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生产函数,是用数学上函数的方法来研究生产系统的投入产出关系。通常是把一个生产系统的产出数量看作是随着系统投入的各生产要素的数量和各要素间的组合方式而变动的,即产出是投入的函数。生产要素,通常归结为资金和劳动,而要素间的组合方式,就反映了广义上的科技水平。至于产出和投入要素及其组合的具体对应关系,经济学者提出了很多假设。每种假设都有一定的实际的社会经济数据作为基础,有一定的道理,有一定的适用性,也有其局限性。从中,我们选择了较为多用的增长速度方程,作为研究钢铁工业科技进步状况的数学模型。
The production function is to study the input-output relationship of the production system by means of mathematical functions. The output quantity of a production system is usually regarded as the quantity of each factor of production invested by the system and the combination of elements, that is, output is a function of input. The factors of production are usually attributed to capital and labor, and the combination of elements reflects the scientific and technological level in a broad sense. As for the specific correspondences between output and input elements and their combinations, economists have put forward many assumptions. Each hypothesis has some actual socio-economic data as a basis, which has some truth, some applicability, and also has its limitations. From that, we have chosen a more versatile growth rate equation as a mathematical model for studying the state of science and technology in the steel industry.