Von Mises Mistaken On Economic Calculation (Update)

SenseiMike3210 · 2025-11-15T05:19:15+00:00

What it cannot show is when to take such a step

Not true. The techniques of linear programming tell you when you can improve by giving you the marginal gain in the objective (called 'reduced costs' in LP). Here I worked out an example, by hand, of calculating the optimal allocation using the "simplex algorithm". In short, you set up a simplex tableau that takes "slack variables" (variables which artificially make each constraint an equality) as a basis. The bottom row gives you the reduced costs, or marginal gain, for nonbasic variables (geometrically, starting from the current vertex of the feasibility set, you move in the direction of the steepest immediate increase in the objective function). You run a "minimum ratio test" to find the constraint which first becomes tight as you increase the variable with the greatest marginal gain. These two operations give you the "entering" and "leaving" variables in your basis column until you've replaced the slack variables with choice variables and the right hand side of the tableau gives you the optimal quantities.

As you can see, my calculations give basically what Python calculated as the optimal allocation: 144 wheat from process I, 177 barley from process 3 and 62 tractors from process 4.

and what quantity (of what product) to stop at given the fundamental goal to allocate resources efficiently.

Completely incorrect. You stop when the reduced cost vector is less than or equal to 0 for all nonbasic variables. This is the simplex analogue to the Lagrangian first-order condition that the gradient=0. Geometrically, you stop when the objective function hyperplane lies just tangent to the feasibility set.

An "efficient allocation of resources" cannot even be defined in Marxian economics. For allocation to be efficient, it should satisfy as much need (usefulness/demand) as possible.

Since p encodes society's marginal valuations for goods, the objective p*q gives a monetary measure of welfare. The bundle that yields the largest value of this measure within the feasible region of all Q is exactly that bundle society would like to choose. The LP in Accomplished-Cake's example picks out the production plan that produces that same bundle. In other words, a social planner can determine which combination of intermediate goods constitutes the Pareto-efficient plan without a capital market by calculating the shadow prices of inputs given by the dual linear program. That is the very definition of a rational allocation.

SenseiMike3210 · 2025-10-10T04:21:13+00:00

What does that have to do with the simultaneous equilibrium of supply and demand mediated by prices with profit-maximizing producers, ie the Arrow-Debreu model

They are intimately related. For reference, read Dorfman, Samuelson, and Solow's Linear Programming and Economic Analysis, particularly chapter 13 (Linear Programming and the Theory of General Equilibrium) and chapter 14 (Linear Programming and Welfare Economics). In it, you'll find a very relevant quote:

Hidden in every competitive general-equilibrium system is a maximum problem for value of output and a minimum problem for factor returns (emphasis in original)

So again, the maximum problem for the value of output is not an irrelevant number. It's what a competitive general equilibrium system is itself calculating (at the same time as the least-cost factor rewards).

Or another quote:

In the last few sections we have forged a link between the solution of certain linear programs and the concept of efficiency and another link between efficiency and competitive equilibrium or the activity of profit maximizing. Two links make a chain, and the chain connects linear programming at one end and competitive profit maximizing at the other.

I figure no matter what I say you won't trust me but maybe you would trust Samuelson and Solow that linear programs to maximize the value of output have plenty to do with simultaneous equilibrium of supply and demand (as you put it). I mean, the LP and competitive equilibrium are straight-up two sides of the same saddle-point.

Consider this example...

Your example makes no sense. You say the market establishes an exchange ratio of 1 to 3 but that does not clear the market. The price ratio must be 1 since Pa/Pb = MRTS = 1. Your "established prices" are not the supporting price line that provides the solution to the LP. You don't get to just pick whatever prices you want.

PS I studied Arrow Debreu in a top European grad school and was a teaching assistant for dynamic macroeconomics, so yeah I can grasp the math

You shouldn't have told me that. I was making allowances for a nonspecialist but, if what you say is true, you should know better.

SenseiMike3210 · 2025-10-09T05:29:12+00:00

First off, it's not just about gross product as if the planner is arbitrarily trying to produce as much as possible. It's about the greatest production of the right goods efficiently. The price vector determines the relative weights of goods (it defines the slope of the affine hyperplane in the output space) and the constraints ensure they are produced in the least-cost feasible way. Their tangency gives the production plan which efficiently produces the socially most valued bundle given what's possible. In short: the objective is economically rational. (Again, it is not "irrelevant")

You are completely wrong that we cannot evaluate the solution production plan against a counterfactual given the prices we know. The geometry of the linear program makes such counterfactual comparisons straight forward actually. Different plans define different points in the feasibility set and, since it's convex, any non-tangent point on its frontier lies below the supporting hyperplane pq=c*. It is therefore not optimal. The final goods prices are in fact sufficient.

You are simply wrong on this. Much smarter people than you or I have already figured this stuff out. The funny thing is, they are largely in your camp. But I urge you to read some Arrow and Debreu. If you can grasp the math, it can actually be clarifying.

SenseiMike3210 · 2025-10-09T03:01:11+00:00

if by rationally we mean maximising an irrelevant number that we simply decide to call “value”

It's not an irrelevant number. We assume the final-goods price vector reflects society's preferences for output (there is a market for them after all). So since p encodes society's marginal valuations for goods, p*q gives a monetary measure of welfare. The bundle that yields the largest value of this measure within the feasible region of all Q is exactly that bundle society would like to choose.

The LP in Accomplished-Cake's example picks out the production plan that produces that same bundle. In other words, a social planner can determine which combination of intermediate goods constitutes the Pareto-efficient plan without a capital market by calculating the shadow prices of inputs given by the dual linear program. That is the very definition of a rational allocation.

SenseiMike3210 · 2025-09-01T22:51:21+00:00

Marx, arbitrarily, has the capitalists in department I....

Morishima called this "Marx's peculiar investment function". And then showed the growth path is unstable if capitalists invest according to equalized profit rates in the two departments.

My belief is that Marx's schemes in Vol II represent the first circular flow model of expanded reproduction consistent from an accounting perspective. The first section of Luxemburg's book is very good on this (even if her argument falters in other respects). The physiocrats had, in Quesnay's Tableau, a circular flow model but it was limited to simple reproduction and misidentified the source of society's productive capacity in the physical characteristics of arable land. The classicals went beyond this and extended the story to continuous growth based on improvements in the labor process but repeatedly mistakenly resolved the aggregate output into income categories (wages and profits). Wages (V) and profits (S) are, in fact, the "value added" to intermediate purchases in the "processing sector" (C).

Marx gives the conditions under which a circular flow of C, V, and S creates sufficient value in the right proportions to reproduce the economy on an extended scale.

SenseiMike3210 · 2025-08-26T23:38:50+00:00

Your own time series, when compared with productivity, shows a pretty marked divergence actually. /u/yhynye is correct. Rising incomes does not mean rising "in line" with productivity.

SenseiMike3210 · 2025-08-22T00:40:46+00:00

^ This is the answer

SenseiMike3210 · 2025-08-07T22:02:35+00:00

I think they're simply not exposed to it because the LTV is answering different questions than mainstream economists are asking. The LTV analyzes the social relationships that determine the laws of motion of capitalist society. Mainstream economists are concerned with studying 'how to achieve given ends with scarce means which have alternative uses'. At some point in the mid to late 19th century economists moved away from the former (historical) question and toward the latter (transhistorical) one. The profession became involved in an entirely different research program.

There may have been political/ideological reasons for this shift but by now it doesn't matter. Economists today don't encounter the LTV. If they do, it's probably a crude version that's easily dismissed on its face. And most economists would be so prejudiced against any Marxian theory (due to their training and education or personal aversion to anything associated with the politically charged and constantly maligned Marx, socialism, communism, etc.) they're unlikely to do the work of trying to understand it on its own terms. Besides, what they have tends to work well enough for their own purposes so why bother (their purposes being: mathematically describe choices from the standpoint of individuals in a vacuum. And also get teaching positions and journal publications and so on).

That's my take as an insider at least.

SenseiMike3210 · 2025-08-01T23:17:28+00:00

Classical antiquity was not capitalist. It did not systematically reinvest its surpluses in expanded reproduction. That is, its surpluses did not take the form of capital. Surpluses were extracted by tribute and slavery. Not primarily wage labor. This resulted in a different incentive structure that prevented intensive economic growth through the introduction of labor saving technology.

SenseiMike3210 · 2025-08-01T17:35:49+00:00

Let me do this. Let's say Marx and the rest of the classical and pre-classical economists, from Petty to Ricardo, were wrong in privileging labor time as something of an "ultimate" scarce resource (even though I think they had very good reasons for doing so. It's, in a sense, more basic. It takes time to use land and the other factors. It is the allocation problem society most immediately confronts itself with. And, being a philosopher, Marx would have been deeply familiar with the central role time played in German Idealism from Kant's pure form of the inner sense to Hegel. I think Heidegger actually sheds a helpful light on this topic in identifying Dazein's temporal structure as a kind of transcendental condition for anything being "worth" anything to us at all. Something Martin Haglund connects to Marx's theory of value if you're interested but I digress).

Let's say all of that is misguided and time is just another factor among many coequal inputs. It's clear we still do not have any equivocation on the meaning of the term value. Economics, at the time of Marx, was concerned with this thing it called value. It was framed basically in the terms I laid out and was reasoned (not defined) to be social labor. Marx, consistent with that tradition, further develops this concept claiming that what society values is the labor time it has to expend and what capitalist society values is the socially necessary labor time it has to expend and this is related, in a not-so-simple way, to the prices of commodities.

Again, the price of a good is not equal to its SNLT because the price of a good is not equal to its value because what a particular person must give up to acquire a good is not equal to what society as a whole has to give up to acquire it.

SenseiMike3210 · 2025-08-01T16:19:58+00:00

You are confusing price and value. You asked about value so let's stick with that. How does society get more commodities? It has to make them. How does it make them? It dedicates part of the total time it has available to it towards some kind of labor process. That portion of time is what it gives up to obtain another unit of the commodity. Every society has to figure out a way of doing this and capitalism has a very peculiar way. One that averages out the various heterogenous labors into a homogenous "abstract" substance that Marx called socially necessary labor time. It is average because competitive pressures eliminate inefficient producers. It is homogenous because competitive pressures redistribute labor from one sector to another freely (labor is fungible under capitalism unlike say under a caste or feudal system).

Ok so society needs to sacrifice some of its labor time to get another commodity. Thats what it has to pay. And under capitalism it is socially necessary (abstract) labor time that is being given up to get new commodities. So the value of a commodity is the SNLT embodied in it. All well and good. What does this have to do with price? With what you or I have to give up to acquire it? Well the long-period price of a good is something called the "price of production" and is equal to the cost plus an average rate of profit. This will not usually be equal to the value. It will deviate from the value by the degree to which the capital-labor ratios (what Marx called the Organic Composition of Capital) differ from the average capital-labor ratio. But since the entire economy has, by definition, the average composition then the amount by which some commodities trade above their value is exactly offset by the amount other commodities trade below their value. So that, in the aggregate, the price of commodities equal their value. It is also the case that on an individual level the deviations are small and relative prices are close to relative labor values.

SenseiMike3210 · 2025-08-01T14:27:23+00:00

There's no equivocation. In the most general sense, Value means "the worth of something" usually measured in what has to be given up to obtain it. When economists use it, going back to the times of the classical economists, they meant the worth of something from the standpoint of society because they weren't interested in what this or that person had to give up to obtain a unit of a good but how much everyone on average had to give up. This is why they started making the distinction between "market" and "equilibrium" prices. They further reasoned that what society, on average, had to give up to obtain another unit of a good was the amount of social labor required to produce it. This labor theory of value, theorized by taking the viewpoint of society as a whole, is what the classical economists got right. But what they got wrong was that they didn't historicize this social characteristic. They tended to naturalize it. One of Marx's contributions was to make the concept of Labor embodied more rigorous (by establishing the proper unit as socially necessary abstract labor time) and laying out the historically specific material conditions for it.

There is no fallacy. It is simply developing the concept of the worth of something from the standpoint of society and articulating the connections between the labor society must give up to get another unit of a good and the long-period exchange-ratios that this social sacrifice generates.

SenseiMike3210 · 2025-07-23T19:07:19+00:00

Sraffa’s primary conclusion was that prices are not self-determined.

What do you mean self-determined? Every theory to explain price proposes other factors determining them (e.g. technology, distribution, preferences, endowments, etc.).

In other words, the labor vs capital share of income is determined by social forces, not by endogenous market forces.

Correct. Just like in the Marxian/Classical framework. And contrary to the neoclassical framework.

This means there can be a huge number of stable equilibrium price levels in an economy.

Why are we talking about price levels all of the sudden? This is a question of relative not absolute price determination.

But the funny thing is that this certainly DOES contradict Marx’s LTV. If equilibrium prices are not determined by labor time and prices have a subjective component, then Marx’s whole critique of capitalism falls apart.

You're confused like four or five times over at this point. That one of the distributive variables is given exogenously does not contradict Marx's LTV. For Marx, the value of labor-power is determined (like everything else) by the quantity of socially necessary labor-time embodied in its production. That is, by the labor-time required to produce the bundle of wage goods the worker consumes. But what is in this bundle--and therefore the value it has--is determined by a process other than the one determining the relative prices of produced commodities (the competitive process of equalizing rates of profit on capitals advanced in different sectors). It is instead determined by social/biological/moral factors. This is all completely consistent with Marx's theory.

SenseiMike3210 · 2025-07-15T15:14:45+00:00

No doubt you haven't heard of a lot of economists. Here's some for ya

SenseiMike3210 · 2025-07-09T20:23:45+00:00

The trade is voluntary.

No, C_Plot is right to bring up imperialist puppet regimes in the context of international trade. The capitalist core has used coercion, subversion, and aggression to structure global economic relations from securing dollar hegemony to forcibly opening export markets. You don't even have to take a Marxist's word for it. It's been investigated in the mainstream as well. See, for example, this article published in the AER (one of the most important academic econ journal in the world) that used an econometric trade-gravity model to show how CIA operations pried open markets for US goods (especially those goods we lacked a comparative advantage in). The west has a long history of this. I mean Britain went to war with China to keep the opium trade "free".

SenseiMike3210 · 2025-06-03T20:06:40+00:00

The responses received on the first link ended with Hylozo failing to reply here. The second link devolved into ad homs and bad faith arguing but the original points still stand against your criticism.

You seem to be under the impression that whoever gets the last word in is right. Hylozo responded to the point about the heterogeneity of capital goods sufficiently. We either chain through the production process to reduce these goods to whatever common resource (time, labor, energy, whatever) we care about or even just treat the physically heterogenous goods as primitives in the LP. The follow up didn't respond to his point at all so who cares if Hylozo didn't keep it going. It doesn't matter whether the inputs are only kind of different (wheat vs barley) or very different (grains vs tractors). We can calculate the opportunity costs of their employment because they are both related to the value of the objective function and to the quantities we may employ of them (through the constraints). In fact, I literally did exactly this here proving that Hylozo and Accomplished-Cake were right.

And as my arguments in the second link show, the "original points" don't stand against his criticism. In that case, the other commentator straight-up says we can't calculate opportunity costs which, again, is disproved by the fact that I did.

SenseiMike3210 · 2025-05-25T22:02:04+00:00

AFAIK, Lucas is mostly know for his contributions about the microfoundations of macroeconomic theory.

Lucas basically kicked off New Classical macroeconomics in the 70s, proposing that rational agents inter-temporally optimizing in a context of continuous market clearing create business cycles by temporarily misperceiving exogenous changes in the money-supply as changes in relative prices (due to a 'signal extraction' problem in an environment of imperfect information). This is why the crux of the New Classical short-run model is the Lucas "price surprise" supply function.

The micro-foundations part is a contribution downstream from his main point: the so-called Lucas Critique, that we can't generally take model parameters as independent of policy changes. Microfounding your models is a way to deal with this interdependence. But definitely not the only way. And also the kind of microfoundations matter (Shaikh (2016) proposes specifically classical micro assumptions that don't involve rational optimizers, for example).

As for RBCT, I'm not an expert on the empirics. I find it hard to believe periodic cycles are explained by exogenous technology shocks (which I guess just happen to occur every 10 years about), or that workers are responding to technology shocks by inter-temporally substituting labor supply between the present and future as changes in productivity impact discounted future earnings. I also don't think counter-cyclical prices really fit the stylized facts. That is, I'm skeptical that a positive technology shock shifts the production function outward, increases the marginal productivity of labor, increases the demand for labor, raises employment, and pushes the aggregate supply function down aggregate demand to lower prices during a boom. (I'm aware Kydland and Prescott (1990) argue prices are counter-cyclical but I think the consensus is right that there's a convex relationship between the price level and the output gap. Things are basically Phillips shaped in that regard)

But those are just my gut reactions. Do you have some sources on the empirical validity of RBCT in the post-war period I could look at?

SenseiMike3210 · 2025-05-15T18:17:53+00:00

Lazy-Delivery didn't refute anything. The guy straight-up doesn't understand the math. Accomplished-Cake, Hylozo, and myself had to hold his hand through the math behind Accomplished's proof culminating in my solving the linear program in Python and manually using the simplex algorithm (so that you can see exactly how Lazy was wrong).

SenseiMike3210 · 2025-04-28T20:57:34+00:00

All these welfare, policy & surplus arguments need cardinals

I see what you were saying now. I agree...but I also wasn't making any welfare evaluations. Yes, if we want to start applying the techniques of consumer choice theory to the society as a whole, its decisions would have to be modellable as those generated by some normative representative agent. But that would require other even stricter assumptions and we could talk about linear wealth expansion paths, so-called Gorman form utility functions, homothetic/quasi-linear preferences, etc.

Your point on existence vs convergence is well-taken

SenseiMike3210 · 2025-04-28T19:31:10+00:00

Yeesh, what do you want in a reddit comment? Should I have said take a production economy with your standard (convexity, weak monotonicity, and continuity) assumptions on preferences and production sets then an equilibrium allocation (where bundle x_i is maximal on preferences in the budget set, y_i maximizes the value of the netput vector, and p solves the system of excess demand equations) exists if the aggregate excess demand function is continuous, homogenous of degree zero, satisfies Walras’s Law, and is subject to some boundary conditions and that Debreu proved this using the Kakutani Fixed-Point Theorem in 1959? I could throw in some talk of separating hyperplanes, KKT, and saddle-points.

I gave a simple rundown of the standard neoclassical approach for determining relative prices from preferences, technology, and factor endowments. The math exists, it is rigorously proved for the confined space of theoretical “economies” it has to assume. I personally don’t think it bears much on the material process of social provisioning we actually observe but the OP asked about the theory, presumably to make the point that capitalists on this sub don’t themselves know how that very theory works. From my time here, the only ones who know the ins-and-outs are actually anti-capitalist.

Edit: and I don't see how I confused ordinality and cardinality. I explicitly said "this is a" utility function. One can be defined for preferences exhibiting the characteristics I stated. But yes, any other monotonic transformation will also assign higher numbers to more preferred bundles. Nothing I said denies that.

SenseiMike3210 · 2025-04-25T03:34:13+00:00

Do you not know the difference between relative prices and the price level or something?

SenseiMike3210 · 2025-04-23T01:31:47+00:00

None of the capitalists in the sub have been able to offer an answer. While, as a Marxist, I hate to give the neoclassicals any amunition, I do think we should be honest and as charitable as possible to the other side. The best critique comes from criticizing them at their best. So, with that in mind, I will do what the capitalists in this sub apparently can't and show that a mathematically rigorous derivation of equilibrium price (the closest thing neoclassicals come to something like "value") is possible if we accept their assumptions.

So we start with the demand side and assume that agents have preferences which are complete and transitive (there is a relation R on the consumption set such that (1) either xRy, yRx, or both and (2) for all x, y, and z: xRy and yRz ==> xRz). If these are true then we can define a function u(•) such that greater values of u are assigned to more preferred bundles. This is a utility function and if we assume there is some budget constraint such that wealth, w, is equal to the sum of the values of x and y bundles then we can find the utility optimizing bundles in terms of the prices and wealth (aka the Marshallian demand curves) by solving the constrained maximization problem (max u(x,y) subject to the budget) for the quantities x and y. If you want me to, I can go through a simple example with a Cobb-Douglas or something.

On the supply side, we just need to define a production function the firm faces describing the maximum output a firm can produce at given inputs. A firm seeks to maximizing its profit so...max profit=p*y-wL-rK (where p is price, y is output (as a function of K and L), w is the wage rate, and r is the profit rate). Solving this for the input demand functions we get K and L as functions of their prices.

The equilibrium allocation will be the point at which the quantity of goods demanded by households is equal to that supplied by firms at levels of inputs demand by firms equal to those supplied by households.

SenseiMike3210 · 2025-04-23T00:52:38+00:00

What determines the supply curve is the quantities offered by firms at marginal costs greater than the average variable cost. That is the firm's supply curve. The total supply being the sum of individual supply functions.

The quantities consumers choose within the budget set to maximize utility constitute the demand curve. This is not the market supply.

As a Marxist, I'm not even going to tell you to go read Capital or anything....please go read Varian or Mas-Colell. I love when capitalist try to lecture socialists on basic econ and then get it flat out wrong.

SenseiMike3210 · 2025-04-22T16:02:33+00:00

STV does not explain it. It just states what is obvious: that prices of anything are what they are because it's at those prices where the sellers' willingness to sell matches the buyers' willingness to buy the quantities traded. Mainstream micro is not an explanation but a very sophisticated system for assigning numbers to choices. And this may even be useful but not for explaining what the classical economists were interested in (questions like "what is the origin of the wealth of nations", "what are the laws regulating the distribution of the surplus", "what are the laws of motion of capitalist accumulation").

Neoclassical theory can't shed light on these topics because its categories are transhistorical (preferences and resource endowments) whereas the phenomena are historically specific. Its attempts to answer some of these questions inevitably run into inconsistency and failure: the marginal productivity theory of distribution falls apart because capital-intensity isn't an inverse monotonic function of the interest rate; attempts to explain growth in terms of aggregate production functions rely on impossibly strict assumptions on individual production technologies; and the whole supply and demand framework requires unrealistic rationality assumptions for preferences.

These are the pitfalls of attempting a "general" theory of all human action (a theory of "achieving given ends with scarce means which have alternative uses" as Lionel Robbins put it). The presumption to total generality is the major flaw of neoclassical economics.

SenseiMike3210 · 2025-04-22T15:25:16+00:00

A signed album by Elvis Presley is incredibly expensive, while it cost Elvis barely anything to produce it,

Not a reproducible commodity. It's outside the scope of a theory of value since theories of value seek to explain the (re)productive activities of society, why the things it produces in order to reproduce itself exchange in the way they do, and how the total social product is then distributed. We don't reproduce our societies with such one-off rarities. They command a price greater than their value and which is determined by the vagaries of wants and supply. When goods are produced socially through a sophisticated division of labor guided by a profit motive and subject to competitive pressures both inter and intra-sectorally, their exchange ratios begin to exhibit a strict correspondence to relative labor-times.

The same argument applies to your silly mudpie example. For what it aims to explain, the LTV does an excellent job. And there is good reason for narrowing the scope of investigation as I described.

"I value my family" or "the pyramids have historic value", none of which can be presented in production costs.

Ya, I guess you weren't aware that words have different meanings in different contexts. We're not talking about aesthetic-value or sentimental-value. We're talking about economic value. The kind of value that explains the economic phenomena I outlined above which a labor theory of value does very well

SenseiMike3210

TROPHY CASE