.E.Slutsky's theorem, which establishes a relationship between the comparative statics indicators of this theory. In production theory (of the firm), the main problems are similar to those of consumption theory. Therefore, it is of interest to obtain a similar result within the theory of the firm. Similar results can be found in the academic literature across various approaches to formulating the problem of the firm. In this paper, we obtain relationships between the comparative statics indicators of the theory of the firm, which are analogous to Slutsky's theorem in consumer theory as interpreted by J.Hicks.

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