Abstract
A new model of economic production process is proposed (in the form of a set of ODEs) based on an idea that nonconsumable factors of production facilitate the conversion of inputs to output in much the same catalytic way as do enzymes in living cells when transforming substrates into different chemical compounds. The output of a converging, multi-resource, single-product supply chain network is shown to depend on the minimum of its inputs in the form of the Leontief--Liebig production function, providing the validity of the clearing function approximation. In turn use of the clearing function is legitimate when the machine processing time is much shorter than the machine loading time.
Highlights
In its broad meaning, factor of production is any entity which can lead to increased output as its availability is increased
There is nothing surprising in that biological systems with their basic variables—concentrations of substances—are similar to economic ones, where variables are the quantities of products or commodities, and the role of enzyme concentration is played by the number of machines in a shop or automatic line
It is important to recognize that we use the notation of chemical reactions to describe things that combine and the things that they produce, and that this framework can be used to model higher-order phenomena in a similar way. It is comprehended from the above analysis, that kinetics of any oneproduct supply chain of arbitrary length with multiple resources would lead to the overall production function of the Leontief type, providing individual production nodes of the chain follow the generic mechanism similar to that of the enzyme catalysis
Summary
The neoclassical production function is a mathematical statement relating the rate of production of a certain finished, or partly finished, intermediate, commodity (output), Y , to a set of the involved factors of production, φ1, φ2, . . . , φn (e.g., [33]):. Funds are not materially transformed into an output they produce They are transforming tools that turn the involved inputs into a product, but are not themselves embodied physically in the product. A special case of production function implying zero substitutability between inputs is the Leontief technology [18, p. In the basic version of the Leontief technology, intended for static analysis, inputs are meant to be resource influxes In such sectors as agriculture, forestry and fishery the use of production function with stock arguments proved to be more appropriate because it is dictated by the very specifics of the relationship between yield (harvest, crop, catch, etc.) and nutrients. A path from primary resources to a finished product may run through a complex supply chain network of “elementary” production units—IO converters. We rather accentuate the emergent self-regulation in the system being considered, which is not due to external interference of any rational agents
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