How sensible is the Leyden individual welfare function of income

Abstract The Leyden economists contend that the individual welfare function (utility function) of income is best represented by a lognormal distribution function. They have presented ample data to document the good empirical fit of the lognormal hypothesis. This paper presents, reexamines, and criticises the theoretical foundations of the lognormal hypothesis and finds that this edifice is not built on solid ground, neither from the point of view of economic theory, nor of experimental psychology. Moreover, it investigates the paradox of the good empirical fit of the lognormal hypothesis in spite of its theoretical deficiencies. It is shown that the lognormal hypothesis is observationally equivalent to the logarithmic (power) welfare function when respondents evaluate welfare according to a normal (lognormal) distribution function.

[1]  S. S. Stevens,et al.  Psychophysics: Introduction to Its Perceptual, Neural and Social Prospects , 1975 .

[2]  R. Luce,et al.  On the possible psychophysical laws. , 1959, Psychological review.

[3]  Arie Kapteyn,et al.  Further evidence on the individual welfare function of income: An empirical investigatiion in The Netherlands , 1973 .

[4]  S. Dubnoff,et al.  Evaluation Questions and Income Utility , 1988 .

[5]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[6]  S. S. Stevens,et al.  Ratio scales and category scales for a dozen perceptual continua. , 1957, Journal of experimental psychology.

[7]  J. Merkel.  Die Abhangigkeit zwischen Reiz und Empfindung , 1889 .

[8]  Utility and gambling decisions: Experiments and equations , 1975 .

[9]  R. Duncan Luce,et al.  A generalization of a theorem of dimensional analysis , 1964 .

[10]  S. Danziger.  The Direct Measurement of Welfare Levels: How Much Does It Cost to Make Ends Meet? , 1984 .

[11]  B.M.S. van Praag,et al.  Household Cost Functions And Equivalence Scales , 1985 .

[12]  S. S. Stevens.  On the psychophysical law. , 1957, Psychological review.

[13]  H. Sinn.  Psychophysical laws in risk theory , 1985 .

[14]  A. Kapteyn,et al.  The poverty line: A pilot survey in Europe , 1980 .

[15]  E. Galanter,et al.  Some invariances of the isosensitivity function and their implications for the utility function of money. , 1967, Journal of experimental psychology.

[16]  Arie Kapteyn,et al.  Empirical comparison of the shape of welfare functions , 1981 .

[17]  S. S. Stevens.  Matching functions between loudness and ten other continua1 , 1966 .

[18]  Wilhelm Krelle,et al.  Personal Income Distribution. , 1980 .

[19]  J. Aitchison,et al.  The Lognormal Distribution. , 1958 .

[20]  Hannes Eisler,et al.  ON THE PROBLEM OF CATEGORY SCALES IN PSYCHOPHYSICS , 1962 .

[21]  K. Lancaster.  A New Approach to Consumer Theory , 1966, Journal of Political Economy.

[22]  G. Debreu,et al.  Theory of Value , 1959 .

[23]  K. Lancaster,et al.  Consumer Demand. A New Approach. , 1972 .

[24]  H. Eisler.  EMPIRICAL TEST OF A MODEL RELATING MAGNITUDE AND CATEGORY SCALES , 1962 .

[25]  Eugene Galanter,et al.  Handbook of mathematical psychology: I. , 1963 .

[26]  G. Duncan,et al.  The Perception of Poverty. , 1987 .

[27]  A. Kapteyn,et al.  The Poverty Line: Concept and Measurement , 1977 .

[28]  J. Aczél,et al.  On scientific laws without dimensional constants , 1986 .

[29]  B. V. Praag,et al.  POVERTY IN EUROPE1 , 1982 .

[30]  A. Kapteyn,et al.  Two Subjective Definitions of Poverty: Results from the Wisconsin Basic Needs Study , 1983 .

[31]  S. S. Stevens,et al.  A metric for the social consensus. , 1966, Science.

[32]  B. V. Praag,et al.  The welfare function of income in Belgium: An empirical investigation , 1971 .

[33]  D. K. Osborne.  Further extensions of a theorem of dimensional analysis , 1970 .

[34]  R. L. Hamblin.  Mathematical experimentation and sociological theory: A critical analysis: 247. , 1971 .

[35]  Robert L. Hamblin.  Ratio Measurement for the Social Sciences , 1971 .

[36]  E. Galanter,et al.  Cross Modality Matching of Money against Other Continua. , 1974 .

[37]  Max Henrion,et al.  Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis , 1990 .

[38]  E. Boring,et al.  The derivation of subjective scales from just noticeable differences. , 1958, Psychological review.

[39]  Aram J. Thomasian,et al.  The structure of probability theory with applications , 1971 .

[40]  Hannes Eisler,et al.  Magnitude scales, category scales, and Fechnerian integration. , 1963 .

[41]  A. Kapteyn,et al.  Interdependent welfare functions and optimal income distribution , 1980 .

[42]  A. Kapteyn.  A theory of preference formation , 1979 .

[43]  L. L. Thurstone,et al.  Fechner's law and the method of equal appearing intervals. , 1929 .

[44]  A. Kapteyn,et al.  A new approach to the construction of family equivalence scales , 1978 .

[45]  K. Breault.  Psychophysical measurement and the validity of the modern economic approach: A presentation of methods and preliminary experiments , 1983 .

[46]  C. Kam,et al.  An operational concept of the ability to pay principle (With an application for The Netherlands, 1973) , 1983 .

[47]  G. Ekman,et al.  Is the Power Law a Special Case of Fechner's Law? , 1964, Perceptual and motor skills.

[48]  E. Galanter,et al.  The direct measurement of utility and subjective probability. , 1962, The American journal of psychology.

[49]  Arie Kapteyn,et al.  Twelve thousand individual welfare functions , 1977 .

[50]  H. Sinn.  Economic Decisions Under Uncertainty , 1983 .

[51]  B. V. Praag,et al.  Individual Welfare Functions and Consumer Behaviour , 1972 .

[52]  J. Hartog.  Review: Poverty and the Measurement of Individual Welfare , 1988 .