劳动价值论中的测度问题及数理表达——兼议价值与价格的矢量逻辑

Measurement Problem and Mathematical Expression on Labor Theory of Value——Vector Logic of Value and Price

市场活动空间是多维的,所以描述其活动的基础变量应该是矢量或者张量,但由于缺乏经济行为活动的背景空间,故把变量归结为一系列没有方向的标量。为寻找价值和价格表征为矢量形式的数理定义,更好地对经济学进行测度进而走精确化道路,以及更全方位地和自然进行对话,克服经济系统在调节部分自然问题上的乏力。根据惯性和劳动力假设,借助行为分析工具即矢量,先用一组正交且完备的指标分量构造商品的功能距离空间,并在其基础上定义影响价值的供给项因子即生产路线和劳动力,以及调制价值生成价格的反映消费者偏好的需求项因子即价格函数和赋价路线,并分析其间的相互作用。给出价值取决于供给项因子的命题,其表征为劳动力与按照其作用的生产路线的矢量点乘,即劳动力做的功;而价格在受供给项因子影响的同时,其还受需求项因子"赋价路线"的调制,其表征为劳动力、赋价方向以及生产路线在赋价路线上的投影间的矢量点乘,即劳动力做的有用功。最后为陈述价值和价格的关系,通过引入价值的表达系数,给出价值和价格的深层联络;同时为更好地理解价值和价格生成的推导过程,用实例加以演示。

The activity space of market is multidimensional, so vector and tensor should be the basic variables to describe its activities. However, due to the lack of background space of economic activities, variables are concluded as a series of scalar without direction. The authors try to find mathematical definition by taking price and price characterization as vector forms, measure e- conomics better to be more precise, and have a more comprehensive dialogue with nature to adjust the inadequacy of economic system in solving some of the natural issues. Under the assumption of inertia and labor force, and by borrowing vector as behavior analysis tool, the functional distance space of products is constructed. Based on this, supply factors such as product route and labor which influence value, and demand factors which represent consumer preferences are defined. More analysis is made on the relationships among the variables. The proposition that value depends on supply factors is proposed, characterized by the work done by labor; while price is influenced by supply factors, it is also modulated by demand factor, which is characterized by useful work done by labor. Finally, coefficient to express value is used to describe the relationship between price and labor, and examples are used to explain the forming process value and price.