criteria of resolvability of the integral linear equation of the ¬rst kind. His last work

appeared in 1961, when his bad health prevented him from dedicating time to

research, as a volume on the natural laws of economics. In more than half a century

of scienti¬c research, the area of study that attracted him the most and to which he

made the most important contributions was without doubt economic science. Most

notable, are some books in which he skilfully synthesized his most important results;

in particular, we refer the interested reader to his Economic Mechanics (1942), in

which he collected his lectures given in 1940 “1941 at the National Institute of

Higher Mathematics. In the topics dealt with in this volume, Amoroso used

sophisticated mathematical tools to reach his objectives and, in extreme synthesis,

presented the main results concerning the generalization of Walras™s and Pareto™s

equilibrium, which is static, through the dynamic consideration of the factors that

intervene in the optimal solution of consumer and producer problems. In his Lessons

269

A.6 RAFFAELE D™ADDARIO

on Mathematical Economics (1921), he lucidly outlined the methods, limits, and

aims of mathematical economics, whereas in The Natural Laws of Economics (1961)

he laid out a de¬nitive description of the fundamental aspects of his favorite

scienti¬c problem, that is, the parallelism between mechanical and economic

phenomena and the transfer of mechanical laws in the economic world. Finally, we

must mention Amoroso™s (1925) contribution on the analytical representation of

income distribution, with which he proposed an equation that is an extension and

generalization (see D™Addario, 1936) of those proposed by March and Vinci,

suitable for describing, according to the value of the parameters, both unimodal and

zeromodal distributions.

REFERENCES

Amoroso™s full bibliography (150 scienti¬c works) appears in Luigi Amoroso: Discorsi

commemorativi pronunciati dai Lincei Mauro Picone e Volrigo Travaglini (1967), Rome:

Accademia Nazionale dei Lincei.

Amoroso, L. (1909). La teoria dell™equilibrio economico secondo il Prof. Vilfredo Pareto.

Giornale degli Economisti, 39 (Series 2), 353“ 367.

Amoroso, L. (1910). Sulla risolubita della equazione lineare di prima specie. In: Rendiconti

`

dell™Accademia dei Lincei. Rome: Classe di scienze ¬siche, matematiche e naturali,

Accademia Nazionale dei Lincei.

Amoroso, L. (1921). Lezioni di economia matematica. Bologna: Zanichelli.

Amoroso, L. (1925). Ricerche intorno alla curva dei redditi. Annali di matematica pura e

applicata, 2 (Series 4), 123“ 157.

Amoroso, L. (1942). Meccanica Economica. Citta di Castello: Macr± Editore.

` `

Amoroso, L. (1961). Le leggi naturali dell™economia politica. Turin: UTET.

D™Addario, R. (1936). Sulla curva dei redditi di Amoroso. In: Annali dell™Istituto di Statistica

`

dell™Universita di Bari, Vol. 10. Bari: Macr± Editore.

`

Giva, D. (1988). Amoroso Luigi. In: Dizionario degli Italiani, Rome: Istituto della

Enciclopedia Italiana fondata da Giovanni Treccani, Vol. 34, pp. 113“ 116.

A.6 RAFFAELE D™ADDARIO*

Born: December 17, 1899, Grottaglie, Italy.

Died: September 1, 1974, Rome, Italy.

Before he was even eighteen years old, Raffaele D™Addario served in World War I,

an unforgettable experience that remained with him for all of his life. After the war

he enrolled at Bari University from which he graduated in 1924 with a degree in

economics and business administration. Carlo Emilio Bonferroni supervised

*The following biography is a slightly edited version of text provided to the authors by Professor Giovanni

M. Giorgi of the La Sapienza University in Rome.

270 BIOGRAPHIES

D™Addario in the writing of his thesis and soon thereafter D™Addario became

Bonferroni™s assistant in mathematics. Later he resigned from the University of Bari

and moved to Rome. Here he worked for ISTAT, the National Institute of Statistics,

where he became head of the Of¬ce of Studies in 1929 and met Corrado Gini who at

that time was president of the institute. However, D™Addario did not remain long at

ISTAT. According to some biographers, it may have been due to incompatibility with

the president; others maintain that it was because he met Luigi Amoroso who, as

administrator of the company Le Assicurazioni d™Italia, appointed him as the

company™s technical consultant in October 1931. The experience that he gained ¬rst

at ISTAT and then in the ¬eld of insurance gave D™Addario not only the opportunity

to analyze concrete phenomena, but also provided stimuli for continuing theoretical-

methodological studies within the university environment. He was awarded the

libera docenza, which quali¬ed him to teach statistics at the university level, in 1931,

and in 1936 he was appointed to the chair of statistics at the Faculty of Economics

and Business Administration at the University of Bari. During the academic year

1950 “1951 he moved to Rome University (now La Sapienza University) to

the Faculty of Political Science, of which he was dean from the academic year

1963 “1964 until the time of his death.

D™Addario held important public positions at the National Council of Labour and

Economics, the Higher Council for Public Education, and the Higher Council

for Statistics. He was a member of various societies and scienti¬c bodies, including

the Lincei Academy, the International Statistical Institute, the International Institute

of Public Finance, the International Union for the Scienti¬c Study of the Population,

the Econometric Society, the Italian Actuarial Institute, the Italian Society of

Economists, and the Italian Society of Economics, Demography and Statistics.

D™Addario™s scienti¬c interests were rather wide and may be classi¬ed into the

following main groups: the distribution of personal income and wealth, the economics

and statistics of insurance, and the division of taxes. His most important studies belong

to the ¬rst group. D™Addario was motivated to study income distribution following the

results obtained by Pareto on the topic. After having ascertained (D™Addario, 1934) that

of the three curves [called ¬rst (I), second (II), and third (III) approximation] by which

the Paretian model is expressed (the literature at that time mainly dwelled on the I-type

curve), he investigated the analytical properties of the II-type curve and proposed

three methods for determining its parameters. Subsequently, he studied the subject in

more detail and suggested a further method for calculating the parameters. D™Addario

(1936, 1949, 1953) also showed that the functions proposed by various authors (e.g.,

Pareto, Kapteyn, March, Vinci, Amoroso, Davis, Mortara, and Benini, etc.) for the

analytical representation of the income and patrimony distributions are particular cases

of a more general function that formally synthesizes Boltzmann, Bose“Einstein, and

Fermi“Dirac statistics.

As far as research in the ¬eld of insurance is concerned, we can brie¬‚y say that

D™Addario dealt, among other things, with the “rational evaluations” of the “rates”

and “reserves,” and of the existence”restricted to the branch of accidents and civil

liability”of a speci¬c law for the distribution of damages. Furthermore, he analyzed

insurance problems in relation to ¬‚uctuations in currency value.

271

A.7 ROBERT PIERRE LOUIS GIBRAT

Finally, D™Addario™s studies on the division of taxes were mainly concerned with

the issues relating to progressive taxation. In this context he proposed some methods

for measuring the structural progressivity of taxation and a general method for

establishing the scale of tax rates. He also investigated the in¬‚uence of a proportional

property tax on corresponding incomes as well as the in¬‚uence of a proportional

income tax on corresponding property.

REFERENCES

D™Addario, R. (1934). Sulla misura della concentrazione dei redditi. Rome: Poligra¬co dello

Stato.

D™Addario, R. (1936). Le trasformate Euleriane. In: Annali dell™Istituto di Statistica

`

dell™Universita di Bari, Vol. 8. Bari: Macr± Editore.

`

D™Addario, R. (1936). Sulla curva dei redditi di Amoroso. In: Annali dell™Istituto di Statistica

`

dell™Universita di Bari, Vol. 10. Bari: Macr± Editore.

`

D™Addario, R. (1939). La curva dei redditi: sulla determinazione numerica dei parametri della

`

seconda equazione paretiana. In: Annali dell™Istituto di Statistica dell™Universita di Bari,

Vol. 12. Bari: Macr± Editore.

`

D™Addario, R. (1939). Un metodo per la rappresentazione analitica delle distribuzioni

`

statistiche. In: Annali dell™Istituto di Statistica dell™Universita di Bari, Vol. 16. Bari:

Macr± Editore.