Marginal productivity

Economic terminology

Marginal productivity theory It's neoclassical economic theory The cornerstone of. The theory of marginal productivity is used to clarify various kinds of cooperation in production production factors Or a way of getting paid for resources. Usually, when the number of other factors remains unchanged, the unit of a certain factor of production leaves (or joins) Production process The decrease (or increase) in the output value of commodities caused by time is equal to the service remuneration or other remuneration of a unit of the factor of production. stay Neoclassical theory Medium, general production function To show the technical relationship between input and output.

Chinese name: Marginal productivity
Foreign name: Marginal productivity
Form: Marginal productivity theory There are two element forms and multi element forms to illustrate production factors Of requirement 。 The two elements refer to total capital and total labor. In this form, production function In the form of Y=F (L, K), L and K are respectively the amount of labor and capital invested in the production process.

Interpretation: Increasing returns to scale It is an inevitable phenomenon in modern production, so the marginal productivity theory must explain this contradictory increasing returns to scale.
Field: Economics

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Marginal productivity theory There are two element forms and multi element forms to illustrate production factors Of requirement 。 The two elements refer to total capital and total labor. In this form, production function In the form of Y=F (L, K), L and K are respectively the amount of labor and capital invested in the production process.

Multi factor refers to the types of distinguishable factors used in the production process, which is the form adopted at the beginning of this article. The two factor form can simplify the marginal productivity theory, but this model has a fatal weakness, that is, how to sum up the heterogeneous labor and capital invested by a manufacturer, (Note: The problem of aggregation is the biggest difficulty encountered by the theory of marginal productivity. Marginal productivity requires a concept of total labor and capital. The aggregation of capital can only be achieved by aggregating its value (lattice), and the price of capital is affected by the marginal productivity of capital（ Interest rate ）That is the Wicksell effect, which makes the marginal productivity theory a Circular argument 。）

This is also in the last century Cambridge Capital Debate The most intense question. Multi factor form avoids the aggregation of different labor and capital, but this form is far from reality.

Because this form will make production function The nature of continuous differentiation is difficult to hold: many manufacturers' input factors are Fixed scale , it is impossible to add or subtract one production factors Without adding or subtracting other factors of production, that is, there is no substitutability between factors of production, so there is no way to obtain the marginal productivity of one factor, so the theoretical scope of application of marginal productivity is very limited.

What this article analyzes here is Marginal productivity theory Therefore, the two factor production model is adopted here, which abstractly divides the input of manufacturers into labor and capital, and how to put aside the problem of heterogeneous capital and labor aggregation, but abstractly believes that labor and capital are homogeneous.

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Increasing returns to scale Is an inevitable phenomenon in modern production, then Marginal productivity theory It is necessary to explain this contradictory increasing returns to scale.

One explanation is that there is no Increasing returns to scale The reason for increasing returns to scale is that production factors Was ignored by people.

As long as new production factors are added, production function There will be no phenomenon of increasing scale: the production function of the two factors cannot explain the real situation of the real economy. 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...), Thus, the production function becomes more and more complex. After such processing, the production function becomes linear Homogeneity We can be satisfied with the total amount, and even further find out the role of science and technology, knowledge, education, etc. in the production process. There is an obvious mistake in this theory production factors The production factors play two roles, one is the inputs in the production process, and the other is to get corresponding rewards in the production process. Although we can calculate the marginal productivity of science, technology, knowledge and education through complex calculations, who gets its reward according to the marginal productivity of these elements?

Are they workers, capitalists or scientists? In addition, science, technology and knowledge are embodied in labor and capital, and cannot be separated from labor and capital, production function The form of should be Y=F [L (T, I, E......), K (T, I, E......)]. In this way, from the mathematical logic, independent variable They must be independent, that is, they have complete degrees of freedom. If technology, knowledge, education, labor and capital exist relevance , they cannot be used as independent variables of the production function at the same time, that is, they can be production factors 。 Therefore, there is a way to make the production function with multiple factors of production linear homogeneous so that it can meet the total amount Logical contradiction 。

Another method of explanation is to change the production function. It is believed that the production function is constantly changing, that is, the production function is dynamically changed into Y=F [, t] (L, K). It is believed that there is no Increasing returns to scale , only exists Constant return to scale The reason why Return to scale Because over time, production function Has changed, and the main reason for this change is attributable to technical progress This leads to the movement of the production function.

Here, we use mathematical form to explain: in static state, the form of production function is Y=F (L, K). Since the scale reward is unchanged, that is, there is linear homogeneity, we can get: Y/L=F (L, K)/L=F (1, K/L), and Y/L is the output of unit labor, that is labour productivity , we use y, K/L is Capital labor ratio , we use k to express, then the production function can be expressed as y=F (1, k), we use a new function f (k) to represent F (1, k), then we can conclude that the linear homogeneous production function can be expressed in the form of: labor productivity is a function of the capital labor ratio, generally, this function is Convexity , that is, f ′ (k) ＞ 0, f ″ (k) ＜ 0 (as f [, 1] (k) in the figure).

Over time, technological progress has changed production function The production function moves from f (, 1) (k) of time t [, 1] to f [, 2] (k) of time t [, 2]. In this way, at each static time point, the production function is linear homogeneous, so the principle of total amount equality can be met, thus production factors We can get corresponding remuneration according to the marginal productivity. At different times, the movement of this production function reflects the impact of technological progress on the production process. The changing production function is not conducive to mathematical analysis Therefore, the production function Y=F [, 1] (L, K) is transformed into Y=F (L, K, t), where t represents time.

Further, Neoclassical theory And expand the production function to the macro Aggregate production function , factor t does not include Increase capital and Labor input Its contribution to technological progress is the rest after deducting the impact of increased labor and capital input. Obviously, this processing method It is the same as the former method, except that the factors such as technology, knowledge and education are all attributed to the change of time.

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