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In economics, the relationship between the input and output in production is called the production function. Production function refers to the relationship between part of the input and output as well as the relationship between all of the input and output.
So, it is a mathematical relationship between the amount produced and the factor of production used.
This study focuses on the production function with electricity consumption. It is the electricity consumption as an input. The enterprise production function with electricity can reflect both the technology level and management level of the production.
The production functions with electricity that we discussed above are the relationship between electricity consumption and production output, namely, the relationship between the changes of electricity consumption and those of production output.
As we all know, electricity consumption is also the function of other production factors. This means that a change in electricity consumption involves the changes in other production factors. As a result, the production functions with electricity describe the relationship between the one output and several production factors as inputs. However, it does not consider the mutual replacement of the production factors.
Electricity used for production has the following characteristics. First, necessity electricity is required for almost any type of production, for example, the irrigation, threshing, and storage of the provisions; the production of the secondary industry; as well as the distribution, operations, and service of the tertiary industry. Second, accuracy electricity consumption is a physical quantity which can be read from meters. Electricity consumption data is objective and unbiased. It can also be checked by electricity generation minus loss of transmission and distribution equals to electricity consumption. Thirdly, accessibility a smart meter can provide us with the electricity consumption per hour from the electrical equipment or the production line in a visualized manner. Finally, representativeness as a productive input, electricity consumption is in proportion to the other production inputs.
At a certain level of production process and technology, a unit of electricity as an input requires a corresponding and relatively constant input from other production factors. Therefore, electricity consumption can serve as the representative input indicator of production factors in the enterprise production. Conversely, the output can be described by quantity of product, sales revenue, profits, value added, and other enterprise production indicators, that is, a single representative input indicator and multiple output indicators. Therefore, the enterprise production functions with electricity is composed of production function of the quantity product, production function of revenue, production function of profit, production function of value added, and so on.
Cobb–Douglas production function is introduced, and readers can analyze and compare the difference between the production functions with electricity and the Cobb–Douglas production function (Harribey).
Because of these later it is a mathematical relationship between the amount produced and the factor of production used which are energy and population in our study so a mathematical model is an abstract, simplified, mathematical construct related to a part of reality and created for a particular purpose (Bender, 1978).
A model is a simplified mathematical representation of a system. In our system Figure 1, many features are likely to be important. Not all of them, however, should be included in the model. Only the few relevant features that are thought to play an essential role in the interpretation of the observed phenomena should be retained (Boccara, 2004).
Figure 1. Mind map of the system study
Energy security, the impact of energy use on the environment, fuel prices and fuel poverty are all issues at the forefront of public attention. The economics of energy is a vital element which contributes to our understanding of these complex issues and influences policy makers’ thinking as energy policy is determined (Evans, 2009).