Profitability condition in the Leontief model

We consider a model input-output model of Leontief, in which each industry supplies its products to other industries and, accordingly, purchases products from them. In the case where the profit of the industries and the costs of output are given, the model dual to the model of Leontief allows us to calculate the equilibrium prices. The paper assumes that the price of products and production costs are set by the industries themselves. For the prices set by the industries, the task is to study their impact on the preservation of the interindustry balance. If we assume that industries are monopolists who, taking advantage of their monopoly position, seek to increase their profits by increasing the price of their products, then the problem arises of determining the conditions of profitability, that is, determining such a set of prices for the products of industries in which all industries make a profit. Assuming that the state cannot influence the prices of the monopolist, measures are proposed to influence the monopolists by the state by imposing restrictions on their profitability or by using cost-saving mechanism. The effectiveness of these measures is evaluated. For the proposed measures to influence monopolies, the conditions for maintaining the interindustry balance and the conditions for profitability are determined.