О свойствах производственных CES-функций в модели производства с промежуточными товарами

Экономика и математические методы. 2016. Т. 52. № 2. С. 91–102.

Matveenko V., Бронштейн Е. М.

CES production functions are widely used in economic growth and development researches. However, it is not always taken into account that properties of different specifications of CES functions (continual or discrete, with the weights or without them) are rather differ. The properties of CES production functions, essential for analysis of economic models, are studied. We prove that the CES function with a finite number of arguments with normalized weights increases with the elasticity of substitution parameter, while under the absence of weights the function decreases in this parameter. Pattern of behavior of the CES function with argument x(i), defined on a continual set [0,N], is operated by the value N. Under N = 1 the function with continual argument behaves (in respect of the elasticity of substitution) similarly to the function with a finite number of arguments with weights, but under N > 1 its behavior is quite different. There are important differences between the continual and the discrete CES functions when the elasticity of substitution parameter converges to zero. We show the mistakes when continual CES functions are applied to models of production with intermediate goods which have gained popularity in recent years. We also show some shortcomings of continual models with intermediate goods when using these models for the analysis of economic development problems.

Keywords: производственная функция, production function, CES-функция, minimum, CES functions, continuous and discrete economic models, essential infimum, континуальные и дискретные модели экономики, монотонность по параметру, минимум, существенный инфимум