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In economics, there are many equilibrium concepts, like equilibrium under perfect competition, Monopolist equilibrium, competitive equilibrium, general equilibrium, nash equilibrium, equilibrium price, market-clearing price, etc.

So, how to understand the equilibrium in economics. I think there should exist an universal and standard theory to describe an equilibrium.

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There are multiple notions of what equilibrium is when it comes to economics although they are all related.

There is a paper fully dedicated to this topic by Backhouse (2004). Following Robinson (1956: 57):

The word equilibrium, in ordinary speech, describes a relation between bodies in space. The scales of a balance are in equilibrium when the balance is at rest. . . . If we are continually throwing coppers at random into either scale, the balance is continually wobbling and never reaches equilibrium; but, at any moment, there is a definite equilibrium position which it would quickly reach if, from that moment, we left it alone.

Equilibrium analysis can be viewed as sort of thought experiment where to organize your thinking passage of time is held constant. Now thinking about equilibrium analysis in the way above still has few issues.

Again Robinson (1956: 59) writes:

Nor can we apply the metaphor of a balance which is seeking or tending towards a position of equilibrium though prevented from actually reaching it through constant disturbances. In economic affairs the fact that disturbances are known to be liable to occur makes expectations about the future uncertain and has an important effect on any conduct (which, in fact, is all economic conduct) directed towards future results. . . . A belief that a particular share is going to rise in price causes people to offer to buy it and so raises its price. . . . This element of ‘thinking makes it so’ creates a situation where a cunning guesser who can guess what the other guessers are going to guess is able to make a fortune. There are then no solid weights to give us analogy with a pair of scales in balance. The metaphor of equilibrium is treacherous. . .

However, this issue was later addressed as discipline evolved Backhouse (2004):

There is, however, an alternative way to think of equilibrium, not as the static equilibrium analogous to that of a pendulum, but as inter-temporal equilibrium where expectations are fulfilled (Milgate 1979, 1987, Phelps 1987). Because this idea is now so strongly associated with the New Classical Macroeconomics and related theories, it is worth noting that Erik Lindahl and his Swedish colleagues used the notion to attack the MisesHakek notion of neutral money. If expectations were correctly anticipated, any rate of inflation was consistent with monetary equilibrium. The door was opened to discretionary monetary policy. (see Laidler 1999: 58–60).

Furthermore, Backhouse (2004) also argues:

... This is the notion that equilibrium is where (a) agents’ decisions are compatible with each other and (b) no agent has any reason to change his or her behavior. The second part of this condition (which might be thought to encompass the first) is often represented by saying that agents are maximizing utility subject to the constraints they face.

Consequently, in economics there are several possible notions of equilibria:

  1. Equilibrium as the absence of endogenous tendencies for change.
  2. Equilibrium as balance of forces (using a mechanical analogy).
  3. Equilibrium as correct expectations.
  4. Equilibrium as meaning that no agent has any reason to change his or her behavior.

Which one of the 1-4 is author talking about is case dependent but most graduate level models will use either notion 3 or 4, speaking from my experience.

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  • $\begingroup$ Sorry, I cannot understand point 3 saying Equilibrium as correct expectations. Could you give some examples? Is this correct expectation meaning from the inter-temporal equilibrium? $\endgroup$
    – DevinY
    Apr 7, 2022 at 8:13
  • $\begingroup$ @DevinY not just that it is an equilibrium concept used when uncertainty is involved. For example, consider some game theory problem where you have just one time period but there is some uncertainty involved, like rock, paper, scissors where people play R, P and S with some probability p, q and 1-p-q. $\endgroup$
    – 1muflon1
    Apr 7, 2022 at 8:17
  • $\begingroup$ So, that means one's response shuold be best given their expectations of uncertainties and the results will form a equilibria? That sounds like being similar to concept like perfect bayesian equilibrium with beliefs and best responses. $\endgroup$
    – DevinY
    Apr 7, 2022 at 8:22
  • $\begingroup$ @DevinY yes that’s exactly what it is $\endgroup$
    – 1muflon1
    Apr 7, 2022 at 9:59
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The general idea of equilibrium is borrowed from physics: An equilibrium is a state of a given system such that all forces acting on it are counterbalanced and the state therefore doesn't change on its own. In economics, states may be production/consumption plans, strategy profiles, or the like, and the forces may be "market forces" or incentives for deviation. I don't think that a "universal and standard theory" of equilibrium exists beyond this general idea. Specific equilibrium concepts of course have to be formally defined.

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Of course the concept of equilibrium in economics is borrowed from physics, in particular from mathematical physics, mechanics and dynamical systems. When a system is described by ordinary differential equations, equilibrium is defined as a constant solution of the differential equations system. That is, a solution that is invariant with respect to time. In economics we have such dynamic models, for instance the demand/supply forces that make prices change, until demand and supply are equal, or growth models, as the Solow growth model. But the concept of equilibrium in economics has evolved and is gone beyond such a physical notion, in particular because many economic models are not dynamic, but are static models. As a consequence, the notion of equilibrium must be indipendent of the idea of the passage of time (even if that idea may be in the background), and may assume different forms in relation to the model under consideration. The most famous definition of equilibrium is perhaps equilibrium in markets as equality between demand and supply of the goods, in particular the definition of equilibrium in walrasian model, as in modern general equilibrium theory (for instance Debreu). Or the equality between output and demand in keynesian models. Even if in the background may still exist an idea of an underliyng dynamics, nonetheless these are static models in their formal definition, at best they are ‘comparative statics’ models. And the mathematical tools employed in the search for existence of equilibria are not borrowed from differential equations theory or analysis, but for instance from fixed point theorems and topology . This indipendence from dynamics can be seen also considering the different notion of equilibrium given in non-walrasian models, that is in models in which the equilibrium in markets differs from a walrasian one, in that there is no equality between walrasian (often called 'notional') demand and supply, but 'effective' demand and supply, which can result from rationing. In such models (se for instance Malivaud) there is no explicit dynamics of the economy. So, in my opinion, the concept of equilibrium in economics is different in different models, and must be defined separately in each model. What can be a common feature of the notion of equilibrium in economics is maybe the concept of a 'state of rest' or, better, following Machlup (1958) a constellation of variables in a model such that there is no inherent tendency to change, which emphasizes the dependence of the definition of equilibria on the particular formal model under consideration, and the variables involved. Under this definition, as the economy is made of agents, is subsumed a definition of equilibrium as a situation in which the economic agents have no reasons for changing their choices.

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