Using the formalism of Lyapunov potential function it is shown that the stability principles for biomass in the ecosystem and for employment in economics are mathematically similar. The ecosystem is found to have a stable and an unstable stationary state with high (forest) and low (grasslands) biomass, respectively. In economics, there is a stable stationary state with high employment, which corresponds to mass production of conventional goods sold at low cost price, and an unstable stationary state with lower employment, which corresponds to production of novel goods appearing in the course of technological progress. An additional stable stationary state is described for economics, the one corresponding to very low employment in production of life essentials such as energy and raw materials. In this state the civilization currently pays 10% of global GDP for energy produced by a negligible minority of the working population (currently ~0.2%) and sold at prices greatly exceeding the cost price by 40 times. It is shown that economic ownership over energy sources is equivalent to equating measurable variables of different dimensions (stores and fluxes), which leads to effective violation of the laws of energy and matter conservation.
Biomass of any type exists in the biosphere in the state of dynamic ecological equilibrium sustained by the balance of synthesis and decomposition. Biomass is synthesized by living organisms, i.e. by living biomass itself. At zero biomass the rate of its synthesis is zero. It grows with increasing biomass of the synthesizing organisms. However, biomass synthesis is ultimately limited by the incoming flux of solar radiation. When all the solar radiation available for synthesis is claimed by the synthesizing organisms, the rate of biomass synthesis reaches its maximum value, which is biomass-independent.
In contrast, decomposition of organic matter by living organisms does not depend on solar radiation. There are no physical limits to biological decomposition, which could, in principle, occur at any rate exceeding the rate of synthesis. If the rate of decomposition permanently exceeded the rate of synthesis, all biomass would have been destroyed and life on Earth ceased. In this paper, using the formalism of Lyapunov potential function, we determine the quantitative conditions accounting for the stability of life and explore why these conditions are apparently fulfilled in the biosphere (Section 2).
The amounts of goods and services instantly available in the market are, similarly to biomass in the biosphere, maintained in the state of dynamic equilibrium by the processes of their production and consumption, i.e. by the balance of offer and demand. We demonstrate that the equations for biomass change in the biosphere are mathematically equivalent to the equations for employment in the output of goods and services in economics. In economics a universal monetary indicator (market price) of the amounts of goods and services available in the market is employed. Using Lyapunov function we determine conditions for the stability of market prices on goods and services (Section 3). It is found that there is a non-zero stable equilibrium value of market price, which can be meaningfully interpreted as equal to the cost price, the latter numerically defined in terms of labor costs associated with the production of goods and services.
For the novel expensive goods, i.e. goods that appear as products of technological progress, market prices are found to be unstable. Such goods are characterized by an unsaturated demand and, at the moment of their appearance in the market, have a market price significantly in excess of their cost price. Expansion of the output of such goods with an increase in the number of people involved in the corresponding production processes leads to an increase of the amount of goods available in the market and fall of their high initial price. With market price of the novel expensive goods diminishing towards their cost price and with gradual saturation of the demand, the goods enter the category of conventional goods, i.e. goods that, at any time of civilization development, make up most of the consumer basket and have a stable market price (Section 4).
Energy and raw materials are used as the indispensable foundation for production of all goods in the civilization and, as such, represent a very special phenomenon in economics, being fundamentally distinct from any other economic realities. If these distinctions are ignored (as is the case in modern economic theory) and energy and raw materials are considered as free market commodities, then, as follows from analysis of Lyapunov function, their market price, unlike that of novel expensive goods, remains stable at its maximum value. By analyzing the world employment data for the energy sector, it is estimated that the average cost price of energy is several dozens of times lower than its modern market price (Section 5).
Unlike with novel expensive goods, the maximum market price of raw materials and energy can never be reduced, because consumption of raw materials and energy is, at any time, saturated and cannot be dramatically increased. Neither can production of raw materials be increased by rising employment in the corresponding economics sectors. Therefore, market price of raw materials and energy remains fixed at its maximum value. This value is the maximum price that the world economy can still afford to pay without self-destruction, currently spending on energy about one tenth of global gross domestic product. Therefore, with increasing global gross domestic product market prices of energy can only grow (Section 6).
The dimensional analysis of stores and fluxes in economics proves that privatization of sources of raw materials and energy is equivalent to equating measurable variables of different dimensions. This violates the laws of matter and energy conservation in economics (Section 7), thus decelerating technological progress and economic growth, destabilizing modern civilization and barring solutions of global environmental problems (Section 8).
Temporal changes of the amount M (dimension kg) of any type of biomass in the biospher
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