Consumer behavior, cost of living measures, and the income tax
The theory of cost of living indices is generalized in such a way that income tax is taken into account. After a general introduction, in part II first a short introduction into consumer theory is given, for the case where income consists of wage and non labor income and consequently, leisure is a consumption good, but where there is no income tax. Then, along the same lines, consumer behavior is studied when there is a (progressive) income tax on total income (nonlabor income and earned wages) which implies that the budget set becomes smaller and that there is a tax deductibility on leisure. For this case known concepts from consumer theory, e.g. indirect utility, Marshallian and Hicksian demand functions are defined, and the different versions of the expenditure function that now exist. Many properties of the original theory remain valid (e.g. theorems of Shephard and Roy), but others are lost, particularly the homogeneity of the budget and of the two types of demand functions. In part III some theory on index numbers (in the absence of tax and without the distinction between labor and nonlabor income) is summarized, emphasizing the Konus and Frisch indices (true cost of living indices). This theory is first generalized so as to take care of the two types of income, which leads to the definition of both a ''nonlabor income-based cost of living index'' and a ''real wage index'', giving the increases of non-wage income (wages) necessary to maintain the level of utility after an increase of prices of goods and of the wage rate (nonlabour income). Then in Part IV the income tax is introduced and the indices are defined again for that case. Different cost of living indices exist, serving different purposes. Particularly, indices giving changes of non-wage income or of the wage rate, necessary to maintain a given level of utility after price changes, are defined while indices based on taxable income or on expenditures are distinguished. In part V some remarks are made on virtual prices and on aggretation and in an example different computed cost of living indices are compared. The last chapter deals with the incorporation of government services and changes in the tax code (both endogenous and exogenous). The book is clearly written and the authors have adapted with care and patience known theory for the case of taxes and found new concepts where necessary. It is a very useful exercise since it is obvious that in the presence of (progressive) taxation the traditional indices loose their significance.
scientific article; zbMATH DE number 3976681