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Balanced Equilibrium

Basic Olicognograph: Switches Perspectives

The Basic of Economics

Construction of concepts like “demand,” “supply,” “equilibrium,” “scarcity,” or “commitment” (or compromise) are practically more complex than generally conceived by traditional economy and must flexibly and variably relate to what people do effectively. They look like needing two by two matching in an equality as demand with supply, commitment with reward. Meanwhile others concept should immediatly and iterativally suggest more questions so is scarcity; coming close after the ideas if the piecemeal need more than a minimum. Economical "sciences", when soon after started debating on how to do, needs few steps out of social violence, then focus on qualification and quantification out God(s)' help(s). Then when economics turned a science to eat, teach and obey for common public, aim has been to convince yourself which best sort of curve of supply or demand exist and use as simple or real object: an evidence expressing the need of economists' magical services. Socially, pre-ideas are often safer as norms rather than as truth, as in used dressed curves.

Our concern for a popular management to introduce the question of prior to the piece of information to calculate the value of concepts and as important is the good way things (product or service) have been done, giving right ground in the frame of an informative concept that can be managed, discussed and helpfully applied. With equilibrium, calculus of economics have found an extraordinary ground for self-justification, use of sophisticated methods, include the mechanics calculus in its marginal or differential form has provided by Newton and Leibnitz. Huge efforts have been deployed to develop and complete the theory since a few small core set of concepts has made before the rhetoric of theology, with more fruitful mathematical extensions but plenty of weird assumptions, that did not prevent the blurring of proximity neither served common sense of persons.

Now for some common on something still so omnipresent in economic literature. The 3 fundamental theorems of general equilibrium theory are the propositions that, under appropriate hypotheses:

  1. A competitive equilibrium exists,
  2. A competitive equilibrium is Pareto efficient (called the First Welfare Theorem),
  3. A Pareto efficient allocation can be decentralized as a competitive equilibrium with transfer payments (the Second Welfare Theorem).

This very short abstract does not reflect that it took more than a century, since the efforts of economists at the start of the industrial revultion, to involve newtonian mechanics. Than the marginalist inclusion and interpretation of Walras (Pareto was his heir) almost fifty years later, addition of many other basic concepts (preference, utilities) up to Arrow-Debreu which after one hundred years achieved the mathematical and logic coherence of a complete system, but to restart the debates of general time tamed equilibrium criticized by new logical systems of mathematics as with theory of games or evolutionnary economics. Arrow-Debreu's theorem has been established during the fifties of past century:

  • Market mechanism cannot do (or deliver) better in such a way that each and all have better utility for all. This has justified originally the concept of a dictatorial hand.
  • may be we could add that the dictatorial hand can be the general overall theoretical democratic consensus, as a residue of social utility, when averyone as safe a minimum enough share (with residual minimum harm for strength care).

"Direct econometric approaches, which started during the same decade of the fifties (of past century) to estimating computable general equilibrium (CGE) models have been used. However, lack of data, computational and conceptual difficulties in estimation, and uncertainty concerning the validity of resulting estimates have comprised ... barriers to application of the econometric approach... Econometric estimates are almost always obtained using annual data. The elasticities obtained are short run. However, many CGE analyses consider a significantly longer adjustment time frame, often three to five years. Short run elasticities are likely to understate the response capacity of agents over this longer time frame. Second, given the large number of parameters to be estimated, long time series data for numerous variables are required to provide sufficient degrees of freedom for estimation. In many cases, the economy is likely to have undergone structural changes over the period, which may or may not be appropriately reflected in the estimation procedure. Finally, even those econometric estimates designed specifically to feed parameters estimates to CGE models undertake estimation without imposition of the full set of general equilibrium constraints. While the estimated parameters might provide a highly plausible description of historical production and consumption data sets, the estimated values will not be fully compatible with the general equilibrium system they are designed to represent.

The market equilibrium (ME) approach is similar to the traditional econometric approach in that 1) the full historical record can be employed, and 2) statistical tests for estimated parameter values are available. It is similar to the multiperiod validation / calibration approach in that 1) the full model tracks the historical record, and 2) the ME approach can be applied in the absence of copious data. The ME approach allows one to use all available data, take into account all relevant constraints, employ prior information about parameter values, and apply variable weights to alternative historical targets".

At different levels and corner of general equilibrium remain many problems. For example "If the economic environment were held constant, profitable firms would grow and unprofitable firms would shrink. In the general equilibrium model, prices change as factor demands and output supply evolves. Without capital markets, when firms can grow only through retained earnings ... model verifies Friedman’s claim that natural selection favors profit maximization. But .... this does not imply that equilibrium allocations converge over time to efficient allocations. Consequently, Koopmans critique of Friedman was correct. When capital markets are added, and firms grow by attracting investment, Friedman’s claim may fail. In either model the longrun outcomes of evolutionary market models are not well described by conventional General Equilibrium analysis with profit maximizing firm". (L. E. Blume & D.Easley).

Relationship between the stability of a competitive equilibrium and the price adjustment mechanism used to attain that equilibrium point. Using two specific examples, a three-commodity exchange economy with a unique competitive equilibrium (Scarf’s global instability example) and a two-commodity, two-trader type exchange economy with multiple competitive equilibria, we show that the stability of a competitive equilibrium depends critically upon the dynamics of the price adjustment mechanism. A particular competitive equilibrium may be unstable under one price adjustment mechanism but stable under another. The joint dynamics of the chosen price adjustment mechanism and the given economy determines the overall stability of its competitive equilibrium. Our results suggest that context-rich studies of economic systems which focus on a specific price adjustment mechanism may provide insights into the dynamics and stability of economic systems that are often not revealed through a context-independent analysis.

Everything in one Thing ?

"The mathematical model of the walrasian economy was a masterpiece of parsimony, but the existence proof of an efficient price system was obtained at the cost of providing a model that could not be played as an experimental game without providing considerable extra detail to convert it into a fully defined process model. ... Wald’s study of the incompleteness of walrasian general equilibrium observed that an incomplete theory or axiomatic system (as a whole) may still be testable if it entails at least one testable statement.

"Efficient Markets Hypothesis (EMH), a powerful idea that traced back to Paul Samuelson (1965), as in his article: 'Proof that Properly Anticipated Prices Fluctuate Randomly': - in an informationally efficient market, price changes must be unforecastable if they are properly anticipated, i.e., if they fully incorporate the expectations and information of all market. This concept of informational efficiency has a ... counter-intuitive and seemingly contradictory price changes generated by such a market must be, and the most efficient market of all is one in which price changes are completely random and unpredictable".

"The desire to build financial theories based on more realistic assumptions has led to new strands of literature, including psychological approaches to risk-taking behavior [Kahneman and Tversky (1979), Thaler (1993), Lo (1999)], evolutionary game theory [Friedman (1991)], and agent-based modeling of financial markets [Arthur et al. (1997), Chan et al. (1998)]. Although there are obvious differences between evolution in biological systems and evolution in financial systems, there are also many similarities".

For other out of frames remarks expressing the way equilibrium concept turned almost hegemonic in the "scientific provision":

  • "Pareto optimal allocation whether each consumer vanishes or survives is determined entirely by discount factors and beliefs. Since equilibrium allocations in economies with complete markets are Pareto optimal, ... results characterize the limit behavior of these economies (normative psychological involvement).
  • The neoclassical theory that all individuals are maximizers can be true only if all markets are in equilibrium. For an equilibrium to exist, there cannot be any incentive for individuals to change their behavior, that is, change their choices (positivist social normation).
  • All else equal, the market selects for consumers who use Bayesian learning with the truth in the support of their prior and selects among Bayesians according to the size of the their parameter space (incorporation of a type of methods of empirical statistics).
  • For Economies with incomplete markets these conclusions may not hold. Payoff functions can matter for long run survival, and the market selection hypothesis fails (imperfections of market).
  • The case of imperfect competition,which everyone agrees is ‘more realistic’, is, however, much more complicated. It is more complicated merely because we cannot say ‘given the going prices in the market’ since the firm’s decision affects its prices as well as its level of output. And so the prices are not‘given’ (the reaction of common sense turns to need to get involved in the mathmatical en logical formulation (most marxist dialecticians fail in that, meanwhile modern marxist economics schools - during the sixties and seventies of past century - retook happily that time the marginalist methods and matrix optimization in central planification).
  • They are strategic market games based on ... strategic forms and solved utilizing the noncooperative equilibrium and market games based on the coalitional form and solved primarily for the core of the game in coalitional form. Without going into detail, some basic observations can be made concerning the relationship among market games, modified market games, strategic market games and the competitive equilibrium exchange economy" (theory of games represent today the major source of critics against the general equilibrium theory meanwhile also emerging too has the major candidate as provider of a new economical paradigm, diversity misunderstood).

Formally, we may say that reproduction of patterns have often been mistaken, forcing overgenerailized concept like of general stable equilibrium calculus. As if every expressions of pieces could be, neutrally priced and equal all independent relative vectors of speculated changes (never democratically approached). Meanwhile, if managing paradoxes, less clear dynamics and contradictory balances to operate in a less academics way there can be many uses of similar concepts extending reasonings in roots of knowledge, with scientific essential knowledge, were equivalent, but more fundamental issues and/or more substantial invariants exist.

There is a need to look at more concepts and frames of equilibrium, coincidental matching, consistent equalities, dynamic transformations; especially seeking to preserve essential units of maximum complexity reached most important being biological and ecological, then put after what should stay of economics issues. Then to consider so what sorts of changes, trends, metastable states could be managed; in multiple registers of applications or approaches. Intent to involve more inspired social infrastructures, environmental transformations and to promote in the mean time those caring the renewals of natural environments. In the hope that there have still mechanisms of sustainability that can help policies to be efficient and positive.

A formal general economical dynamic equilibrium could be just a conceptual chimera poorly applicable in reality (almost always with the same ambition to serve an imaginary dictator), waste too much time and ressources, miss to care the intermediate different positions we have in macrounit, for a positive effect. Because, for negative effects and artificial macro-units like geopolitical ones, they can be very relevant to the problems there and just how to get out of thems. Overall seeking perspective(s), wholist ones, sort of mixtures looking more like general solution of common aspiration, and able to include illusions on materialistic renewal processes.

Being nurtured by Sun's positive energetic inputs, regular maintainance (dynamic economic stability), to compensate metabolic turnovers, so the need to preserve essential identity. Our essential identities being composed of invariants landmarks: complex structured coincidences of matter, functional subsystems working for the whole, varying in average life, local supplies of energetic releases, provisions of self-raw materials; maintain supports of information, energetic and material economical metabolisms with inputs, so as to sustain, at least, the essential, plenty of less cared deficits, gaps and consistent satisfactions to work with, and probably as able as many vanity fairs to provide satisfaction and happyness.

More Fundamental Concept ?

On this concept of general equilibrium, as thought by economists, there should be something like a frame of heterogeneous and diverse complex and complicated concepts, to intent to control our human mental disorders with economics, by critical multidisciplinarity thinking and promotion of good 'collateralism' in social projects. Projects framed at responsible level of close territorial collectivities. Allowing the matching of values and engineered material quantities and qualities, to maintain and develop humane sustainabilities. More robust if better including social systems of cooperation and preserve some organized characteristics (eventually into hierarchies of essential flows by non central means). In our mind, a social system shall cover or cover enough complexities, as those it produces, as well as those that can be cared by legitimate citizens. Disposing some densities of options and diversity for good resilience, that is also care vital supports.

To restart with basic of “Equilibrium” (Webster’s 7th New Collegiate Dictionary):

  • A static or dynamic state of balance between opposing forces or actions (or concepts sharing a matching)
  • A state of adjustment between opposing or divergent influences or elements (see mechanisms of adjustment).
  • The normal oriented state of the animal body in respect to its environment.

A thermodynamic sense is more stringent (Zemansky & Dittman):

  • Mechanical equilibrium: There are no unbalanced forces or torques acting on any part of the system or the system as a whole (but a potential expression of non linear effect if a lone or oriented break).
  • Thermal equilibrium: There are no temperature differences between parts of the system or between the system and its surroundings (more complicated with open biological systems).
  • Chemical equilibrium: There are no chemical reactions within the system and no motion of any chemical constituent from one part of a system to another part".
  • It can be good to consider also a entropy induced / neguentropy equilibrium and its phenomenological expression as 'information' (where we prefer the word 'communication').

Highest complex unit turns to be one able to manage hierarchical complex networks of its collection of subsystems 'definying its identity'. Overall complexity makes evolution. Possibly because reaching a "higher complex construction" means somehow that complex sorts of dynamic equilibria or regular static arranged transformations help to preserve the overall logic of the system, identity or unity. They cannot be repeated exactly the same way, from the start of the origin, but somehow can be reproduced and modelled in reproducible information support (DNAs or RNAs in biology). Two plates of foods are never exactly the same everything taken into account; including environment and situations. But some metabolic pathways and alternatives will operate either, assume flexibility and balance essentiel priorities. Imperfections have turned essential engines to adaptation partly making the potential of evolution and have been systemized to create more diversity, under the shadow (or the umbrella) of thermodynamics limits of higher complicated units.

'Permanent' transformations are essential because obliged by disorganization (and disaggregation) induced by entropy. Open maintained systems are able to prevent disaggegation by catching in their environment around, their maintenance and restore themselves via regular metabolic pathways. Preserve some unity happens since having pieces of information "recalling" good pathways without redoing all since the beginning of ages (only in the accelerated kit-being of the embryo). Trajectories may at some limits look more like strange attractors or chaotic motions. Especially when memories grow up: it is not only one pathway that helps you adapt to complexity of intricated complex subsystems. Since, in our idea, a material generally calculable complex varied unity (non commutative four dimensioned-parametrized-characteristic exponentiated at least) which use too areas, separations, lines, circles, chains, cascades or subvolumes to develop structures and run functions which characteristically are mixed and crossed by strange attractors, not being themselves the only mechanisms of complexities).

Study of these concepts would care for example the concept of "displacement of equilibrium" with the exploration of critical limits. Compare the posivity of changes with the explosive changes of definition. Consider that in a material (physics) world things cannot go too far (not necessarilly at our scale) but very different from the laziness of homogeneity. See that a forest fire will extend more if unlimited by homogeneity of good conditions of propagation and slower if limited by heterogeneity. Conceive that butterfly's effect may need the support of a catastrophic unadvert disposal of Hadley's cells. "The interaction details between reactants and those for interacting populations are of course quite different both in form and motivation. In biological systems there is generally more complexity as regards the necessary order of the differential equation model. However, this is often compensated by the presence of enzyme catalysts and thus a biological justification for reducing the order considerably".

Now it would be to take into consideration the human phenomena of extroverted or expansive speculations. Pictures of general natural equilibrium, as provided by Biosphere in absence of critical humans or; local assymetries and heterogeneous-non perfect mixtures, make still very relativelly confused maps of distributions of matters (materials) and energies (exoenergetics materials' transformations a large part of our level). They set sorts of "environments at stacks of equilibria" like: climax or climacic ecosystems. Those change because of what we do. Hope them, for humane reasons, to let enough space to tomorrow's tribes of humans. Artificial sorts of human engineering systems of transformations of environment, with conceivable speculative management of "general equilibrium models of precautions"; if those could catch better the limits. Even when these models could be non linear but calculable.

May be the sort of complex reasonable highest social unit able to be productive, wise and peacefull could be communities in regional environments shared sense of common humanity, meanwhile national regulations would have the purpose to preserve excessive distorsions induced by exogenous alienations. Communities having often enough skilled members to care the future of their ressources if not forced to fight in destructive conflicts.