Eco-mechanisms within economic evolution – Schumpeterian approach

Supporting eco-innovations and economic eco-activities is one of a important challenge to decision makers. The above is related to the problem of specification of mechanisms resulting in introducing eco-innovations. The original vision of the economic evolution determined by innovation was firstly presented by Joseph Schumpeter who identified essential innovative changes as well as indicated different mechanisms governing the economic evolution. The aim of the paper is to suggest a cohesive topological approach maintained in the stream of Schumpeter’s thought, to study changes in the economy, which result in the elimination of at least one harmful commodity or technology from the market, by incorporating Hurwicz apparatus in a suitably modified competitive economy. Qualitative properties of mechanisms which can occur within the economic evolution are also analyzed.


Introduction
"Eco-innovation is any innovation resulting in significant progress towards the goal of sustainable development, by reducing the impacts of our production modes on the environment, enhancing nature's resilience to environmental pressures, or achieving a more efficient and responsible use of natural resources" (Europa.eu› eu › pubs › pdf › factsheets › ec). In the interest of each community is introducing eco-innovations and eco-activities and the above should be the most important task and the challenge to decision makers. In this context economic ecomechanisms, i.e. economic mechanisms bringing changes beneficial for the environment, are worth to be studied. The concept of eco-innovation was widely explored (see Arundel, Kemp 2009, Joller 2012Rennings 2000;Carrillo-Hermosilla, del Rio and Könnölä 2010;Faucheux, Nicolaï, 2011;Antonioli, Borghesi and Mazzanti 2016;Crespi, Mazzanti and Managi 2016;Leal-Millán, Leal-Rodríguez and Albort-Morant 2017;Szutowski, Szulczewska-Remi and Ratajczak 2017;Dewick, Maytorena-Sanchez and Winch 2019).
Defining and analysis of the rules governing economic life were in the focus of interest of Joseph Schumpeter (1912Schumpeter ( , 1934Schumpeter ( , 1950Schumpeter ( , 1964. Schumpeter (1950)  The Schumpeter's ideas found many followers. Nelson and Winter (1982) initiated the neoschumpeterian research program as well as significantly developed the Schumpeterian ideas, among others, by, respecting the paradigm of the bounded rationality (see for instance Hayek 1945;Alchian 1950;Simon 1947Simon , 1957 and criticism of the principles of the perfect rationality as they were not reflected in the economic life, focusing, opposite to the neoclassical and Keynesian conceptions, on the mesosphere of the economy as it was the area of occurrence of innovative processes as well as applying the strict methodology of mathematical modeling of economic development. Howitt (1992, 1998), who laid down the beginning of the theory of endogenous economic growth, saw the source of economic development in the effectiveness of activities of the R&D sector, but not in the accumulation of capital, as it was in case of the Solow's neoclassical theory of economic growth (Romer 2012).
Our analysis takes static as well as dynamic forms of the economy. Such approach is fundamentally different from the main stream of modern studying of the Schumpeterian evolution which includes two paths of economic theorizing, i.e., neo-Schumpeterian research program (Hanusch, Pyka 2007;Day 2007;Andersen 2009;Foster 2011;Freeman 1982;Malerba, Orsenigo 1995, 1997Nelson 2016;Witt 2017) and Schumpeterian endogenous growth theory (Dosi et al. 2010, Assenza et al. 2015Dawid et al. 2019;Almudi et al. 2019aAlmudi et al. , 2019b. The difference can be seen in the mathematical setting based on the set-theoretical and topological apparatus which is borrowed from general equilibrium theory. The motivation for using the general equilibrium framework in our paper is clear -Schumpeter's vision on economic evolution was strongly inspired by Walrasian thinking (cf. Hodgson 1993;Andersen 2009). However, it should be emphasized that the central idea of general equilibrium has been only a starting point for Schumpeter's study on economic development which runs far beyond equilibrium schemata (Malawski 2013;Malawski 2005Malawski , 2008Malawski, Woerter 2006;Ciałowicz, Malawski 2011;Lipieta, Malawski 2016). On the one hand, the employment of such specific methodology maintains our research in the main stream of Schumpeter's thought, on the other hand gives an opportunity to avoid some strong mathematical assumptions (such as differentiability of utility functions) not realistic in the analysis of economic objects. However, above all, we aim at analysis and specification of various kinds of mechanisms that can occur or be implemented within the evolution of the economy with particular focus on ecomechanisms. Some partial results on modelling mechanisms of economic change within which harmful commodities or technologies were reduced from agents' activities were presented in (Lipieta 2010(Lipieta , 2015. In difference to the above, we suggest a model of Schumpeterian economic evolution within which, at its every stage, eco-mechanisms can be implemented (Example 1, Theorems 1 -3).
The mechanisms presented are formed in the conceptual apparatus of the Hurwicz theory (see Hurwicz, Reiter 2006), while the economic transformation is modelled as an adjustment process (Hurwicz 1987). The Hurwicz mechanism design theory begun with the paper by Leonid Hurwicz (Hurwicz 1960). It aimed at formalizing institutions and economic processes to examine how they could achieve optimal outcomes (Hurwicz 1987). Later, in mechanism design theory the problems of incentives (Hurwicz 1972), uncertainty (Marschak & Radner 1971;Radner 1972) as well as the roles of the signals based on agents' private information (Mount and Reiter 1974) were taken into account. The above made that economic mechanisms in the sense of Hurwicz could be applied in many areas of economic theory.
The paper consists of five parts. In the second part, the economy in the form of the circular flow is modelled, the third part takes characterization of innovative changes. The fourth part is devoted to the mathematical model of the economic evolution, while in the fifth part various kinds of eco-mechanisms in the framework of the economic evolution are specified.
The paper is closed with Conclusions.

The economy in the form of the circular flow
Schumpeter distinguished two forms of economic life: the circular flow and the economic development (Schumpeter 1912(Schumpeter , 1934(Schumpeter , 1950(Schumpeter , 1961, however, the relationship between these two forms has not been presented by Schumpeter in a satisfactory way (see Shionoya 2015; Lipieta, Malawski 2016). As it was emphasized (Schumpeter 1961;Lipieta, Malawski 2016), the economy in the form of the circular flow due to Schumpeter's analogy reminds of the circulation of blood in a living organism. Thus, in the form of the circular flow, an economic system has the tendency to equilibrium state to determine prices and quantities of goods, the changes in activities of economic agents do not occur, or are so small that they do not influence current economic processes as well as operating of firms and consumers. The above lead us to the modelling the economy in the form of the circular flow by the use of the apparatus of theory of general equilibrium (Arrow, Debreu 1954;Mas-Colell et al. 1995).
At the beginning, we focus on the case when the activities of economic agents do not change within the given time interval. It is convenient to consider the countable number of inactive agents and a finite number of active agents, endogenously determined in the model. Such setting reflects the main premises of the creative destruction principle, namely that an unknown number of potential future producers "wait" for the proper time for themselves to enter the market or some of them are, or will be, eliminated from the economic life. Similarly, an unknown number of consumers may appear on the market in the future. First the production sphere of an economy will be defined. Let

•
= ( ) ∈ℕ -be a countable set of producers, • : ∋ → ⊂ ℝ ℓ -be a correspondence of production sets, which to every producer assigns a non-empty production set ( ) = ⊂ ℝ ℓ of the producer's feasible production plans as well as • ∈ ℝ ℓ be a price vector.
The producer for which ( ) = {0} is called the inactive producer while the producer for which ( ) ≠ {0} is called the active one. The elements of set ( ) are called the optimal plans of producer . Let us recall (Lipieta, Malawski 2016) that, in the spirit of the assumption of bounded rationality (Simon 1955), in the quasi-production system, the aims of producers are not specified, while in the production system, producers maximize profits at given prices and technologies.
Definition 2. The three-range relational system = ( , ℝ ℓ , Ξ; , , , ) is called the quasi-consumption system. If, for every ∈ , then the quasi-consumption system is called the consumption system and denoted by .
Similarly to the case of producers, the consumer for which ( ) = {0} is called the inactive consumer while the consumer for which ( ) ≠ {0} is called the active one. In the quasiconsumption systems, the upper bound for preference relation on a consumer's budget set does not have to exist. However, according to the assumption of perfect rationality, every consumer realizes one of his optimal plans of action if any exists. Now, we can assume the following definition, which is a slight modification of the original Arrow and Debreu economy (compare to Arrow, Debreu 1954;Debreu 1959;Mas-Colell et al. 1995;Lipieta 2010): Let ̃= { 1 , … , } and ̃= { 1 , … , }.
If is the production system ( = ) and is the consumption system ( = ), then private ownership economy with almost all inactive agents ℇ will be denoted by ℇ = (ℝ ℓ , , , , ) or in short ℇ = ℇ.
The private ownership economy with almost all inactive agents operates as follows. Let a price vector ∈ ℝ ℓ be given. Every producer ∈̃, realizes a production plan ̃∈ ( ).
For > , it is assumed that ̃= 0 ∈ ℝ ℓ . It means that, for > , producer is not active in the economy at the given moment ( ∈ \̃). The profit of each active producer ( ∈̃) by realization of the plan ̃, is divided among all active consumers according to function .
Without loss of generality we can also assume that ℓ ≤ ℓ ′ .
In an imitative transformation of a given quasi-production system, there appear neither new firms nor new commodities (conditions 1 and 2) as well as there is no new technologies at time ′ with respect to time (condition 2). In a cumulative transformation of a quasi-production system, additionally, the commodities and technologies used at time can be used at time ′ (condition 3) as well as economic positions of producers at time ′ (see Lipieta, Malawski 2016) are not worse than at time (condition 4). Precisely speaking, condition 4 means that adequate profits in system ( ′ ) are not less than in system ( ). Let us also notice that, if Suppose that quasi-consumption systems ( ) = ( , ℝ ℓ , Ξ ; , , , ( )) and ( ′ ) = ( ′ , ℝ ℓ ′ , Ξ ′ ; ′ , ′ , ′ , ( ′ )) are mathematical models of consumption sphere at time and ′ , respectively. System ( ′ ) is called the transformation of system ( ), which is noted by Similarly, as in case of a production sector, it is assumed that if ( ) ⊂ ( ′ ), then = ′ and ℓ ≤ ℓ ′ .
Definition 5. Quasi-consumption system ( ′ ) is said to be the imitative transformation of If ( ) ⊂ ( ′ ) and additionally, then quasi-consumption system ( ′ ) is called the cumulative transformation of quasi- In an imitative transformation of a given quasi-consumption system, neither new consumers nor new commodities appear (conditions 1 and 2) at time ′ with respect to time .
In a cumulative transformation of a given quasi-consumption system, additionally, consumers' commodity bundles demanded at time are still wished by consumers at time ′ (condition 3) as well as initial endowments are non-decreasing (condition 4). If ( ) = ′ ( ), then the preference relation of consumer at time ′ is the same as his preference relation at time ; if ( ) ⊊ ′ ( ), then the preference relation of consumer at time ′ is the extension of his preference relation from time (condition 5). Finally, consumers' commodity bundles that can be realized at time ′ are preferred not less than consumption plans feasible to realization at time (condition 6). On the basis of the above, it can be said that if ( ) ⊂ ( ′ ), then the economic positions of consumers in system ( ′ ) are not worse than in system ( ) (Lipieta, Malawski 2016). It is obvious that, if ( ) ⊂ ( ′ ), then ( ) ⊂ ( ′ ).
If the economy is in equilibrium, then economic agents can realize their optimal plans of action The specification of the transformations at time ′ is determined on the basis of the properties of the economy at time . However, it is easy to notice that features "being the imitative transformation" or "being the cumulative transformation" have properties transitivity i.e., for , ′ , ′′ ∈ {1,2, … }, < ′ and ′ < ′′ , the following is true: To model innovative changes that can be observable in the economy, we have to formulate conditions that enable us to recognize that innovations appear at time ′ compared to time , 1 ≤ < ′ . Following Schumpeter's ideas, we admit that the creative natures of entrepreneurs make they generate new products or new technologies. The producers who introduce innovations are called the innovators. An innovator may achieve the increase in the profit or not.

Innovative changes in the economy
As earlier, , ′ ∈ {1,2, … }, < ′ . Let us consider quasi-production systems ( ) and ( ′ ), where ( ) ⊂ ( ′ ). If some innovations are visible at time ′ compared to time , then it is said that quasi-production system ′ is the innovative transformation of the quasiproduction system (compare to Lipieta 2018). More formally, we suggest: Definition 7. Quasi-production system ( ′ ) is called the innovative transformation of quasi- Let us notice that if ( ) ⊂ ( ′ ) and ℓ = ℓ ′ , then new technologies are the only innovations at time ′ with respect to time (condition 1). If ( ) ⊂ ( ′ ) and ℓ < ℓ ′ , then a new commodity is introduced as well as at least one innovator introduces new technology into the production sphere (condition 2) at time ′ with respect to time . The producer satisfying condition 1 or 2 is the innovator. If producer 0 is the innovator, then the vectors 0 ( ′ ) satisfying condition (2) by Definition 7 are called (his) innovative plans. We assume that, if ( ) ⊂ ( ′ ), then at time ′ at least one innovator realizes one of his innovative plans. The above is coherent with Schumpeter's theory. If ( ) ⊂ ( ′ ) and additionally then innovative plan 0 ( ′ ) gives a higher profit at price vector ( ′ ) to innovator 0 than any plan 0 ( ) at price vector ( ). In that case the economic position of the innovator satisfying one of the above conditions, is better in system ( ′ ) than in system ( ). If innovative changes are observable in the production sector at time ′ with respect to time , then the economy is not in the form of the circular flow and the economic development has already been started.
1. If, for every , ℇ () ⊂ ℇ (̃+ 1), then the economy is in the form of the circular flow in in the period from to ′ .
2. If ℇ ( ) ⊂ ℇ ( ′ ), then the economy is in the form of the economic development in the period from to ′ .
3. If, in the period from to ′ , the economy is neither in the circular flow nor in the economic development, then we say that the economy is in the regression.
On the basis of the previous considerations, it is seen that nature of economic processes is quite complex because their properties also depend on the duration of a period analyzed. The definitions presented below are borrowed from (Hurwicz 1987) and adapted to the economy with the countable number of agents. Let countable set denote the set of economic agents. All characteristics, determining an individual as the -th agent ( ∈ ) in the given economic process, form the so called economic environment of that agent. The economic environment of agent at time is denoted by ( ). The symbol ( ) stands for the set of all feasible economic environments of agent at time . The set is called the set of economic environments at time , vector = ( 1 ( ), 2 ( ), … ) ∈ is called the economic environment at time . Economic agents consciously or unconsciously send some messages to other agents. The set of messages to be used on the market by agent at time is denoted by ( ), while its elements (messages) by ( ). The vector where, for every ∈ , ( ) ∈ ( ), is called the message at time . The process of exchanging messages may be represented by a system of equations of the form: where = 1 × … × , = 1 × … × −1 , ℎ = ℎ 1 × … × ℎ , is called the adjustment process.
The number of commodities in the economy under study can be changed in time. Let ℓ ∈ {1,2, … } mean the dimension of the commodity space at time ∈ {1, … , }. Without loss of generality, we can assume that ℓ = ℓ 1 ≤ ⋯ ≤ ℓ . Let ≝ ∪ be the set of economic agents. For every and ℓ : Consequently, the set of environments at time ∈ {1, … , } is of the form in restriction to space ℝ ℓ , where for every ∈ , economic environment ( ) defined in (3) for = 1, … , . The response function is of the form where is, for = 1, … , − 1, given by (1). So, in reply to prices ( + 1), every agent chooses his plan of action at time + 1. The feasible plans of action at time + 1 form sets ( + 1) and ( + 1), respectively.
Ad. b) In the model under study technologies are described by production plans. If consumers do not want to buy the commodities which are produced by the use of some detrimental technologies, their consumption sets might satisfy condition (9) for a subspace .
Therefore, if conditions (a) or (b) or (c) are satisfied, then producers can decide to change their activities on the market.
At the end, let us notice that to get equilibrium in economy ℇ(2) a person or an institution established by an unspecified decision maker, should determine a direction (vectors 1 , … , ) of the transformation process presented.

□
In Example 1, we design an adjustment process transforming economy ℇ(1) being in equilibrium into such economy ℇ( ) in which there is equilibrium at the same prices as well as ∀ ∈ ( ) ⊂ .
Example 1 shows that it is possible to guide the economic system being in the form of the circular flow into its transformation also being in the form of the circular flow introducing ecochanges into production sphere. The production sets satisfying the above condition are called the linear production sets (Moore 2007). Finally, it should be added that the assumptions considered by Arrow and Debreu (1954) were not assumed for economy ℇ(1).

Mechanisms of economic evolution as the components of the adjustment process
On competitive markets, the economic agents do not behave strategically and they do not cooperate. In the spirit of the perfect rationality assumptions (Simon 1955), producers and consumers realize their optimal plans of action, while according to the bounded rationality conditions, innovators realize or will realize their innovative plans. Innovators introduce new products or new technologies into production to get higher profits now or in the future. Thus, now or in the near future, profits may not be increased. Eco-innovators introduce ecoinnovations above all to protect the environment and only in the second instance, if at all, to increase the profits.
In the model under study, if innovators do not operate at a given period, then the aim of economic agents is to realize the plans of action which guarantee maximum profits or maximizing the preferences on the budget sets, respectively. If the economy is in equilibrium as well as the producers do not have ideas for creating new commodities or implementation new technologies etc. to increase the profits, then the economic agents do not have motivations to change their plans of action. That is why, in the model considered, only innovators or the influence of external factors can move an economy from its equilibrium state. In this research, we focus only on the innovators' activities.
To analyze and to explore the nature of economic evolution, the Hurwicz's economic mechanisms (see for instance Hurwicz, Reiter 2006) were used in our previous research. It enabled us to emphasize the role of information within economic processes as well as distinguish price, qualitative and adapting mechanisms among all possible economic mechanisms of economic evolution (Lipieta, Malawski 2016).
First we recall the definition of the economic mechanism in the sense of Hurwicz. Let ≠ ∅ be a set of economic environments, -a set of outcomes.
Below the relationship between Hurwicz mechanisms and the transformation process of a private ownership economy with almost all inactive agents (see Definition 10) is indicated.
On the basis of the above reasoning the following can be concluded: • if  is an imitative mechanism and ℇ ( ) ≠ ℇ ( + 1), then  carries only insignificant changes into agents' economic activities, • if ℇ ( ) = ℇ ( + 1), then also ℇ ( ) ⊂ ℇ ( + 1); in such a case, economic agents do not change their activity on markets in the period from to + 1.
Combining the results of the Example 1 and Theorem 1, we easy conclude that an ecomechanism can be implemented at every step of an adjustment process. Dependently on initial conditions and prices that mechanisms can be innovative, imitative, cumulative or regressive.
Below further examples of mechanisms in the sense of Hurwicz are presented. Those examples take the form of mathematical theorems and correspond to Schumpeter's description of economic evolution. In the proof of the following theorem, an explanation, why a private ownership economy with almost all inactive agents, which is an example of an economic organizational structure, is a mechanisms in the sense of Hurwicz, can be found. The idea of the proof relies on the interpretation of realized allocations as messages and outcomes of the mechanism under study. Firstly, the following is proposed:  (15) is a mechanism in the sense of Hurwicz.
In contrast to Theorem 1, the mechanism defined in the proof of Remark 2 (see Appendix) is static: message correspondence assigns to the environment at time , messages at the same time. That mechanism is eco-mechanism if ∀ ∈ * ( ) ∈ and ∀ ∈ * ( ) ∈ , where subspace is determined by one of the conditions (a), (b) or (c) analyzed in Example1.
If every producer maximizes his profit ( = ) and every consumer maximizes his preference on the budget set ( = ), then it can be also proved that the economy ℇ = ℇ is a Hurwicz mechanism. However, in that case, the agents' aims are different. Hence the set of messages is defined in another way, i.e. Mechanism defined in Remark 2 does not make positions of economic agents worse because producers and consumers realize their optimal plans of action in given environments. Therefore, it is concluded that the mechanism defined in Remark 2 is the cumulative mechanism, which additionally confirms that every economy ℇ ( ) is in the form of the circular flow.

Now, we focus on modelling some examples of mechanisms resulting in equilibrium in
the economy under study. Assuming that at some prices, every agent can realise his aims, i.e.
producers maximize profits, consumers maximize preferences on the budget sets, we will show how to reach equilibrium in a transformation of the initial economy under some additional mathematical assumptions interpreted in economic theory.

Theorem 2. If
as well as then there exists a cumulative mechanism  which results in equilibrium at price vector ( + 1) = , in economy ℇ ( + 1) in which characteristics of economic agents are the same as in economy ℇ ( ).
Assumption (17) means that sequence (( * ( )) ∈ , ( * ( ) ∈ , ) satisfies Walras Law, whereas assumption (18) indicates that excess or deficiency of some commodities on markets can be fulfilled by producers' activity. The mechanism defined in the proof of Theorem 2 relies on changing producers' activities under feasible technologies at time , to cover surpluses or deficiencies of commodities revealing in total consumption plan * ( ) compared to total endowment ( ).
It can be noticed that, under the assumption ( ) = , the mechanism defined in the proof of Theorem 2 is the cumulative mechanism since this mechanism requires changes in producers' activities whereas maximal profits are not changed (conditions (22) and (23)).
Hence, in that case the economic positions of economic agents are not worse. If in the economy satisfying assumptions of Theorem 2, there exist 0 ∈ such that 0 * ( ) + ∈ 0 ( ), which means that in decomposition (19) At the end, we show that if the difference between the total demand and the total endowment cannot be fulfilled by producers under feasible technologies, then would be the equilibrium price vector in an innovative transformation of economy ℇ ( ). As earlier we assume that there is an allocation (( * ( )) ∈ , ( * ( )) ∈ ) (see (10)), where at price system , * ∈ ( ), for every ∈ , * ∈ ( ), for every ∈ , which means that ℇ ( ) = ℇ( ).

Proof. As condition
The consumption sets, preferences and endowments at time + 1 are assumed to be the same as at time , while Components of mechanism  are defined in the same way as in the proof of Theorem 2.

□
The producers satisfying (25) are innovators. Innovativeness of producers revealing within the mechanism defined in Theorem 3 is the result of disequilibrium on markets of some commodities. The mechanism defined in Theorem 3 could change the position of some economic agents. For instance, if 0 ≤ ( ) = • , for 0 < < 1, then the maximal profit of producer for which ∘ * ( ) > 0 increases at time + 1. However, if ( ) = , then producers' plans maximizing profits, consumers' plans maximizing their preferences on budget sets at time remain the same as at time . Consequently maximal profits stay at the same level.
It could be caused by too high costs of introducing innovations with regard to their prices.
Hence it is worth to study innovative mechanisms which will generate small changes into production activities. The distribution 1 , … , of vector satisfying conditions (19), (22) and (24) is not the only one, hence in some cases it seems to be possible to specify such a mechanism for which the changes to be introduced are sufficiently small in the given metrics.
The mechanisms defined in the proofs of Theorem 1 or Theorem 2 are eco-mechanisms, if, as earlier, where subspace is determined by one of the conditions (a), (b) or (c) analysed in Example1.
Let us notice that, at given prices, maximal profits and plans maximizing consumers' preferences on budget set would be the same in both cases: as a result of an eco-mechanism or without any changes in agents' activities.
At the end we present an example of the mechanism defined in the proof of Theorem 3 which results in equilibrium in a transformation of economy ℇ ( ). As we will see, in economy ℇ ( ) neither the assumptions considered in Example 1 nor the assumptions posted by Arrow and Debreu (1954) are satisfied. 2) design a mechanism which leads, at prices = (1,1), to equilibrium in a transformation of economy ℇ ( ).

Solution.
In economy ℇ ( ) some assumptions of the First Existence Theorem for Competitive Equilibrium (Arrow, Debreu 1954, p. 266) are not satisfied i. e. set ( ) = 1 ( ) does not satisfy assumptions I.b, I.c (ibid. p. 267), the utility function determined by preference relation ≼ 1 does not satisfy assumption III. c (ibid. p. 269). We show that at any price system there is no equilibrium in that economy.
If 1 = 0, then the consumer does not maximize his preference on the budget set.
By the above there is no equilibrium in economy ℇ ( ). Moreover, condition (9) is not satisfied in that economy.
□ Remark 3. The mathematical set-up presented above leads us to specifying the relationship between the circular flow and the economic development. Within the evolution of the economy, cumulative or regressive or innovative mechanisms appear. Economic evolution can be viewed as a sequence of Hurwicz mechanisms which includes at least one innovative mechanism and a cumulative mechanism is the first element in that sequence. On the basis of the above, due to the use of the tools of Hurwiczian theory, we can conclude, that the circular flow is an environment, or an intermediate point, or an outcome of the economic development.

Conclusions
Modelling mechanisms of economic evolution in the Hurwicz's apparatus confirms the Day's ideas (2007) on the differences between mechanisms within the circular flow and the economic development, as well as contrary to the Schumpeter's concept, showed that mechanisms governing the innovative and non-innovative processes are naturally divided into more than two groups. What is more, it was shown that at every stage of the economic evolution eco-mechanisms can be implemented. The eco-mechanisms defined in the paper in many cases can improve the position of economic agents. Moreover, if an eco-mechanism were not be implemented, then the agents' economic position would not be better.
The model presented reveals the significant role of information and the ways of exchanging messages during innovative processes. Diversification of analyzed mechanisms reflects the complexity of economic processes and their results. In the set of outcomes of an innovative mechanism, the effects of creative destruction are also revealed; besides new commodities, technologies and organizational structures visible on the market, the old, unattractive or harmful products and technologies as well as the uncompetitive in a new economic reality firms, can disappear from the market.
Axiomatization of mechanisms of the evolution of the economy by the use of Hurwicz's apparatus exposed the positive, from the producers' and consumers' points of view, qualitative properties of the examined mechanisms. Moreover, it gave us the criterion for identifying in the set of analyzed mechanisms, the qualitative mechanisms with respect to the given set of agents, i.e. the mechanisms in which at least one agent from the given set would be better off due to a given criterion, without making the rest of agents from this set worse off.
Specification of an optimal eco-mechanism towards equilibrium considering agents' incentives remain under our research perspectives.
On the basis of the above, the structure  = ( , , ℎ ) for = 1, … , is the mechanism in the sense of Hurwicz.

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Funding
This work is supported by National Science Centre in Poland, GRANT 2014/13/B/HS4/03348

Authors' contributions
Andrzej Malawski: conceptualizing the idea Agnieszka Lipieta: conceptualizing the idea, analysis and writing