<p>It is not so evident or even clear that &quot;any price would be pushed/converge to equilibrium&quot;. For this type of argument to make sense, you need some kind of price adjustment process which determines in what direction and to what degree prices will adjust if, for example, for some markets supply is not equal to demand.</p>
<p>The most well known adjustment process is called the <strong>tâtonnement</strong> process. In this process one assumes that the change in (relative) price of a certain good is proportional to the excess demand for that particular good. So prices increase if demand is greater than supply an vice versa if supply exceeds demand.</p>
<p>There is a lot of (quite difficult) theoretical literature on this topic but the end results are rather mixed. In general a given equilibrium does not need to be tâtonnement stable, not even locally. In fact, there might be equilibria which are very unstable under the tâtonnement process or equilibria that have some kind of strage saddle point type of behaviour.</p>
<p>On the other hand, many (theoretical) economists assume from the start that the economy is always in equilibrium. In this case, there is no need to talk about a price adjustment process towards equilibrium (as we never deviate from equilibrium). Moreover, the price adjustment process (e.g. tâtonnement) is only interesting from an as-if exercise, as it is quite unclear who actually does the price adjustment to bring the markets back to equilibrium (is it the market participants themselves? or is it some benevolent auctioneer). Besides, it is quite strange to talk about price adjustment processes if the underlying economic model is static (what happens during the time that we need to adjust the prices to equilibrium).</p>

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2023-08-02T15:14:29.787Z
Why is assuming equilibrium from the start reasonable?
Vivaan Daga
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2023-08-02T17:41:52.020Z
Hi @VivaanDaga. If agents within the economy acted according to neo-classical assumptions and like tdm said there was some source of tantonment (such as adjustment through expectations), then it may be reasonable to assume that the economy is in equilibrium. Moreover, equilibrium is an operationally important assumption. For example, computable general equilibrium (CGE) models (i.e. very large systems of equations) are parameterised/calibrated on baseline data which is assumed to be in equilibrium. Following this assumption, counterfactual shocks can be introduced into the model.
EB3112
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2023-08-02T20:05:05.873Z
@EB3112 there seems to be a self-defeating argument here. tdm mentions a tatonnement process may not exist or may not lead to a stable equilibrium, hence most economists just assume an equilibrium state; you argue equilibrium state is a reasonable assumption because tatonnement leads to it.
Giskard
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2023-08-03T07:02:59.767Z
Hi @Giskard. I disagree. I don't think it is 'self-defeating' to admit that it may be reasonable for economists to draw from neo-classical behavioural assumptions and market clearing-type assumptions when assuming the economy is in an equilibrium state. The fact that they're somewhat contentious/contested assumptions doesn't mean people do not assume them in the background. And even if the modeller didn't assume these, it is indefensible just to say 'I assume equilibrium. End-of." Therefore, I was suggesting to VivD why it may be reasonable; not why it is always and everywhere correct.
EB3112
CC BY-SA 4.0
2023-08-03T08:28:48.093Z
@EB3112 okay, cool, but can you please provide a reference for these neo-classical behavioral assumptions that will definitely cause a GE model to converge to a stable equilibrium? Right now the existence of these is just a claim.
Giskard
CC BY-SA 4.0
2023-08-03T09:19:29.360Z
Hi @Giskard. I never made a definitive statement, and I would not claim to have a single reference in which certain neoclassical assumptions definitely cause (with 100 percent certainty) a stable equilibrium. Instead I say that there is assumed to be the existence of an equilibrium (a stable point) given certain neoclassical assumptions, yet the stability of the equilibrium is a slightly different matter. Which someone like Arrow addressed differently. Please, however, clarify all my points for VivD. I only endeavoured to give hints to VivD (a high schooler), not get embroiled in debate.
EB3112
CC BY-SA 4.0
2023-08-03T09:22:57.807Z
@EB3112 Okay, I was just having difficulties parsing [your sentence](https://economics.stackexchange.com/questions/55983/how-does-equilibrium-work/55984?noredirect=1#comment91744_55984) "*If agents within the economy acted according to neo-classical assumptions and like tdm said there was some source of tantonment (such as adjustment through expectations), then it may be reasonable to assume that the economy is in equilibrium.*" because I didn't see how it demonstrates the reasonableness in any way, and I was curious. Have nice day!
Giskard
CC BY-SA 4.0
2023-08-03T09:28:04.410Z
@Giskard. You too. I do believe however, that if you can provide a fuller reasonable justification, then you should. If it is an unreasonable to presume, I think you should also identify why. My points reside only as a broad comment.
EB3112
CC BY-SA 4.0
2023-08-03T09:48:30.273Z
@EB3112 I did not see any academic work on this. Personally I think that equilibrium is a poor assumption. For starters, the law of one price is violated all the time; you need to bring in additional variables such as travel and/or search costs to account for this. Second, most real world markets have fairly quickly changing circumstances, making it difficult for the tatonnement process to reach its end before the market becomes too different. Third, I think rationality based models don't fit real life behavior very well, and equilibrium relies on rationality at least implicitly.
Giskard
CC BY-SA 4.0
2023-08-03T10:00:57.217Z
Hi @Giskard. I am in agreement with many of your points. However, I think given that equilibrium is such a pervasive concept in economics, and equilibrium-modelling is the dominant paradigm, that is reasonable to assume from the perspective of a professional modeller. For example, you'd hope that an economics degree would inform you about economic truths, the same way a physics degree may inform you of physical truths.  If however, someone is a keen theorist looking to re-write the foundations of economics, then equilibrium is perhaps an unreasonable assumption. You're right to be sceptical.
EB3112
CC BY-SA 4.0
2023-08-02T15:07:19.517Z
2023-08-02T15:07:19.517Z
tdm
<p>As the previous answer by TDM says in static equilibrium there is no adjustment. You either are in equilibrium or you are not. In static game everything happens instantaneously. Firms make actions but they occur in an instant.</p>
<p>There is also dynamic equilibrium where adjustment occurs over time, but equilibrium point itself is an equilibrium point precisely because no other agent wants to deviate form it. That is equilibrium occurs when no person wants to do something else than what they are doing now. So in dynamic equilibrium there are no changes, unless it is perturbed by new forces. An physics analogy is pendulum. Pendulum recorded over time is a dynamic system, but equilibrium occurs once pendulum stops swinging. All forces acting on pendulum like gravity etc are in balance (equilibrium is Latin for balance).</p>
<p>Similarly economic dynamic equilibrium occurs when economic forces (e.g. supply, demand, peoples preferences, resources, technology etc) made people act in a such way they don't want to do something different unless there is some shock to the system (change in preferences, technology etc).</p>
<p>Also, even <strong>profit maximizing</strong> firm, acting <strong>completely rationally</strong> might end up in low or zero profit in equilibrium under competitive pressure. Profit maximization only refers to an objective of firm, not outcome that will happen, and firm cannot simply choose profit they like because it is constrained by actions of other firms and customers.</p>
<p>Consider the following simple 'game' between two firms A and B respectively. Both firms can choose two strategies:</p>
<p>Charge high price (H), or low price (L).</p>
<p>If firm A charges H, and firm B also H they both split the market at high price and earn 10 million profit each (suppose H=\$10 and there is 2 million customers with max willingness to pay \$10).</p>
<p>If firm A charges L and B charges H, A captures whole markets but does so at a low price (lets say \$7) so it gets 14 million profit and B gets zero. The reverse happens when B charges L and A charges H.</p>
<p>If both firms charge low price they will split market like with high price but now they both get low profit of 7 million.</p>
<p>This is represented in the payoff table below:</p>
<p><span class="math-container">$$
\begin{array}{|c|c|c|}
\hline
\text{A\B} &amp; H &amp; L\\\hline
H &amp; 10, 10 &amp; 0,14 \\\hline
L &amp; 14,0 &amp; 7,7 \\
\hline
\end{array}
$$</span></p>
<p>We also assume the firms cannot sign contracts that would change payoffs due to antitrust laws, and firms can't observe what the other firm is doing so they have to choose simultaneously.</p>
<p>To find the Nash equilibrium, which tells us what would the rational profit maximizing firms do we have to check their best response against what other firm is doing.</p>
<p>If firm <strong>B</strong> charges <strong>H</strong>, the <strong>best response</strong> of firm <strong>A</strong> is to charge <strong>L</strong>. This is because it will get firm A <strong>maximum profit</strong> 14 million given constraints imposed by B (playing H) and customers.</p>
<p>If firm <strong>B</strong> charges <strong>L</strong> the <strong>best response</strong> of firm <strong>A</strong> is to charge <strong>L</strong> again. This will again give firm A <strong>maximum profit</strong> 7 million under constraints imposed by B's action (playing L) and customers.</p>
<p>Consequently, in the case above it is always the best course of action for firm A to charge low price.</p>
<p>Next we can redo all of the above for firm B, and we will in this game get the same result (since the game is set up to be symmetric). Firm B will also charge low price because it is always the best response.</p>
<p>Hence the equilibrium outcome in the game below is for both firms to charge low price. Equilibrium strategies and pay offs are highlighted red.</p>
<p><span class="math-container">$$
\begin{array}{|c|c|c|}
\hline
\text{A\B} &amp; H &amp; \color{red}{L}\\\hline
H &amp; 10, 10 &amp; 0,14 \\\hline
\color{red}{L} &amp; 14,0 &amp; \color{red}{7,7} \\
\hline
\end{array}
$$</span></p>
<p>In the case above, the firms are rational and profit maximizing yet due to competition they both end up with low profit of 7 million instead of the pareto efficient outcome where they would both get larger profit of 10 million. This might sound counterintuitive given the profit maximizing assumption but again the low 7 million profit is the maximum profit under the constraint of other firms.</p>
<p>If you want to have some adjustment mechanism, you can turn the game above into a game where people play the game repeatedly, in such case sometimes firms can enforce the high price by certain strategies such as so called grim-trigger strategy where rational firms starts playing 'nice' and avoids competing until the other firm tries to screw it and then forever deviates.</p>
<p>What the outcome will be in such dynamic game depends on additional assumptions such as how much impatient each firm is etc.</p>

CC BY-SA 4.0
2023-08-02T16:55:04.500Z
Why does equilibrium occur when demand and supply are equal? What stops a firm from moving the price up?
Vivaan Daga
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2023-08-02T17:10:01.873Z
@VivaanDaga Because it would hurt the firms. For example, suppose supply is given by $S=p$ and demand is given by; $D=100-p$, in such case when $S=D$ equilibrium price is $p_m=50$ and  equilibrium quantity is also $q_m=50$. Producer surplus of all firms with simple linear demand above is $PS= p_mq_m - \int^{q_m}_0 S(q) dq = 2500$. Suppose all firms decide to charge 60, now market quantity is 40, and producer surplus now would be: $PS = p_mq_m - \int^{q_m}_0 S(q) dq =1600$ Firms are significantly worse of by charging price above equilibrium. Now do the opposite experiment  firms charge
1muflon1
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2023-08-02T17:12:00.203Z
less 40, at that price market quantity will be also 40, so producer surplus is 800, even worse than before. You can do trial and errors if you want but you will find that producer surplus is maximized when firms charge equilibrium price and provide equilibrium quantity.
1muflon1
CC BY-SA 4.0
2023-08-02T17:35:43.127Z
In the case of linearity yes, but is that an assumption we must make?
Vivaan Daga
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2023-08-02T18:01:34.443Z
@VivaanDaga no it works with non linear demand and supply but for that I can’t do the integral in my head so I used it to be able to quickly do the calculations
1muflon1
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2023-08-03T03:22:40.640Z
If you are talking how firms would respond, then shouldnt we also consider what B does after A makes its decision of high or low?
Vivaan Daga
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2023-08-03T09:54:32.640Z
@VivaanDaga yes, but I do consider it. Read my answer carefully. I have written you can do the same steps I did for A for B. I on purpose created a symmetric problem so firms mirror each other and when you calculate what one does you immediately know what other does. I did this again to make calculation faster, but you can also just manually find best response for firm B, it will be low. So equilibrium strategy is Low Low, or Low for both A and B
1muflon1
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2023-08-03T11:37:00.467Z
well, if A goes high, then B would go high then A would go high and they all earn more profit. now suppose someone breaks the cycle, then only the other person goes low. so they both wait for the other to break the cylce, which would be never!
Vivaan Daga
CC BY-SA 4.0
2023-08-03T12:09:06.560Z
@VivaanDaga no in the example I provided when A goes H, B wants to go low. B will always be better of by going low. If A goes H and B goes L B gets 14 million profit. If both go H B gets 10 million, 14 million is clearly > 10 million
1muflon1
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2023-08-03T12:27:04.500Z
In the short run not the long run. In the long run you loose out since eventually both would go low.
Vivaan Daga
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2023-08-03T12:27:25.617Z
Why should firms want to loose out in the long run?
Vivaan Daga
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2023-08-03T13:04:55.700Z
@VivaanDaga they don’t want to… they want to maximize profit, but they are constrained by other people’s action… I explained it in my answer did you miss it? For example, if I open bakery in Utrecht the highest profit I might theoretically get given overall utrecht demand for cakes is perhaps by charging 30 bucks per cake. But my bakery won’t be the only bakery in town, if another person starts baking and charges 29e can I still get the max profit charging 30e? If I then undercut him by charging 28e can he still charge 29e? Read my answer carefully I address it in second half
1muflon1
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2023-08-03T13:36:04.093Z
But the rational thing for other person to do would be not to undercut you for that would lead to lower long term profit.
Vivaan Daga
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2023-08-03T13:37:34.900Z
@VivaanDaga thats were you wrong, its rational to undercut, as shown in the example in my full answer, and you can prove logically it is rational to undercut the other player (in many market settings of course there are exceptions), you can even prove it mathematically.
1muflon1
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2023-08-03T13:39:09.273Z
It’s rational to undercut for immediate profit, but you loose long term profit!!
Vivaan Daga
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2023-08-03T13:40:34.030Z
@VivaanDaga no it is rational to undercut even if you loose both short and long term profit. In example in my answer both firms loose both short and long term profit yet they are 100% rational. In my example there was zero deviation from rationality, they were pure rational profit maximizing firms, yet the most rational choice was to choose low price for both of them
1muflon1
CC BY-SA 4.0
2023-08-03T13:43:48.010Z
look let me give you another example. Nuclear arms race. Nuclear weapons are in some sense stupid. They are expensive, they can lead to bad nuclear accident, terrorists might steal them, they have zero tactical use on battlefield and even their strategic use only makes sense when other party does not have one. Yet the thing is that if your opponent lets say China or Russia has them, you have to have them, even though its bad deal for a country to spend money on them. Everyone would be better off if they did not exist
1muflon1
CC BY-SA 4.0
2023-08-03T13:44:59.410Z
but at the same time if there is only 1 single power that has them they have extremely large value. If everyone has them there is no value because of mutually assured destruction only cost. So even though everyone having them is the worst case scenario, it is the rational scenario. If others dont get nuclear weapons its rational for you to invest in them, if others have them you have to have them
1muflon1
CC BY-SA 4.0
2023-08-03T13:46:11.370Z
there are ways how to prevent this prisoner dillema, for example in real world you have anti nuclear weapon proliferation treaties but still all major global powers have them and those that dont dont have them because they are aligned with one of the global powers that has them like Japan or South Korea that are aligned with US, and this is despite that this is the worst case for whole world and there is nothing irrational about this and necessity of this system is upheld by pretty much all military/strategic experts
1muflon1
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2023-08-03T14:17:11.120Z
My point is you should let the other person make the first move, and if they don’t  you both profit!
Vivaan Daga
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2023-08-03T14:20:09.223Z
@VivaanDaga 1. That can sometimes be rational, in fact what you suggest is so called Grimm-Trigger strategy, but it doesn’t work always. 2. In example, I made such strategy is not possible. If I would change the game it might become possible but it’s not always workable it depends on peoples impatience, sometimes it can be stable equilibrium 3. The whole point is that rational profit maximizing agents will not always manage to get the best outcome even when acting purely rationally
1muflon1
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2023-08-03T14:33:56.643Z
Why is it not possible in your example?
Vivaan Daga
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2023-08-03T14:39:28.510Z
@VivaanDaga because it is a finite static example, not dynamic one, such strategies are only possible in infinite dynamic games, subject to other conditions of course for example with too much impatience such outcome is not possible even in such games.
1muflon1
CC BY-SA 4.0
2023-08-03T15:30:05.020Z
but the real world is dynamic?
Vivaan Daga
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2023-08-03T16:59:35.567Z
@VivaanDaga it is dynamic in a sense that time progresses and things change, however, many economic interactions can be thought of as in essence being static. For example, government opens bidding for a road, nobody can see other persons bid or even know who are the other bidders to contact them. All bids are revealed simultaneously. In that case you are dealing with a static interaction even if of course in real time passage of time is unstoppable. Or for example suppose due to various policies and regulations or menu costs its very expensive to change prices every time so you have to make
1muflon1
CC BY-SA 4.0
2023-08-03T17:01:34.450Z
decision once and then stick with it for foreseeable future. Or suppose you are entering into contract that is too expensive to revoke, or building a house in a place without developed housing market so house cannot be resold etc. Next sometimes even dynamic interactions can be simplified into static model without model loosing to much in predictive power etc. For example, map is a simplified 2D model of 3D reality but still has its uses. Similarly sometimes the time dimension can be gotten rid of without rendering the model useless even if there might be some costs in accuracy/realism
1muflon1
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2023-08-05T19:16:12.263Z
Ok. But these seem like outliers the fact that entire economic theory is based on this is a bit dissatisfiying
Vivaan Daga
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2023-08-05T22:03:05.637Z
@VivaanDaga who says entire economic theory is based on it? 1. Real life problems that can be modeled as static are more common than you think even if they are less common than dynamic problems. 2. Large body of economic theory is dynamic. I work on intersection of macro and public policy. Macro is almost all just dynamic models and public policy is about 50/50. 3. You might get the impression from 101 textbooks but the problem there is that for most dynamic problems you need excellent command of differential calculus and most first year undergraduates are not  equipped to handle that
1muflon1
CC BY-SA 4.0
2023-08-16T16:03:51.337Z
Can you give an example of a genuine market that acts like this?
Vivaan Daga
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2023-08-16T16:04:29.050Z
Maybe it is pushed to equilibrium because if firms are making supernormal profits other firms join the market?
Vivaan Daga
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2023-08-16T16:05:03.633Z
Also some people say the price is pushed down because suppliers are unable to sell their product, this reasoning is incorrect?
Vivaan Daga
CC BY-SA 4.0
2023-08-17T19:56:23.383Z
@VivaanDaga as mentioned earlier government procurement is an excellent example. Also note modes are like maps. 100% realistic 3D map of a city is useless as it would be just a perfect recreation and you would still stay lost. Same way models sometimes reduce dimension like time to make other aspects of problem more clear. I think that while not perfect the example I gave you is decent approximation of duopoly in some town competing on prices. For example, in town where I was born there were only 2 ice cream sellers, I think the model above is good enough representation of their strategic
1muflon1
CC BY-SA 4.0
2023-08-17T19:59:26.197Z
Interaction. Also note the model above is just simple example. I could give you dynamic complex problem and derive equilibrium using Hamiltonian or some other method but what’s a point of all that math if you are just novice asking very basic question. Equilibrium exists even in physics and if you would ask physicist for an example of equilibrium you would also get some simplified mathematical example of pendulum in vacuum chamber and they would not throw at you field equations or some dynamic equilibrium that describes flow of gas in sun
1muflon1
CC BY-SA 4.0
2023-08-17T20:01:40.207Z
“ Maybe it is pushed to equilibrium because if firms are making supernormal profits other firms join the market?” <- not in model above, but indeed there are other models that allow for entry where this also pushes price down. Such models exist but in my example there isn’t any new entrant (btw this is why models are powerful, the model above shows that price can be pushed down even without allowing entrants to join under some situation). But sure entry of other firms also pushes price down IRL and in other models
1muflon1
CC BY-SA 4.0
2023-08-17T20:03:14.713Z
“ Also some people say the price is pushed down because suppliers are unable to sell their product, this reasoning is incorrect?” <- again correct reasoning, in some markets this is the reason but it’s again not necessity. In some models this causes price to fall but it’s not the only reason. Also IRL you can get combinations of effects working together.
1muflon1
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2023-08-18T05:52:51.880Z
but even in your model you have ton put several unrealisitic assumptions.
Vivaan Daga
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2023-08-18T08:06:25.193Z
@VivaanDaga of course because it’s a model. A model of solar system you find in a school textbook also has ton of unrealistic assumptions. Completely realistic model of solar system would be useless because it would have to be 1:1 recreation of solar system. The unrealistic assumptions in the model are there to reduce complexity of the problem to showcase that things like entry pressure are not necessary to lower prices. Rationality and imperfect information are enough
1muflon1
CC BY-SA 4.0
2023-08-02T16:19:59.160Z
2023-08-02T16:27:47.430Z
2023-08-02T16:27:47.430Z
1muflon1
<p>It is well known that in a perfectly competitive market, any price would be pushed to equilibrium. Say for instance, that the price was higher than the equilibrium price than a firm lacking demand for their products, would have incentive to lower their price slightly to increase their profit, this process would repeat until all firms are at the equilibrium price. Unfortunately, I feel there is an issue with this argument, the problem is that the firms profit might actually reduce when they reach equilibrium price. So, by that argument not lowering the price would be the rational decision, so how is equilibrium achieved?</p>

CC BY-SA 4.0
2023-08-02T14:37:49.853Z
Hi @Vivaan. Equilibrium is a point of stability where there is no economic incentive to change. A price-taking perfectly competitive firm may therefore lose profit upon converging upon the equilibrium price. The overall point is the perfectly competitive market converges on a point where all profit have been completely exhausted. Why? Because if price-taking firms in a perfectly competitive market did not act like this, then market behaviour would be missing a profit opportunity, and it could be argued that there is superior/more efficient forms of economic organisation if that was the case.
EB3112
CC BY-SA 4.0
2023-08-02T14:48:28.890Z
@EB3112 Missing a profit in the short run, but winning on the long run!
Vivaan Daga
CC BY-SA 4.0
2023-08-02T16:31:39.017Z
@VivaanDaga actually not necessarily, price taking firms will not earn economic  profit even in long run, there simply is too much competition. All profits are competed away in such case, even when firms are profit maximizing. Profit maximization does not mean firm can pick any profit it wants
1muflon1
<microeconomics>
How does equilibrium work?
Vivaan Daga
# How does equilibrium work?

(Asked by: username_0 on 2023-08-02)

It is well known that in a perfectly competitive market, any price would be pushed to equilibrium. Say for instance, that the price was higher than the equilibrium price than a firm lacking demand for their products, would have incentive to lower their price slightly to increase their profit, this process would repeat until all firms are at the equilibrium price. Unfortunately, I feel there is an issue with this argument, the problem is that the firms profit might actually reduce when they reach equilibrium price. So, by that argument not lowering the price would be the rational decision, so how is equilibrium achieved?

**Tags:** microeconomics

> **Comments:**
> **username_1**: Hi @Vivaan. Equilibrium is a point of stability where there is no economic incentive to change. A price-taking perfectly competitive firm may therefore lose profit upon converging upon the equilibrium price. The overall point is the perfectly competitive market converges on a point where all profit have been completely exhausted. Why? Because if price-taking firms in a perfectly competitive market did not act like this, then market behaviour would be missing a profit opportunity, and it could be argued that there is superior/more efficient forms of economic organisation if that was the case.  
> **username_0**: @username_1 Missing a profit in the short run, but winning on the long run!  
> **username_2**: @VivaanDaga actually not necessarily, price taking firms will not earn economic  profit even in long run, there simply is too much competition. All profits are competed away in such case, even when firms are profit maximizing. Profit maximization does not mean firm can pick any profit it wants  

---

## 2 answers

### Answer by username_3 on 2023-08-02. Score: 3

It is not so evident or even clear that "any price would be pushed/converge to equilibrium". For this type of argument to make sense, you need some kind of price adjustment process which determines in what direction and to what degree prices will adjust if, for example, for some markets supply is not equal to demand.

The most well known adjustment process is called the **tâtonnement** process. In this process one assumes that the change in (relative) price of a certain good is proportional to the excess demand for that particular good. So prices increase if demand is greater than supply an vice versa if supply exceeds demand.

There is a lot of (quite difficult) theoretical literature on this topic but the end results are rather mixed. In general a given equilibrium does not need to be tâtonnement stable, not even locally. In fact, there might be equilibria which are very unstable under the tâtonnement process or equilibria that have some kind of strage saddle point type of behaviour.

On the other hand, many (theoretical) economists assume from the start that the economy is always in equilibrium. In this case, there is no need to talk about a price adjustment process towards equilibrium (as we never deviate from equilibrium). Moreover, the price adjustment process (e.g. tâtonnement) is only interesting from an as-if exercise, as it is quite unclear who actually does the price adjustment to bring the markets back to equilibrium (is it the market participants themselves? or is it some benevolent auctioneer). Besides, it is quite strange to talk about price adjustment processes if the underlying economic model is static (what happens during the time that we need to adjust the prices to equilibrium).

> **Comments:**
> **username_0**: Why is assuming equilibrium from the start reasonable?  
> **username_1**: Hi @VivaanDaga. If agents within the economy acted according to neo-classical assumptions and like username_3 said there was some source of tantonment (such as adjustment through expectations), then it may be reasonable to assume that the economy is in equilibrium. Moreover, equilibrium is an operationally important assumption. For example, computable general equilibrium (CGE) models (i.e. very large systems of equations) are parameterised/calibrated on baseline data which is assumed to be in equilibrium. Following this assumption, counterfactual shocks can be introduced into the model.  
> **username_4**: @username_1 there seems to be a self-defeating argument here. username_3 mentions a tatonnement process may not exist or may not lead to a stable equilibrium, hence most economists just assume an equilibrium state; you argue equilibrium state is a reasonable assumption because tatonnement leads to it.  
> **username_1**: Hi @username_4. I disagree. I don't think it is 'self-defeating' to admit that it may be reasonable for economists to draw from neo-classical behavioural assumptions and market clearing-type assumptions when assuming the economy is in an equilibrium state. The fact that they're somewhat contentious/contested assumptions doesn't mean people do not assume them in the background. And even if the modeller didn't assume these, it is indefensible just to say 'I assume equilibrium. End-of." Therefore, I was suggesting to VivD why it may be reasonable; not why it is always and everywhere correct.  
> **username_4**: @username_1 okay, cool, but can you please provide a reference for these neo-classical behavioral assumptions that will definitely cause a GE model to converge to a stable equilibrium? Right now the existence of these is just a claim.  
> **username_1**: Hi @username_4. I never made a definitive statement, and I would not claim to have a single reference in which certain neoclassical assumptions definitely cause (with 100 percent certainty) a stable equilibrium. Instead I say that there is assumed to be the existence of an equilibrium (a stable point) given certain neoclassical assumptions, yet the stability of the equilibrium is a slightly different matter. Which someone like Arrow addressed differently. Please, however, clarify all my points for VivD. I only endeavoured to give hints to VivD (a high schooler), not get embroiled in debate.  
> **username_4**: @username_1 Okay, I was just having difficulties parsing [your sentence](https://economics.stackexchange.com/questions/55983/how-does-equilibrium-work/55984?noredirect=1#comment91744_55984) "*If agents within the economy acted according to neo-classical assumptions and like username_3 said there was some source of tantonment (such as adjustment through expectations), then it may be reasonable to assume that the economy is in equilibrium.*" because I didn't see how it demonstrates the reasonableness in any way, and I was curious. Have nice day!  
> **username_1**: @username_4. You too. I do believe however, that if you can provide a fuller reasonable justification, then you should. If it is an unreasonable to presume, I think you should also identify why. My points reside only as a broad comment.  
> **username_4**: @username_1 I did not see any academic work on this. Personally I think that equilibrium is a poor assumption. For starters, the law of one price is violated all the time; you need to bring in additional variables such as travel and/or search costs to account for this. Second, most real world markets have fairly quickly changing circumstances, making it difficult for the tatonnement process to reach its end before the market becomes too different. Third, I think rationality based models don't fit real life behavior very well, and equilibrium relies on rationality at least implicitly.  
> **username_1**: Hi @username_4. I am in agreement with many of your points. However, I think given that equilibrium is such a pervasive concept in economics, and equilibrium-modelling is the dominant paradigm, that is reasonable to assume from the perspective of a professional modeller. For example, you'd hope that an economics degree would inform you about economic truths, the same way a physics degree may inform you of physical truths.  If however, someone is a keen theorist looking to re-write the foundations of economics, then equilibrium is perhaps an unreasonable assumption. You're right to be sceptical.  

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### Answer by username_2 on 2023-08-02. Score: 1

As the previous answer by TDM says in static equilibrium there is no adjustment. You either are in equilibrium or you are not. In static game everything happens instantaneously. Firms make actions but they occur in an instant.

There is also dynamic equilibrium where adjustment occurs over time, but equilibrium point itself is an equilibrium point precisely because no other agent wants to deviate form it. That is equilibrium occurs when no person wants to do something else than what they are doing now. So in dynamic equilibrium there are no changes, unless it is perturbed by new forces. An physics analogy is pendulum. Pendulum recorded over time is a dynamic system, but equilibrium occurs once pendulum stops swinging. All forces acting on pendulum like gravity etc are in balance (equilibrium is Latin for balance).

Similarly economic dynamic equilibrium occurs when economic forces (e.g. supply, demand, peoples preferences, resources, technology etc) made people act in a such way they don't want to do something different unless there is some shock to the system (change in preferences, technology etc).

Also, even **profit maximizing** firm, acting **completely rationally** might end up in low or zero profit in equilibrium under competitive pressure. Profit maximization only refers to an objective of firm, not outcome that will happen, and firm cannot simply choose profit they like because it is constrained by actions of other firms and customers.

Consider the following simple 'game' between two firms A and B respectively. Both firms can choose two strategies:

Charge high price (H), or low price (L).

If firm A charges H, and firm B also H they both split the market at high price and earn 10 million profit each (suppose H=\$10 and there is 2 million customers with max willingness to pay \$10).

If firm A charges L and B charges H, A captures whole markets but does so at a low price (lets say \$7) so it gets 14 million profit and B gets zero. The reverse happens when B charges L and A charges H.

If both firms charge low price they will split market like with high price but now they both get low profit of 7 million.

This is represented in the payoff table below:

$$
\begin{array}{|c|c|c|}
\hline
\text{A\B} & H & L\\\hline
H & 10, 10 & 0,14 \\\hline
L & 14,0 & 7,7 \\
\hline
\end{array}
$$

We also assume the firms cannot sign contracts that would change payoffs due to antitrust laws, and firms can't observe what the other firm is doing so they have to choose simultaneously.

To find the Nash equilibrium, which tells us what would the rational profit maximizing firms do we have to check their best response against what other firm is doing.

If firm **B** charges **H**, the **best response** of firm **A** is to charge **L**. This is because it will get firm A **maximum profit** 14 million given constraints imposed by B (playing H) and customers.

If firm **B** charges **L** the **best response** of firm **A** is to charge **L** again. This will again give firm A **maximum profit** 7 million under constraints imposed by B's action (playing L) and customers.

Consequently, in the case above it is always the best course of action for firm A to charge low price.

Next we can redo all of the above for firm B, and we will in this game get the same result (since the game is set up to be symmetric). Firm B will also charge low price because it is always the best response.

Hence the equilibrium outcome in the game below is for both firms to charge low price. Equilibrium strategies and pay offs are highlighted red.

$$
\begin{array}{|c|c|c|}
\hline
\text{A\B} & H & \color{red}{L}\\\hline
H & 10, 10 & 0,14 \\\hline
\color{red}{L} & 14,0 & \color{red}{7,7} \\
\hline
\end{array}
$$

In the case above, the firms are rational and profit maximizing yet due to competition they both end up with low profit of 7 million instead of the pareto efficient outcome where they would both get larger profit of 10 million. This might sound counterintuitive given the profit maximizing assumption but again the low 7 million profit is the maximum profit under the constraint of other firms.

If you want to have some adjustment mechanism, you can turn the game above into a game where people play the game repeatedly, in such case sometimes firms can enforce the high price by certain strategies such as so called grim-trigger strategy where rational firms starts playing 'nice' and avoids competing until the other firm tries to screw it and then forever deviates.

What the outcome will be in such dynamic game depends on additional assumptions such as how much impatient each firm is etc.

> **Comments:**
> **username_0**: Why does equilibrium occur when demand and supply are equal? What stops a firm from moving the price up?  
> **username_2**: @VivaanDaga Because it would hurt the firms. For example, suppose supply is given by $S=p$ and demand is given by; $D=100-p$, in such case when $S=D$ equilibrium price is $p_m=50$ and  equilibrium quantity is also $q_m=50$. Producer surplus of all firms with simple linear demand above is $PS= p_mq_m - \int^{q_m}_0 S(q) dq = 2500$. Suppose all firms decide to charge 60, now market quantity is 40, and producer surplus now would be: $PS = p_mq_m - \int^{q_m}_0 S(q) dq =1600$ Firms are significantly worse of by charging price above equilibrium. Now do the opposite experiment  firms charge  
> **username_2**: less 40, at that price market quantity will be also 40, so producer surplus is 800, even worse than before. You can do trial and errors if you want but you will find that producer surplus is maximized when firms charge equilibrium price and provide equilibrium quantity.  
> **username_0**: In the case of linearity yes, but is that an assumption we must make?  
> **username_2**: @VivaanDaga no it works with non linear demand and supply but for that I can’t do the integral in my head so I used it to be able to quickly do the calculations  
> **username_0**: If you are talking how firms would respond, then shouldnt we also consider what B does after A makes its decision of high or low?  
> **username_2**: @VivaanDaga yes, but I do consider it. Read my answer carefully. I have written you can do the same steps I did for A for B. I on purpose created a symmetric problem so firms mirror each other and when you calculate what one does you immediately know what other does. I did this again to make calculation faster, but you can also just manually find best response for firm B, it will be low. So equilibrium strategy is Low Low, or Low for both A and B  
> **username_0**: well, if A goes high, then B would go high then A would go high and they all earn more profit. now suppose someone breaks the cycle, then only the other person goes low. so they both wait for the other to break the cylce, which would be never!  
> **username_2**: @VivaanDaga no in the example I provided when A goes H, B wants to go low. B will always be better of by going low. If A goes H and B goes L B gets 14 million profit. If both go H B gets 10 million, 14 million is clearly > 10 million  
> **username_0**: In the short run not the long run. In the long run you loose out since eventually both would go low.  
> **username_0**: Why should firms want to loose out in the long run?  
> **username_2**: @VivaanDaga they don’t want to… they want to maximize profit, but they are constrained by other people’s action… I explained it in my answer did you miss it? For example, if I open bakery in Utrecht the highest profit I might theoretically get given overall utrecht demand for cakes is perhaps by charging 30 bucks per cake. But my bakery won’t be the only bakery in town, if another person starts baking and charges 29e can I still get the max profit charging 30e? If I then undercut him by charging 28e can he still charge 29e? Read my answer carefully I address it in second half  
> **username_0**: But the rational thing for other person to do would be not to undercut you for that would lead to lower long term profit.  
> **username_2**: @VivaanDaga thats were you wrong, its rational to undercut, as shown in the example in my full answer, and you can prove logically it is rational to undercut the other player (in many market settings of course there are exceptions), you can even prove it mathematically.  
> **username_0**: It’s rational to undercut for immediate profit, but you loose long term profit!!  
> **username_2**: @VivaanDaga no it is rational to undercut even if you loose both short and long term profit. In example in my answer both firms loose both short and long term profit yet they are 100% rational. In my example there was zero deviation from rationality, they were pure rational profit maximizing firms, yet the most rational choice was to choose low price for both of them  
> **username_2**: look let me give you another example. Nuclear arms race. Nuclear weapons are in some sense stupid. They are expensive, they can lead to bad nuclear accident, terrorists might steal them, they have zero tactical use on battlefield and even their strategic use only makes sense when other party does not have one. Yet the thing is that if your opponent lets say China or Russia has them, you have to have them, even though its bad deal for a country to spend money on them. Everyone would be better off if they did not exist  
> **username_2**: but at the same time if there is only 1 single power that has them they have extremely large value. If everyone has them there is no value because of mutually assured destruction only cost. So even though everyone having them is the worst case scenario, it is the rational scenario. If others dont get nuclear weapons its rational for you to invest in them, if others have them you have to have them  
> **username_2**: there are ways how to prevent this prisoner dillema, for example in real world you have anti nuclear weapon proliferation treaties but still all major global powers have them and those that dont dont have them because they are aligned with one of the global powers that has them like Japan or South Korea that are aligned with US, and this is despite that this is the worst case for whole world and there is nothing irrational about this and necessity of this system is upheld by pretty much all military/strategic experts  
> **username_0**: My point is you should let the other person make the first move, and if they don’t  you both profit!  
> **username_2**: @VivaanDaga 1. That can sometimes be rational, in fact what you suggest is so called Grimm-Trigger strategy, but it doesn’t work always. 2. In example, I made such strategy is not possible. If I would change the game it might become possible but it’s not always workable it depends on peoples impatience, sometimes it can be stable equilibrium 3. The whole point is that rational profit maximizing agents will not always manage to get the best outcome even when acting purely rationally  
> **username_0**: Why is it not possible in your example?  
> **username_2**: @VivaanDaga because it is a finite static example, not dynamic one, such strategies are only possible in infinite dynamic games, subject to other conditions of course for example with too much impatience such outcome is not possible even in such games.  
> **username_0**: but the real world is dynamic?  
> **username_2**: @VivaanDaga it is dynamic in a sense that time progresses and things change, however, many economic interactions can be thought of as in essence being static. For example, government opens bidding for a road, nobody can see other persons bid or even know who are the other bidders to contact them. All bids are revealed simultaneously. In that case you are dealing with a static interaction even if of course in real time passage of time is unstoppable. Or for example suppose due to various policies and regulations or menu costs its very expensive to change prices every time so you have to make  
> **username_2**: decision once and then stick with it for foreseeable future. Or suppose you are entering into contract that is too expensive to revoke, or building a house in a place without developed housing market so house cannot be resold etc. Next sometimes even dynamic interactions can be simplified into static model without model loosing to much in predictive power etc. For example, map is a simplified 2D model of 3D reality but still has its uses. Similarly sometimes the time dimension can be gotten rid of without rendering the model useless even if there might be some costs in accuracy/realism  
> **username_0**: Ok. But these seem like outliers the fact that entire economic theory is based on this is a bit dissatisfiying  
> **username_2**: @VivaanDaga who says entire economic theory is based on it? 1. Real life problems that can be modeled as static are more common than you think even if they are less common than dynamic problems. 2. Large body of economic theory is dynamic. I work on intersection of macro and public policy. Macro is almost all just dynamic models and public policy is about 50/50. 3. You might get the impression from 101 textbooks but the problem there is that for most dynamic problems you need excellent command of differential calculus and most first year undergraduates are not  equipped to handle that  
> **username_0**: Can you give an example of a genuine market that acts like this?  
> **username_0**: Maybe it is pushed to equilibrium because if firms are making supernormal profits other firms join the market?  
> **username_0**: Also some people say the price is pushed down because suppliers are unable to sell their product, this reasoning is incorrect?  
> **username_2**: @VivaanDaga as mentioned earlier government procurement is an excellent example. Also note modes are like maps. 100% realistic 3D map of a city is useless as it would be just a perfect recreation and you would still stay lost. Same way models sometimes reduce dimension like time to make other aspects of problem more clear. I think that while not perfect the example I gave you is decent approximation of duopoly in some town competing on prices. For example, in town where I was born there were only 2 ice cream sellers, I think the model above is good enough representation of their strategic  
> **username_2**: Interaction. Also note the model above is just simple example. I could give you dynamic complex problem and derive equilibrium using Hamiltonian or some other method but what’s a point of all that math if you are just novice asking very basic question. Equilibrium exists even in physics and if you would ask physicist for an example of equilibrium you would also get some simplified mathematical example of pendulum in vacuum chamber and they would not throw at you field equations or some dynamic equilibrium that describes flow of gas in sun  
> **username_2**: “ Maybe it is pushed to equilibrium because if firms are making supernormal profits other firms join the market?” <- not in model above, but indeed there are other models that allow for entry where this also pushes price down. Such models exist but in my example there isn’t any new entrant (btw this is why models are powerful, the model above shows that price can be pushed down even without allowing entrants to join under some situation). But sure entry of other firms also pushes price down IRL and in other models  
> **username_2**: “ Also some people say the price is pushed down because suppliers are unable to sell their product, this reasoning is incorrect?” <- again correct reasoning, in some markets this is the reason but it’s again not necessity. In some models this causes price to fall but it’s not the only reason. Also IRL you can get combinations of effects working together.  
> **username_0**: but even in your model you have ton put several unrealisitic assumptions.  
> **username_2**: @VivaanDaga of course because it’s a model. A model of solar system you find in a school textbook also has ton of unrealistic assumptions. Completely realistic model of solar system would be useless because it would have to be 1:1 recreation of solar system. The unrealistic assumptions in the model are there to reduce complexity of the problem to showcase that things like entry pressure are not necessary to lower prices. Rationality and imperfect information are enough  

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