から。競争のモード。 –。現象の種類


プロデューサー。 -、、。一般的な均衡。 –から。味覚に関する平衡。終点で、または経路と無関心曲線の間の接点で、経路の平衡がどのように行われるか。 –から。生産者の均衡。 –。最大利益のライン。 –から。好みと障害の均衡。 –から。平衡点を決定する一般理論。 –から。交換平衡のモードと形態。さまざまな平衡点。安定した平衡と不安定な平衡。 –。 ophelimityの最大値。 –から。生産における均衡のモードと形態。最大利益のライン。プロデューサー間の競争。 –から。価格。 -、。交換価値。 –。別の観点からの商品の価格。 –から。価格の概念を使用して説明される経済現象。 –から。価格と第2の障害。定価および変動価格。 –。個人の予算。 –。生産者の予算–、、。生産コスト。 –から。需要と供給。 –。供給曲線と需要曲線。 -、、。需要と供給は、経済均衡のすべての状況に依存します。 –から。均衡点での需要と供給の平等。 –。需要と供給が異なる方法。 –。生産コストと販売価格の平等。 –。需要と供給の概念を持つ安定した均衡と不安定な均衡。 –から。一般的な場合の交換均衡。 –から。一般的な場合の交換と生産の均衡。 -、。一般的な場合の安定および不安定な平衡。 -、。数学の使用が役立つ方法と理由。 –から。この使用が不可欠である数学の使用を無視することに起因するエラー。 –。価値の唯一の原因の検索は役に立たず、決定的ではありません。 –。これまでのところ、純粋な経済のみが、経済現象の総合的な概念を私たちに与えることに成功しています。



…
付録（）、PP。 –§。付録の目的。 –から。無関心の線。 –、、。喜びのインデックス、または楽観的なインデックス、およびそのレベルカーブの表面。 –。経験を通じて眼球限界を判断できる場合。 –。基本的な順応性の等価性。 –。無関心線のプロパティ。 –。無関心線の特性から推測される指標の特性。 –。 ophelimityのもう1つの特徴。 –。 ophelimityの特性から推定される無差別曲線の特性。 –。消費が独立したいくつかの経済財。 –。さまざまな種類の依存。 –。数学の使用の難しさ。 –。無関心線の代わりに使用できる他の線。 -、。障害物。 –から。 2人の個人の交換の平衡。 –。この平衡を決定する方程式の性質。 –。定価。 –。独占。 –から。一般的な場合の交換の平衡。 –。一定価格での交換の均衡。 –から。製造。 -、。の均衡
製造。 –。変動価格との自由競争の場合の生産の均衡。 -、。一定価格での自由競争の場合の生産の均衡。 –。生産係数と配分の決定方法。 –。一定の価格での個別生産。 -、。最大限の光学限界を備えた個々の生産。 -、。集合生産。 –。最大限の光学的限界を備えた集合生産。 –。両替。 –。平衡の特性。 -、。交換の場合の有限のバリエーション。付録（）、PP。 –§。付録の目的。 –から。無関心線。 –から。観測によって提供される微分方程式。 -、。方程式の積分と喜びとの対応。 –から。観察から視野限界を推測する方法。 -、。 1人の個人と2つの商​​品の場合の均衡。 -、。いくつかの経済財の場合。 -、。障害物の方程式。 –から。 1人の個人の独占。 –。無料の競争。 –。検討されたケース間の比較。 –。 3つの商品。 –。価格。 –。予算。 –。変動価格。 –。例。 –。 1人の個人、任意の数の商品、および定価の場合の均衡。 –。 Ophelimityおよび需給曲線。 –。需給曲線から推測される経済的均衡。 -、。無関心線のプロパティ。 –から。インデックスの特性。 –。無関心線の複雑さ。 –から。需要と供給の一般法則。 –から。お金の制限を一定とみなした経済学者の誤り。 –から。一定の価格で交換する一般的なケース。 –。 1人の個人と1つの商品の独占。 -、。 2人の個人と1つの商品の独占。 –。 2人の個人と2つの商​​品の独占。 –から。独占のこれらの異なるケースに関する考慮事項。 -bis。例。 –。製造。 –。生産係数。 –。生産コスト。 –。消費者の均衡。 –。企業の均衡。 –。生産の均衡。 –。無料の競争。 –から。生産における独占。 –。コミュニティーのophelimityの最大値の定義。 –から。最大値の決定

生産の限界。 –から。例。 –から。生産係数の変動性。 –。企業間の数量の分布。 –。生産係数に関する通常のエラー。 –から。経済均衡の特性と、その最大限界との関係。 –。個人の場合。 –から。 ophelimityの最大条件。 –から。有限変位に関連したophelimityの最大値。 –から。 ophelimityの最大値の経済的意味。 –から。概要：制約。 –。経済システムの分解。 から。インデックス機能。 –。 ophelimityのインデックス。 –。一般的なインデックス関数。 –から。経済タイプ。 –。インデックス関数の二次導関数。 –。経済的均衡を決定する方程式のシステム。 –。経済均衡の特性;経済的対立。 –から。 ophelimityの最大値。 –。有限のバリエーション。 –。平衡のさまざまなポイント。




以下は別の書籍

一般社会学提要（名古屋大学出版会古典翻訳叢書）（日本語）単行本– 1996/3
ヴィルフレドパレート（著）、Vilfredo Pareto（原著）、姫岡勤（翻訳）


https://www.britannica.com/biography/Vilfredo-Pareto
彼の最も影響力のある作品である彼のマニュアル経済学（1906）で、彼はさらに純粋な経済学の理論と予言的限界（満足を与える力）の分析を発展させました。彼は、パレート最適と呼ばれる概念で現代の福祉経済学の基礎を築き、少なくとも1人の個人が自分自身でより良くすることができる限り、社会の資源の最適な配分は達成されないと述べた。他の人が自分の推定で以前と同様にオフに保ちながら推定。彼はまた、「無関心の曲線」、分析


1930年代まで普及しなかった楽器。













市場と社会6
www.rikkyo.ne.jp/univ/nakaj/nakajima/mha1106.htm
 -キャッシュ
...有限な土地が障害に→土地公有論パレート（V. Pareto、1848-1923） 『経済学提要』（1906）、 『一般社会...











パレート的社会情報学への試論パレート語の試論...-J-Stage（Adobe PDF）
www.jstage.jst.go.jp/article/jasi/24/0/24_0.../_pdf
2パレートの社会学に関する主要著作について整理しておこっています... 3社会的異質性の定義に関しては、Pareto（1906）、第7章2。











経済学提要（けいざいがくていよう）とは-コトバンク
kotobank.jp/word/経済学提要-167606
 -キャッシュ
イタリアの経済学者ウィルフレド・パレートの主著。レオン・ワルラスの著作とともに一般均衡理論の古典。1906年刊。1909年刊行...












パレートとは-コトバンク
kotobank.jp/word/パレート-117606
 -キャッシュ
ブリタニカ国際大百科事典小項目事典-パレートの用語解説-[生] 1848.7.15。 ...経済学提要 』Manuale d'economia politica（1906）、『一般社会学概論 』Trattato di sociologia generale（2巻、1916）など著書多数。
付録の邦訳
https://hosei.repo.nii.ac.jp/?action=repository_action_common_download&item_id=2042&item_no=1&attribute_id=22&file_no=1

福岡論考
https://core.ac.uk/download/pdf/145739456.pdf

https://cruel.org/econthought/essays/paretian/paretequil.html
パレティア体系：I-均衡

パレティアシステム
I-均衡

________________________________________________________
「我々の研究の主要な主題は経済的均衡である。この均衡は、男性の嗜好とそれらを満足させる障害との対立から生じることがすぐに分かる。我々の研究には、3つの異なる部分が含まれる。 °障害の研究; 3±これら2つの要素が結合して平衡に達する方法の研究。
（ヴィルフレド・パレート、政治経済学マニュアル、1906年：p.106）
「私の科学的概念は、ウォルラスの科学的概念と反対です。もし望むなら、ウォルラスのそれとは何の共通点もないように、平衡の理論を提示できたでしょう。」
（ビルフレド・パレート、グイド・センシーニへの手紙、1911年）
「ヒュー・ダルトン（当時、経済学部の一時長）は、「イタリア語を読んで、パレートを読むべきだ」と言った。だから、経済理論を始めたマニュアルを読んでいた。マーシャルの外に。」
（ジョン・ヒックス、1979年、「経済学者の形成」、バンカナツィオナーレデルラヴォロクォータリーレビュー、9月）

CHAP TER I I I, PP. – The General Concept of Economic Equilibrium § , . The object of political economy. –. Difficulties of the economic problem, and how it is worthwhile to use mathematics in order to remove some of these difficulties. –, , . How the economic problem is simplified; pure economy. –. Three parts of pure economy –, , . Economic statics. One studies a continuous phenomenon. –, . Two classes of theories; the first aims at comparing the sensations of a man, the second aims at comparing the sensations of different men. Political economy deals exclusively with the former. –. The way we shall follow in this study. –, . We shall study the tastes, the obstacles, and how, from their contrast, economic equilibrium is born. –, , . Economic goods and the sensations they provide. –. The elements that must be combined are tastes and obstacles. –, . Qualitative and quantitative combinations of economic goods. –. Definition of economic equilibrium; real movements and virtual movements. –, , , . Data pertaining to the equilibrium problem. –. How, in general, equilibrium is determined. –, . Men’s tastes; the imperfect concept one used to have of it through the economists’ notion of value in use. –, . How, by rectifying erroneous concepts, the theory of pure economy was born. – to  [and bis]. Ophelimity. –. The constraints that exist between the conditions of the economic phenomenon. –. We shall endeavor to explain the theories of pure economy without using algebraic symbols. –. Direct and indirect effects of tastes. – to . Types of phenomena derived from tastes; free competition; monopoly. –. Type of the socialist system. –, . How the types mix and how they must be considered. – to . The indifference lines of tastes. –, . Indices of ophelimity. –, , . How the tastes of an individual are represented; the hill of pleasure. –, . How the condition of a man who successively has various quantities of an economic good may be illustrated with a path. –, , . Considerations on the paths; terminal points and points of tangency with the indifference lines. –, , . Continuous and discontinuous variations. –. Obstacles. –. First kind of obstacles. –, , . Transformations of economic goods. –, . Second kind of obstacles. –. Indifference lines of obstacles in objective transformations. –. The indifference lines of the producer. – to . Analogies between the indifference lines of tastes and indifference lines of obstacles. –.The hill of profit. –. Competition. –. Competition in the case of exchange. –. Competition in the case of production. –. One starts by studying a community separated from the others. – to . Modes of competition. –. Types of phenomena concerning

producers. –, , . Equilibrium in general. – to . Equilibrium with regard to tastes; how the equilibrium on a path takes place at a terminal point, or at a point of tangency between the path and an indifference curve. – to . Equilibrium of the producer. –. The line of maximum profit. – to . Equilibrium of tastes and obstacles. – to . General theory that determines the point of equilibrium. – to . Modes and forms of exchange equilibrium. Various points of equilibrium. Stable equilibrium and unstable equilibrium. –. Maxima of ophelimity. – to . Modes and forms of equilibrium in production. The line of maximum profit. Competition among producers. – to . Prices. –, . Value in exchange. –. The price of a commodity in terms of another. – to . Economic phenomena described using the concept of price. – to . Prices and the second kind of obstacles. Constant prices and variable prices. –. The budget of the individual. –. The budget of the producer –, , . The cost of production. – to . Supply and demand. –. Supply curve and demand curve. –, , . Supply and demand depend on all the circumstances of economic equilibrium. – to . Equality between supply and demand, at the point of equilibrium. –. Ways in which supply and demand vary. –. Equality between the cost of production and the selling prices. –. Stable equilibrium and unstable equilibrium, with the concepts of supply and demand. – to . Exchange equilibrium, in the general case. – to . Exchange and production equilibrium, in the general case. –, . Stable and unstable equilibrium in the general case. –, . How and why the use of mathematics is helpful. – to . Errors that had their origin from neglecting the use of mathematics where this use was indispensable. –. The search for one sole cause of value is useless and inconclusive. –. Only pure economy has so far succeeded in giving us a synthetic conception of the economic phenomenon.

…

APPENDIX (), PP. – § . Aim of the Appendix. – to . Lines of indifference. –, , . Surface of the indices of pleasure, or of ophelimity, and its level curves. –. When it is possible to determine ophelimity through experience. –. Equivalence of elementary ophelimities. –. Properties of indifference lines. –. Characteristics of the indices inferred from those of the indifference lines. –. Another characteristic of ophelimity. –. Characteristics of indifference curves deduced from those of ophelimity. –. Several economic goods, the consumption of which is independent. –. Various kinds of dependence. –. Difficulty in the use of mathematics. –. Other lines that can be substituted for the indifference lines. –, . Obstacles. – to . Equilibrium of exchange for two individuals. –. Nature of the equations that determine this equilibrium. –. Constant prices. –. Monopoly. – to . Equilibrium of exchange in the general case. –. Equilibrium of exchange with constant prices. – to . Production. –, . Equilibrium of 

production. –. Equilibrium of production in the case of free competition with variable prices. –, . Equilibrium of production in the case of free competition with constant prices. –. How production coefficients and allocation are determined. –. Individual production with constant prices. –, . Individual production with maximum ophelimity. –, . Collective production. –. Collective production with maximum ophelimity. –. Exchange. –. Properties of equilibrium. –, . Finite variations in the case of exchange. APPENDIX (), PP. – § . Aim of the Appendix. – to . Indifference lines. – to . Differential equation provided by observation. –, . Integral of the equation and its correspondence with pleasure. – to . How it is possible to infer ophelimity from observation. –, . Equilibrium in the case of one individual and two goods. –, . The case of several economic goods. –, . Equation of the obstacles. – to . Monopoly of one individual. –. Free competition. –. Comparison between the cases that have been considered. –. Three goods. –. Prices. –. Budget. –. Variable prices. –. Example. –. Equilibrium in the case of one individual, any number of goods, and constant prices. –. Ophelimity and supply and demand curves. –. Economic equilibrium inferred from supply and demand curves. –, . Properties of indifference lines. – to . Characteristics of the indices. –. Complexity of indifference lines. – to . The general laws of supply and demand. – to . Error of the economists who considered the ophelimity of money as constant. – to . General case of exchange with constant prices. –. Monopoly of one individual and one commodity. –, . Monopoly of two individuals and one commodity. –. Monopoly of two individuals and two commodities. – to . Considerations on these different cases of monopoly. –bis. Example. –. Production. –. Production coefficients. –. Costs of production. –. Consumers’ equilibrium. –. Equilibrium of the firms. –. Equilibrium of production. –. Free competition. – to . Monopoly in production. –. Definition of maximum of ophelimity for a community. – to . Determining the maximum

of ophelimity of production. – to . Example. – to . Variability of the production coefficients. –. Distribution of the quantities among firms. –. Usual errors with regard to the production coefficients. – to . Properties of economic equilibrium and its relations with the maximum of ophelimity. –. The case of one individual. – to . The conditions for the maximum of ophelimity. – to . The maximum of ophelimity in relation to finite deplacements. – to . Economic meaning of the maximum of ophelimity. – to . An overview: constraints. –. Decomposition of the economic system.  to . Index-functions. –. The indices of ophelimity. –. Index-functions in general. – to . Economic types. –. Second derivatives of the index-functions. –. The system of equations that determines economic equilibrium. –. Properties of economic equilibrium; economic antagonisms. – to . Maximum of ophelimity. –. Finite variations. –. The different points of equilibrium.

以下は別の書籍

一般社会学提要 (名古屋大学出版会古典翻訳叢書) (日本語) 単行本 – 1996/3

ヴィルフレド パレート (著), Vilfredo Pareto (原著), 姫岡 勤 (翻訳)

https://www.britannica.com/biography/Vilfredo-Pareto
In his Manuale d’economia politica (1906), his most influential work, he further developed his theory of pure economics and his analysis of ophelimity (power to give satisfaction). He laid the foundation of modern welfare economics with his concept of the so-called Pareto Optimum, stating that the optimum allocation of the resources of a society is not attained so long as it is possible to make at least one individual better off in his own estimation while keeping others as well off as before in their own estimation. He also introduced “curves of indifference,” analytic instruments that did not become popular until the 1930s.

市場と社会6

www.rikkyo.ne.jp/univ/nakaj/nakajima/mha1106.htm

-キャッシュ

... 有限な土地が障害に → 土地公有論 パレート（ V. Pareto, 1848-1923 ）『経済学提要』（1906）、『一般社会 ...

パレート的社会情報学への試論 An Trial Essay on Paretian ... - J-Stage

（Adobe PDF）

www.jstage.jst.go.jp/article/jasi/24/0/24_0.../_pdf

2 パレートの社会学に関する主要著作について整理しておこ ... 3 社会的異質性の定義に関しては、Pareto(1906),第 7 章 2.

経済学提要(けいざいがくていよう)とは - コトバンク

kotobank.jp/word/経済学提要-167606

-キャッシュ

イタリアの経済学者ウィルフレド・パレートの主著。レオン・ワルラスの著作とともに一般均衡理論の古典。1906年刊。1909年刊行 ...

パレートとは - コトバンク

kotobank.jp/word/パレート-117606

-キャッシュ

ブリタニカ国際大百科事典 小項目事典 - パレートの用語解説 - [生]1848.7.15. ... 経済学提要』Manuale d'economia politica（1906），『一般社会学概論』Trattato di sociologia generale（2巻，1916）など著書多数。

付録の邦訳
https://hosei.repo.nii.ac.jp/?action=repository_action_common_download&item_id=2042&item_no=1&attribute_id=22&file_no=1

福岡論考
https://core.ac.uk/download/pdf/145739456.pdf

https://cruel.org/econthought/essays/paretian/paretequil.html

The Paretian System: I - Equilibrium

The Paretian System  I - Equilibrium

________________________________________________________

"The principal subject of our study is economic equilibrium. We shall see shortly that this equilibrium results from the opposition between men's tastes and the obstacles to satisfying them. Our study includes, then, three distinct parts: 1ï½° the study of tastes; 2ï½° the study of obstacles; 3ï½° the study of the way in which these two elements combine to reach equilibrium."

(Vilfredo Pareto, Manual of Political Economy, 1906: p.106)

"My scientific concept is the opposite to that of Walras. If I wanted, I could have presented my theory of equilibrium in such a way that it would seem to have nothing in common with that of Walras."

(Vilfredo Pareto, Letter to Guido Sensini, 1911)

"Hugh Dalton (then temporary head of the economics department) said to me, "you read Italian, you ought to read Pareto". So it was reading the Manuale which started me off on economic theory. I was deep in Pareto before I got much out of Marshall."

(John Hicks, 1979, "The Formation of an Economist", Banca Nazionale del Lavoro Quarterly Review, September)

________________________________________________________

Contents

(1) Introduction
(2) Graphical Illustration: A two-sector model
(3) A General Paretian Model

Selected References

Back

(1) Introduction

The "Paretian System" refers to the approach to general equilibrium theory initiated largely by Vilfredo Pareto's Manual of Political Economy (1906). Although often employing tools developed by his predecessors such as Leon Walras (1874), Francis Y. Edgeworth (1881) and Irving Fisher (1892), the hallmark of the Paretian approach is its concentration on agent optimization in a price-taking, multi-market scenario - and thus the emphasis on differentiability and efficiency. 

The 1930s and 1940s represent the height of the Paretian approach, particularly as channeled through the L.S.E. of Arthur L. Bowley (1924), John Hicks and Roy G.D. Allen (1934), Abba Lerner (1932, 1934, 1944), Nicholas Kaldor (1939), Tibor de Scitovsky (1941, 1942) and, most influentially, through John Hicks's masterpiece, Value and Capital (1939). Elsewhere, the Paretian approach sounded forth in the masterful efforts of Maurice Allais (1943), Oskar Lange (1942) and Paul Samuelson (1947).

The basic structure of the Paretian model is similar to the static Walras-Cassel model, although, unlike that construct, everything is now cast in the "tastes-and-obstacles" structure that is the signature of the Paretian system, rather than the "demand-and-supply" functions of the older Lausanne system that the Walras-Cassel model exhibits. As Koopmans was to write many years later:

"It is worth point out that in this particular study our authors have abandoned demand and supply functions as tools of analysis, even as applied to individuals. The emphasis is entirely on the existence of a some set of compatible optimizing choices...The problem is no longer conceived as that of proving that a certain set of equations has a solution. It has been reformulated as one of proving that a number of maximizations of individual goals under interdependent restraints can be simultaneously carried out." (T.C. Koopmans, 1957: p.60)

Perhaps the greatest advantage of the Paretian system is its simple graphical intuition: indifference curves, Edgeworth-Bowley boxes, production possibilities frontiers, community indifference maps, etc. all come together in a simple way to illustrate the conditions for general equilibrium. The great cost is its reliance upon the assumption of differentiability of the various functions employed. The development of the Neo-Walrasian economcs in the postwar period, notably the Arrow-Debreu system of the 1950s, retained the tastes-and-obstacles optimization structure of the Paretian system, but it essentially eschewed its differentiability assumptions and effectively reproduced the same results without it - although the question of whether its reliance on convexity is, in fact, more "general" is a thorny issue. The differentiable approach to general equilibrium lived on largely in international trade theory and only really re-emerged in Neo-Walrasian general equilibrium theory in the 1980s.

In the main Paretian model, all agents respond to prices parametically, i.e. they take prices as given, what Pareto (1906: p.115) calls "Type I" behavior. Edgeworth (1881) justified this assumption as a limiting case of a recontracting exchange process when there are an infinite number of agents. Pareto, on the other hand, justified it on the basis of the impossibility of manipulative behavior in a sufficiently complex economy; as he writes:

"A farmer can easily calculate, at the market prices, whether it is more advantageous for him to use the power of a horse or that of a steam engine to run a pump; but neither he, nor anyone in the world, is capable of knowing either the effect the substitution of a steam engine for a horse will have on the prices of horses and steam engines, or the greater quantity of vegetables which will be consumed when consumers enjoy the savings resulting from that substitution." (V. Pareto, 1906: p.245).

Households possess factor endowments and desire produced goods for consumption; firms possess nothing, but merely organize production by demanding factors from households and supplying produced goods. The rest of the Paretian system thus follows as in a Walrasian one: given a set of output and factor prices cried out by the "auctioneer", households choose their supplies of factors and demand for goods via a utility-maximization exercise whereas firms decide upon their demand for factors and supply of produced goods via a profit-maximization exercise (as noted, incorporating this last point was one of Pareto's main contributions to the Walrasian system). An equilibrium is then defined as a market-clearing set of prices in both output and factor markets. 

(2) Graphical Illustration: A two-sector economy

Arguably, the greatest advantage of the Paretian system is its intuitive structure and amenability to simple diagrammatic exposition - and thus quite effective as a heuristic device. Graphical illustrations of the Paretian system inevitably require confinement to a simple "two-sector" economy - i.e. an economy with two outputs (and firms), two factors and two households - and thus is quite similar in structure to the "Hecksher-Ohlin" model of international trade. The nomenclature for the two-sector case is then the following:

Households: A and B
Factor endowments: K and L (factor returns are r and w respectively)
Produced Outputs (Firms): X and Y (output prices are p_X and p_Y respectively).

Agents possess factor endowments and desire outputs. In order to present this diagramatically, we shall ignore factor supply functions and thus assume that agents are "forced" to place all their factors on the marketplace, i.e. K and L are supplied inelastically by agents. As a result, we can capture the consumer's decision as follows. Let U^A(X^A, Y^A) is the utility function of agent A which increases with the acquisition of produced goods (X^A, Y^A) and let endowment of agent A be e^A = (K^A, L^A). Obviously, for B, we have U^B(X^B, Y^B) and e^B = (K^B, L^B). Together, consumers cannot demand more outputs than are available, thus feasibility requires that:

X^A + X^B ï½£ X

Y^A + Y^B ï½£ Y

where X and Y are the total amounts of goods X and Y produced. Utility functions are assumed differentiable. Thus, given prices, p_X, p_Y, r, w, consumer A faces the following optimization problem:

max U^A(X^A, Y^A)

s.t. 

p_XX^A + p_YY^A ï½£ rK^A + wL^A

The first order conditions for a maximum are then:

ｶU^A/ｶX^A = l_Ap_X

ｶU^A/ｶY^A = l_Ap_Y

p_XX^A + p_YY^A = rK^A + wL^A

where l_A is the Lagrangian multiplier for agent A (or his "marginal utility of income"). Letting U^A_X = ï½¶U^A/ｶX^A represent the A's marginal utility of good X and the same for the other goods and factors, then the consumer will choose to demand outputs until:

U^A_X/U^A_Y = p_X/p_Y

the ratio of marginal utilities between outputs (also known as the "marginal rate of substitution between X and Y", or simply MRS^A_XY) is equal to the price ratio, p_X/p_Y. This is the familar condition for a tangency between the budget constraint (with slope equal to - p_X/p_Y and pinned down by the income from the sale of endowments) and the highest indifference curve (with slope equal to - MRS^A_XY). This is obvious in Figure 1 to be at point E = (X^A, Y^A) which yields utility U^A(X^A, Y^A) Bundle G, which yields utility U^{Aï½¢ ï½¢} is unattainable given the budget constraint. Conversely, bundles F and H, both of which yield utility U^Aï½¢ , are attainable but suboptimal for agent A.

Figure 1 - Household Utility-Maximization

As agent B faces the same problem, then his conclusion will also be that MRS^B_XY = U^B_X/U^B_Y = p_X/p_Y at his optimum. Thus, assuming a price-taking economy, as prices faced by agent A and B are the same, then when agents optimize, then it will be true that:

MRS^A_XY = p_X/p_Y = MRS^B_XY

the marginal rates of substitution between the two goods will be the same for both agents.

We assume a firm only produces one output, so the production function for the firm that produces good X is X= ï½¦ ^X(K_X, L_X), which says that the output of X is some function (ｦ ^X) of the factors it employs (K_X, L_X). Similarly, the firm that produces good Y faces the production function Y = ï½¦ ^Y(K_Y, L_Y) where the output of Y is a function (ｦ ^Y) of the factors it employs (K_Y, L_Y). Together, firms cannot employ more factors than are supplied by the agents, thus letting K = K^A + K^B be the total supply of factor K and L = L^A + L^B be the total supply of factor L, then the feasibility condition is that:

K_X + K_Y ï½£ K

L_X + L_Y ï½£ L

Each firm attempts to maximize profits subject to given prices factor and output prices. Thus letting p ^X be the profits of firm X, then the firm's optimization problem is:

max p^X = p_XX - rK_X - wL_X

s.t. 

X = ï½¦^X(K_X, L_X)

and the same applies for firm Y if we replace X with Y. Assuming the production functions are differentiable, then the first order conditions for a maximum are:

r = p_X(ｶｦ^X/ｶK)

w = p_X(ｶｦ^X/ｶL)

Letting ï½¦^X_K = (ｶｦ^X/ｶK) and ï½¦^X_L = (ｶｦ^X/ｶL) be the marginal physical products of K and L respectively, then the firm will employ factors (and thus produce output X) until:

ｦ^X_K/ｦ^X_L = r/w

i.e. the ratio of marginal products is equal to the factor price ratio. The ratio of marginal products is also known as firm X's "marginal rate of technical substitution" between K and L, or MRTS^X_KL = ï½¦ ^X_K/ｦ ^X_L. The MRTS^X_KL is the slope of the firm's isoquant, thus this condition claims that the firm will hire factors (and thus produce) until where the slope of its isoquant is tangent to the isocost line - once we fix one. 

We can see this diagramatically below in Figure 2. A given factor price ratio (r/w), will determine an entire series of isocost lines. At any isocost line, the firm will maximize profits by choosing input combinations (K_X, L_X) and level of output (X) such that the slope of the isoquant (= MRTS^X_KL) is equal to the slope of the isocost line (r/w). Thus, in our diagram, points E, Eï½¢ and Eï½¢ ï½¢ all represent profit-maximizing choices of inputs and output levels that maximize profits given different isocost lines. The thick line passing through E, Eï½¢ and Eï½¢ ï½¢ , denoted "E path", represents firm X's "output expansion path" given r/w and, in this diagram, its constant slope indicates that the firm's technology exhibits homotheticity (e.g. the production function is homogeneous of some degree). 

Figure 2 - Firm Profit-Maximization

If r/w was different, we would have a different output expansion path. For instance, if r/w was lower, then our first order conditions tell us that firm X would employ more K relative to L. We can see this in Figure 3 where we compare (r/w)^E > (r/w)^F. At a particular level of output X, we can see that the optimal input combination for factor returns (r/w)^E is given by K_X^E and L_X^E and for factor returns (r/w)^F, we have K_X^F and L_X^F. Thus, as r/w falls, the optimal input combination for a given X involves an increase in K and a fall in L. By homogeneity of whatever degree of the production function, this would be true at every level of output, e.g. X and Xï½¢ , thus we could draw two output expansion paths, the E path and the F path, corresponding to different levels of X where the E path refers to factor returns (r/w)^E and the F path refers to the lower factor returns (r/w)^F.

Figure 3 - Firm Profit-Maximization at two sets of factor prices

Nonetheless, at a given r/w, in order to obtain the precise input combinations that firm X produces it is thus necessary to either fix total costs and have the firm maximize output or set a particular output level and permit the firm to minimize costs. The interesting question that emerges is what will be the levels of K_X, L_X and X that the firm chooses when maximizing profit for a given p_x and r/w if we do not arbitrarily pin down a particular cost level or output level? In fact, if we consider firm X in isolation, we cannot pin these down at all unless we assume ideas about Marshallian increasing costs/diminishing returns via factors specific to the firm - which, as Piero Sraffa (1926) has shown, are nonsensical for a single firm in a perfectly competitive economy. What is necessary, as insinuated by Sraffa, is to consider the firm in a general equilibrium framework as that will provide the necessary "increasing cost" properties that permit us to pin down the levels of output and inputs demanded in each industry. (see our survey of production theory for more details.)

To understand this, recall that value, as the more faithful Neoclassical economists (e.g. Wieser, 1889, Knight, 1928; Robbins, 1934), insisted repeatedly, arises solely from opportunity cost and opportunity cost will not arise unless there is scarcity, i.e. there are fixed supplies of resources upon which demands are made. In this context, this means that we cannot consider the firm in isolation and hope to determine what K_X, L_X and X will be as we cannot restrict costs or outputs arbitrarily. We must consider what the impact its output and factor demand decisions will be on other firms. The greater the output of firm X, the more resources it will require and thus the less available to firm Y. Such a notion, of course, may conflict with the idea of perfect competition as the increase in output of a firm will influence not only its own cost conditions but also those of other firms, and in a two-sector model such in inevitable, but we have so far considered X as a single firm. There is no reason not to assume that it is instead an aggregate of "perfectly competitive" firms producing output X, arbitrarily divided. 

The basic notion, then, is that as long as there is an inelastic supply of factors and all are fully employed, then for the output of X to rise, factors must be released from firm Y and thus the output of firm Y must fall. However, unless both X and Y use effectively the same technology, the amount of factors released by a reduction in output of industry Y will be of a different proportion to the absorption requirements of industry X. Hence, an increase in the output of industry X requires an increase in demand for K and L which is different from the factors released by a decline in output of industry Y. As a result, the factor which industry X uses more intensively will rise in price relative to the factor it uses less intensively. As Joan Robinson put it, "for any commodity considered separately, .... an increase in the output of any commodity turns the relative factor prices against itself." (J. Robinson, 1941).

This process can be understood by using an Edgeworth-Bowley box for production, as in Figure 4. Total factor supplies K and L set the size of the box. A particular point in the box represents an allocation of resources K and L between the different industries, X and Y. Notice that full employment is assumed, thus at an allocation point such as F, industry X employs L_X and K_X and industry Y employs K_Y and L_Y and, by the full emploment assumption, K_X + K_Y = K and L_X + L_Y = L. Seeing the bottom left and the upper right corners of the box as the origins of an isoquant map for industries X and Y respectively, we can thus figure out the levels of output in each industry which correspond to allocation F. 

[Historical note: the misnamed box as drawn here was first introduced by Pareto (1906: p.138) and is only implicit in Edgeworth (1881: p.28) and drawn differently in Bowley (1924: p.5). Although Allais (1989: p.67, 620), defying "intellectual gangsterism", has reverted to calling it a "Pareto box", we shall sheepishly retain its conventional usage.]

Figure 4 - Production Edgeworth-Bowley Box

The curved line connecting O_X and O_Y represents the "contract curve" between industries X and Y which represents the set of allocations where the isoquants of each industry are tangent to each other. In this particular diagram we assume that industry X is more intensive in K and less intensive in L relative to industy Y. Thus, starting from the origin O_X, we can see that as output of industry X rises that of industry Y falls, then industry X is "turning" the factor prices against itself. In other words, as X increases from, say, X to Xï½¢ , then factor returns rise from (r/w)^F to (r/w)^E - and thus firm X will choose a different input combination. In terms of our earlier Figure 3, think of firm X being shunted from the F path to the E path as output climbs from X to Xï½¢ and factor prices increase from (r/w)^F to (r/w)^E. In this sense, as we increase the output of industry X and decrease the output of industry Y, then output expansion rays from O_X rotate counterclockwise for X. 

Thus, unlike the consumption case, in a production Edgeworth-Bowley box, the contract curve connecting O_X and O_Y has a precise, curved shape of Figure 4 reflecting different factor intensities in both industries. If we drew a diagonal line from O_X to O_Y, then, save for the origins, the contract curve would lie completely to one side of it. Notice that, in contrast, if X were relatively more intensive in L than X, then the curvature of the contract curve would be reversed and it would lie on the other side of the box so that as X rises, the output expansion rays from O_X would rotate clockwise. 

We can represent the locus of tangencies in Figure 4, the contract curve, as a "production possibilities frontier" (PPF) or "transformation surface" as depicted in Figure 5, first introduced by Abba Lerner (1932) and Gottfried Haberler (1933: p.176). What may be called the production possibilities set (PPS) is the area below the PPF curve and above the axes. The PPF represents the trade-offs between outputs X and Y. As output X increases, output Y decreases, etc. In Figure 5, points E and F represent output combinations equivalent to those in Figure 4. Notice that the curvature of X and Y represents not diminishing returns or any Marshallian paraphenelia (recall both our industries have constant returns to scale), but rather the different relative factor proportions which each industry uses, the "turning" of factor prices against one's self as factors are released from one industry to another. The PPF would be linear only if industries X and Y had the same relative technology and thus each industry absorbs factors in exactly the same proportion as they are released by the other industry.

Figure 5 - Production Possibilities Frontier (PPF)

It is a simple matter to notice that the (negative of the) slope of the PPF is merely the "marginal rate of product transformation" betwen outputs X and Y (also known as MRPT_XY). Notice that as we increase output of good X and decrease output of good Y, then, at the margin, we release dL from Y to X, then output of X increases by dX = ï½¦^X_LdL while output of Y falls, or -dY = ï½¦^Y_LdL. Thus, combining these two via dL, we obtain the result that 

- dY/dX = ï½¦^Y_L/ｦ^X_L

Thus, the negative of the slope of the PPF is merely the ratio of the marginal products of labor in each industry, ï½¦^Y_L/ｦ^X_L. This ratio is the marginal rate of product transformation (MRPT_XY). If we had released K instead by marginal amount dK, then we would obtain the result that -dY/dX = ï½¦^Y_K/ｦ^X_K. Thus, it must be that 

MRPT_XY = ï½¦^Y_L/ｦ^X_L = ï½¦^Y_K/ｦ^X_K

By cross-multiplying, we can rewrite this last equality as:

ｦ^X_K/ｦ^X_L = ï½¦^Y_K/ｦ^Y_L

which simply states the familiar condition that MRS^X_KL = MRS^Y_KL, the marginal rates of substitution in both industries are equal - the condition implied by the tangency of the isoquants in the Edgeworth-Bowley box in Figure 4. Thus, a point on the PPF in Figure 5 indeed represents points on the contract curve in Figure 4. 

However, we can say something more. The production possibilities frontier in Figure 5 permits one to connect output prices (p_X, p_Y) and factor prices (r, w). Recall from the first order conditions for profit maximization for firm X we obtained the result that w = p_Xｦ^X_L and for firm Y we obtained w = p_Yｦ^Y_L, thus combining:

p_X/p_Y = wｦ^Y_L/wｦ^X_L

As MRPT_XY = ï½¦ ^Y_L/ｦ ^X_L, then this is equivalent to stating that:

p_X/p_Y = MRPT_XY

Thus, drawing a price line (as in Figure 5) with slope equal to the (negative of) output prices, p_X/p_Y, we obtain that the only point on the PPF where p_x/p_Y = MRPT_XY (i.e. the price line and PPF are tangent) is at point F. Thus, only output combination X and Y are consistent with profit-maximization. A different price ratio (noted as p_Xï½¢ /p_Yï½¢ in Figure 5), would be tangent to the PPF at point E, thus E would be the only output combination (noted here Xï½¢ and Yï½¢ ) which is consistent with profit-maximization. 

Additionally, note that the marginal cost of increasing output by firm X is merely w/ｦ ^X_L while the marginal cost of increasing output by firm Y is w/ｦ ^Y_L. Thus, when we can rewrite the profit-maximizing condition as:

p_X/p_Y = MRPT_XY = (w/ｦ^X_L)/(w/ｦ^Y_L)

which effectively yields two things: (i) that MRPT_XY can be regarded as the ratio of marginal costs for each firm; (ii) that the profit maximization exercise implies that output price equals marginal cost of output for each firm, i.e. p_X = w/ｦ^X_L and p_Y = w/ｦ^Y_L. 

Finally, note that the second order condition for profit-maximization implies that for firm X, p_Xｦ^X_LL ï½£ 0, p_xｦ^X_KK ï½£ 0 and ï½¦^X_KKｦ^X_LL - ï½¦^X_KLｦ^X_LK ï½³ 0. This implies that the production function for firm X, ï½¦^X(K, L) must be concave in the neighborhood of the maximum. As a result, a maximum cannot be achieved where the marginal products of both inputs are increasing locally, i.e. we cannot allow for local increasing returns to scale. Translated to the PPF world, the implication is that we cannot have non-convexities in the production possibilities set. 

From these exercises, we can immediately begin to see the "imputation" idea of Friedrich von Wieser (1889) in this context. Given output prices, we can "impute" what the corresponding factor prices have to be. Namely, given p_X/p_Y, we know that output has to be (X, Y) in Figure 5, and we can then translate this, via the corresponding point F in the Edgeworth-Bowley Box in Figure 4, we can notice that the factor returns ratio has to be (r/w). If we are given different output prices (p_Xï½¢ /p_Yï½¢ ), then we know output has to be Xï½¢ , Yï½¢ and thus, via point E, we know that the factor returns ratio has to be (r/w)ï½¢ . Thus, by merely knowing output prices, we can then determine outputs, factor prices and factor employments in different industries. 

However, there are two exogenous elements here: the supply of factors and output prices - exactly like in the linear Walras-Cassel model. Once we know these, the rest (output produced, factors employed and factor prices) follows. One ought then to suspect that, like the Walras-Cassel model, the supply of factors and output prices both emerge from the household utility-maximization exercise. We presumed, for purposes of graphical presentation, that households supply factors inelastically, but it would not be difficult to notice that if we allow household factor supplies to vary, we would be varying the size of the Edgeworth-Box and the PPF. What about output prices? In principle, households take these as given and then, via utility-maximization, we obtain demands for commodities. However, suppose that given certain output prices, the corresponding household demands for commodities are not equivalent to the output of commodities that are implied by the same price ratio operating on the PPF? In this case, we cannot say we have an "equilibrium". For an equilibrium, the outputs demanded must equal the outputs supplied - and, hopefully, there is such a price ratio. 

To see this in diagrammatic form, we need only consider the issue of allocation of output. Given output prices p_X and p_Y, we obtain a given amount of commodities produced X and Y. These will form the dimensions of a consumer Edgeworth-Bowley box as depicted in Figure 6. As a particular output price ratio determines r/w, and as we are assuming supply of factors are supplied exogenously, we can pin down the income of each household A and B as m^A = rK^A + wL^A and m^B = rK^B + wL^B. As we are given p_X/p_Y, then each household will maximize utility subject to such a constraint. We have an equilibrium if the resulting demands are equal to output. In Figure 6, as we can immediately see visually, this is indeed not the case as we have an excess supply of good X (as X^A + X^B < X) and an excess demand for good Y (as Y^A + Y^B > Y).

Figure 6 - Consumer Edgeworth-Bowley Box

Consequently, we have an equilibrium only if the output prices are such that maximizing utility, the sum of demands of both housholds will be equal to the amount supplied by firms. This will only be true if the indifference curves are at a tangency to each other. This is visualized in Figure 7 where we have fitted a consumer Edgeworth-Bowley Box within the Production Possibilities Frontier by taking our origin the origin of the diagram as the origin of consumer A (O_A) and point F as the origin of consumer B (O_B). At equilibrium prices, p_X/p_Y, we can define X and Y as the profit-maximizing point F on the PPF. At that same output price ratio, p_X/p_Y, within the consumer Edgeworth-Bowley box, indifference curves of agents A and B are tangent to each other at point C. At that tangency, the outputs demanded by households are X^A + X^B = X (thus the market for X clears) and Y^A + Y^B = Y (thus the market for Y clears). 

Figure 7 - General Equilibrium

We achieve a general equilibrium if all markets clear - which means that output prices and factor prices are such that the demand for each factor equals the supply of each factor and the demand for each good equals the supply of each good, i.e. there is a set of prices (p_X, p_Y, r, w) such that:

X^A + X^B = X

Y^A + Y^B = Y

K_X + K_Y = K

L_X + L_Y = L

where (X^A, Y^A), (X^B, Y^B) satisfy the consumers' utility-maximzation exercise and (K_X, L_X), (K_Y, L_Y) satisfy the producers' profit-maximization exercise. Is there such a set of prices? The early employers of this model did not answer this question satisfactorily. Rather, they proceeded to count equations and unknowns and, once these were found to be equal, were satisfied that a solution existed. The situation depicted in Figure 7 represents a general equilibrium situation because all of the following hold:

(i) Output markets are clearing (as X^A + X^B = X and Y^A + Y^B = Y)

(ii) Factor markets are clearing (a point on the PPF represents a situation where K_X + K_Y = K and L_X + L_Y = L at imputed factor prices r/w).

(iii) firms are maximizing profits (p_X/p_Y is tangent to the PPF at point F)

(iv) households are maximizing utility (households indifference curves are tangent to the budget constraint defined by the same p_X/p_Y and imputed r/w).

As a consequence, it is obvious that the conditions for an equilibrium are that:

(i) MRTS^X_KL = r/w = MRTS^Y_KL (tangency of firms' isoquants at equilibrium factor prices)

(ii) MRS^A_XY = p_X/p_Y = MRS^B_XY (tangency of household indifference curves at equilibrium output prices)

(iii) MRS^A_XY = MRPT_XY = p_X/p_Y (households and firms face the same output prices).

All these conditions are obvious. The last is the condition that the p_X/p_Y which is tangent to the PPF is the same as the p_X/p_Y that is in the interior of the Edgeworth-Bowley box forming the tangency to the households's indifference curves, thus MRS_XY^A = MRPT_XY. We can see this last point more clearly by constructing a "community indifference curve" (CIC) which has the same slope at F on the PPF, as the consumers have at point C in the interior of the box. The third condition, then, can be represented by saying that the slope of the community indifference curve (CIC) must be equal to the PPF. We shall postpone the construction of the CIC until later, when we consider welfare theory more carefully.

(3) A General Paretian Model

The structure of the two-sector model can be expanded into a multi-sectoral model where we have m factors, n goods, F firms and H households. In this case, we do not need to place any arbitrary restrictions: we allow firms to produce several outputs, for instance, and allow households to possess a factor supply function which arises from utility-maximization rather than imposing that these be supplied inelastically. Furthermore, we shall allow households to own shares of firms, thus their income is no longer confined to the sale of endowment but also to the profit shares they own. Of course, with all this, the model is no longer amenable to diagrammatic representation, but similar conclusions can effectively be reached. 

Our primary task is to tackle the issue of the existence of an equilibrium in a multi-sectoral model. Like Walras (1874), Vilfredo Pareto (1906: p.446-8; 482-3) was content to count equations and unknowns to establish the existence of an equilibrium. Given the resemblance of the Paretian structure to the Walras-Cassel structure, we shall attempt to maintain more or less the same notation we had before. The notation and environment is as follows:

(1) H households, F firms, n commodities, m factors.

(2) Commodities

(i) x^h is a vector of commodities demanded by household h
(ii) x^f is a vector of commodities supplied by firm f
(iii) p is the vector of commodity prices.

(3) Factors:

(i) v^h is a vector of factors supplied by household h
(ii) v^f is a vector of factors demanded by firm f
(iii) w is the vector of factor prices.

(4) Private Ownership:

(i) p ^f is the profit of firm f
(ii) q ^hf is the share of firm f's profit owned by household h.

To ease notation, we assume that all price vectors are row vectors and all quantity vectors are column vectors. We also assume, for simplicity, that there are no intermediate goods, thus firms do not demand produced goods.

Each firm f = 1, .., F has a production function (technology) represented by the implicit function F ^f(x^f, v^f) = 0 which transforms factors demanded (v^f) into outputs supplied (x^f) by the fth firm. It is assumed that output increases and inputs increase. Firms seek to maximize profits, thus the fth firm's profit (p^f) arises from the difference between total revenue from the sale of commodities (px^f) and total costs from factor payments (wv^f). Thus, the fth firm has the following optimization problem:

max p ^f = px^f - wv^f

s.t. F ^f(x^f, v^f) = 0 

As there are F firms, there are F such profit-maximizing programs. 

Profits obtained by firms are distributed to households as profit income. Thus, letting q^hf denote the hth household's share of firm f's profits, then a fully privately owned economy implies that we can normalize profit shares as ãƒ»/font> _h=1^H q ^hf = 1, i.e. the sum of firm f's shares is equal to one. It is assmed that profit shares are not unknowns in this economy, but rather are given as data.

We assume each household h = 1, ..., H has a utility function (U^h) representing preferences and a particular endowment of factors, only v^h of which is supplied to the economy. Utility of the hth household is a function of outputs consumed (x^h) and factors supplied (v^h) - increasing with the former and decreasing with the latter. Thus, households seek to maximize U^h(x^h, v^h). Households obtain income from the sale of factors (wv^h) and the profit shares (q^h p ) where q ^h = [q ^hf]_f=1^F is the vector of shares owned by the hth households (i.e. q^h is household h's "portfolio") and p = [p^f]_f=1^F is the vector of firms' profits. It uses the proceeds from factor sales and profit shares to demand produced commodities, thus total purchases of household h, px^h cannot exceed income (wv^h + q^h p ). The hth household's utility maximization problem is then:

max U^h = U^h(x^h, v^h)

s.t. px^h ï½£ wv^h + q^h p

As there are H households, there are H such optimization programs.

Let us now establish the number of equations. From the H utility maximization and F profit-maximization problems we obtain the following first order conditions (note: m ^h is the Lagrangian multiplier for the hth household; m ^f is the Lagrangian multiplier for the fth firm). From the household's optimization problem we obtain the following:

(1)  ï½¶U^h/ｶx_i^h = m^hp_i for i = 1, .., n; h = 1, .., H.

as we have n commodities and H households, we have nH such equations (one per commodity per household).

(2)  ï½¶U^h/ｶv_j^h = - m^hw_j for j = 1, .., m; h = 1, .., H.

as we have m commodities and H households, we have mH such equations (one per factor per household).

(3)  px^h = wv^h + q ^h p for h = 1, .., H

we have H budget constraint equations (one per household).

From the firms' optimization problem, we obtain the following first-order conditions:

(4) p_i = -m^f (ｶF^f/ｶx_i^f) for i = 1, .., n; f = 1, .., F.

as we have n commodities and F firms, we have nF such equations (one per commodity per firm)

(5) w_j = m^f (ｶF^f/ｶv_j^f) for j = 1, .., m; f = 1, .., F.

as we have m factors and F firms, we have mF such equations (one per factor per firm)

(6)  F^f(x^f, v^f) = 0 for f = 1, ..., F.

we have F such equations (one per firm)

We now have to impose market-clearing for equilibrium. Thus:

(7)  ãƒ»/font> _h=1^H x_i^h = ãƒ»/font> _f=1^F x_i^f for i = 1, .., n

is the market clearing condition for commodity i. We have n commodities, thus we have n such equations (one per commodity).

(8)  ãƒ»/font> _h=1^H v_j^h = ãƒ»/font> _f=1^F v_j^f for j = 1, .., m

is the market clearing condition for factor j. We have m factors, thus we have m such equations (one per factor).

Thus, adding up, we obtain the following:

Number of equations = (n + m + 1)(H + F) + n + m

We can remove one equation by Walras's Law. Summing up budget constraints over households and recognizing that the profits shares for a particular firm f equate to one and then plugging in firms' profits yields, after some rearrangement:

(9)  ãƒ»/font> _i=1ⁿ p_i [・/font> _h=1^H x_i^h - ãƒ»/font> _f=1^F x_i^f] + ãƒ»/font> _j=1^m w_j [・/font> _f=1^F v_j^f - ãƒ»/font> _h=1^H v_j^h] = 0

or, in vector form:

p[x^h - x^f] + w[v^f - v^h] = 0

which is the familiar statement of Walras's Law. Note that if all markets clear but one, then that last one will necessarily clear too. Thus, we can exclude one of the market-clearing conditions from our list. Thus, now, the number of equations becomes:

(n + m + 1)(H + F) + n + m - 1

Let us now turn to the establishing the number of unknowns. From household h's optimization problem, the unknowns are x_i^h for each good i = 1,.., n; v_j^h for each factor j = 1, .., m and m ^h (Lagrangian multiplier from utility-maximization), thus for each household we have n+m+1 unknowns. As we have H households, then we have (n + m + 1)H unknowns from the household side. From firm f's optimization problem, unknowns are x_i^f for each good i =1,.., n; v_j^f for each factor j = 1, .., m and m ^f (Lagrangian multiplier from profit-maximization), thus for each firm we have n + m + 1 unknowns. As we have F firms, then we have (n+m+1)F unknowns from the firm side. From the market-clearing situations, we have p_i from every commodity market, i = 1, .., n and w_j for every factor market j = 1, .., m, thus we have n + m unknowns. Thus, for the entire system we have:

Total number of unknowns = (n + m + 1)(F + H) + n + m

It seems to exceed equations, but we forgot the numeraire good. We can thus set, say, the price of the first commodity to one (i.e. p₁ = 1) and so one of the unknowns drops out. Thus total unknowns are now:

(n + m + 1)(F + H) + n + m - 1

Thus, in conclusion, the total number of equations is equal to the total number of unknowns. Pareto (1906) concluded that this was enough to establish the existence of a general equilibrium for the economy.

(On to the Paretian System II: Efficiency)

Selected References

Maurice Allais (1943) Trait・d'ﾉconomie Pure, 1952 edition of ï¾ la Recherche d'une Discipline ﾉconomique, Paris: Impremerie Internationale.

Francis M. Bator (1957) "The Simple Analytics of Welfare Maximization", American Economic Review, Vol. 47, p.22-59.

Gottfried von Haberler (1933) The Theory of International Trade: with its applications to commercial policy. 1937 translation, New York: Macmillan.

John Hicks (1939) Value and Capital: An inquiry into some fundamental principles of economic theory. 1946 Edition, Oxford: Clarendon Press.

Frank H. Knight (1928) "A Suggestion for Simplifying the Statement of the General Theory of Price", Journal of Political Economy, Vol. 36 (3), p.353-70.

Oskar Lange (1942) "The Foundations of Welfare Economics", Econometrica, Vol. 10 (3), p.215-28.

Abba P. Lerner (1932) "The Diagrammatical Representation of Cost Conditions in International Trade", Economica, Vol. 12, p.346-56.

Abba P. Lerner (1934) "The Concept of Monopoly and the Measurement of Monopoly Power", Review of Economic Studies

Abba P. Lerner (1944) The Economics of Control: Principles of welfare economics. New York: Macmillan.

Vilfredo Pareto (1906) Manual of Political Economy. 1971 translation of 1927 edition, New York: Augustus M. Kelley.

Lionel C. Robbins (1934) "Remarks upon Certain Aspects of the Theory of Costs", Economic Journal, Vol. 44, p.1-18.

Joan Robinson (1941) "Rising Supply Price", Economica, Vol. 8, p.1-8.

Paul A. Samuelson (1947) Foundations of Economic Analysis. 1983 edition. Cambridge, Mass: Harvard University Press.

Tibor Scitovsky (1941) "A Note on Welfare Propositions in Economics", Review of Economic Studies, Vol. 9, p.77-88.

Tibor Scitovsky (1942) "A Reconsideration of the Theory of Tariffs", Review of Economic Studies, Vol. 9, p.89-110.

Friedrich von Wieser (1889) Natural Value. 1971 reprint of 1893 translation, New York: Augustus M. Kelley.

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https://cruel.org/econthought/profiles/pareto.html

ヴルフィレド・パレート (Vilfredo Pareto)

　イタリアの経済学者ヴルフィレド・パレートはローザンヌ学派指導者の一人で、新古典派革命第二世代の代表者だ。存命中はほどほどの影響力にとどまったが、一般均衡理論に対する「嗜好と障害」アプローチは1930年代のパレート復興で蘇り、その後経済学に大きな影響を与え続けている。

　ヴィルフレド・パレートは1848年にパリで、イタリア人貴族の家庭に生まれた。トリノ大学で数学と機械的な均衡の発想に惹かれ、その後フィレンツェで鉄道会社や製鉄会社の重役を務めたが、1889年に退職、文無しのロシア娘と結婚してフィエソーレに隠居して執筆活動に入った。フィレンツェ時代には政治活動を盛んに行っていたために当局に目をつけられ、かなりの苦労を強いられたものの、イタリアの新古典派経済学の星だったマフェオ・パンタレオーニの知己を得たことで、ワルラス派経済理論を学び、関連論文を発表するようになった。

　折しもそのレオン・ワルラスはローザンヌ大学での後継者を探しており、パンタレオーニに推挙を受けて、パレートが1894年にその座を次ぐこととなった。ただしワルラスとパレートは、政治的見解や気質の面で正反対で、両者は必ずしも仲がよいわけではなかったという。

　パレートは政治活動も続けつつ、三巻に渡る講義録『政治経済学講義』 (1896, 1897) を刊行した。決して数式による純理論の書ではなく(数式はむしろ脚注などに追いやられている）、手法論や社会学的な考察も大きな割合を占める。おそらく最も重要な経済学的考察は、所得分配の「パレート法則」だろう。あらゆる時代と国で、所得と富の分配は規則正しい対数関数であらわされるという:

logN=logA+mlogx ここでN は、x より所得の高い人々の数であり、A と m は定数である。長年にわたり、パレート法則は実証的にきわめて頑健であることが示されている。

　それ以外にも、効用概念に対する批判（人は自分に「望ましい」ものを選ぶのであり、必ずしもそれは当人の厚生に関係しない）や、分配の限界生産性理論批判、均衡概念からくる社会的な経済の「計算可能性」示唆などは重要な論点となっている。

　1906年にパレートは大著『政治経済学マニュアル』を発表。純粋経済学の大著で、これによりパレートはワルラスの影から飛び出した。『講義』とはちがい、純粋経済学を数学的に記述することが重視された（特に1909年の改訂フランス語版）。ワルラスの方程式はまだ見られるが、重視されているのはむしろ、個人の「目的と制約」の解として均衡を実現することだ。このため、 エッジワースの無差別曲線 (1881) が多用されている——消費者理論でも、そして目新しい点としては生産者の理論でも。「エッジワース＝ボウリー」ボックスと（誤って）呼ばれるようになったものが初めて登場するのも、この「マニュアル」だ。

　アーヴィング・フィッシャー (1892) と同じく、パレートも明示的な効用はなしでもすませられることに気がついた。原初的な指向を示すのは選好であり、効用は選好序列の表現にすぎないというわけだ。これによりパレートは現代ミクロ経済学を創始しただけでなく、経済学と 効用主義の「卑しい連合」を破壊した。かわりにかれはパレート最適の概念を導入した。これは万人について、だれかの厚生を増すときに他人の厚生を減らさなくてはならないときに、社会は「最大の ophelimity (これはパレートが効用にかわって導入した概念)」を実現している、という発想だ（詳細はパレート一般均衡体系の説明を見てね)。

　1900年にパレートは、ベネデット・クローチェとの論争を経て経済学の有用性に不満を抱き、人間行動が必ずしも合理的ではないことが原因と考えた。ここから社会学的な研究が始まった。1907年にはローザンヌを退職して大量のネコたちとチェリグニーに隠居し（妻にはすでに逃げられていたが、別のフランス人女性が終生の伴侶となった）社会学の大著『一般社会学考察』(Trattato di sociologia generale, 1916) を発表した。人間は不合理な性向で行動し、後付でそれを合理化する、という基本的な発想に基づき、パレートは人を第一種（革新的）と第二種（保守的）に分類する。社会はこの二種類の人々の混合で決まるが、この両者は長期的には均衡するという。

　パレートはそれ以前にも、1900年の論説でマルクス経済学を始めとする各種イデオロギーが、あるエリート層を別のエリート層に置き換えるための茶番でしかないと看破し、社会主義の階級闘争概念は支持したものの、社会主義革命で階級が消えるというマルクスの主張を徹底批判していた。その後も社会学について二冊本を書き (1920, 1921)、その半ば神秘的な議論はイタリアのファシスト（ムッソリーニも含む）を惹きつけ、かれらの自己正当化に利用されることとなる。パレートはファシスト運動にあまり関心はなかったが、ファシストによる言論統制には反発した。パレートはムッソリーニ政権樹立後10か月で死亡し、ファシスト支配の悪い面を見ずにすんだ。

　ファシズムとの関係にもかかわらず、パレートの社会学的な業績は真剣に受け止められ、人気の高まりと、批判的な検討の時期とを繰り返している。フロイト心理学はパレートの概念の一部をかなり重視している。パレートに対する批判は、その主な主張に対するものではなく。むしろその粗雑さ、単純さ、不完全性が主な原因だ。

　だがずっと大きな影響があったのは、パレートの経済学だ。パレートは ローザンヌ時代にも学派を形成し、内外に支持者を持っていた。その最大の影響は、死後1930年代と1940年代の、「パレート復興」とも呼ぶべきものだ。需要に対する「嗜好と障害」アプローチはジョン・ヒックスと R.G.D. アレン (1934) が復活させた。また厚生経済学の検討はハロルド・ ホテリングやオスカール・ランゲと「新厚生経済学」運動が採用した。最後に、共産社会の効率性に関するパレートの考察は、 パレート派とオーストリア学派の 社会主義計算論争で採り上げられた。

ヴィルフレド・パレートの主要著作

• Principii Fondamentali della Teorie dell' Elasticità,, 1869.
• "Della logica delle nuove scuole economiche", speech to Accademia dei Gerogofili, 1877.
• "L'Italie économique", 1891, Revue des deux mondes
• "Les nouvelles théories économiques", 1892, Le monde économique
• "Considerazioni sui principi fondamentali dell'economia politica pura", 1893, Giornale degli Economisti.
• "Introduction" to K. Marx, Capital, 1893.
• Leçon d'économie pure à l'Universit de Lausanne, 1893 (unpublished)
• "The Parliamentary Regime in Italy", 1893, American Poli Sci Quarterly
• La liberté économique et les événements d'Italie.
• "La courbe des revenus", 1896, Le Monde economique (French/Italian)
• Cours d'économie politique professé à l'université de Lausanne, 3 volumes, 1896-7.
• "The New Theories of Economics ", 1897, JPE.
• "Comment se pose le problème de l'économie pure?", Notes to Association Stella,1898 (publ. 1965)
• "Un' Applicazione di teorie sociologiche", 1900, Rivista Italiana di Sociologia(transl. in English as The Rise and Fall of the Elites)
• "On the Economic Phenomenon", 1900, GdE (repr. 1953, IEP)
• "Le nuove toerie economiche (con in appendice le equazioni dell' equilibrio dinamico)", 1901, GdE
• "De l'économique, discours d'installation de M.V. Pareto professeur ordinaire", Lausanne, 1901 (publ. 1965)
• Les systèmes socialistes, 1902.
• L'économie pure, resumé du cours donné a l'Ecole des Hautes Etudes Sociales de Paris, 1902
• "Review of Aupetit", 1902, Revue d'econ politique
• "Anwendungen der Mathematik auf National(ﾟ konomie", 1903, Encyklopödie der Mathematischen Wissenschaften
• "Il Crepuscolo della Libertà", 1905, Rivista d'Italia.
• Manual of Political Economy , 1906 (Italian; French transl., 1909, English transl, 1971).
• "L'économie et la sociologie au point de vue scientifique", 1907, Rivista di Scienza.
• "Economie mathématique", 1911, in Gauthier-Villars, Encyclopedie des sciences mathematiques.
• Le mythe vertuiste et la littérature immorale. 1911
• "Introduction" to G. Osorio, Théorie mathematique de l'échange, 1913.
• Trattato di Sociologia Generale, 1916. (transl. in English as Mind and Society. Extracts (1) , (2), (3); extract in Spanish)
• "Discorso per il Giubileo", 1917, La Riforma Sociale - Jubillee speech manuscript
• "Formi di fenomeni economici e previsioni", 1917, Riv di Sci Banc
• Fatti e Teorie, 1920
• Trasformazione della Democrazia, 1921.
• Mon Journal, 1958
• Scritti sociologici di Vilfredo Pareto, 1966.
• Oeuvres complètes de Vilfredo Pareto, ed. G. Busino

ヴィルフレド・パレートに関するリソース

• HET ページ: パレート体系: 均衡, 効率性, 社会厚生, the 生産決定, 分配の限界生産性理論
• "Review of Bortkiewicz's Anwendungen and Pareto's Anwendungen", by Francis Ysidro Edgeworth, 1903, EJ 
• "Review of Pareto's Manuale di Economia Politica", by Philip H. Wicksteed, 1906, EJ
• "Recent Contributions to Mathematical Economics, I & II", by Francis Ysidro Edgeworth,1915, EJ
• "Review of Pareto's Cours d'économie politique, Vol. 1" by Georges Sorel, 1896, Le devenir social, Ann. 2, N. 5, May. 
• "Review of Pareto's Cours d'économie politique, Vol. 2" by Georges Sorel, 1897, Le devenir social, Ann. 3, N. 5, May. 
• "Review of Pareto's Manuale di Economia Politica" by M. Halbwachs, 1906, L'année sociologique, Ann. 10
• "Review of Jevons's Theory, Pareto's Manuel and Marshall's Principles" by François Simiand, 1909, L'année sociologique, Ann. 11
• "Review of Pareto's Manuel d'économie politique" by E. d'Eichthal, 1909, Revue critique d'histoire et de littérature
• "Review of Pareto's Trait・de sociologie générale" by C. Bougl・ 1919, Revue historique
• "Review of Pareto's Trait・de sociologie générale" by F. Bd., 1919, Revue critique d'histoire et de littérature
• Cercle d'études Paretiennes at Lausanne.
• Centre d'études interdisciplinaires Walras-Pareto at Lausanne
• Le Fonds Pareto at CWP Lausanne
• Il Fondo Pareto of the Banca Popolare de Sondria
• Annoucement of Oeuvres complètes de Vilfredo Pareto, ed. G. Busino
• Biographie de Pareto at CWP Lausanne
• Biography of Pareto - in English.
• "Vilfredo Pareto: Concise Overview of His Life, Works, and Philosophy" by Fr. James Thornton
• "Pareto in Toscana" by Alberto Zanni, 1999, SdPE.
• "More on Slutsky's Equation as Pareto's Solution", by C.E. Weber, 1999, HOPE
• "La raccolta dei documenti di Vilfredo Pareto", by P. C. Ferrara, 1997
• Vilfredo Pareto page at Dead Sociologists Index
• Vilfredo Pareto page at Marxists.org
• "Vilfredo Pareto: Il Gioco del Potere?" by Franco Gianola
• Pareto dressed as a Bedouin Arab on the way to a masked ball. (source)
• Pareto Page at McMaster
• Pareto Page at Akamac
• Pareto Page at Laura Forgette
• Selected Primary and Secondary Works of Vilfredo Pareto at Bristol, UK
• Pareto Page at R. Dixon, Melbourne
• Walras, Pareto: L'Ecole de Lausanne - in French
• Essay on "Pareto Analysis" 
• Other Images of Pareto - (1), (2)
• Books on Pareto
• Pareto page at Britannica.com
• Philosophy of Pareto
• Pareto Page (in French)
• Pareto Consulting?! (don't ask)

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免責条項、© 2002-2004 Gonçalo L. Fonseca, Leanne Ussher, 山形浩生

https://www.nri.com/jp/knowledge/glossary/lst/ha/pareto_princ

パレートの法則

Pareto principle

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「80：20の法則」ともいわれ、「売上げの8割は2割の社員に依存する」といった傾向をさす。集団の報酬や評価が一部の構成員に集中するという経験則。

イタリアの経済学者ビルフレッド・パレート（1848～1923）が1880年代の欧州の経済統計から「個人の所得額」と「その所得額以上の所得を得ている人の数」との間に見出した法則をいいます。

「80：20」の数値に絶対的な意味はなく、集団の報酬や評価の集中傾向を端的に表すにすぎません。その由来について、園芸家でもあったパレートが、エンドウ豆の80％が20％のサヤから収穫されたことに着想を得たともいわれています。

「選択と集中」を裏づける経験則

この法則は「べき法則」と呼ばれる数理法則の一部で、同様の傾向が、英単語の使用頻度、都市の人口規模、河川やインターネットの結節点の次数など、社会や自然の様々な領域で観察されています。

企業経営に当てはめると、売上げや利益が一部の社員や顧客に集中的に依存することが明確になり、選択と集中の必要性の根拠として注目されるようになりました。ABC分析にもこの法則が応用されています。

経営にどう応用するかが重要

「パレートの法則」が観察される状態が、社会や集団にとって好ましいとは限りません。観測される集中傾向をより強めるのか、弱めるのかを判断することが重要です。

金融サービス等で、ターゲットを富裕層に特化する動きは、集中の度合いを強めていく方向といえます。

逆に、従来、収益の主要な源泉とはみなされなかった発注頻度の少ない商品を重視する「ロングテール」は、商品の管理コストの低下を背景に、特定の売れ筋商品への依存傾向を弱める方向といえます。

また、独占禁止法、地方交付税、累進課税制度、最低賃金法などの制度は、一部の企業や構成員に対する報酬や評価の集中を是正するための制度と捉えることができます。

パレート分布と正規分布