Özet:

The purpose of the article is to substantiate and systematize theoretical knowledge about Allen production function and it is an attempt to apply it in the tasks of modelling, analysis, and production forecasting at enterprises. Methodology. In the presented work, estimation’s questions of unknown parameters of Allen function based on the least squares method and regression analysis on the basis of standard programs of the Excel are discussed; its belonging to neoclassical functions, as well as the most important economic and mathematical characteristics. In particular, in the framework of Allen production function, the formulas for average return of resources (capital productivity and productivity), marginal returns of resources, elasticity of output on factors need for productive resources, when there is a production output and one of the factors is given, also the replacement of resources (capital assets), the marginal rate of substitution of factors, the elasticity of replacement of resources (labour with capital). Results. Based on the assumption that Allen function belongs to the group of substitutional functions according to the equivalence principle, the formula of optimal capital formation is determined, which maximizes output at given total capital expenditures on the main production funds and labour remuneration (minimizes the total capital expenditures for a given volume of production). In addition, the calculation formulas for determining the maximum output (minimum total cost of capital) in terms of optimal capital stock are given. All the above indicators are summarized in the summary table of the main economic and mathematical characteristics of Allen production function. Practical implications. In the case when the model is based on empirical data that varies in time, for example, at one enterprise in a number of years, we are proposed to use the dynamic Allen production function, which explicitly includes the time factor. In both cases, the volume of the information base (sample size) is determined, which will ensure the representativeness of future conclusions regarding unknown parameters that are subject to evaluation. The article also considers Allen production function as an instrument for evaluating the economic efficiency of future investment in production in the usual and dynamic variants. Value/originality. The obtained theoretical and methodological aspects of Allen two-factor production function are illustrated in a practical example of construction, economic interpretation, and practical use of the model.

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