Discussion on marginal productivity papers

First, the 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, under the condition that the number of other factors remains unchanged, the decrease (or increase) of commodity output value caused by a certain factor unit leaving (or joining) the production process is equal to the labor remuneration or other remuneration of the factor unit. 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 express the technical relationship between input and output. The theory of marginal productivity is expressed by mathematical formula:

The production function of the manufacturer is y = f (x, x, x …), y is the output in the production process, 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 the equivalent increase of any production factor will inevitably lead to the increase of 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. When the output decreases, there is no need for manufacturers to increase the input of one factor. The second-order partial derivative is less than zero, that is, the convexity 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 that the first derivative is greater than zero, which is a common law of diminishing marginal products in economics. In fact, this is not a rule, but the same feature in most production processes. (Noe: Fan Lian: Microeconomics: A Modern Viewpoint, Shanghai Sanlian Publishing House and Shanghai People's Publishing House, 1994, p. 395. In the production process, if the reward of any factor exceeds the output value lost when using this factor less, then a unit of this factor of production will use less. If this imbalance is not eliminated, the use of this factor of production will continue to decrease until it is equal, that is, the attached figure. (Note: In fact, the reward of the factor should be equal to the marginal income of the product. Neoclassical marginal productivity theory mainly studies the perfectly competitive market, not the value of marginal products, so the two are equal in quantity. ) where w[, i] is the reward (price) of 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 manufacturer's maximum profit.

The marginal productivity theory has two elements and multiple elements to explain the demand of production factors. These 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-factors refer to the types of distinguishable factors used in the production process, which is the form adopted at the beginning of this paper. The two-factor form can simplify the theory of marginal productivity, but this model has a fatal weakness, that is, how to add up the labor of different quality and the capital of different quality invested by a manufacturer. (Note: Sum problem is the biggest difficulty in marginal productivity theory, and marginal productivity needs a concept of total labor and total capital. The sum of capital can only be realized by the sum of its value (lattice), and the price of capital is affected by the marginal productivity (interest rate) of capital. This is also the most intense issue in the capital debate in Cambridge in the last century. Multi-factor form avoids adding different labor and capital, but it is far from reality, because it will make it difficult to establish the continuously differentiable of production function: many manufacturers' input factors are fixed, and it is impossible to increase or decrease one production factor without increasing or decreasing other production factors, that is, there is no substitution between production factors, so the marginal productivity of one factor cannot be obtained, 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. How to put aside the problem of heterogeneity of capital and labor sum and think that labor and capital are homogeneous abstractly? 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 a wage graph, and the remuneration of capital is also a profit (interest) rate graph.

Second, the total matching problem (addition problem)

Marginal productivity is easily accepted intuitively, because it embodies a basic principle of economic theory, 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, is the output of the manufacturer equal to the marginal product of all production factors, that is, Y = MP [,L] × L+MP [,K ]× K In 1894, Wexter elaborated this point in detail in On the Coordination of Distribution Laws. (Note: palgrave Dictionary of Economics, Vol. 1, Economic Science Press, 1986, pp. 22-23; Schumpeter: History of Economic Analysis (Volume 3), Commercial Press, 1996, pp. 407-409. ) The detailed description of this conclusion is that 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, the euler 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 to get y× p = w× l+r× k. The (excess) profit of the manufacturer is equal to the income (gross output value) of the manufacturer minus the total reward (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 that the production function must be linear homogeneous, that is, the scale return 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) satisfies the condition: P(ax, ay)=a[n]F(x, y), then the function is homogeneous n times. If n= 1, it is linear homogeneous, that is, F(ax, ay)=aF(x, y). If a production function is n homogeneous production function, then when n > 1, the production function shows increasing returns to scale, when n < 1, it shows decreasing returns to scale, and when n= 1, it shows constant returns to scale. This means that the total matching can only be established if the scale income remains unchanged. It is also easy to prove 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 returns of various production factors, and there is a "total shortage"; When n > 1, that is, there is an increasing return to scale, the total output of the manufacturer is greater than the sum of the returns 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 marginal productivity theory 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 the 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 appears in the real economy. Therefore, it is generally believed that the return of economies of scale is constant and increasing.

Third, there is 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 centralized, large-scale production can be divided into divisions, advanced equipment can be adopted, senior experts can be hired, and management costs can be saved, all of which can improve production efficiency, which is enough to show that modern production must be growing in scale. Smith first proposed that the 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 the Journal of Economics 1926 12, pointing out that "under the condition of pure competition, as long as the increase of output is accompanied by the internal economy, manufacturers will not be in a state of complete equilibrium" and "the increase of income is also inconsistent with the assumption of complete competition". Since then, the prelude to the theory of imperfect competition has been opened. There are also some economists who admit that there is increasing returns to scale, but "according to the viewpoint of replication, constant returns to scale are the most natural phenomenon, but this does not mean that other situations cannot happen ... Incremental returns to scale are usually applicable within a certain output range." It is doubtful to explain the existence of constant returns to scale by copying, which is far from reality, because in the real world, people basically can't see that manufacturers expand their production on the original scale instead of building new factories to copy the original factories. Fan Lian made a metaphysical mistake. However, it is hard to deny the existence of increasing returns to scale.

Fourthly, the marginal productivity theory explains the increasing returns to scale.

Because 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 of increasing returns to scale is that a production factor that promotes increasing returns to scale has been ignored. As long as new production factors are added, the scale of production function will not increase: the production functions of the two factors can not explain the real situation of the real economy. In modern economy, the factors of production are also diversified, and factors such as science and technology, knowledge and education have been added to the production function. The production function becomes y = f (L, k, t, that is ...), which makes the production function more and more complicated. After this treatment, the production function becomes linear homogeneous, which can meet the total amount, thus making the marginal productivity theory more perfect, and even further finding out the role of science and 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 to invest 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 will be paid according to the marginal productivity of these elements? Are they workers, capitalists or scientists? In addition, 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, that is ...), k (t, I, e...)]. In this way, from the logical analysis of mathematics, the independent variable must be independent, that is, it has complete freedom. If there is correlation among technology, knowledge, education, labor and capital, they can't be independent variables of production function at the same time, that is, they can also become production factors. Therefore, there is a logical contradiction in using the production function of multiple production factors to make it linear homogeneous and satisfy the total amount.