Inverse problems of demand analysis and their applications to computation of positively-homogeneous Konüs-Divisia indices and forecasting

Journal of Inverse and Ill-posed problems. 2016. Vol. 24. No. 4. P. 367–391.

Klemashev N., Шананин А. А.

According to Pareto's theory of consumer demand a rational representative consumer should choose their consumption bundle as the solution of mathematical programming problem of maximization of utility function under their budget constraint. The inverse problem of demand analysis is to recover the utility function from the demand functions. The answer to the question of solvability of this problem is based on the revealed preference theory. If the problem is unsolvable, one should apply regularization procedure by introducing irrationality indices. When recovering the utility function one puts a priori requirements on it. In this paper, we suggest including positively-homogeneity property into these requirements. We compare the setups with and without this requirement both theoretically and empirically and provide evidence in favor of requiring this property when computing economic indices for consumer representing consumption behavior of large number of various households for large time intervals.

Keywords: forecasting, прогнозирование, математическое программирование, обратная задача, mathematical programming, revealed preferences, inverse problem, выявленное предпочтение, economic indices, экономические индексы