INDIRECT TAXES AND RELATIVE PRICES: AN APPLICATION OF LEONTIEF MODELS

The generalized Leontief model is particularly suitable for the study of indirect taxation and, yet, to my knowledge, it had not been extended to a world where taxes are levied. Three features of the model distingush it from others usually employed in the study of public finance. First, it assumes the existence of one primary factor or, if more than one, the relative prices between them is kept constant so that they can be treated as if there was only one combined factor. This limits the validity of the analysis to the study of short-run phenomena but, on the other hand, makes the model extremely manageable enabling one to derive a series of results on the effects of taxes by means of simple geometry. Second, it admits the possibility of substitution in production instead of fixed-coefficient production functions that characterize the simple Leontief model and which is the version commonly used in the study of taxes. Unlike the fixed-coefficient version that rules out the possibility of inefficiencies being introduced in an economy due to the existence of taxes, in the generalized version of the Leontief model it is seen that most partial taxes shift downward the production possibility frontier. Finally, unlike the standard neo-classical model in "net" terms, the model explicitly deals with intermediate flows of goods. As a consequence of the existence of taxation on intermediate transactions, one can show, for instance, that the claim that the method of collection of value-added taxes (VAT) has no economic effect is, in general, false. A partial VAT collected via the accounts method always provokes inefficiencies in production while a partial VAT collected via the invoice method is only inefficient if there exists exemptions. Furthermore, the nature of the inefficiency of the latter tax is necessarily distinct from that of the former. If smooth, differentiable production functions are best suited for the development of theoretical (graphical) results, the assumption of a finite number of activities describing the technology of each sector seems more appropriate for an empirical application of the model to the study of Brazilian indirect taxes. The information needed to construct these activities can be derived from input-output tables of several countries, transforming those matrices which are expressed in value terms into quantity indexes coefficients by means of some elementary operations on matrices. The effects that taxes have on producers' prices can, then, be determined with the use of linear programming. Taking the number of activities to be finite, tax rates have to be sufficiently large to induce a producer to switch from an activity to another in order to maximize profits. There is reason to believe that Brazilian tax rates levied on intermediate transactions are not large enough to lead to such switching of activities so that a fixed-coefficient production function leads to approximate results on the effects of taxes on producers' prices. Note, however, that the use of a fixed-coefficient production function, in such a procedure, is adopted as a result of experimenting with a model that admits substitution, its validity not being assumed from the outset. Once producers prices are estimated, prices for consumers are easily obtained by adding taxes on final sales. In models with only one primary factor, prices are technologically determined and as a consequence, the set of consumers' prices estimated is independent of demand