<p>No it does not for several reasons. Labor theory of value (LTV) central tenant is that there is some intrinsic component to value determined objectively by labor  (see Brue and Grant History of Economic Thought  7ed). This implies that there exist some unit of labor in which every value could be measured. In addition, it means that the value (<span class="math-container">$V$</span>) is some sort of function labor <span class="math-container">$L$</span> i.e. <span class="math-container">$V=f(L)$</span>. As stated by Adam Smith in Wealth of Nations who first developed the LTV (and as mentioned in the comments as well):</p>
<blockquote>
<p>&quot;The value of any commodity ... is equal to the quantity of labour which it enables him to purchase or command. <strong>Labour, therefore, is the real measure of the exchangeable value of all commodities.</strong></p>
</blockquote>
<p>Hence, at the core of labor theory of value is proposition that all value can be somehow objectively measured by labor, and that it should depend on labor.</p>
<p>Well there are several problems with that proposition:</p>
<ol>
<li>What about things that require great labor inputs but are worthless (which is situation that can and empirically does arise even in competitive markets as preferences and tastes change and something that was once desired might be trash today)?</li>
</ol>
<p>The LTV actually has no good answer for that. Adam Smith tried to
answer this objection by distinguishing between value in use and
value in exchange. As Smith further writes in his Wealth of Nations:</p>
<blockquote>
<p>The word value, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and sometimes the power of purchasing other goods which the possession of that object conveys. The one may be called &quot;value in use&quot;; the other, &quot;value in exchange.&quot; The things which have the greatest value in use have frequently little or no value in exchange; and, on the contrary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarce anything; scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it.</p>
</blockquote>
<p>This is basically the argument that Marx repeats (although he had different name for it), as mentioned above (indeed I am always surprised that Marx is often quoted regarding LTV given he did not do virtually any original work on the LTV and just took it from Ricardo and Smith).</p>
<p>The problem with this is that it is already quite scientifically undesirable as it is essentially a cop-out. Labor is the source of value, well, except in cases where it isn't because the object is not useful. So already LTV from the get go admits it is not a theory that can explain all value, which is scientifically undesirable as we want to generalize as much as possible. Now, if we would not have alternative theories of value this could be forgiven but given we do have them and they can explain more this in itself is argument for ditching LTV (e.g. we can safely ditch Newtons theory of gravity in favor of relativity as the latter is more general, but even though theory of relativity can't explain everything we cannot ditch because there is no other competing theory that can).</p>
<p>With regards to your main question, already this point 1 proves that in competitive markets LTV does not need to hold as it is completely valid outcome under perfect competition that value of produced good will be 0 (or indeed even negative like with <a href="https://www.reuters.com/article/us-global-oil-idUSKBN2210V9" rel="nofollow noreferrer">oil futures</a>).</p>
<ol start="2">
<li>How to measure value in labor (the problem of transformation)?</li>
</ol>
<p>One of the central tenets of labor theory of value as mentioned
above is that labor must be some sort of real measure of value of
all commodities. However, due to the problem mentioned in point 1 it is also necessary to argue that value of labor will not correspond exactly to the  price.</p>
<p>Hence, this gives raise to the question how to actually establish some correspondence between prices and labor which is also known as the problem of transformation (see <a href="https://www.jstor.org/stable/2721055?seq=1#metadata_info_tab_contents" rel="nofollow noreferrer">Samuelson; 1971</a>). This was in fact a problem that Ricardo devoted considerable amount of time to solve, although he was ultimately unsuccessful.
Samuelson argues there is no general solution to the problem, and although there are some scholars claiming to solve it  there are no generally accepted solutions.</p>
<p>In regards to your question, assuming competitive market does not provide solution to the above problem and without the above being possible it is very hard to sustain claim that value can be somehow objectively measured by labor.</p>
<ol start="3">
<li>Empirically value seems to be orthogonal on labor inputs and this hold regardless of how competitive industry is.</li>
</ol>
<p>There simply does not seem to be any relationship between value and labor inputs. Relative prices fluctuate widely even when labor inputs stay same. This can occur both in theoretical models of perfect competition (e.g. consider two perfectly sectors two goods model with some idiosyncratic demand shocks), and frequently occurs in reality.</p>
<p>Now even if there would be a discrepancy between price and the value of labor that went into producing the product, if there is any objective value determined by labor then you would at the very least expect relative prices to depend on relative labor inputs but they do not and there is no indication that they start doing so in competitive industries. Hence <span class="math-container">$V \perp L$</span>.</p>
<p>This also connects to the previous point, but for LTV to hold it is simply not enough to just show that something that was produced with labor is happens to have value - the value of it should depend on labor input and ultimately be measurable.  What even more it should be <em>the</em>  measuring stick of the value. But this is clearly inconsistent with observation that relative prices change and fluctuate widely even when labor inputs do not.</p>

CC BY-SA 4.0
2020-12-23T10:16:44.993Z
Does point 3 mean there is no direct relation or also no indirect relation? Because to me it sounds logical that the amount of labor input is part of the supply and thus indirectly contributes to the value. Like if there is a demand for something and it takes 1 day to make something more people will try to make it then if it takes 1 year to make it. Thus labor input will influence the supply and thus the price. Maybe I'm missing the definition of value, but I thought it would be price in modern economic theories.
Hakaishin
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2020-12-23T10:29:52.507Z
@Hakaishin 1. As the point 3 is not enough to show that labor in some cases influences price. Under LTV there labor must be able to serve as some sort of unit of value and so for example something that takes 2h to make should be twice as valuable than something that takes 1h to make - we do not observe that empirically. 2. Yes value should be closely related to price (although does not need to be exactly equivalent in all cases) - this is already failure of LTV and why modern economics uses subjective theory of value instead - LTV always needs some hot fixes because price does not have any
1muflon1
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2020-12-23T10:35:49.650Z
discernible relationship with labor inputs. For example, labor inputs of firms are relatively stable - companies usually do not fire employees at a whim on hourly basis. Yet prices can fluctuate even hourly at commodity markets for example. Even in general markets again usually when people are fired hired it is long process yet stores change prices sometimes daily. So the question is why they do that if labor component of the goods is same. LTV does not have any good answer for that save for saying that they fluctuate due to the value of usefulness- which is already half abandoning the LTV
1muflon1
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2020-12-23T10:41:10.403Z
In addition to prices fluctuating *relative* prices fluctuate as well. The last nail to the coffin is that it seems it is even impossible to solve the transformation problem generally (hence labor cannot serve as measurement of value). Now subjective theory of value that states that value depends on people’s subjective judgments and preferences (marginal utility) can explain everything what LTV does and  even things  that LTV cannot, hence there really is no use for LTV anymore.
1muflon1
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2022-03-04T16:13:42.910Z
"What about things that require great labor inputs but are worthless" Isn't one way of addressing that to assume the labor theory of value is talking about the "natural price" that would emerge in the *equilibrium of a competitive market*, after supply and demand have already corrected wasted effort of this nature? For example, suppose we have two models of chairs that both require the exact same amount fo labor time to make, model A is widely considered comfortable and aesthetic, model B is widely considered unconfortable and ugly (but it does have some fans).
Hypnosifl
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2022-03-04T16:18:08.060Z
(cont.) If model A and model B are initially being offered in equal numbers, demand for model B will be much lower, and likely the manufacturers will initially have to lower the price. But in the long term this will result in manufacturers investing less money in making units of model B, and as supply goes down, price will go up; at the equilibrium of [perfect competition](https://archive.ph/ZIdIx), where all prices are equal to production costs, one would expect far less of B to be made than A, in exactly the right ratio so that both can sell at their production cost.
Hypnosifl
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2022-03-04T16:20:15.813Z
@Hypnosifl but what you describe is not labor theory of value anymore. That would be like saying can’t we fix Newtonian physics by assuming that mass bends space time? Sure you can do that but you are replacing Newtonian physics with General Relativity. Under labor theory of value labor has to be the final measuring stick for value. The particular solution which you propose in last two paragraphs of first comment is the marginalist subjective value theory (if people are fans of something they will pay for it - value is dependent on subjective perceptions). That certainly solves all LTV
1muflon1
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2022-03-04T16:27:15.240Z
paradoxes but its a different theory.
1muflon1
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2022-03-04T17:09:45.880Z
@1muflon1 - What aspect of my explanation do you think conflicts with the labor theory of value? Marx did explicitly say that his notion of "value" corresponded to natural price at the equilibrium of supply and demand. Granted, in the microeconomic model of perfect competition there is no profit so Marx's ideas can't fit this model, but one feature of that model is that production rates exactly match consumption rates, I think if we modify this to have a simple model of an expanding economy where prices and proportions are in equilibrium but total numbers are growing, it fits Marx.
Hypnosifl
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2022-03-04T17:24:27.253Z
@Hypnosifl  Demand is literally given by people's subjective valuations of how they value product. Also, no Marx said on LTV literally: "a value determined, as in the case of every other commodity, by the labour time necessary for the production, and consequently also the reproduction, of this special article." - Das Kapital p 120. It is simply incorrect to state that Marx believed value is determined by supply and demand
1muflon1
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2022-03-04T17:32:28.273Z
@1muflon1 - I think your argument depends on ambiguity in the phrase "determined by supply and demand". In the equilibrium of the perfect competition model, the price is "determined by supply and demand" in the sense that there is a background assumption that the back-and-forth between supply and demand will drive an out-of-equilibrium state towards the equilibrium one, but in the equilibrium state itself, prices are always exactly equal to production costs and so in another sense they do not "depend on supply and demand". I would argue that Marx had similar ideas about his version of the LTV.
Hypnosifl
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2022-03-04T17:33:51.647Z
@Hypnosifl "but in the equilibrium state itself, prices are always exactly equal to production costs" - but this is simply demonstrably false.
1muflon1
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2022-03-04T17:34:09.107Z
(cont.) For support for this interpretation of Marx, see [Chapter 6 of his book *Value, Price and Profit*](https://www.marxists.org/archive/marx/works/1865/value-price-profit/ch02.htm#c6) where he writes: *"It suffices to say the if supply and demand equilibrate each other, the market prices of commodities will correspond with their natural prices, that is to say with their values, as determined by the respective quantities of labour required for their production. But supply and demand must constantly tend to equilibrate each other,*
Hypnosifl
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2022-03-04T17:34:55.020Z
(cont.) *a rise by a fall, and vice versa. If instead of considering only the daily fluctuations you analyze the movement of market prices for longer periods, as Mr. Tooke, for example, has done in his History of Prices, you will find that the fluctuations of market prices, their deviations from values, their ups and downs, paralyze and compensate each other; so that apart from the effect of monopolies and some other modifications I must now pass by, all descriptions of commodities are, on average, sold at their respective values or natural prices.”*
Hypnosifl
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2022-03-04T17:37:20.013Z
@1muflon1 "but this is simply demonstrably false" Are you saying it's demonstrably that false that this is a characteristic of the perfect competition model you will find in any textbook on microeconomics, or are you just saying the perfect competition model doesn't match the real world? (It isn't supposed to, it's meant as a simplified approximate model that can be used as a starting point to add more realistic considerations, much like the simplified models used as starting points in the natural sciences, like frictionless motion or treating planets as point particles)
Hypnosifl
CC BY-SA 4.0
2022-03-04T17:40:28.733Z
@Hypnosifl if you can show me single textbook that would show that in perfect competition prices equal production costs I will literally eat my diploma. What you probably mean is that price will equal to the **marginal** cost of production and **marginal** cost of production is the derivative of production costs not production costs
1muflon1
CC BY-SA 4.0
2022-03-04T17:43:29.527Z
moreover, even if you mean marginal costs it is not true that even in perfect competition prices always equal marginal costs, that is long run result in short run that can be violated even in simply textbook models of perfect competition
1muflon1
CC BY-SA 4.0
2022-03-04T17:44:10.897Z
@Hypnosifl also going back to Marx quotes you posted. okay, but this is different argument than what you previously stated in your previous comments. Marx argues here that value is determined by labor value, and market forces happen to equilibrate on that labor value. So this is exactly opposite argument. Here the argument is that value is determined by the labor and then supply and demand makes sure prices are equal to that value. But this is not the same as the argument you put forward in your comments (or maybe you wanted to make this argument but misrepresented it).
1muflon1
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2022-03-04T17:46:39.447Z
also, literally the Marx argument that market should equilibrate on labor value of products, is precisely what can be used to disprove labor theory of value because an implication of that is that in long run the ratio of prices of different objects should correspond to labor inputs of those objects, this was empirically intensively tested in previous century with conclusion that data do not support labor theory of value
1muflon1
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2022-03-04T17:52:32.527Z
in addition, in marx time the concept of supply and demand was not as developed as now. For example, in Marx time it was not yet known that demand depends on subjective marginal utility from consumption, so that is moot point because demand does not even necessarily works as Marx assumed it does. Demand and supply certainly not help to equilibrate on labor value
1muflon1
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2022-03-04T17:53:12.697Z
@1muflon1 - I am talking about the long run outcome of perfect competition. I already supplied a [link to an online textbook on perfect competition](https://archive.ph/ZIdIx) which discusses perfect competition in the long run in section 6.3 and says "In theory, due to competition, homogeneous goods, and perfect information, firms will continue to match and undercut other firms on the price, until the price drops to the point where all remaining firms make an economic profit of zero." Do you think this is wrong, and if not, is it different from saying prices are equal to production costs?
Hypnosifl
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2022-03-04T17:55:26.407Z
@Hypnosifl economic profit will be zero when **revenue** is equal to production costs (including opportunity cost btw, firm can still record even million dollar accounting profit). Revenue is price times quantity. Price itself is equal to marginal costs of production.
1muflon1
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2022-03-04T17:59:11.770Z
@Hypnosifl btw the source you linked to also literally states that: "Otherwise, [meaning in long run when economic profits are driven to zero] the firm should operate at the level where price is equal to marginal cost." - this is how textbook perfect competition works
1muflon1
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2022-03-04T18:02:02.833Z
@1muflon1 - OK, I was speaking imprecisely, I should have said "production-cost-per-unit". Do you agree that in the long run of perfect competition, production-cost-per-unit is equal to the price of a unit of the same good? And so if we assume that all production costs on a given unit boil down to labor costs, and all forms of manual labor that go into making that unit pay the same hourly wage, then in perfect competition with these additional assumptions, price will be proportional to labor time.
Hypnosifl
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2022-03-04T18:08:31.223Z
but its marginal costs (MC) not "production-cost-per-unit". e.g., if cost of first unit is \$60 second unit \$80 and third unit \$100, there wont be 3 different market prices, the market price simply will be 100 dollars - MC. Only if you assume some simple cost function such as C(q)= cq marginal cost = cost per unit. Also let me stress this as it is really important that this includes opportunity cost. e.g., if the capitalist could invest the same money they invest in company into bonds yielding \$100 profit, the competitive price must cover this lost profit that in econ is considered cost.
1muflon1
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2022-03-04T18:14:51.643Z
if you assume simple cost function, like C(q) = L*q where L is some labor input, assume away any opportunity cost, and assume long run perfect competition, without any perturbations to the system, then yes price in perfectly competitive market would in long run be proportional to labor input, but that in itself does not prove LTV because first, even if you assume subjective theory of value you will get the same result so you cannot judge which theory of value is correct based on this thought experiment. Second, most of those assumptions you need to make are not realistic anyway and this result
1muflon1
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2022-03-04T18:18:51.673Z
would not be robust to change in extremely unrealistic assumptions (such as assuming away any opportunity costs), or assuming that production depends only on labor inputs, or even assuming that cost function can be simply described in a way marginal costs are constant (although that in itself would not be as unrealistic as the first two)
1muflon1
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2022-03-04T18:20:01.110Z
@1muflon1 - But in the long run equilibrium of perfect competition, the number of units produced per unit time, the total production cost per unit time, and the total revenue per unit time are all completely fixed for each and every firm, if any of these numbers are varying with time that indicates the system hasn't yet reached the long run equilibrium--do you disagree? If not, the production-cost-per-unit in the equilibrium state can simply be defined as yearly total production cost in making a type of good divided by yearly number of units of that good produced.
Hypnosifl
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2022-03-04T18:29:16.240Z
@Hypnosifl I am getting confused by your non-standard terminology. What exactly is production cost per unit? Because in my mind that is the cost of a unit produced for example if I have 3 widgets and w1 costs 10 w2 costs 20 and w3 costs 30 then I understand it as that cost per unit of w1 was 10, w2 was 20 and w3 was 30 but based on your last comment it looks like you want to talk about **average** costs TC/Q. To avoid any conclusion, could you please give me equation you would use to calculate production cost per unit?
1muflon1
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2022-03-04T18:49:56.933Z
@1muflon1 - Yes, apologies if I'm using non-standard terminology, my background is in physics rather than economics, but I've read enough about perfect competition and the LTV to think there are some logical connections there. So here I'm just talking about averages at equilibrium, if we consider firms that only produce a single type of good such as a widget, the per-unit production cost I'm interested in (feel free to pick whatever term you like for this) could just be defined as (total production costs for all widgets made per year)/(total number of widgets made per year).
Hypnosifl
CC BY-SA 4.0
2022-03-04T18:50:28.560Z
But as a side note, I would have thought, just based on a general knowledge of what simplified equilibrium models are like in other sciences, that one of the simplifying assumptions is that the rates of all processes are treated as constant no matter how finely you divide up time. So I’d have guessed that in the long run equilibrium of perfect competition, we could for example meaningfully talk about number of widgets per microsecond, production costs per microsecond etc.,
Hypnosifl
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2022-03-04T18:51:01.533Z
and that these rates would be fixed from one microsecond to the next, it wouldn’t be as if widgets were costing more to produce on a microsecond on day 1 vs. a microsecond on day 4, and that the ratio only attained a fixed value when averaged over some longer time span like a year; instead the ratio would be the same regardless of the time interval chosen. Is my assumption about what "equilibrium" means here incorrect?
Hypnosifl
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2022-03-04T18:57:44.697Z
@Hypnosifl that would be average cost (AC) then. Also, in long run you can certainly show that MC=AC because firms will enter or exit until that will happen. Well the issue is that the models you refer to (for example, the link you sent) are not dynamic models. Long-run and short-run in economics does not refer to passage of time. i.e. there is not some amount of units of $t$ after which you can say we are in long run. Long run is defined as a situation where firms can enter and exist market freely. The simple textbook model basically has two modes (short run mode where entry is prohibited)
1muflon1
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2022-03-04T18:58:05.237Z
long run mode where entry is allowed, and then you simply derive equilibrium under both modes. Also we don't really call it mode thats just a word that I use because maybe it will be easier for you to imagine.
1muflon1
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2022-03-04T19:02:28.953Z
in perfect competition both in short run (SR) and long run (LR) firm maximizes profit subject to its output as a control variable $\Pi = PQ -C(q)$, as a physicist you must be familiar with calculus, so you should see from this that the condition to maximize profit will be $p=C'(q)$ or price is equal to marginal cost. But in the LR firms are allowed to enter and exist industry where the entry condition for new firm is that $\Pi > 0$ and exit condition is that $\Pi<0$, as a consequence it would be valid to say that in LR price also happens to be equal to AC as otherwise $\Pi \neq 0$
1muflon1
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2022-03-04T19:03:52.743Z
but price is still determined by condition $p=C'(q)$  just entry and exit make sure that  $p=C'(q)=C(q)/q$ at least under standard cost functions used in many intro textbooks
1muflon1
CC BY-SA 4.0
2022-03-04T19:04:33.220Z
@1muflon1 - "that would be average cost (AC) then" So in that case would you agree that in the long run of perfect competition, average cost of a good is equal to market price of that good? Also, when I talked about time I wasn't talking about some kind of transition from short run to long run--I assume, again in analogy with equilibrium models in other branches of science, that we treat the system as if it remains in the same equilibrium state from t=-infinity to t=+infinity. But there is still a temporal coordinate so we can talk about number of widgets made per day vs. per year etc., no?
Hypnosifl
CC BY-SA 4.0
2022-03-04T20:05:09.620Z
@Hypnosifl sure in the simple textbook version of perfect competition with its assumptions on cost function in LR you price will happen to be also equal to AC, I can agree on that. No the textbook version of a perfect competition is not dynamic model. Essentially the simple textbook version is not one model but two models. A model of how perfectly competitive firms behave in SR and model how they behave in LR. You can have a dynamic model but that does not work exactly the same way as the undergraduate version. In dynamic model also firm maximizes expected profit not actual profit etc
1muflon1
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2022-03-04T20:30:25.513Z
@1muflon1 - When you say it's not a dynamic model do you mean that all the variables have fixed values in time, or do you mean there isn't a time coordinate at all, so that when you consider equations with derivatives they are just the derivatives of one economic variable wrt another, not with regard to time? Even if it's the latter case, aren’t the equilibrium values at least conceptually understood as attractors for some time-based process where the economic variables converge on those values, and then remain at those values at all later times?
Hypnosifl
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2022-03-04T20:30:55.603Z
For example, [this section](https://en.wikipedia.org/wiki/General_equilibrium_theory#Walrasian_equilibrium) of the wiki article on general equilibrium theory says “Walras also proposed a dynamic process by which general equilibrium might be reached, that of the tâtonnement or groping process.” Even if economists have not developed any standard time-based differential equations stating the rate of change of one economic variable given the instantaneous values of other vbls, and shown that these equations cause convergence to equilibrium,
Hypnosifl
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2022-03-04T20:31:59.387Z
I’d guess it would at least be possible to develop some agent-based numerical model (with agents and firms having the properties assumed by the perfect competition model, like perfect information) where one could observe such a convergence “empirically” if one starts the simulation in a state where the variables deviate (perhaps by a small amount) from the equilibrium values.
Hypnosifl
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2022-03-04T20:35:45.660Z
@Hypnosifl in the undergraduate textbook model of perfect competition you referenced there is no temporal dimension.  Of course there is a graduate version where there is one but there results are not exactly same eg you work with expected profit there is only zero economic profit in ex ante expectations not actually realized zero profit etc. Yes in the simple undergraduate model variables are not functions of time so derivative wrt time would not make sense.
1muflon1
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2022-03-04T20:37:07.563Z
@Hypnosifl right but I am not saying that in economics we dont have dynamic models. You can have dynamic walrasian models, but let me stress again, the *undergraduate version of perfect competition model* you referenced does not have any temporal dimension, thats simply too complex for average undergraduate to handle because once you introduce dynamics you need to deal with expectations and those are quite complex
1muflon1
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2022-03-04T20:39:17.387Z
you can have also agent based models. Again dynamic models and agent based models exist but the model of perfect competition that you referenced simply does not have it. That would be like me picking a textbook model from physics textbook that assumes no air resistance and then asking if physics did not yet developed such models. I presume that all 101 textbook physics models have their more complex counterparts. If not, then in economics they certainly have, in intro classes we typically get rid of most of the temporal dynamics except for stuff like growth theory where its impossible
1muflon1
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2022-03-04T22:41:16.773Z
@1muflon1 - Thanks for the clarification on how the perfect competition model is actually defined. If there are *some* more complex models with a temporal dimension that predict the same unchanging equilibrium values for the same variables that are solved for in perfect competition, then perhaps you could substitute the name of such a model for "perfect competition" in my earlier comments about the per-unit-production-cost of a widget being the same as its average production cost? Leaving aside the part about Marx and LTV for now, would you still object to my comments in that case?
Hypnosifl
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2022-03-04T22:41:28.557Z
Also, even without naming such a specific model, isn’t it fair to say that when economists refer to the notion “perfect competition” they may not be referring only to the mathematical elements, but also to some conceptual background elements of a simple hypothetical economy the equations are supposed to characterize? For example, textbooks will refer to buyers having perfect information, but the equations in an undergraduate textbook wouldn’t include variables that characterize what knowledge buyers have, would they?
Hypnosifl
CC BY-SA 4.0
2022-03-04T22:41:42.203Z
And if “perfect competition” can be said to refer to some background conceptual assumptions as well as to the equations, I think it would be reasonable to include the idea that the model economy had arrived at these values for the variables after some time-based “groping process” of the kind suggested by Walras, and that once it arrived at them (or got arbitrarily close) it continued to stay at them (or arbitrarily close) at all subsequent times.
Hypnosifl
CC BY-SA 4.0
2022-03-04T22:53:41.310Z
@Hypnosifl in a dynamic setting it would no longer be true that there has to be zero economic profit ex post so there is no reason to believe price should be equal to average costs of production in long run. Also to further clarify perfect competition is a market structure. This market structure can be modeled in various ways. A perfect competition would be equivalent for let's say gravity that could be modeled using Newtonian dynamics or GR. But from your comments its clear that you were talking about the undergraduate model of perfect competition not some dynamic model of perfect competition
1muflon1
CC BY-SA 4.0
2022-03-04T22:56:02.830Z
yes, I think I accidentally got you confused. perfect competition is market structure, but this market structure can be modeled in various ways. Statically, dynamically, with different assumptions on cost function etc. This can yield different results sometimes. For example, you can have model of perfect competition with heterogenous firms - where firms have different cost structure, where now some firms can earn positive profits  (but don't confuse it with models with heterogenous products that would not be perfect competition anymore)
1muflon1
CC BY-SA 4.0
2022-03-04T22:59:09.177Z
perfect competition is a market structure where you have large number of sellers (approaching infinity), all firms are price takers and products are homogenous. Also there should not be any market failures present. Furthermore, entry and exit has to be assumed to be free. If some of the above is violated then we would talk about different market structure, if goods are differentiated then it would be a model of monopolistic competition. If the goods are homogenous but number of firms is small oligopoly etc.
1muflon1
CC BY-SA 4.0
2022-03-04T23:13:05.407Z
@Hypnosifl yea but once you involve dynamics the problem changes. Because for example, if firm maximizes $E[ \sum_{t=0}^T\beta^t\Pi]$, then things get more complicated because expectations imply there is some randomness in the system. Profit will be some distribution and firm will try to maximize the expected value of that distribution. In that case its not guaranteed that in equilibrium profit will be constant quantity.Equilibrium is situation where no agent would like to deviate from strategy they pursue. Firms and consumers may pick production and consumption schedules that max their
1muflon1
CC BY-SA 4.0
2022-03-04T23:17:41.897Z
welfare in ex ante expectation, but then ex post due to random error there is no guarantee what the utility will end up being. For example, if someone offers you choice between two gambles A: 50\%*100e 50\%*0e and B:   50\%*1000e 50\%*0e and assuming you are risk neutral and want to maximize your expected payoff clearly option B is your preferred choice and that would be equilibrium strategy you would keep choosing but there is no guarantee you will get 1000e you might get 0e
1muflon1
CC BY-SA 4.0
2022-03-04T23:46:17.833Z
@1muflon1 "But from your comments its clear that you were talking about the undergraduate model of perfect competition not some dynamic model of perfect competition" Well, I'm talking about a dynamic economic model which matches the conceptual features that define perfect competition (perfect information etc.) and which converges over time on the actual time-independent values of economic variables predicted by the undergraduate model (or if it has those values to start, then the dynamics keep it fixed on those values). Are you saying that no such dynamic model is known to economists?
Hypnosifl
CC BY-SA 4.0
2022-03-04T23:49:48.140Z
Just doing some googling, there are some papers by Mark Satterthwaite and Artyom Shneyerov that seem to be talking about "Convergence to Perfect Competition" in models of markets that have a dynamic element, see [here](https://www.kellogg.northwestern.edu/faculty/satterthwaite/Research/2007-0718a%20dda%20exogexit%20final.pdf) and [here](https://www.kellogg.northwestern.edu/faculty/satterthwaite/research/Dynamic%20Matching.pdf) and [here](http://papers.economics.ubc.ca/legacypapers/dp0504.pdf)
Hypnosifl
CC BY-SA 4.0
2022-03-05T07:28:18.757Z
@Hypnosifl 1. those are 2 papers the first two links are 2 links to 2 version of the same paper. 2. Also previously you stated you want to talk about models of perfect information and these models are models of imperfect information. 3. These are auction models they don't even have production in them. The cost there are opportunity costs of trade not production costs. 4. As the paper in first two links states the competitive price is such that "That the resulting allocations give traders the expected utility they would realize in a
1muflon1
CC BY-SA 4.0
2022-03-05T07:32:13.543Z
perfectly competitive market follows"". **This is exactly what I was trying to explain**. Results in these dynamic models are results that hold in expectations. Let me give you simple example, I will talk about profit not to complicate things with utility. If the probability distribution of revenue is such that with 50\% revenue is 100 and with 50\% rev. is 0 and seller has opportunity cost of 50, then you will get zero economic profit in expectation since expected revenue $E[R] = 0.5 \cdot 100+ 0.5 \cdot 0= 50$ so with 50 opportunity cost the expected economic profit is zero $E[\Pi]=50-50=0$
1muflon1
CC BY-SA 4.0
2022-03-05T07:35:59.263Z
but that is different from claiming that realized (ex post) profit will be 0, the ex post profit can be either 100-50= 50  or 0-50 = -50. It cannot actually be 0, the same way as the coin toss cannot be 0.5 even though thats the expected value you would expected from fair coin (if tail is 1 and face is 0). What could happen is that once you repeat the game over a large amount of time the *cumulative* profit over all time periods would converge to zero, but in this case you can really claim that prices equal  average costs of those products
1muflon1
CC BY-SA 4.0
2020-12-23T04:28:05.357Z
2020-12-23T04:28:05.357Z
1muflon1
<p>Most criticisms of the Labor Theory of Value I have come across go something like this quote from Carl Menger:</p>
<blockquote>
<p>There is no necessary and direct connection between the value of a
good and whether, or in what quantities, labor and other goods of
higher order were applied to its production. A non-economic good (a
quantity of timber in a virgin forest, for example) does not attain
value for men since large quantities of labor or other economic goods
were not applied to its production. Whether a diamond was found
accidentally or was obtained from a diamond pit with the employment of
a thousand days of labor is completely irrelevant for its value.</p>
</blockquote>
<p>This is perfectly obvious and Marx even mentions this:</p>
<blockquote>
<p>A commodity, such as iron, corn, or a diamond, is therefore, so far as
it is a material thing, a use value, something useful. This property
of a commodity is independent of the amount of labour required to
appropriate its useful qualities.</p>
</blockquote>
<p>But putting aside the natural resource example for a moment, in the long term in a competitive market isn't it the case that if there is a situation where someone is able to sell something for more than the cost of the labor that went into it, someone else should be able to step in and sell that thing for a lower price? Eventually prices will go down until they are stopped by another constraint. That constraint being the cost of all the labor required to produce the product.</p>
<p>In situations where this doesn't happen isn't it an indication of some anti-competitive force?
Monopoly of a natural resource, monopoly of a technology through a patent, externalities that result in a small number of large companies, cooperation between large companies to set prices, etc...</p>
<p>So is it fair to say that in the long term in competitive markets the labor theory of value holds?</p>
<p>If the theory is &quot;at any point in time a commodity is worth as much as the cost of labor that went into it&quot; then it is obviously wrong and I can't imagine any classical economist would have believed it.
But if the theory is &quot;over time the cost of a good will tend towards the cost of the amount of labor that went into it assuming the market is competitive&quot; then it still seems plausible.</p>

CC BY-SA 4.0
2020-12-23T02:40:26.187Z
What happened 1870? Léon Walras and his pioneering 1874 work Elements of Pure Economics
Jesper Hybel
<competition><pricing><marxism>
Does the Labor Theory of Value hold in the long term in competitive markets?
markv12
# Does the Labor Theory of Value hold in the long term in competitive markets?

(Asked by: username_0 on 2020-12-23)

Most criticisms of the Labor Theory of Value I have come across go something like this quote from Carl Menger:

> There is no necessary and direct connection between the value of a
> good and whether, or in what quantities, labor and other goods of
> higher order were applied to its production. A non-economic good (a
> quantity of timber in a virgin forest, for example) does not attain
> value for men since large quantities of labor or other economic goods
> were not applied to its production. Whether a diamond was found
> accidentally or was obtained from a diamond pit with the employment of
> a thousand days of labor is completely irrelevant for its value.

This is perfectly obvious and Marx even mentions this:

> A commodity, such as iron, corn, or a diamond, is therefore, so far as
> it is a material thing, a use value, something useful. This property
> of a commodity is independent of the amount of labour required to
> appropriate its useful qualities.

But putting aside the natural resource example for a moment, in the long term in a competitive market isn't it the case that if there is a situation where someone is able to sell something for more than the cost of the labor that went into it, someone else should be able to step in and sell that thing for a lower price? Eventually prices will go down until they are stopped by another constraint. That constraint being the cost of all the labor required to produce the product.

In situations where this doesn't happen isn't it an indication of some anti-competitive force?
Monopoly of a natural resource, monopoly of a technology through a patent, externalities that result in a small number of large companies, cooperation between large companies to set prices, etc...

So is it fair to say that in the long term in competitive markets the labor theory of value holds?

If the theory is "at any point in time a commodity is worth as much as the cost of labor that went into it" then it is obviously wrong and I can't imagine any classical economist would have believed it.
But if the theory is "over time the cost of a good will tend towards the cost of the amount of labor that went into it assuming the market is competitive" then it still seems plausible.

**Tags:** competition, pricing, marxism

> **Comments:**
> **username_1**: What happened 1870? Léon Walras and his pioneering 1874 work Elements of Pure Economics  

---

## 1 answers

### Answer by username_2 on 2020-12-23. Score: 4 | Accepted answer

No it does not for several reasons. Labor theory of value (LTV) central tenant is that there is some intrinsic component to value determined objectively by labor (see Brue and Grant History of Economic Thought 7ed). This implies that there exist some unit of labor in which every value could be measured. In addition, it means that the value ($V$) is some sort of function labor $L$ i.e. $V=f(L)$. As stated by Adam Smith in Wealth of Nations who first developed the LTV (and as mentioned in the comments as well):

> "The value of any commodity ... is equal to the quantity of labour which it enables him to purchase or command. **Labour, therefore, is the real measure of the exchangeable value of all commodities.**

Hence, at the core of labor theory of value is proposition that all value can be somehow objectively measured by labor, and that it should depend on labor.

Well there are several problems with that proposition:

1. What about things that require great labor inputs but are worthless (which is situation that can and empirically does arise even in competitive markets as preferences and tastes change and something that was once desired might be trash today)?

The LTV actually has no good answer for that. Adam Smith tried to
answer this objection by distinguishing between value in use and
value in exchange. As Smith further writes in his Wealth of Nations:

> The word value, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and sometimes the power of purchasing other goods which the possession of that object conveys. The one may be called "value in use"; the other, "value in exchange." The things which have the greatest value in use have frequently little or no value in exchange; and, on the contrary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarce anything; scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it.

This is basically the argument that Marx repeats (although he had different name for it), as mentioned above (indeed I am always surprised that Marx is often quoted regarding LTV given he did not do virtually any original work on the LTV and just took it from Ricardo and Smith).

The problem with this is that it is already quite scientifically undesirable as it is essentially a cop-out. Labor is the source of value, well, except in cases where it isn't because the object is not useful. So already LTV from the get go admits it is not a theory that can explain all value, which is scientifically undesirable as we want to generalize as much as possible. Now, if we would not have alternative theories of value this could be forgiven but given we do have them and they can explain more this in itself is argument for ditching LTV (e.g. we can safely ditch Newtons theory of gravity in favor of relativity as the latter is more general, but even though theory of relativity can't explain everything we cannot ditch because there is no other competing theory that can).

With regards to your main question, already this point 1 proves that in competitive markets LTV does not need to hold as it is completely valid outcome under perfect competition that value of produced good will be 0 (or indeed even negative like with [oil futures](https://www.reuters.com/article/us-global-oil-idUSKBN2210V9)).

2. How to measure value in labor (the problem of transformation)?

One of the central tenets of labor theory of value as mentioned
above is that labor must be some sort of real measure of value of
all commodities. However, due to the problem mentioned in point 1 it is also necessary to argue that value of labor will not correspond exactly to the price.

Hence, this gives raise to the question how to actually establish some correspondence between prices and labor which is also known as the problem of transformation (see [Samuelson; 1971](https://www.jstor.org/stable/2721055?seq=1#metadata_info_tab_contents)). This was in fact a problem that Ricardo devoted considerable amount of time to solve, although he was ultimately unsuccessful.
Samuelson argues there is no general solution to the problem, and although there are some scholars claiming to solve it there are no generally accepted solutions.

In regards to your question, assuming competitive market does not provide solution to the above problem and without the above being possible it is very hard to sustain claim that value can be somehow objectively measured by labor.

3. Empirically value seems to be orthogonal on labor inputs and this hold regardless of how competitive industry is.

There simply does not seem to be any relationship between value and labor inputs. Relative prices fluctuate widely even when labor inputs stay same. This can occur both in theoretical models of perfect competition (e.g. consider two perfectly sectors two goods model with some idiosyncratic demand shocks), and frequently occurs in reality.

Now even if there would be a discrepancy between price and the value of labor that went into producing the product, if there is any objective value determined by labor then you would at the very least expect relative prices to depend on relative labor inputs but they do not and there is no indication that they start doing so in competitive industries. Hence $V \perp L$.

This also connects to the previous point, but for LTV to hold it is simply not enough to just show that something that was produced with labor is happens to have value - the value of it should depend on labor input and ultimately be measurable. What even more it should be *the* measuring stick of the value. But this is clearly inconsistent with observation that relative prices change and fluctuate widely even when labor inputs do not.

> **Comments:**
> **username_3**: Does point 3 mean there is no direct relation or also no indirect relation? Because to me it sounds logical that the amount of labor input is part of the supply and thus indirectly contributes to the value. Like if there is a demand for something and it takes 1 day to make something more people will try to make it then if it takes 1 year to make it. Thus labor input will influence the supply and thus the price. Maybe I'm missing the definition of value, but I thought it would be price in modern economic theories.  
> **username_2**: @username_3 1. As the point 3 is not enough to show that labor in some cases influences price. Under LTV there labor must be able to serve as some sort of unit of value and so for example something that takes 2h to make should be twice as valuable than something that takes 1h to make - we do not observe that empirically. 2. Yes value should be closely related to price (although does not need to be exactly equivalent in all cases) - this is already failure of LTV and why modern economics uses subjective theory of value instead - LTV always needs some hot fixes because price does not have any  
> **username_2**: discernible relationship with labor inputs. For example, labor inputs of firms are relatively stable - companies usually do not fire employees at a whim on hourly basis. Yet prices can fluctuate even hourly at commodity markets for example. Even in general markets again usually when people are fired hired it is long process yet stores change prices sometimes daily. So the question is why they do that if labor component of the goods is same. LTV does not have any good answer for that save for saying that they fluctuate due to the value of usefulness- which is already half abandoning the LTV  
> **username_2**: In addition to prices fluctuating *relative* prices fluctuate as well. The last nail to the coffin is that it seems it is even impossible to solve the transformation problem generally (hence labor cannot serve as measurement of value). Now subjective theory of value that states that value depends on people’s subjective judgments and preferences (marginal utility) can explain everything what LTV does and  even things  that LTV cannot, hence there really is no use for LTV anymore.  
> **username_4**: "What about things that require great labor inputs but are worthless" Isn't one way of addressing that to assume the labor theory of value is talking about the "natural price" that would emerge in the *equilibrium of a competitive market*, after supply and demand have already corrected wasted effort of this nature? For example, suppose we have two models of chairs that both require the exact same amount fo labor time to make, model A is widely considered comfortable and aesthetic, model B is widely considered unconfortable and ugly (but it does have some fans).  
> **username_4**: (cont.) If model A and model B are initially being offered in equal numbers, demand for model B will be much lower, and likely the manufacturers will initially have to lower the price. But in the long term this will result in manufacturers investing less money in making units of model B, and as supply goes down, price will go up; at the equilibrium of [perfect competition](https://archive.ph/ZIdIx), where all prices are equal to production costs, one would expect far less of B to be made than A, in exactly the right ratio so that both can sell at their production cost.  
> **username_2**: @username_4 but what you describe is not labor theory of value anymore. That would be like saying can’t we fix Newtonian physics by assuming that mass bends space time? Sure you can do that but you are replacing Newtonian physics with General Relativity. Under labor theory of value labor has to be the final measuring stick for value. The particular solution which you propose in last two paragraphs of first comment is the marginalist subjective value theory (if people are fans of something they will pay for it - value is dependent on subjective perceptions). That certainly solves all LTV  
> **username_2**: paradoxes but its a different theory.  
> **username_4**: @username_2 - What aspect of my explanation do you think conflicts with the labor theory of value? Marx did explicitly say that his notion of "value" corresponded to natural price at the equilibrium of supply and demand. Granted, in the microeconomic model of perfect competition there is no profit so Marx's ideas can't fit this model, but one feature of that model is that production rates exactly match consumption rates, I think if we modify this to have a simple model of an expanding economy where prices and proportions are in equilibrium but total numbers are growing, it fits Marx.  
> **username_2**: @username_4  Demand is literally given by people's subjective valuations of how they value product. Also, no Marx said on LTV literally: "a value determined, as in the case of every other commodity, by the labour time necessary for the production, and consequently also the reproduction, of this special article." - Das Kapital p 120. It is simply incorrect to state that Marx believed value is determined by supply and demand  
> **username_4**: @username_2 - I think your argument depends on ambiguity in the phrase "determined by supply and demand". In the equilibrium of the perfect competition model, the price is "determined by supply and demand" in the sense that there is a background assumption that the back-and-forth between supply and demand will drive an out-of-equilibrium state towards the equilibrium one, but in the equilibrium state itself, prices are always exactly equal to production costs and so in another sense they do not "depend on supply and demand". I would argue that Marx had similar ideas about his version of the LTV.  
> **username_2**: @username_4 "but in the equilibrium state itself, prices are always exactly equal to production costs" - but this is simply demonstrably false.  
> **username_4**: (cont.) For support for this interpretation of Marx, see [Chapter 6 of his book *Value, Price and Profit*](https://www.marxists.org/archive/marx/works/1865/value-price-profit/ch02.htm#c6) where he writes: *"It suffices to say the if supply and demand equilibrate each other, the market prices of commodities will correspond with their natural prices, that is to say with their values, as determined by the respective quantities of labour required for their production. But supply and demand must constantly tend to equilibrate each other,*  
> **username_4**: (cont.) *a rise by a fall, and vice versa. If instead of considering only the daily fluctuations you analyze the movement of market prices for longer periods, as Mr. Tooke, for example, has done in his History of Prices, you will find that the fluctuations of market prices, their deviations from values, their ups and downs, paralyze and compensate each other; so that apart from the effect of monopolies and some other modifications I must now pass by, all descriptions of commodities are, on average, sold at their respective values or natural prices.”*  
> **username_4**: @username_2 "but this is simply demonstrably false" Are you saying it's demonstrably that false that this is a characteristic of the perfect competition model you will find in any textbook on microeconomics, or are you just saying the perfect competition model doesn't match the real world? (It isn't supposed to, it's meant as a simplified approximate model that can be used as a starting point to add more realistic considerations, much like the simplified models used as starting points in the natural sciences, like frictionless motion or treating planets as point particles)  
> **username_2**: @username_4 if you can show me single textbook that would show that in perfect competition prices equal production costs I will literally eat my diploma. What you probably mean is that price will equal to the **marginal** cost of production and **marginal** cost of production is the derivative of production costs not production costs  
> **username_2**: moreover, even if you mean marginal costs it is not true that even in perfect competition prices always equal marginal costs, that is long run result in short run that can be violated even in simply textbook models of perfect competition  
> **username_2**: @username_4 also going back to Marx quotes you posted. okay, but this is different argument than what you previously stated in your previous comments. Marx argues here that value is determined by labor value, and market forces happen to equilibrate on that labor value. So this is exactly opposite argument. Here the argument is that value is determined by the labor and then supply and demand makes sure prices are equal to that value. But this is not the same as the argument you put forward in your comments (or maybe you wanted to make this argument but misrepresented it).  
> **username_2**: also, literally the Marx argument that market should equilibrate on labor value of products, is precisely what can be used to disprove labor theory of value because an implication of that is that in long run the ratio of prices of different objects should correspond to labor inputs of those objects, this was empirically intensively tested in previous century with conclusion that data do not support labor theory of value  
> **username_2**: in addition, in marx time the concept of supply and demand was not as developed as now. For example, in Marx time it was not yet known that demand depends on subjective marginal utility from consumption, so that is moot point because demand does not even necessarily works as Marx assumed it does. Demand and supply certainly not help to equilibrate on labor value  
> **username_4**: @username_2 - I am talking about the long run outcome of perfect competition. I already supplied a [link to an online textbook on perfect competition](https://archive.ph/ZIdIx) which discusses perfect competition in the long run in section 6.3 and says "In theory, due to competition, homogeneous goods, and perfect information, firms will continue to match and undercut other firms on the price, until the price drops to the point where all remaining firms make an economic profit of zero." Do you think this is wrong, and if not, is it different from saying prices are equal to production costs?  
> **username_2**: @username_4 economic profit will be zero when **revenue** is equal to production costs (including opportunity cost btw, firm can still record even million dollar accounting profit). Revenue is price times quantity. Price itself is equal to marginal costs of production.  
> **username_2**: @username_4 btw the source you linked to also literally states that: "Otherwise, [meaning in long run when economic profits are driven to zero] the firm should operate at the level where price is equal to marginal cost." - this is how textbook perfect competition works  
> **username_4**: @username_2 - OK, I was speaking imprecisely, I should have said "production-cost-per-unit". Do you agree that in the long run of perfect competition, production-cost-per-unit is equal to the price of a unit of the same good? And so if we assume that all production costs on a given unit boil down to labor costs, and all forms of manual labor that go into making that unit pay the same hourly wage, then in perfect competition with these additional assumptions, price will be proportional to labor time.  
> **username_2**: but its marginal costs (MC) not "production-cost-per-unit". e.g., if cost of first unit is \$60 second unit \$80 and third unit \$100, there wont be 3 different market prices, the market price simply will be 100 dollars - MC. Only if you assume some simple cost function such as C(q)= cq marginal cost = cost per unit. Also let me stress this as it is really important that this includes opportunity cost. e.g., if the capitalist could invest the same money they invest in company into bonds yielding \$100 profit, the competitive price must cover this lost profit that in econ is considered cost.  
> **username_2**: if you assume simple cost function, like C(q) = L*q where L is some labor input, assume away any opportunity cost, and assume long run perfect competition, without any perturbations to the system, then yes price in perfectly competitive market would in long run be proportional to labor input, but that in itself does not prove LTV because first, even if you assume subjective theory of value you will get the same result so you cannot judge which theory of value is correct based on this thought experiment. Second, most of those assumptions you need to make are not realistic anyway and this result  
> **username_2**: would not be robust to change in extremely unrealistic assumptions (such as assuming away any opportunity costs), or assuming that production depends only on labor inputs, or even assuming that cost function can be simply described in a way marginal costs are constant (although that in itself would not be as unrealistic as the first two)  
> **username_4**: @username_2 - But in the long run equilibrium of perfect competition, the number of units produced per unit time, the total production cost per unit time, and the total revenue per unit time are all completely fixed for each and every firm, if any of these numbers are varying with time that indicates the system hasn't yet reached the long run equilibrium--do you disagree? If not, the production-cost-per-unit in the equilibrium state can simply be defined as yearly total production cost in making a type of good divided by yearly number of units of that good produced.  
> **username_2**: @username_4 I am getting confused by your non-standard terminology. What exactly is production cost per unit? Because in my mind that is the cost of a unit produced for example if I have 3 widgets and w1 costs 10 w2 costs 20 and w3 costs 30 then I understand it as that cost per unit of w1 was 10, w2 was 20 and w3 was 30 but based on your last comment it looks like you want to talk about **average** costs TC/Q. To avoid any conclusion, could you please give me equation you would use to calculate production cost per unit?  
> **username_4**: @username_2 - Yes, apologies if I'm using non-standard terminology, my background is in physics rather than economics, but I've read enough about perfect competition and the LTV to think there are some logical connections there. So here I'm just talking about averages at equilibrium, if we consider firms that only produce a single type of good such as a widget, the per-unit production cost I'm interested in (feel free to pick whatever term you like for this) could just be defined as (total production costs for all widgets made per year)/(total number of widgets made per year).  
> **username_4**: But as a side note, I would have thought, just based on a general knowledge of what simplified equilibrium models are like in other sciences, that one of the simplifying assumptions is that the rates of all processes are treated as constant no matter how finely you divide up time. So I’d have guessed that in the long run equilibrium of perfect competition, we could for example meaningfully talk about number of widgets per microsecond, production costs per microsecond etc.,  
> **username_4**: and that these rates would be fixed from one microsecond to the next, it wouldn’t be as if widgets were costing more to produce on a microsecond on day 1 vs. a microsecond on day 4, and that the ratio only attained a fixed value when averaged over some longer time span like a year; instead the ratio would be the same regardless of the time interval chosen. Is my assumption about what "equilibrium" means here incorrect?  
> **username_2**: @username_4 that would be average cost (AC) then. Also, in long run you can certainly show that MC=AC because firms will enter or exit until that will happen. Well the issue is that the models you refer to (for example, the link you sent) are not dynamic models. Long-run and short-run in economics does not refer to passage of time. i.e. there is not some amount of units of $t$ after which you can say we are in long run. Long run is defined as a situation where firms can enter and exist market freely. The simple textbook model basically has two modes (short run mode where entry is prohibited)  
> **username_2**: long run mode where entry is allowed, and then you simply derive equilibrium under both modes. Also we don't really call it mode thats just a word that I use because maybe it will be easier for you to imagine.  
> **username_2**: in perfect competition both in short run (SR) and long run (LR) firm maximizes profit subject to its output as a control variable $\Pi = PQ -C(q)$, as a physicist you must be familiar with calculus, so you should see from this that the condition to maximize profit will be $p=C'(q)$ or price is equal to marginal cost. But in the LR firms are allowed to enter and exist industry where the entry condition for new firm is that $\Pi > 0$ and exit condition is that $\Pi<0$, as a consequence it would be valid to say that in LR price also happens to be equal to AC as otherwise $\Pi \neq 0$  
> **username_2**: but price is still determined by condition $p=C'(q)$  just entry and exit make sure that  $p=C'(q)=C(q)/q$ at least under standard cost functions used in many intro textbooks  
> **username_4**: @username_2 - "that would be average cost (AC) then" So in that case would you agree that in the long run of perfect competition, average cost of a good is equal to market price of that good? Also, when I talked about time I wasn't talking about some kind of transition from short run to long run--I assume, again in analogy with equilibrium models in other branches of science, that we treat the system as if it remains in the same equilibrium state from t=-infinity to t=+infinity. But there is still a temporal coordinate so we can talk about number of widgets made per day vs. per year etc., no?  
> **username_2**: @username_4 sure in the simple textbook version of perfect competition with its assumptions on cost function in LR you price will happen to be also equal to AC, I can agree on that. No the textbook version of a perfect competition is not dynamic model. Essentially the simple textbook version is not one model but two models. A model of how perfectly competitive firms behave in SR and model how they behave in LR. You can have a dynamic model but that does not work exactly the same way as the undergraduate version. In dynamic model also firm maximizes expected profit not actual profit etc  
> **username_4**: @username_2 - When you say it's not a dynamic model do you mean that all the variables have fixed values in time, or do you mean there isn't a time coordinate at all, so that when you consider equations with derivatives they are just the derivatives of one economic variable wrt another, not with regard to time? Even if it's the latter case, aren’t the equilibrium values at least conceptually understood as attractors for some time-based process where the economic variables converge on those values, and then remain at those values at all later times?  
> **username_4**: For example, [this section](https://en.wikipedia.org/wiki/General_equilibrium_theory#Walrasian_equilibrium) of the wiki article on general equilibrium theory says “Walras also proposed a dynamic process by which general equilibrium might be reached, that of the tâtonnement or groping process.” Even if economists have not developed any standard time-based differential equations stating the rate of change of one economic variable given the instantaneous values of other vbls, and shown that these equations cause convergence to equilibrium,  
> **username_4**: I’d guess it would at least be possible to develop some agent-based numerical model (with agents and firms having the properties assumed by the perfect competition model, like perfect information) where one could observe such a convergence “empirically” if one starts the simulation in a state where the variables deviate (perhaps by a small amount) from the equilibrium values.  
> **username_2**: @username_4 in the undergraduate textbook model of perfect competition you referenced there is no temporal dimension.  Of course there is a graduate version where there is one but there results are not exactly same eg you work with expected profit there is only zero economic profit in ex ante expectations not actually realized zero profit etc. Yes in the simple undergraduate model variables are not functions of time so derivative wrt time would not make sense.  
> **username_2**: @username_4 right but I am not saying that in economics we dont have dynamic models. You can have dynamic walrasian models, but let me stress again, the *undergraduate version of perfect competition model* you referenced does not have any temporal dimension, thats simply too complex for average undergraduate to handle because once you introduce dynamics you need to deal with expectations and those are quite complex  
> **username_2**: you can have also agent based models. Again dynamic models and agent based models exist but the model of perfect competition that you referenced simply does not have it. That would be like me picking a textbook model from physics textbook that assumes no air resistance and then asking if physics did not yet developed such models. I presume that all 101 textbook physics models have their more complex counterparts. If not, then in economics they certainly have, in intro classes we typically get rid of most of the temporal dynamics except for stuff like growth theory where its impossible  
> **username_4**: @username_2 - Thanks for the clarification on how the perfect competition model is actually defined. If there are *some* more complex models with a temporal dimension that predict the same unchanging equilibrium values for the same variables that are solved for in perfect competition, then perhaps you could substitute the name of such a model for "perfect competition" in my earlier comments about the per-unit-production-cost of a widget being the same as its average production cost? Leaving aside the part about Marx and LTV for now, would you still object to my comments in that case?  
> **username_4**: Also, even without naming such a specific model, isn’t it fair to say that when economists refer to the notion “perfect competition” they may not be referring only to the mathematical elements, but also to some conceptual background elements of a simple hypothetical economy the equations are supposed to characterize? For example, textbooks will refer to buyers having perfect information, but the equations in an undergraduate textbook wouldn’t include variables that characterize what knowledge buyers have, would they?  
> **username_4**: And if “perfect competition” can be said to refer to some background conceptual assumptions as well as to the equations, I think it would be reasonable to include the idea that the model economy had arrived at these values for the variables after some time-based “groping process” of the kind suggested by Walras, and that once it arrived at them (or got arbitrarily close) it continued to stay at them (or arbitrarily close) at all subsequent times.  
> **username_2**: @username_4 in a dynamic setting it would no longer be true that there has to be zero economic profit ex post so there is no reason to believe price should be equal to average costs of production in long run. Also to further clarify perfect competition is a market structure. This market structure can be modeled in various ways. A perfect competition would be equivalent for let's say gravity that could be modeled using Newtonian dynamics or GR. But from your comments its clear that you were talking about the undergraduate model of perfect competition not some dynamic model of perfect competition  
> **username_2**: yes, I think I accidentally got you confused. perfect competition is market structure, but this market structure can be modeled in various ways. Statically, dynamically, with different assumptions on cost function etc. This can yield different results sometimes. For example, you can have model of perfect competition with heterogenous firms - where firms have different cost structure, where now some firms can earn positive profits  (but don't confuse it with models with heterogenous products that would not be perfect competition anymore)  
> **username_2**: perfect competition is a market structure where you have large number of sellers (approaching infinity), all firms are price takers and products are homogenous. Also there should not be any market failures present. Furthermore, entry and exit has to be assumed to be free. If some of the above is violated then we would talk about different market structure, if goods are differentiated then it would be a model of monopolistic competition. If the goods are homogenous but number of firms is small oligopoly etc.  
> **username_2**: @username_4 yea but once you involve dynamics the problem changes. Because for example, if firm maximizes $E[ \sum_{t=0}^T\beta^t\Pi]$, then things get more complicated because expectations imply there is some randomness in the system. Profit will be some distribution and firm will try to maximize the expected value of that distribution. In that case its not guaranteed that in equilibrium profit will be constant quantity.Equilibrium is situation where no agent would like to deviate from strategy they pursue. Firms and consumers may pick production and consumption schedules that max their  
> **username_2**: welfare in ex ante expectation, but then ex post due to random error there is no guarantee what the utility will end up being. For example, if someone offers you choice between two gambles A: 50\%*100e 50\%*0e and B:   50\%*1000e 50\%*0e and assuming you are risk neutral and want to maximize your expected payoff clearly option B is your preferred choice and that would be equilibrium strategy you would keep choosing but there is no guarantee you will get 1000e you might get 0e  
> **username_4**: @username_2 "But from your comments its clear that you were talking about the undergraduate model of perfect competition not some dynamic model of perfect competition" Well, I'm talking about a dynamic economic model which matches the conceptual features that define perfect competition (perfect information etc.) and which converges over time on the actual time-independent values of economic variables predicted by the undergraduate model (or if it has those values to start, then the dynamics keep it fixed on those values). Are you saying that no such dynamic model is known to economists?  
> **username_4**: Just doing some googling, there are some papers by Mark Satterthwaite and Artyom Shneyerov that seem to be talking about "Convergence to Perfect Competition" in models of markets that have a dynamic element, see [here](https://www.kellogg.northwestern.edu/faculty/satterthwaite/Research/2007-0718a%20dda%20exogexit%20final.pdf) and [here](https://www.kellogg.northwestern.edu/faculty/satterthwaite/research/Dynamic%20Matching.pdf) and [here](http://papers.economics.ubc.ca/legacypapers/dp0504.pdf)  
> **username_2**: @username_4 1. those are 2 papers the first two links are 2 links to 2 version of the same paper. 2. Also previously you stated you want to talk about models of perfect information and these models are models of imperfect information. 3. These are auction models they don't even have production in them. The cost there are opportunity costs of trade not production costs. 4. As the paper in first two links states the competitive price is such that "That the resulting allocations give traders the expected utility they would realize in a  
> **username_2**: perfectly competitive market follows"". **This is exactly what I was trying to explain**. Results in these dynamic models are results that hold in expectations. Let me give you simple example, I will talk about profit not to complicate things with utility. If the probability distribution of revenue is such that with 50\% revenue is 100 and with 50\% rev. is 0 and seller has opportunity cost of 50, then you will get zero economic profit in expectation since expected revenue $E[R] = 0.5 \cdot 100+ 0.5 \cdot 0= 50$ so with 50 opportunity cost the expected economic profit is zero $E[\Pi]=50-50=0$  
> **username_2**: but that is different from claiming that realized (ex post) profit will be 0, the ex post profit can be either 100-50= 50  or 0-50 = -50. It cannot actually be 0, the same way as the coin toss cannot be 0.5 even though thats the expected value you would expected from fair coin (if tail is 1 and face is 0). What could happen is that once you repeat the game over a large amount of time the *cumulative* profit over all time periods would converge to zero, but in this case you can really claim that prices equal  average costs of those products  

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