price changes, their proximity and PSR-FSR query

bump.

You and your posts abs...

2. This process seems of equilibration seems like it could be quite complex in a most cases, since central to Misesian analysis is the variable convertibillity of capital employed in market processes. Has anyone attempted a detailed analysis of how such changes could and do proceed? Indeed, can we even prove that an ERE would eventually be produced, since this involves more than just changes in supply of a specific good with response to supply/demand, given the effects of connexity?

In a really strict sense, no. Because how the market reacts is subjective. We can try to make all these predictions about how people will respond to prices, but its just psychological speculation. You can probably come up with a very good empirical model, or a very good theoretical model with a few constraining assumptions, but nothing a priori.

3. If the second query in 2. cannot be answered in the positive, then does this lend credence to Lachmann's doubts about whether the market necessarily tends towards an equilibrium at all? My gut tells me he's wrong, but I am curious about whether it can be proved.

Lachmann is going to be wrong in practice 999/1000 times. Though he may be wrong all the time if his theory is wrong even if he is right in his conclusions.

4. Mises, talks about how price adjustments to changes in market data require time to a variable extent, some more some less. To say anything more accurate in any particular case would thereby seem to present a challenging empirical, or should I say historical problem. Given, that some adjustments could occur quite quickly however, can we rule out completely as he does, the possibility of market prices matching final prices, perhaps temporarily? Hence adjustments could occur and finish BEFORE new data appear.

From what you've presented here, I'd go against mises on this issue. If you have completely static consumption/production patterns, and stretch time to infinity, you would expect prices to stabilize. Although that is under the assumption that there is entrepreneurial/speculative agreement on prices.

Speculators might even all agree but guess wrong about the right equilibrium price. Its possible that while they miss some subtle pieces of information that causes them to choose the wrong price.

But, equilibrium theory basically says there's some Objective Function being minimized out there. But if the market gets stuck in a local minimum it may never get out (trough). There could be multiple absolute minimums.

^If you don't know what an objective function is then ask, because its not quite what it sounds like. Though I think you know because you're a grad student :)

However, this DOESN'T mean changes couldn't occur AFTER these final prices have been reached, then upsetting the established equilibrium. Mises discounts this equilibrium ever arriving, asserting an ERE would be produced. This makes sense to me, if we assume that no further changes occur at all, forever, but given (I assume) that price adjustments would take a finite amount of time, why couldn't we have the scenario, albeit unlikely that these adjustments can occur in full, before future disturbances arrive?

Right so oil prices have fluctuated between 40 and 160, and the optimal daily (secondly) price has probably been reached at some point. But we're either wrong or moving off to another equilibrium.

This would seem to imply that equilibrium theory has no good applications in worlds that aren't static. It probably works in the wheat market, probably fails in the oil market. Nuff said.

[edit]

Oh, and since the "final price" has to be a number, and since the # of numbers between 0 and n is infinity... you can't ever know if you've minimized the objective function since some other price the market hasn't tried yet might minimize it further.

Forgive me for my ignorance, but in this case, is the objective function your talking about utility or something else? If utility, surely, it would reach a local maximium and not a minimium, right (ignoring for a second issues with cardinality)?

 

Also, my point on Lachmann, I'm not sure if you really got what I meant. What I mean is that, given that price changes can occur in so many variable directions, whether it can be proved in the aggregate, going step by step from the individual changes, that eventually adjustments will be such that they will stabilise and no further price changes occur. I suspect this can be done.

 

Moreover, the goal of such a project would be more theoretical, almost pedagogical, to provide an appendix of possible pathways that can occur given a market with X conditions, in place and a change in the data, e.g. an increase in demand for a good G. It might be pointless, and I suspect, I might learn like perhaps Hayek did with PTOC, the limits of positve exposition in economics.

 

P.S. Thanks for responding.

Forgive me for my ignorance, but in this case, is the objective function your talking about utility or something else? If utility, surely, it would reach a local maximium and not a minimium, right (ignoring for a second issues with cardinality)?

An objective function is how your mathematical optimizer knows how to tweak variables. Usually you'll say that the objective function is equal to the sum of the squared errors and then the optimizer will try to minimize it.

The problem is that you can have many local minimums that the optimizer might stop at without getting to the global minimum. So, let's say that there are local minimums when entrepreneurs charge $2, $5, and $10 per loaf of bread. If the market gets to $5, it might stick there even though $2 is the global minimum.

This is because equilibrium theory essentially states that there is some objective function out there, that is maybe equal to the sum of the squared errors between the market price and some true price, and that the objective function tends to minimize. So, then you get all the problems in optimization, and the equilibrium theory explodes because the way you prove you've reached a global minimum is analytically.

Also, my point on Lachmann, I'm not sure if you really got what I meant. What I mean is that, given that price changes can occur in so many variable directions, whether it can be proved in the aggregate, going step by step from the individual changes, that eventually adjustments will be such that they will stabilise and no further price changes occur. I suspect this can be done.

I think you have to make some assumptions here, like that everyone is forecasting properly and interpreting prices in the correct way...

There's also sort of a circular element here. Becuase the final price is not only dependent on supply, but on what people think. So if someone thinks bread should cost 10 cents, they're "wrong" about the final equilibrium price. But in a way, he's "right" because his opinion lowers the equilibrium price since he doesn't buy bread for $5.

abskebabs:

I'll try to make this as little of a ramble as possible, but please forgive me if at times it appears so. I've been trying to get my head around some parts of the PSR-FSR analysis(plain state of rest - final state of rest) Mises employs in his price theory and this has brought to the fore some things I've been puzzling for a while.

Exactly what is PSR and FSR is context dependent, and it really depends on who you ask.  Here is a discussion between myself and BlackNumero about the topic:

http://mises.org/Community/forums/t/17956.aspx

The FSR is defined as the hypothetical future state of rest that would be achieved by the market travelling forward in time given the appearance of any given PSR, assuming no further changes in data that would affect market prices. Mises describes, that there would be a tendency toward a final price, I assume with regard to a single commodity. Now, I'm guessing that this FSR describes a kind of "general equilibrium" for the entire market right?

Yes.

Has anyone attempted a detailed analysis of how such changes could and do proceed? Indeed, can we even prove that an ERE would eventually be produced, since this involves more than just changes in supply of a specific good with response to supply/demand, given the effects of connexity?

The ERE, FSR, etc, are purely theoretical constructs that are entirely detached from reality. Economics employs such constructs in order to better elucidate extremely complex and inter-related phenomena while abstracting from billions of variables. The ERE is an unattainable state because it requires a set of conditions that can never come to fruition (perfect information, complete rationality (in the neoclassical sense), instantaneous price adjustments, stable preferences, etc). Mainstream mathematical economists attempt to fully explain such processes with full mathematical rigor.

That being said, we see the effects of the equilibrating processes that the ERE attempts to illuminate every single day, though it may be impossible to trace them back to the initial cause (why many consider the market to be irrational, chaotic, and "anarchic"). The fact that we have recessions is proof in itself.

Given, that some adjustments could occur quite quickly however, can we rule out completely as he does, the possibility of market prices matching final prices, perhaps temporarily? Hence adjustments could occur and finish BEFORE new data appear.

There's no reason to automatically rule out the possibility of temporary partial equilibrium (single market). At the same time, though, we realize that all markets are inherently interconnected (some more so than others). A single change sets off a chain of events  altering an unknown number of prices, which, in turn, changes optimal production methods and all sorts of other economic phenomena. It would be impossible to accurately describe and or model this without entirely eliminating the element of realism. Thus, it seems impossible that we could reach a state of general equilibrium before new data appears.

It seems I was right in my hunch about Lachmann, and he seems to have shared my concerns about the plausibillity of the partial equilibrium given the connexity of the price and market system. Here's a quote of his taken from page 8 of John Egger's very inciteful review of Arthur Marget's Theory of Prices:

"we can never be sure that the spill-over effects which an equilibrating adjustment in one market has on other markets will always be in an equilibrating direction ...Equilibrium in one market may be upset when the repercussions of the equilibrating adjustments in other markets reach it"[1]

[1]. 1971. "Ludwig von Mises and the Market Process." In Friedrich A.Hayek, ed. Toward Liberty. Menlo Park, Calif.: Institute for Humane Studies. Reprinted in Lachmann 1977. Pp. 190-91.

 

Unfortunately, without having read much of Lachmann (yet), going on 2nd hand interpretations alone, he may well have challenged the plausibillity of general equilibrium as a useful concept on the same grounds, while Misesians would not go so far. I think a future goal of my work may be to try and see analytically which interpretation is closer to the truth. My gut instinct alone sides me with Mises on this issue, but i think the diffusion of the ripple effects of price changes in goods connected by connexity of demand, supply and substition is still something that needs to be demonstrated explicitly if possible, for us to be able to make a final case.

 

EDIT: I misinterpreted Lachmann, it seems he as well as Marget, actually seems the problem with GE as a descriptive tool to describe the market's tendency, as opposed to PE as a limited descriptve tool to describe what occurs in every market. Interesting how they and i come to diametrically different conclusions from analysing the same problem. For me, I guess I've been more doubtful of PE due to the inabillity of isolating price changes of goods from other types of goods which they have a connexity and dependence. Time plays a siginificant factor here, for me any approach to PE would be perturbed in the time it would take to complete an approach, while there may still be a diffusion of initial changes if no further changes in external data occur(preferences, technology etc). For Lachmann, the inverse problem is in place, with changes in single markets sequentially perturbing related ones preventing any realisation of overall equilibrium.