# Econodynamics

Economic dynamics is an empirical science that studies emergences, motion and disappearance of value—a specific concept that is used for description of the processes of creation and distribution of wealth. Any economic theory deals with the interpretation of economic processes based on the law of production of value, and various scientific approaches differ in the choice of factors of production that determine, in the end, the creation of wealth. Marxists insist that only labor creates value, neoclassicists believe that, in addition to labor, capital must also be taken into account as the important source of value. Econodynamics demonstrates, and this is an achievement of V.N. Pokrovskii, that the observed substitution of labour be capital is, in fact, the substitution of labour by work of external energy sources, and the statement about the productive power of capital is a hoax that hides the real role of labor and energy in the production of value. Econodynamics offers a more adequate interpretation of economic growth and other phenomena. Econodynamics is based on the achievements of classical political economy and neo-classical economics and has been using the methods of phenomenological science to investigate evolution of economic system. Econodynamics has been proposing methods of analysis and forecasting of economic processes. The comprehensive review of the problems of econodynamics is given recently by Vladimir Pokrovskii.

## The Fundamentals
### Value and production factors

Economic events are considered as processes of creation, motion and distribution of value that is firstly measured as exchange value. The factor interpretation of the exchange value, accepted by Econodynamics, is based on the Smith-Marx's labour theory of value, according to which efforts of workers $L$ are the most essential production factor. The theory is completed by the law of substitution, which states that the workers efforts in production of value could be substituted by work of production equipment driven with outer sources of power. Econodynamics regards two distinctive characteristics of the production equipment: capital stock as value of production equipment (production capital) and capital service as a substitute for labour. The later is considered as an independent production factor, whereas capital stock is considered to be the means of attracting labour and energy services to the production. Econodynamics introduces a concept of substitutive work $P$, which is true work of production equipment, to characterize the functional role of machinery in production processes. The amount of production equipment is treated as physical capital $K$, measured by its value; the variable $P$ can be considered as a capital service, a concept that was discussed by Robert Solow. Production of value $Y$ can be considered as a function of the three production factors $Y=Y(L,P,K).$ The human efforts $L$ and substitutive work $P$ are the true sources of value, production equipment (physical capital $K$) is passive; the role of various appliances is to attract active factors to production, and in order to characterize this feature of capital, technological characteristics were introduced. The work of people is used directly, the usage of substitutive work is based on the preliminary activity of people in the study of the laws of nature, the design of technological schemes, the manufacture of production equipment and other things. In order to assess the impact of one of the production factors, the marginal productivity of production factors is used
| $\beta ={\frac {\partial Y}{\partial L}},\quad \gamma ={\frac {\partial Y}{\partial P}}.$ | (1) |
Econodynamics considers that not physical capital $K$, that is a measure of the production equipment itself, but its property to fulfill work to replace human efforts in the production of value. The description of mechanism of substitution requires introduction of a special production factor—substitutive work $P$ that is genuine work of production equipment, which fulfills the same operations as workers, but with help of external sources of energy. Capital (production equipment) $K$, as a production factor, is the means by which the active factors of production operate, and one needs some kind of characteristic of the quality of the physical capital used. The function of production equipment $K$ is to provide various means to attract labor $L$ and substitutive work $P$ to production: it is not so important how much equipment we have as what is the benefit of the equipment used. . The characteristic of this ability of capital is the amount of labor and energy per unit (by value) of production equipment
| $\lambda ={\frac {\Delta L}{\Delta K}},\quad \varepsilon ={\frac {\Delta P}{\Delta K}}.$ | (2) |
These quantities determine the necessary amounts, respectively, of labor and productive energy consumption per unit (in value measure) of the equipment introduced, and, therefore, are universal technological characteristics of the production equipment.
Although capital is not a value-producing factor, we can formally determine the marginal productivity of capital. Differentiating the relations $Y=Y(L,P,K),$ we find
| $\kappa ={\frac {\partial Y}{\partial K}}=\beta {\frac {\partial L}{\partial K}}+\gamma {\frac {\partial P}{\partial K}}$ | (3) |
This relation shows that the productivity of capital (production equipment) is reduced to the functioning of active production factors, $L$ and $P$, whereas the characteristics of the quality of capital appear: labor requirement and energy requirement.
The technological description assumes that work $P$ and labor $L$ should be considered as substituting each other, and the amount of production equipment, universally measured by its value $K$, should be considered complementary to the work ($L$ and $P$) of production equipment. Considering that the description should be valid for any starting point of time (the principle of universality), and assuming also that production is homogeneous, that is, the law of production of value does not change when the scale of production changes, we write the production function, which is the expression for the production of value in the form of two alternative relations
| $Y=\left\{{\begin{array}{lll}\xi K,&\quad &\xi >0\\[2mm]\displaystyle {Y_{0}\,{\frac {L}{L_{0}}}\left({\frac {L_{0}}{L}}{\frac {P}{P_{0}}}\right)^{\alpha }},&\quad &0<\alpha <1\end{array}}\right.,$ | (4) |
The subscript zero marks values of quantities in the base year. Time-dependent values of $\alpha$ and $\xi$ are interrelated internal characteristics of the production system. The time-dependent quantity $\alpha$ --- technological index --- is defined through dimensionless technological characteristics of production equipment
| $\alpha ={\frac {1-{\overline {\lambda }}}{{\overline {\varepsilon }}-{\overline {\lambda }}}}.$ | (5) |
The technological index $\alpha$ in equation (4) appears to be connected with technological characteristics, which can be evaluated independently, and, therefore, in contrast to the neoclassical theory the known production function does not contain arbitrary parameters.
That relation (5), the proof of which can be found in the cited monograph [2, Chapter~5], includes the level of technological development into production function. The characteristic of the production system $\alpha$ relates to the quality of the installed production equipment (physical, fixed capital $K$) and determines the efficiency of the usage of social resources, it determines the degree of substitution of the labor with productive energy.
Due to the equation (4), the Smith-Marx theory of labor value is supplemented by the law of substitution, which states that in the production of value, the work of external forces of nature through production equipment replaces the efforts of people; human efforts and the substitute work of external energy sources are the true and only sources of wealth. Two factors of production: labor efforts and the substitutive work of external energy sources are interchangeable and, in this sense, are equivalent, so that labor remains, in the end, in the words of Adam Smith, 'the only universal, as well as the only accurate measure of value, or the only standard by which we can compare the values of various goods at all times and in all places.' At the same time, the work of machines can be appreciated only insofar as machines, replacing the efforts of people, do what a person wants.

### The absolute measure of value

The extension of the labour theory of value with the law of substitution allows us to generalize the Smith-Marx's labour theory of value. and to provide a better correspondence with empirical evidence.
In the Smith-Marx's theory of value, it is postulated that estimate of the efforts of workers $L$ is an ultimate source of all created wealth (products), an absolute measure of value. When one accounts the effect of substitution of workers' efforts with the true work of the production equipment, one could expect, that the total amount of work on the production of value, which is the sum of properly accounted work of humans $L$ and work of production equipment (substitutive work) $P$, both measured in power units, could be an absolute measure of value, and one can write
| $Y\sim P+L$ | (5) |
This relation allows one to estimate the work needed for creation of wealth worth of one monetary units (energy content of monetary unit), which was done for different cases. For example, the mean value of 'energy content' of dollar of year 1996 in years 1960 - 2000 is $1.4\times 10^{5}$ J. The values of the 'energy content' of monetary units that are used for accounting change during the time, which shows that the used units of money do not present constant amounts of 'true' value. The absolute measure of value can be introduced as some amount of energy.
The direct methods of estimation of the substitutive work $P$ are developing for both past and future situations. For example, it is found that the total amount of substitutive work in the U.S. economy in 1999 can be estimated as $10^{18}$ J per year. It is approximately one hundred times less than total (primary) consumption of energy, which was about $97\cdot 10^{18}$ J in 1999. However, the amount of primary energy (energy carriers), which is needed to provide this amount of substitutive work, is about $25\cdot 10^{18}$ J. It is about 26% of total primary consumption of energy. Although one can easily find estimates of the total amount of primary energy carriers in the past, the biggest interest is caused by possible assessments of the future quantity of energy going to the substitution of workers' efforts in processes of the production. This is a problem, which has been considered specially.

### Value, Utility and Entropy

Econodynamics establishes relationship between the real wealth and abstract concepts of value, utility and entropy. The artificial products created by humans: buildings, machines, vehicles, sanitation, clothes, home appliances and so on, can be sorted and counted, so that one consider the amounts of quantities in natural units of measurement $Q_{1},Q_{2},...,Q_{n}$ and the prices of all products $p_{1},p_{2},...,p_{n}$ to be given, so that one can define increase in value of a stock of products as
| $dW=\sum _{j=1}^{n}p_{j}\,dQ_{j}.$ | (6) |
Due to dependence of prices on the amounts of products $p_{i}=p_{i}(Q_{1},Q_{2},...,Q_{n})$, one can hardly expect that form (6) is a total differential of any function. In other words, one cannot say that $W$ is a characteristic of the set of the products which is independent of the history of their creation. However, a function of a state, which is called utility function, can be introduced on the basis of relation (6). Indeed, the linear form (6) can be multiplied by a certain function, which is called integration factor $\phi =\phi (Q_{1},Q_{2},...,Q_{n})$, so that, instead of form (6), one has a total differential of a new function
| $dU=\sum _{j=1}^{n}\phi (Q_{1},Q_{2},...,Q_{n})\,p_{j}(Q_{1},Q_{2},...,Q_{n})\,dQ_{j}.$ | (7) |
The introduced function $U$ is called utility function (objective), taking into account that the properties of function $U$ coincide with those of the conventional utility function, which is introduced as {subjective} utility function connected with sensation of preference of one aggregate of products as against another. The above transformation of value to utility reminds us of the transformation of heat to entropy in thermodynamics. In other terms, analogy between theory of utility and theory of heat was discussed by von Neumann and Morgenstern (see item 3.2.1 of their work).
The artificial objects can be considered, as it was explained by Prigogine with collaborators, as far-from-equilibrium objects (dissipative structures), and to create and maintain them, the fluxes of matter and energy are necessary to run through the system. In our case, energy comes in the form of human efforts $L$ and work of external sources $P$ that can be used by means of the appropriate equipment. The creation of dissipative structures leads to decrease in entropy, and utility $U$ can be considered as a close relation to entropy $S$, though does not coincides with it. Considering that changes of internal energy in production of things can be neglected, one can write a thermodynamic relation
| $dU\approx -dS={\frac {1}{T}}(L+P).$ | (8) |
Reconciliation of the two points of view on the phenomenon of production leads to a unified picture that enables us to relate some aspects of our observations of economic phenomena to physical principles. A flux of information and work eventually determines new organisation of matter, which acquires forms of different commodities (complexity), whereby the production process is considered as a process of materialisation of information. The cost of materialisation of information is the work of production system. To maintain complexity in a thermodynamic system, fluxes of matter and energy must flow through the system.

### Innovation and technological progress

The earlier version of neoclassical production function ignores the technological progress at all. It was introduced later into neo-classical theory by hand, as a time-dependent factor $A(t)$ (growth accounting ). In contrast to this, the technological progress appears to be an internal property of the theory of ecodynamics. It is understood, first of all, as a progress in substitution of labour with work of production equipment in technological processes; the theory gives the expression
| $A(t)=\,\left({\frac {K_{0}}{K}}{\frac {P}{P_{0}}}\right)^{\alpha },\quad 0<\alpha <1$ | (9) |
The exogenous, according to the neo-classical theory, technological progress $A(t)$ appears to be connected with the ratio of substitutive work to stock of capital $P/K$, which can be considered as a measure of technological progress itself, independent on the assumption made in the neo-classical theory. Sometimes it is convenient to use the non-dimensional ratio of substitutive work to labour efforts $P/L$ as a characteristic of technological progress; this quantity can be interpreted as the number of 'mechanical workers', operating in the production processes, in line with an 'alive worker'. To the end of the last century, this ratio reaches, for example, 12 for the USA. Apart from this, equation (9) contains the technological index $\alpha$, which, due to relation (2), determines effectiveness of usage of production factors $L$ and $P$.

## Dynamics of development
### Equations of evolution

Production of value (for year, for example) $Y$ is a money estimate of 'useful' changes in our environment (in the form of useful consumer goods and services), which can be connected with production factors. To formulate the system of evolution equations of the production system, function (1) ought to be specified and dynamic equations for production factors $L$, $P$ and $K$ to be formulated, while necessary technological characteristics of production equipment to be introduced. In result, it came to the set of equations of economic growth—the theory of evolution, dubbed as the technological theory of social production. The theory is formulated both in one-sector, and, using the Wassily Leontief's input-output model, in multi-sector approximations. The data for the U.S. economy in the last century was used to justify the specification of the theory. It was demonstrated that the substitution of worker's efforts with work of the production equipment appears to be more adequate idea than the substitution of worker's efforts with the amount of production equipment (capital in the neo-classical theory of economic growth); work can be replaced only with work, not with capital. The theory demonstrates that the growth of production is caused by achievements in technological consumption of labour and energy. The set of equations determines three modes of economic development, depending on deficit of one of the factors: investment, labour or substitutive work. The changing of modes during the development reveals as short cycles in growth—the business cycles.

### Applications

The theory can be applied to any national economy; principles of consistent analysis and forecast are considered. As an example, dynamics of Russian economy for years 1960 - 2060 is considered in one-sector and three-sector approximations(see. Chapter 8 and 9). The elementary, three-branch model is used (see. Section 2.2.2, Table 2.2 in Chapter 2 and Section 9.5 in Chapter 9) for the description of dynamics of production (the expanded reproduction, in Marx's terms).
The theory allows, being based on the Angus Maddison"s estimates of the Gross World Product and World population, to restore the picture of development of mankind in the previous centuries. It was shown (see, Chapter 12). that one need the theory, based on the effect of substitution of worker's efforts with work of external power (two-factor theory), for the description of the evolution of production activity from approximately year 1000 of our era. Before this time the substitution of human's efforts for outer work practically was not noticeable, and one can use one-factor theory that is taking into account only one production factor—efforts of workers. The theory is stated (see. section 1.3.1, the formula 1.1 in chapter 1 and section 12.3 in chapter 12).

### The principle of evolution

The human population, as any biological population obeys energy principle of evolution, which states that those populations and their associations (ecosystems) which can use the greater amount of energy from their environment have an advantage for survival. One can see that the social production system tries to swallow all available resources, productive energy included. This sentence can be considered as the principle of development of the production system and the human population itself, that has been developing as a self-organising system, trying to catch as much energy as possible.
A lot of energy is used by a human population through improvements of technology, and the managing huge amount of energy allows the human population to survive in every climate zone of the Earth and expand itself in great measure. The enlargement of the human population from a very small group a million years ago till about 7 billion in year 2012 ought to be apparently connected with enhancement of the living conditions. Apparently, it is impossible to explain growth of number of human population, not referring on social production system—the means of adopting the human to conditions of existence.