The production function has always been a focus of research in the field of economics.

Some of the ideas put forward by Marx in his production function theory actually contain some connections that are easily overlooked. For example, there is a fundamental connection between the vertical production function and the variable capital part of Marx's production function. Although this topic is rarely studied in depth, it is indeed worthy of our careful exploration.

Marx's production function has its own uniqueness.

In terms of time, it already existed in the early stages of the development of economics.

Its basic characteristic is a linear production function.

The linear production function here is not just a simple superposition of formulas. It is actually a systematic combing of various logical relationships from cost to output in the production model at that time.

In many traditional manufacturing companies, if the input of human, material and other resources remains stable, Marx's linear analysis method can clearly explain the relationship between output and input.

In addition, when Marx elaborated on the production function, he proposed the formula that W equals c plus v plus m. This formula reveals the composition and circulation process of value. This special setting is the core of accurately grasping its production function.

In the era of the rise of capitalism and the working class in the context of the industrial revolution, the production function proposed by Marx clearly reflected the characteristics of that era.

It reflects the input of production factors and the mode of value generation at that time.

Studying the production function requires certain ideas and methods.

Researchers base their research findings on a scale from specific to general.

It might start by just exploring the production laws of a particular industry, such as the British textile industry in the 19th century. Since this industry is restricted by geographical location and relies heavily on manpower, its production patterns present a unique pattern.

As the research deepens, researchers obtain data from multiple fields and conduct comprehensive analysis.

At this point we noticed that Marx’s production function can be expanded into the form of the CES production function, thus achieving the goal of generalization.

This approach has expanded people's understanding of the production function and is no longer limited to the original form of the production function proposed by Marx.

This research result did not happen overnight.

After a long period of accumulation of economic data, in-depth analysis of cases in various industrial regions around the world, and the unremitting exploration of many economists, these efforts have jointly laid a solid foundation for its development.

After this generalization, the laws of production that were difficult to understand in the past now become clear. Some complex production logic has now become easier to understand.

In the past, some scholars tried to use the Cobb-Douglas function to discuss Marx's production function.

In theory, this seems to be a means of exploring new research paths, but in reality there are many problems.

Taking an international economics collaborative research project as an example, the team modeled Marx's production function based on the Cobb-Douglas function. The results revealed that there were many distorted logics in Marx’s original economic theory.

When elaborating on the concept of variable capital, the Cobb-Douglas function failed to accurately reflect the movement characteristics of variable capital described by Marx and its close relationship with value production.

At that time, many regions, including some traditional industrial countries in Europe, were undergoing a period of transformation. In this context, research results are often difficult to match with actual economic changes.

When we clarify the ideas of Marx's production function, we can bring many benefits to ourselves.

First of all, in model construction, we can break away from the limitation of simply borrowing other functions for interpretation.

Based on Marx's theory, we can build a model that accurately displays productivity and value flow based on specific conditions such as various industries and social structures.

Take the currently emerging Internet industry as an example. Its components are significantly different from traditional industries. Based on Marx's production function theory, we can establish a corresponding data model.

It can also expand the dimension of research and integrate with the viewpoints of other schools of thought.

In the process of postmodern economics challenging traditional theories, we can start from Marx's production function theory and deeply explore the intrinsic connections and differences between the two, so as to enrich and improve the theoretical system in the field of economics.

The decomposition of the variable capital part of Marx's production function has special significance.

In the early stages of industrialization, the main inputs were workers' wages and the value of laborers.

From the perspective of geographical distribution, many large industrial cities in Europe have a large group of workers; in the capital composition of these cities, variable capital accounts for a very high proportion.

Decomposing this part helps to understand the value-added process.

Analyzing from the perspective of economic structure, the current market economy has developed to the financialization stage, and it is indeed more complicated to directly understand variable capital.

Decomposition can explain the direction of value creation and profit distribution logic from the source.

This has important implications for studying contemporary economic inequality and welfare distribution.

The vertical production function is closely related to the variable capital part of the production function proposed by Marx.

From a logical perspective, some elements of McKinsey's 7S model were incorporated into Marx's analysis of variable capital in the production function. This view is formed in the context of the combination of modern business management theory and classical economic theory.

Observing practical applications, we found that in the daily operations and management of large multinational enterprises, enterprises need to comprehensively consider the vertical connections in various aspects such as cost planning, staffing ratios, and production processes.

This connection is like a chain that closely connects all parts of the company's operations. This is similar to how variable capital connects different stages of value creation mentioned by Marx in the productivity function.

Do you find that the business operations or economic phenomena around you are related to these theories?