Abstract
Harold Hotelling believed that integrability was a necessary characteristic of both individual and market demand equations, and he demonstrated that it would hold if consumers did not have a budget constraint. If there was a budget constraint, he contended, the usual integrability condition would be replaced by a condition which assures that an integrating factor can be introduced. This paper shows that this condition can be satisfied only if the consumer's income effect is the same numerically for all goods. Aggregation by summation of individual demands is considered, and it is shown that this form of aggregation is valid if there is a budget constraint only when income effects are the same for all individuals.
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References
Hicks, J. R.; Allen, R. G. D. "A Reconsideration of the Theory of Value, part I,"Economica, n.s.1, 1934, pp. 52–76.
__. "A Reconsideration of the Theory of Value, part II,"Economica, n.s.1, 1934, pp. 196–219.
Hotelling, H. "Edgeworth's Taxation Paradox and the Nature of Supply and Demand Functions,"Journal of Political Economy, 40, 1932, pp. 577–616.
__. "Demand Functions with Limited Budgets,"Econometrica, 3, 1935, pp. 66–78.
__. "The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates,"Econometrica, 6, 1938, pp. 242–69.
Malik, S. C.Mathematical Analysis, New York: Halsted, 1984.
Marhuenda, F. "Distribution of Income and Aggregation of Demand,"Econometrica, 63, 1995, pp. 647–61.
Samuelson, P. A.The Foundations of Economic Analysis, Cambridge: Harvard University Press, 1947.
__. "The Problem of Integrability in Utility Theory,"Economica, n.s.17, 1950, pp. 355–85.
Slutsky, E. E. "On the Theory of the Budget of the Consumer,"Giornale degli Economisti, 51, 1915, pp. 1–26.
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Pfouts, R.W. Integrability and aggregation in the theory of demand. Atlantic Economic Journal 23, 176–188 (1995). https://doi.org/10.1007/BF02299028
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DOI: https://doi.org/10.1007/BF02299028