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## The hidden ideology in the neoclassical production function

In mainstream economics, the students are taught that the distribution of income is the result of an objective, and unbiased variable: productivity. In other words, it is stated that each factor would get what it contributes to the growth of the output, thus, the most productive factor will get a bigger slice of the pie. The purpose of this post is to show in a simple way the flaws of such reasoning and the political message it hides among mathematic equations.

We are taught in economics that increases in capital per worker (K/L) bring about increases in output per worker (Y/L) as more capital goods per person employed boosts the productivity of labor (you can find this idea from Smith to neoclassical economists). Then, a question arises: what portion of the output should go to the owner of the capital good used in the production process and what portion to the workers who operate such a capital?

Definitely, a portion of the income must replenish the worn-out capital goods. For instance, the machinery in any company must be replaced from time to time, then a percentage of the total output needs to be allocated to rebuild that machinery. Nevertheless, here we ran into another question; who should pocket the remaining value, the owner of the capital or the worker?

The Neoclassical economic explanation of income distribution

Neoclassicals have pretended to answer this question in an “objectively way” referring to the theory based on productivities of each factor of production, where labor and capital are paid according to their contribution to the output. In other words, each one gets what they deserve.

The above is illustrated as follows. The output of an economy Y equals their inputs, namely, labor L and capital K, along with their respective payments, wages w, and profits r. Hence, we have the accounting identity:

(1)

Y=wL+rK

Neoclassical economists usually express the relationship between output and inputs by a Cobb-Douglas function:

(2)

Where the growth of Y depends on the number of workers engaged, the value of the capital stock, and a residual A. α and β are the labor and capital shares of income.

The residual A is the so-called Total Factor Productivity (TFP), which means the portion of the output growth that is not accounted for by the growth of each factor of production. The TFP can be interpreted in many ways and is stated as a measurement of efficiency or productivity (after all it is what is explained by neither labor nor capital).

The TFP can be interpreted as all those variables that neither labor L nor capital K accounts for, hence, it could be a matter of externalities, technical change, better management of resources, institutional changes that create new incentives. Well,  who knows.

There is something wrong here, technically speaking

The employment of the production function by neoclassical economics to explain income distribution has some flaws.

First of all, such a production function is, in reality, an accounting identity. As explained by Montier & Pilkington (2019), the “TFP is nothing more than the weighted average of real wage growth and profit growth, pure and simple” (p.4),  and the slowdown of the TFP does not have anything to do with productivity decline, it is the “reflection of the well-documented, very slow wage growth that has been observed.” (p.5).

The argument of Montier & Pilkington (2019) can be illustrated using the accounting identity (equation 1), and the production function (equation 2), making use of log differentiation. Let’s see.

Firstly, we can observe that output change ΔY equals the sum of each component change (stated by Δ).

(3)

ΔY=α(Δw+ΔL)+β(Δr+ΔK)

Secondly, the production function already illustrated in equation 2 can also be presented using log differentiation:

(4)

Y=A+αΔL + βΔK

Then, we can obtain A (the TFP) as a residual:

(5)

A=ΔY-αΔL - βΔK

Substituting ΔY for the definition shown in equation 3 we get the following expression:

(6)

A=α(Δw+ΔL)+β(Δr+ΔK)-αΔL - βΔK

Then, here we have the TFP debunked:

A=αΔw+βΔr

It is clear that the TFP represented as A, is no more than the result of the income distribution,  consequently, if wages lose share of output, the TFP will fall; it does not mean there is an issue with efficiency (productivity).

It takes time to believe it, why do so many researchers go on using the TFP?

Capital measurement is another mess

However, the difficulties related to the production function are not limited to TFP, capital measurement holds some complications too.  While it is well-known that labor is measured by the number of workers engaged or a number of hours worked, capital is made of a constellation of different types of goods with different characteristics.

Given the diversity of capital, it is not measured by a physical magnitude but by using market prices. Here is the main issue, as Robinson (1953-1954) asserted, prices are made of wages and profits, thus, prices of capital goods already incorporate the distribution between labor and capital.

Neoclassical economists cannot scientifically argue that the retribution of each factor of production is the result of their contribution to the output. They cannot demonstrate their argument empirically without tautological reasoning and without using a flawed production function.

The neoclassical tautological reasoning goes as follows. The payment of each factor of production depends on its individual contribution, but to know their contribution it is necessary to know the prices of capital goods, but the prices already embody the income distribution. It is nonsensical.

Capital is a physical object or a production relation?

The issues with capital come from the basics. The concept of capital according to Neoclassical theory is nothing more than the number of physical goods used to produce, such as structures, buildings, machinery, equipment, fertilizers, among others. But such a definition led us to think mistakenly that capitalism has existed since the human being started using capital goods, for example, the pyramids of Egypt or Mexico (which up to date generates rents thanks to tourism).

Capital was well defined by Marx (1865) as a relation of production where there are a group of people who owns the means of production and there are others who possess only the labor-power and sell themselves like any other commodity. Thus, capital is not a physical object or a factor of production as stated by neoclassical economics, it is a relation of production and the machine becomes capital only when the whole system is established and capital walks on its own feet.

From an aggregate and Marxist viewpoint, the Neoclassical concept of capital productivity is as wrong as the TFP. Capital cannot be productive because the only one who can be productive is the worker who is the source of value and the producer of means of production as explained in the post Labor is the cornerstone.

In this order of ideas, the main way to measure productivity from an aggregate perspective is labor productivity, namely, output per worker (Y/L).

The income distribution is a matter of political forces

Just to be clear, in a capitalist system, society should award those who save, invest, and take risks. However, the thing is that in the really existing capitalism a chunk of the capital invested is not the outcome of own effort and savings but is inherited and commands the labor of others in the society. Here ownership is the ruling factor instead of labor.

Then, how much of the output should be pocketed by the capital owners and how much by the workers? The answer must be found in the correlation of forces between the owners of the means of production and the workers, instead of looking for it in the imaginary-perfect competition world and in the mechanistic idea of marginal productivity.

The slice size of the pie taken by one and other is the result of political struggle between those who have contradictory interests as is explained in the post The unavoidable conflict in the income distribution.

If there are several flaws in the use of the production function and in the neoclassical theory of income distribution, why such a problematic subject is not studied deeply in the economics classes, or is not even mentioned? Maybe it is not only about the “sloppy habits of thought handed on from one generation to the next, as asserted by Robinson (1953-1954, p.81), but it has to do with the interest of those who are taken the big slice of the pie and do not want a political discussion of income and wealth distribution.

I tried to write this post in the shortest way possible, therefore, I put aside many criticisms on the production function and the Neoclassical theory of income distribution.

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