# Econodynamics

Econodynamics is an empirical science that studies emergences, motion and disappearance of value—a specific concept that is used for description of the processes of production and distribution of wealth. 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[1].

## The Fundamentals

### Concept of value

Economic events are considered as processes of creation, motion and distribution of value that is understood as exchange value without any factor interpretation. The factor theory of the exchange value is based on the Smith-Marx’s labour theory of value. according to which efforts of workers ${\displaystyle L}$  are the most essential production factor. It was impossible to explain the modern economic growth without introduction the second value-creating factor, closely connected with production equipment. The neoclassical economics has delabourated the ideas about productive force of capital and is using the value of production equipment ${\displaystyle K}$  as a characteristic variable.[2][3] In addition to it, econodynamics has been taking into account the functional role of production equipment, as a set of appliances that allow to substitute efforts of workers with work of outer sources of power. A new concept of substitutive work ${\displaystyle P}$  was introduced, to characterize the functional role of machinery in production processes. The law of substitution, which is one of the main principles of econodynamics, generalized the Smith-Marx’s labour theory of value.[4][5][6] and provide a new interpretation of neo-classical economics. The variable ${\displaystyle P}$  is true work of production equipment and is equivalent to workers’ efforts in entire relationship, so that the production of value ${\displaystyle Y}$  can be considered as a function of the two production factors

${\displaystyle Y=Y(L,P)}$

(1)

The extension of the labour theory of value with the law of substitution allows us to formulate the theory,[7][8] which, in fact, is a modification and re-interpretation of neo-classical theory of production with two production factors: labour ${\displaystyle L}$  and capital ${\displaystyle K}$ . The comparison of the theory with neo-classical theory growth accounting that introduce the technical progress as the exogenous factor ${\displaystyle A(t)}$  gives the expression

${\displaystyle A(t)=\,\left({\frac {K_{0}}{K}}{\frac {P}{P_{0}}}\right)^{\alpha },\quad 0<\alpha <1}$

(3)

The exogenous neo-classical technical progress ${\displaystyle A(t)}$  appears to be connected with the ratio of substitutive work to stock of capital ${\displaystyle P/K}$ , 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 ${\displaystyle P/L}$  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[6]. Technical progress, as an internal property of the theory, is understood as a progress in substitution of labour with work of production equipment in technological processes.

The introduction of the substitutive work ${\displaystyle P}$  could be useful, if one can measure the quantity. Although one can easily find estimates of the total amount of primary energy carriers, the biggest interest for our aims is caused by possible assessments of the quantity of energy going to the substitution of workers' efforts in processes of the production. This is a problem, which has been considered specially.[9] The direct methods of estimation of the substitutive work can be used for both past and future situations. For example, the total amount of substitutive work in the U.S. economy in 1999 can be estimated as ${\displaystyle 10^{18}}$  J per year. It is approximately one hundred times less than total (primary) consumption of energy, which was about ${\displaystyle 97\cdot 10^{18}}$  J in 1999. However, the amount of primary energy (energy carriers), which is needed to provide this amount of substitutive work, is about ${\displaystyle 25\cdot 10^{18}}$  J. It is about 26% of total primary consumption of energy.

### Value, Utility and Entropy

Econodynamics establishes relationship between the concrete 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 ${\displaystyle Q_{1},Q_{2},...,Q_{n}}$  and the prices of all products ${\displaystyle p_{1},p_{2},...,p_{n}}$  to be given, so that one can define increase in value of a stock of products as

${\displaystyle dW=\sum _{j=1}^{n}p_{j}\,dQ_{j}.}$

(4)

Due to dependence of prices on the amounts of products ${\displaystyle p_{i}=p_{i}(Q_{1},Q_{2},...,Q_{n})}$ , one can hardly expect that form (4) is a total differential of any function. In other words, one cannot say that ${\displaystyle W}$  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 (4). Indeed, the linear form (4) can be multiplied by a certain function, which is called integration factor ${\displaystyle \phi =\phi (Q_{1},Q_{2},...,Q_{n})}$ , so that, instead of form (4), one has a total differential of a new function

${\displaystyle dU=\sum _{j=1}^{n}\phi (Q_{1},Q_{2},...,Q_{n})\,p_{j}(Q_{1},Q_{2},...,Q_{n})\,dQ_{j}.}$

(5)

The introduced function ${\displaystyle U}$  is called utility function (objective), taking into account that the properties of function ${\displaystyle U}$  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 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 [10] (see item 3.2.1 of their work).

The artificial products can be considered, as it was explained by Prigogine with collaborators[11][12], as the far-from-equilibrium objects (the 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 ${\displaystyle L}$  and work of external sources ${\displaystyle P}$  that can be used by means of the appropriate equipment. The creation of dissipative structures leads to decrease in entropy, and utility ${\displaystyle U}$  can be considered as a close relation to entropy ${\displaystyle S}$ , 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

${\displaystyle dU\approx -dS={\frac {1}{T}}(L+P).}$

(6)

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 work of production system. To maintain complexity in a thermodynamic system, fluxes of matter and energy must flow through the system.

## Dynamics of development

### Equations of evolution

To formulate the system of evolution equations of the production system, function (1) ought to be specified and dynamic equations for production factors ${\displaystyle L}$ , ${\displaystyle P}$  and ${\displaystyle K}$  to be formulated, while nessasery 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 onky 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.[13] The changing of modes during the development reveals as short cycles in growth—the busyness 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[1]. Chapter 8 and 9). The elementary, three-branch model is used (see[1]. 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 [1], 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[1]. section 1.3.1, the formula 1.1 in chapter 1 and section 12.3 in chapter 12).

### The principle of evolution

One can see on raw of examples that the production system, indeed, tries to swallow all available resources.[7] 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. 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.[14][15] 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.[16]

## The absolute measure of value

Production of value (for year, for example) ${\displaystyle Y}$  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. In the Smith-Marx's theory of value, it is postulated that estimate of the efforts of workers ${\displaystyle L}$  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 ${\displaystyle L}$  and work of production equipment (substitutive work) ${\displaystyle P}$ , both measured in power units, could be an absolute measure of value, and one can write

${\displaystyle Y\sim P+L}$

(7)

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[6]. For example, the mean value of 'energy content' of dollar of year 1996 in years 1960 - 2000 is ${\displaystyle 1.4\times 10^{5}}$  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.

## References

1. Pokrovskii, Vladimir (2018). Econodynamics. The Theory of Social Production. The 3rd Ed. https://www.springer.com/gp/book/9783319720739: Springer, Dordrecht-Heidelberg-London-New York.CS1 maint: location (link)
2. ^ Cobb, G.W. and Douglas, P.N. (1928). "A Theory of Production." American Economic Review, Suppl. (March), pp. 139-165.
3. ^ Solow, R. (1957). "Technical Change and the Aggregate Production Function." Review of Economic Studies, vol. 39 (Aug.), pp. 312-330.
4. ^ Beaudreau, B.C. (1998). Energy and organization: Growth and distribution reexamined. Greenwood Press.
5. ^ Pokrovskii, V.N. (2008). ") An extension of the labour theory of value" (PDF). Pluralist Economics Review (February).
6. ^ a b c Beaudreau, B.C. & Pokrovski, V.N. (2010) On the energy content of a money unit. Physica A: Statistical Mechanics and its Applications, 389 (13), 2597–2606.
7. ^ a b Pokrovski, V.N. (2003). "Energy in the theory of production." Energy 28, 769-788.
8. ^ Pokrovskii, Vladimir (2011). Econodynamics. The Theory of Social Production. https://www.springer.com/physics/complexity/book/978-94-007-2095-4: Springer, Dordrecht-Heidelberg-London-New York.CS1 maint: location (link)
9. ^ Pokrovski, V.N. (2007) Productive energy in the US economy, Energy 32 (5) 816-822.
10. ^ Neumann, John von & Morgenstern, Oskar (1944). Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.
11. ^ Prigogine, I. (1980). From being to becoming: Time and complexity in the physical sciences. New York: Freeman & Company.
12. ^ Nicolis, G.; Prigogine, I. (1977). Self-organisation in non-equilibrium systems: From dissipative structures to order through fluctuations. New York: John Wiley \& Sons.
13. ^ Pokrovskii, V.N. (2011) Pulsation of the growth rate of output and technology. Physica A: Statistical Mechanics and its Applications, Vol. 390 (23-24), 4347-4354.
14. ^ Lotka, A.J. Elements of Physical Biology, Williams and Wilkins, Baltimore, 1925.
15. ^ Odum, H.T. Environmental Accounting. Energy and Environmental Decision Making, John Wiley \& Sons, New York {\it etc}, 1996.
16. ^ V.N. Pokrovski, Physical Principles in the Theory of Economic Growth, Ashgate Publishing, Aldershot, 1999. A revised and extended version of the monograph is published by Springer (2011) as Econodynamics. The Theory of Social Production.