The TD-BU methodology covers a wide range of objects of various "physical" nature and with various analysis tasks. The feature of such objects is that they have a hierarchical structure. Mathematically, they are related by the formalization of upper-level processes by algebraic equations, while lower levels are described by means of mathematical programming. Currently being extensively researched the forecast status of ultra-large hierarchical systems such as "the country's economy -its fuel and energy complex" with certain requirements. The excessive dimensions of such systems create difficulties in their analysis in the classical formulation, so most researchers use diacoptic methods and therefore these tasks TD-BU are labor-intensive. There are a large number of objects to which the TD-BU methodology could be formally applied. We are talking, among other things, about forecasting the volume of production of all types of products, services and demand for them what is necessary for the activities of all sectors of the economy with details at hierarchical levels. For the tasks of this type the key is the problem of discrepancy of the upper and lower levels indicators. This problem cannot be solved by existing TD-BU models. This paper presents a mathematical model and methods for analytical determination of indicators of the upper and lower levels in the above problems, which solve the problem of ambiguity. The mathematical model is formed in such a way that provides an opportunity to find solutions for the upper and each of the lower (sectoral) levels in a unique, analytical form. Therefore, the search for solutions is non-iterative and not laborious. It is carried out in two stages. On the first of them, using known (standard) methods, forecasts are developed for preliminary indicators of the upper and lower levels. At the second stage a special system of algebraic equations is formed, from which analytical dependences for calculation of refined indicators of both levels are defined. This ensures a complete match between the upper indicator and the sum of the lower levels indicators, which is demonstrated by the example of forecasting electricity demand. These mathematical models and methods can also be used to reconcile the reporting indicators of the upper and lower levels of the respective objects (management structures, banks, trade network, etc.). Thus the coordinated decisions are formed in one stage.

At present, monetary models of equilibrium prices have received a very wide and varied application. In this paper it is proved that the application of the currently existing monetary models of the intersectoral balance is associated with significant methodical errors. It is shown that price models based on the input balance provides such a balance only in unreal cases when the prices of all sectors are the same. For realistic conditions, when these requirements are not met, errors for these models reach unacceptable values. This article proposes and thoroughly investigated new price models based on output balances which do not have the said drawbacks. It is mathematically proven that the new models satisfy the output balances and do not have methodical errors. When used, they provide zero output imbalances for both theoretical and realistic data packets. Also in the paper the calculation results are presented both for the existing monetary models of input-output balance and for new price models using a wide set of initial data. The calculations performed confirm the theoretical conclusions of the article. It is also proved that the Leontief price model is a special case of the generalized model of price indices proposed in the work.