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Discussion on marginal productivity papers

I. Limitations of marginal productivity theory

Marginal productivity theory is the cornerstone of neoclassical economic theory. Marginal productivity theory is a method used to clarify the remuneration of various production factors or resources that cooperate with each other in production. Usually, when the number of other factors remains the same, the decrease (or increase) of commodity output value caused by a unit of a certain production factor leaving (or joining) the production process is equal to the service remuneration or other remuneration of a unit of this production factor. It is obvious here that the remuneration of production factors depends on the technical conditions in the production process. In neoclassical theory, production function is generally used to show the technical relationship between input and output. The theory of marginal productivity is expressed by mathematical formula:

the production function of a manufacturer is Y=F(x,x,x,x……), y is the output in the production process, x, x … is the input in the production process, and f is the production function. In general, the production function satisfies the following assumptions: the input of output to production factors satisfies that the first-order partial derivative is greater than zero and the second-order partial derivative is less than zero, that is, the attached figure. The first-order partial derivative is greater than zero, which means that an equal increase in any factor of production will inevitably lead to an increase in physical output, that is, the marginal product is greater than zero, which is very easy to understand and can be said to be an axiom under the condition of market economy. It is not necessary for manufacturers to increase the input of one factor when the output decreases. The second-order partial derivative is less than zero, that is, the convex assumption of the production function, which indicates that the marginal product of a production factor will decrease with the increase of the input of the factor. This is a stronger assumption than the first-order derivative is greater than zero, which is the law of diminishing marginal product often used in economics. "In fact, this is not a law, but the * * * identical characteristics of most production processes". (Noe: Fan Lian: Microeconomics: Modern Viewpoint, Shanghai Sanlian Publishing House, Shanghai People's Publishing House, 199, p. 9. ) In the production process, if the reward of any factor exceeds the output value lost when using this factor less, then one unit of this factor of production will be used less, and if this imbalance is not eliminated, the use of this factor of production will continue to be reduced until it is equal, that is, the attached figure, (Note: In fact, the reward of the factor should be equal to the marginal revenue of product. Instead of the value ofmarginal product, the neoclassical marginal productivity theory mainly studies the perfectly competitive market, so the two are equal in quantity. ) where w[,i] is the reward (price) of the production factor x[,i], and p is the price of the product. This conclusion can be simply drawn from the given production function and the maximum profit of the manufacturer.

the theory of marginal productivity has two-factor forms and multi-factor forms to explain the demand of production factors. The two elements refer to total capital and total labor. In this form, the form of production function is Y=F(L,K), and L and K are the amount of labor and capital invested in the production process respectively. Multi-factor refers to the types of distinguishable factors used in the production process, which is the form adopted at the beginning of this paper. Two-factor form can simplify the theory of marginal productivity, but there is a fatal weakness in this model, that is, how to sum up the labor of different qualities and the capital of different qualities invested by a manufacturer. (Note: the problem of summation is the biggest difficulty encountered by the theory of marginal productivity, and marginal productivity needs a concept of total labor and capital. The summation of capital can only be realized by summing up its value (lattice), and the price of capital is affected by the marginal productivity of capital (interest rate) ) This is also the most heated issue in the capital debate in Cambridge in the last century. Multi-factor form avoids summing up different labor and capital, but it is far from reality, because it will make it difficult to establish the continuous differentiability of production function: many manufacturers' input factors are fixed, and it is impossible to increase or decrease one production factor alone without increasing or decreasing other production factors, that is, there is no substitution between production factors, so there is no way to obtain the marginal productivity of one factor, so the theoretical application scope of marginal productivity is very limited. This paper analyzes the scope of application of marginal productivity theory here. Therefore, a two-factor production model is adopted here, which divides the input of manufacturers into labor and capital abstractly, and how to put aside the problem of heterogeneous capital and labor summation, while abstractly thinking that labor and capital are homogeneous. In this way, the model of marginal productivity can be described as follows: for a manufacturer's production function Y=F(L,K), the remuneration of workers is also the salary chart, and the remuneration of capital is also the profit (interest) rate chart.

. Adding-up Problem)

Marginal productivity is very easy to be accepted intuitively, because it embodies a basic economic theory principle, that is, when other factors are fixed, the marginal income brought by one factor input is equal to the marginal cost, so as to maximize the profits of manufacturers. But there is a problem here: if each unit of each factor is paid according to the corresponding marginal productivity, then whether the output of the manufacturer is equal to the marginal products of all production factors, which is Y = MP [,L] × L+MP [,K ]× K. In 189, Wicksted elaborated this view in detail in "On the Coordination of Distribution Laws", "These distribution shares add up to the net output of each manufacturer." (Note: palgrave Dictionary of Economics, Volume 1, Economic Science Press, 198, pp. -; Schumpeter: History of Economic Analysis (Volume ), Commercial Press, 199, pp. 17-19. ) The detailed description of this conclusion is: when the production function is linear homogeneous, the marginal product of various input production factors multiplied by the sum of their inputs is exactly equal to their output value, which is the total coincidence, that is, Euler's theorem, thus making the marginal productivity more perfect in theory. If expressed by the price of products and the remuneration of production factors, we can get that the sum of the remuneration of various input factors is exactly equal to the total output value. (Note: euler theorem Y=MP[,L]×L+MR[,K]×K is multiplied by the product price P at the same time, and Y×P=w×L+r×K can be obtained. ) The (excess) profit of the manufacturer is equal to the income (gross output value) of the manufacturer minus the total remuneration (total cost) of various production factors, that is, the total amount is consistent and the profit of the manufacturer is zero. But there is a condition here, that is, the production function must be linear homogeneous, that is, the return on scale is constant.

in neoclassical economic theory, the homogeneity of production function is usually used to express the return to scale. Homogeneity is a mathematical concept, which shows that if a function F(x,y) meets the condition: P(ax,ay)=a[n]F(x,y), the function is n-degree homogeneous. If n=1, it is a first-order homogeneity, also known as linear homogeneity, that is, F(ax,ay)=aF(x,y). If a production function is a homogeneous production function of n times, then when n > 1, the production function is an increasing return on scale, when n < 1, it is a decreasing return on scale, and when n=1, it is a constant return on scale. This means that the total matching can only be established when the scale return is constant. It can also be easily proved that when n < 1, that is, when there is diminishing returns to scale, the total output value of the manufacturer is less than the sum of the rewards of various production factors, and there is a "total shortage"; When n > 1, that is, there is increasing returns to scale, the total output value of the manufacturer is greater than the sum of the rewards of various production factors, and there is a "total surplus". So, who will make up for the "shortage" and get the "surplus"? Obviously, in these two cases, the theory of marginal productivity has great defects, because it contradicts the increasing and decreasing returns to scale, unless it can be proved that these two situations do not exist in capitalist economy. It is unlikely that there will be diminishing returns to scale in the economy. If there is diminishing returns to scale, large enterprises can be divided into small enterprises for production, but this phenomenon rarely occurs in the real economy. Therefore, it is generally believed that the economic returns to scale are constant and increasing.

Third, the existence of increasing returns to scale

Increasing returns to scale is a common phenomenon in modern economy and an inevitable result of economic development. Judging from the history of capitalist development, production is gradually concentrated, and large-scale production can be divided into divisions, advanced equipment can be adopted, and senior experts can be hired to save management costs, all of which can improve production efficiency, which is enough to show that there must be an increasing scale in modern production. Smith first proposed that division of labor would lead to specialization, thus improving labor productivity and increasing returns to scale. Sraffa published the Law of Remuneration under Competition in February, 19 in the Journal of Economics, pointing out that "under the condition of pure competition, as long as the increase in output is accompanied by internal economy, manufacturers will not be in a state of complete equilibrium" and "increasing income is also inconsistent with the assumption of complete competition". Since then, it has opened the prelude to the theory of imperfect competition. There are also some economists who admit that there is an increasing return to scale, but "according to the viewpoint of replication, constant return to scale is the most natural phenomenon, but this does not mean that other situations cannot happen ... Incremental return to scale is usually applicable within a certain output range." It is doubtful to explain the existence of constant scale reward by copying, which is far from reality, because in the real world, people basically can't see that the way for manufacturers to expand production is to expand on the original scale, instead of building a new factory to copy the original factory. Fan Lian made a metaphysical mistake in thinking that constant scale reward. However, it is hard to deny the existence of increasing returns to scale.

iv. explanation of increasing returns to scale by marginal productivity theory

since increasing returns to scale is an inevitable phenomenon in modern production, marginal productivity theory must explain this contradictory increasing returns to scale.

One explanation is that there is no phenomenon of increasing returns to scale in the economy. The reason for increasing returns to scale is that there is a factor of production that promotes increasing returns to scale that has been ignored. As long as new factors of production are added, there will be no phenomenon of increasing scale in the production function: the production functions of two factors cannot explain the real situation of the real economy, and in the modern economy, the factors of production are also diversified. Science and technology, knowledge, education and other factors are added to the production function, and the production function becomes y = f (L, K, T, I, E ...), which makes the production function more and more complex. After this treatment, the production function becomes linear homogeneous, which can satisfy the total amount, thus making the theory of marginal productivity more perfect, and even further finding out the technology, knowledge and education in the production process. There is an obvious mistake in this theory. According to the nature of production factors, production factors play two roles, one is the input in the production process, and the other is to get corresponding remuneration in the production process. Although we can get the marginal productivity of science and technology, knowledge and education through complicated calculations, who gets paid according to the marginal productivity of these elements? Are they workers, capitalists or scientists? In addition, science and technology and knowledge are embodied in labor and capital, and cannot be separated from labor and capital. The form of production function should be y = f [L (t, i, e ...), k (t, i, e ...)]. In this way, from the logical analysis of mathematics, the independent variables must be independent, that is, they have complete freedom. If there is a correlation among technology, knowledge, education, labor and capital, it is impossible for them to be independent variables of production function at the same time, that is, to become production factors at the same time. Therefore, there is a logical contradiction in using the production function of multiple production factors to make it linear homogeneous, so that it can meet the total amount.