u/Accomplished-Cake131

I have heard that capitalism is more efficient than socialism. Or that markets are efficient. Or something.

These types of claims raise a question.

What do you mean by 'efficiency'?

It is not in the spirit of the question to look up an answer before responding.

I suppose I can say this question is part of a series:

• What do you mean by the labor theory of value?
• What do you mean by supply and demand?

Milton Friedman was an illogical advocate of right wing capitalism. C. B. MacPherson, in examining Friedman's Capitalism and Freedom, writes "One almost despairs of logic".

But never mind that. This post is about how his descendants engage in LARPing. Do you find them absurd?

Capitalism and Freedom is co-dedicated to Milton's son, David. David continues the silliness with his book, The Machinery of Freedom. His fantasy novel, Salamander, has the system of magic partially taken from LeGuin's Earthsea series and partially built on linear algebra. He is an active participant in the Society of Creative Anachronisms, where he is known as Duke Cariadoc of the Bow. In addition to this LARPing, he writes about saga-period Iceland as a model of how law might work in a capitalist society.

Patri Friedman is the son of Davd Friedman. His confusion about LARPing can be seen in his founding of the Seasteading Institute. He was the executive director at its founding in 2008, with a large donation from Peter Thiel. He continued the LARPing with the founding of the Future Cities Development Corporation. I am sorry that Paul Romer promotes this anti-democratic idea.

This LARPing may strike you as a combination of harmless recreation and silliness with no chance of being implemented. But here we are, with rich effs close to political power.

Marx provides a supposed proof of the labor theory of value (LTV) in the first section of the first chapter of Capital. The worth of his analysis depends on neither the soundness nor the validity of this argument about the third thing. If you are interested in Marx, you should be willing to see where he goes after chapter 1. I find most insightful the last section in chapter 1, the bit on commodity fetishism.

Manufacturing goods in an ongoing society depend on many activities happening in parallel. For example, somebody must be mining iron for the blacksmith to be manufacturing horse shoes out of steel. Under capitalism, nobody is coordinating these activities. For Marx, this coordination results from prices under the anarchy of production characterizing capitalism. Capitalists see whether they are making lots of profits or not in marketing the commodities produced under their direction. Each capitalist adjusts their establishments accordingly.

Marx explains his overall approach to the theory of value in a much-quoted 11 July 1868 letter to Ludwig Kugelmann:

>Dear Friend,

>The children are getting on well, though still weak.

>Thank you very much for the things you sent. Definitely do not write to Faucher, otherwise this mannequin pisse will feel too important. All he has achieved is that, if a second edition appears, I shall aim a few necessary blows at Bastiat where I speak about the magnitude of value. This wasn't done before, since the 3rd volume will contain a separate and extensive chapter about the 'vulgar economy' gentry. Incidentally, you will find it quite natural that Faucher and consorts derive the 'exchange value' of their own scribblings not from the amount of labour power expended, but from the absence of such expenditure, that is from 'saved labour'. Moreover, the worthy Bastiat did not even himself make this 'discovery', so welcome to these gentry, but just 'cribbed' it, in his usual manner, from much earlier authors. His sources are of course unknown to Faucher and consorts.

>As for the Centralblatt, the man is making the greatest concession possible by admitting that, if value means anything at all, then my conclusions must be conceded. The unfortunate fellow does not see that, even if there were no chapter on 'value' at all in my book, the analysis I give of the real relations would contain the proof and demonstration of the real value relation. The chatter about the need to prove the concept of value arises only from complete ignorance both of the subject under discussion and of the method of science. Every child knows that any nation that stopped working, not for a year, but let us say, just for a few weeks, would perish. And every child knows, too, that the amounts of products corresponding to the differing amounts of needs demand differing and quantitatively determined amounts of society's aggregate labour. It is SELF-EVIDENT that this necessity of the distribution of social labour in specific proportions is certainly not abolished by the specific form of social production; it can only change its form of manifestation. Natural laws cannot be abolished at all. The only thing that can change, under historically differing conditions, is the form in which those laws assert themselves. And the form in which this proportional distribution of labour asserts itself in a state of society in which the interconnection of social labour expresses itself as the private exchange of the individual products of labour, is precisely the exchange value of these products.

>Where science comes in is to show how the law of value asserts itself. So, if one wanted to 'explain' from the outset all phenomena that apparently contradict the law, one would have to provide the science before the science. It is precisely Ricardo's mistake that in his first chapter, on value, all sorts of categories that still have to be arrived at are assumed as given, in order to prove their harmony with the law of value.

>On the other hand, as you correctly believe, the history of the theory of course demonstrates that the understanding of the value relation has always been the same, clearer or less clear, hedged with illusions or scientifically more precise. Since the reasoning process itself arises from the existing conditions and is itself a natural process, really comprehending thinking can always only be the same, and can vary only gradually, in accordance with the maturity of development, hence also the maturity of the organ that does the thinking. Anything else is drivel.

>The vulgar economist has not the slightest idea that the actual, everyday exchange relations and the value magnitudes cannot be directly identical. The point of bourgeois society is precisely that, a priori, no conscious social regulation of production takes place. What is reasonable and necessary by nature asserts itself only as a blindly operating average. The vulgar economist thinks he has made a great discovery when, faced with the disclosure of the intrinsic interconnection, he insists that things look different in appearance. In fact, he prides himself in his clinging to appearances and believing them to be the ultimate. Why then have science at all?

>But there is also something else behind it. Once interconnection has been revealed, all theoretical belief in the perpetual necessity of the existing conditions collapses, even before the collapse takes place in practice. Here, therefore, it is completely in the interests of the ruling classes to perpetuate the unthinking confusion. And for what other reason are the sycophantic babblers paid who have no other scientific trump to play except that, in political economy, one may not think at all!

>But satis superque [Enough and more than enough]. In any case, it shows the depth of degradation reached by these priests of the bourgeoisie: while workers and even manufacturers and merchants have understood my book and made sense of it, these 'learned scribes' (!) complain that I make excessive demands on their comprehension.

>I would not advise reprinting Schweitzer's articles, though Schweitzer has made a good job of them for his paper.

>You would oblige me if you sent me a few issues of the Staats-Anzeiger.

>You should be able to get Schnacke's address by enquiring at the Elberfelder.

>Best greetings to your wife and Fränzchen.

>Yours,

>K. M.

>Apropos. I have received an article by Dietzgen about my book; I am sending it to Liebknecht.

I fault Marx for spending so much time in rewriting volume 1 of Capital after its publication. He should have put more time in preparing the later volumes for publication. Some have recommended that on a first reading, you skip the first chapter. If I took some comments here more seriously, I could see an argument that Marx should have worked on rewriting chapter 1 a few more times.

Suppose that you are not a knave and are curious about what socialism is. Then you know that you do not need to rely on a short sentence from some pseudonymous commentator on the Internet. You can find statements, programs, etc. from organizations historically important or of current importance.

For example, I think of the Socialist International as following on from the Second International. Their June 1989 Declaration of Principles is here.

The Democratic Socialists of America (DSA) currently has a certain prominence in the United States. They offer a definition of Democratic Socialism here:

>"Capitalism is a system designed by the owning class to exploit the rest of us for their own profit. We must replace it with democratic socialism, a system where ordinary people have a real voice in our workplaces, neighborhoods, and society.

>We believe there are many avenues that feed into the democratic road to socialism. Our vision pushes further than historic social democracy and leaves behind authoritarian visions of socialism in the dustbin of history.

>We want a democracy that creates space for us all to flourish not just survive and answers the fundamental questions of our lives with the input of all. We want to collectively own the key economic drivers that dominate our lives, such as energy production and transportation. We want the multiracial working class united in solidarity instead of divided by fear. We want to win 'radical' reforms like single-payer Medicare for All, defunding the police/refunding communities, the Green New Deal, and more as a transition to a freer, more just life.

>We want a democracy powered by everyday people. The capitalist class tells us we are powerless, but together we can take back control."

The Rochdale Principles for co-operatives were stated in 1844, and been updated by, for example, the International Cooperative Association. One statement of these principles is here.

Others will have other statements or historical statements they think important. For example, Rosa Luxemburg's Reform or Revolution was of historical importance in responding to Eduard Bernstein's The Preconditions of Socialism and the Tasks of Social Democracy. I will grant that if you are uninterested in socialism, recognizing which documents are of more importance in history might not be obvious.

The laws of supply and demand, as presented in neoclassical economics, are muddled and confused. Demand for consumer goods, for eample, is the result of households maximizing some non-existent utility subject to constraints. A market is an unanalyzed entity, generally with no brokers who make markets, willing to trade on either side. Although not discussed, the market in neoclassical microeconomics is typically a posted price market, corresponding to the lowest level of the Chomsky hierarchy.

Those who specialize in finance might say they observe something like supply and demand in order books. But those curves are not the supply and demand curves in neoclassical microeconomics. These financial markets are structured, with algorithmic rules for matching bids and offers. They often parallel future markets, capable of going into backwardation and contango.

A certain sort of mathematics is needed to fully analyze markets. From one perspective, computers should be designed to execute our algorithms, which are abstract mathematical entities independent of such implementation. Computational complexity is a part of this mathematics. From literature on algorithmic game theory, I know that if P ≠ NP, complexity classes exist in-between. My favorite approach to price theory, concentrating on reproducibility, can be developed with an emphasis on algorithms. I once presented a derivation along this path.

Philip Mirowski explains more about the ideas on which I draw here. Towards the end, after about 19:30, he explains, "There's no such thing as a law of supply and demand."

>"It was thenceforth no longer a question, whether this theorem or that was true, but whether it was useful to capital or harmful, expedient or inexpedient, politically dangerous or not. In place of disinterested inquirers, there were hired prize fighters; in place of genuine scientific research, the bad conscience and the evil intent of apologetic." -- Karl Marx

Suppose you run a restaurant. You think that you could expand if you paved your parking lot or put a deck up out back. You convince your local bank manager. The bank credits their own account with an asset and credits your account with a loan. That asset, for the bank, is a promise from you to pay off the loan. You spend the money in your account by paying a paving or building contractor.

The bank has created money. No third party must first choose to increase their saving rate and deposit money in the bank. You are able to obtain resources to implement plans for increased production.

The author of a prominent introductory textbook for economics has another, confused story:

>"Financial intermediaries are financial institutions through which savers can indirectly provide funds to borrowers. The term intermediary reflects the role of these institutions in standing between savers and borrowers. Here we consider two of the most important financial intermediaries: banks and mutual funds.

>Banks If the owner of a small grocery store wants to finance an expansion of his business, he probably takes a strategy quite different from that of Intel. Unlike Intel, a small grocer would find it difficult to raise funds in the bond and stock markets. Most buyers of stocks and bonds prefer to buy those issued by larger, more familiar companies. The small grocer, therefore, most likely finances his business expansion with a loan from a local bank.

>Banks are the financial intermediaries with which people are most familiar. A primary job of banks is to take in deposits from people who want to save and use these deposits to make loans to people who want to borrow. Banks pay depositors interest on their deposits and charge borrowers slightly higher interest on their loans. The difference between these rates of interest covers the banks’ costs and returns some profit to the owners of the banks." -- Greg Mankiw. 2018. Principles of Economics, 8th edition p. 545.

Mankiw then goes on with archaic nonsense about loanable funds and government spending crowding out private investment.

Why do economists teach balderdash?

Libertarianism is a kind of communism. I need a label for a right-wing, extreme defense of property by those who repudiate many of the functions of government. According to Wikipedia, David Boaz and others call this political philosophy, 'Propertarianism'.

Robert Nozick is the most respected proponent of propertarianism among recent analytical philosophers. Anarchy, State, and Utopia is his attempt at a fairly comprehensive defense of propertarianism. He later repudiated it, but no matter. His utopia is of a federation of free communities, with the federation being a minimal state. People are free to move to the community which has rules closest to what they prefer.

Nozick explicitly says that slavery can exist in some of these communities:

>"The comparable question about an individual is whether a free system will allow him to sell himself into slavery. I believe that it would… But some things individuals may choose for themselves, no one may choose for another… But remember that any individual may contract into any particular constraints over himself and so may use the voluntary framework to contract himself out of it." – Robert Nozick. Anarchy, State, and Utopia. p. 263.

Those who do not know better might think academic economics would be useful for understanding capitalism. But much of academic economics is propaganda and reactionary justification for the ruling class of capitalists.

This post describes two ways of classifying economic theory (Table 1). Even if you had paid attention in class, you probably would have only been exposed to ideas in the column for the neoclassical position in the table.

Table 1: Two Classification Of Economists

	Neoclassical Position	Correct Position
Price Theory	Emphasis on allocating scarce resources	Emphasis on social reproduction
Monetary Theory	Money as a veil	Money Non-Neutral

I have written about the row for price theory before. Classical and Marxian political economy focuses on what needs to hold such that society is reproduced. Neoclassical economics is defined, by many, as being about the allocation of scarce resources.

Post Keynesians and others describe money as having real effects. Many mainstream economists, on the other hand, model capitalist economies as, basically, barter economies. They hold money to be neutral, at least in the long run. They mistakenly think a natural rate of interest would arise in a barter economy. It is the task of the monetary authority to set the money rate of interest equal to this natural rate so that the economy, in the short run, would behave as if it were a barter economy, with no inflation.

The above describes two ways of dividing economists into two groups, for a total of four buckets. For example, an economist could think of prices as scarcity indices and of money as non-neutral. Finance allows entrepreneurs to obtain the resources they need for innovation.

Can you name economists in each of these four buckets?

I turn to Colin Rogers when I want to see the Cambridge Capital Controversy used to criticize Wicksellian monetary theory. My more direct inspiration for this post is Mason and Jayadev's current book, Against Money.

All civilization has been built on slavery. It is endorsed in the Bible, for example, in Paul's letter to Timothy. Are you godless?

Intellectuals in coffee houses with no practical experience can say what they want. They only think they are smart.

Look at what happens when slaves listen to you, like Spartacus and Nat Turner. Nothing but violence and death result.

Our crops can only be grown by many slaves working together on large fields. If they were freed, they would each tend a small field for themselves. Only the master can be expected to have the understanding of a cash crop, like cotton, for sustaining people far away.

You will only hurt the people you are trying to help. Right now, the slave is taken care of and does not face the uncertainty of the master who makes the decisions. The master bears the risk that the crops being grown are the right ones, that they will not be attempting to sell into a glut. If the slave were free, they would have all this uncertainty and become a worse, grasping person.

Sure, some masters are abusive. But no better society has been devised. And the masters have laws and norms to limit abuse.

You want to eliminate innovation. Right now, a freeman with a good idea is at liberty to pledge themself to obtain the needed finance. If he fails, he becomes an indentured servant or slave. But society is vastly improved by successful inventions and innovation.

You want to eliminate civilization and culture. Sculpture, painting, plays can only be created by those with the leisure to do so. Likewise, they need an audience and patrons free to develop their tastes. They cannot be this audience if they are daily grubbing in the muck to earn their keep.

When you grow up, you will begin to understand how the world works. And you will drop these impractical, undeveloped musings of youth. You will realize we cannot get rid of slavery.

In the 1960s economists discovered that much that they taught was unfounded or incorrect. Well-behaved supply and demand functions do not determine prices in the long run.

Jack Birner is an economist of the Austrian school. He wrote a book, Cambridge Controversies in Capital Theory: A Methodological Analysis in 2002. He described the Cambridge Capital Controversies (CCC) as in the title:

>"Four decades ago the best minds in economics were engaged in a confrontation which the entire profession followed in the pages of the leading journals almost as if it were a soccer match. It has become customary to distinguish two opposing groups of economists to the debate." -- Jack Birner (2002: 1)

And he expresses astonishment that the results of this dispute are ignored:

>"What I do want to draw attention to is that the conclusions reached in that debate constitute a rare example of a set of formally proven, uncontestable, undeniably true and reliable results in economics... They can be summarized by saying that the K of the production function that modern economists so confidently and fully rely on for their theoretical and empirical work can only be used in conditions where there is only a single, homogeneous capital good... In other words, not only is there no intuitive justification for the use of aggregate, homogeneous K, we have proofs by Nobel-calibre economists assisted by 100 per cent certain mathematical techniques that demonstrate without a shred of doubt that this K cannot and should not be used for the objectives it is currently used for. Nevertheless, economists go about their business as if these proofs did not exist. That some of them are the very same people who produced these proofs earlier makes things even more curious. The fact that production functions with the same aggregate K figure prominently in all current textbooks of macroeconomics is worse than curious: it is deeply worrying." -- Jack Birner (2002: 1-2)

I wanted to bring attention to the above statements, by an economist who probably generally disagrees with me on lots of matters.

I agree with Birner that the overall point of the CCC is not at all clear from the details of the match. The participants were worrying about local details. I think more was at stake than an aggregate theory. I like to emphasize the labor 'market' in my expositions. Fabio Petri, among others, emphasizes mistakes in what the early marginalists thought could be consistently taken as given in their theory.

If you want to know more about the collapse of neoclassical economics, you could do worse than Cohen and Harcourt's 2003 survey article. I wish their example had a circular structure in production.

Many posts here argue about the labor theory of value (LTV) and the subjective theory of value (STV). I have pointed out that both labels are misleading. For some reason, the pro-capitalists generally assert they do not need to know anything about Marx's work to argue about his theory of value. They also generally ignore all literature of maybe a century setting out a modernized version of classical and Marxian political economy.

But I do not want to argue here for the superiority of, say, Marxian political economy over neoclassical theory.

Rather, I want to point out that you cannot fully understand the literature developing either without some comfort with mathematics.

My thesis does not exclude that during the last century and a half, some developing either did not use much maths in their exposition. Ronald Coase and Joan Robinson are examples. (I read Robinson as if she used maths to develop her ideas and then put them in words I know that is historically inaccurate.) But I include rigorous, logical arguments, from premises to conclusions, as mathematics.

You are much more convincing arguing that economists misuse mathematics if your presentations exhibit familiarity with mathematics. Nicholas Georgescu-Roegen and Philip Mirowski are some who I find interesting on the (ab)use of mathematics in economics. John Maynard Keynes has some remarks in his General Theory and later.

The question of whether a modernized classical and Marxian political economy should be preferred to an exploded neoclassical theory is not closely tied to the question of socialism versus capitalism. Many have noted that 'the LTV' was developed by pro-capitalists and that some (e.g. Oskar Lange) advocated for socialism on the basis of neoclassical theory. If you adopt Leontief's approach for empirical work, you will not automatically become a socialist. It is more the other way around. Widespread opposition to the Vietnam war and questioning of Western imperialism had some connection with academic economists in, say, American universities exploring radical ideas. The connections are not one of rigorous logic and sometimes hard to find.

By the way, a recovered classical and Marxian political economy versus some version of neoclassicism are not the only alternatives. Institutionalism, as in the work of Thorstein Veblen, Wesley Clark Mitchell, John Maurice Clark, John Kenneth Galbraith, Warren Samuels, Clarence E. Ayres, Gunnar Myrdal, and Geoffrey Hodgson is another possibility. Generally, institutionalist eschew theory and emphasize empirical work, including qualitative work.

Many mainstream economists reacted to their defeat in the Cambridge Capital Controversy by turning to General Equilibrium Theory (GET). When the defects in that approach were emphasized in the 1970s - see the Sonnenschein-Mantel-Debreu theorem, game theory became all the rage. Game theory does not seem to provide a general approach, and the folk theorem seems to imply it shares the same lack of empirical implications as GET. Then there are all sorts of specific analyses, also not providing a general vision. I might mention principal agent problems and asymmetric information as examples.

Many socialists suspect that much of academic economics is propaganda for the bourgeois. You can expect hegemonic ideas to present the special interest of the dominant class as the general interest. So it is demotivating to study orthodox economics. I have no objection to some concentrating on activism, organizing labor unions, or whatever. We need students of economics, though, to help staff, say, the New York City Rent Guidelines Board. Lauren Melodia and Sina Sinai, for example, have masters from John Jay's economics department.

I find strange the many pro-capitalists here who proclaim that socialists do not understand economics and go wrong very quickly in discussing neoclassical economics. Unlike in Dragnet, pseudonyms are not named, to protect the guilty.

Do the pro-capitalists know that they need maths to convincingly argue for neoclassical economics?

Sraffa's 1960 book, The Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory, is a work of modern art. (You can find a PDF version by googling.) Much has been stripped away, providing a new way of looking at political economy. I have been putting in some time exploring the six-page chapter on land. The relationship of Sraffa's work to the work of Marx has been much discussed.

For those who have some exposure to linear algebra, Luigi L. Pasinetti's 1977 book, Lectures on the Theory of Production, is another elegant book. This book, too, can be found in a PDF version with a google search, although that transcription has some difficulties.

What other books in political economy do you think are particularly well-written?

I suppose John Kenneth Gabraith's 1958 The Affluent Society and Thorstein Veblen's 1899 The Theory of the Leisure Class are two examples. I am undecided on John Maynard Keynes' The General Theory of Employment, Interest, and Money. The first volume of Marx's Capital might be considered well-written by those who enjoy long Victorian novels. I am limited to English translations.

Ludwig Von Mises' Human Action is a counter-example. It is poorly organized. F. A. Hayek's The Road to Serfdom is poorly written at the level of the individual sentence, although it belongs on the list of works that those interested in political economy must read at some point.

General Equilibrium Theory (GET) is the most rigorous and most developed version of the theory of supply and demand. I note that, before you were born, economists discovered that GET does not support the just so stories many economists still tell. (Experimental economists have validated Scarf's example of instability.)

Franklin Fisher is an authority on the post topic. The New Palgrave is an authoritative reference. Fisher writes the following there:

>"Yet the very power and elegance of equilibrium analysis often obscures that it rests on a very uncertain foundation. We have no similarly elegant theory of what happens out of equilibrium, of how agents behave when their plans are frustrated. As a result, we have no rigorous basis for believing that equilibria can be achieved or maintained if disturbed. Unless one robs words of their meaning and defines every state of the world as an 'equilibrium' in the sense that agents do what they do instead of doing something else, there is no disguising the fact that this is a major lacuna in economic analysis.

>Nor is that lacuna only important in microeconomics. For example, the Keynesian question of whether an economy can become trapped in a situation of underemployment is not merely a question of whether underemployment equilibria exist. It is also a question of whether such equilibria are stable. As such, its answer depends on the properties of the general (dis)equilibrium system which macroeconomic analysis attempts to summarize. Not surprisingly, modern attempts to deal with such systems have been increasingly forced to treat such familiar macroeconomic issues as the role of money." -- Franklin M. Fisher. 1987. Adjustment processes and instability. In J. Eatwell, M. Milgate, P. Newman, The New Palgrave: A Dictionary of Economics. Macmillan.

As far as I know, although some interesting work has been done, this gap still exists.

Can you acknowledge problems with supply and demand?

>"I am in a somewhat peculiar position because due to certain idiosyncrasies of my education I never learned 'neoclassical economics'. The economic theory that I learned was from Herbert Scarf and it was couched entirely in terms of the abstract general equilibrium model... My economic intuition was always that there were no theorems of the following kind: suppose you increase the supply of labour, as a result the equilibrium real wage will fall. I knew there were no such theorems available in general equilibrium theory. I also knew, and maybe this became clearer because of Scarf's mathematical point of view, that once you took the step to a simultaneous general equilibrium vision, you had to give up hope of sustaining some traditional ideas. For one thing, you lost any sense of causality." -- Duncan Foley (2003)

1. Introduction

Neoclassical economics emphasizes equilibria, for example in General Equilibrium models. In equilibria, all agents are optimizing and their plans are all coordinated. But no reason exists for economists to expect actually existing more-or-less capitalist economies to ever be in such equilibria.

This post demonstrates that economies need not be near equilibria by means of an example. This example has been available for two thirds of a century (Scarf 1960) and is often referenced. The example is of a pure exchange economy. No trading occurs at any prices other than equilibrium prices. Since the example has one locally unstable equilibrium, equilibrium prices are never achieved.

(This post assumes the reader knows about how utility theory relates to the demand for consumer goods and that consumer demand is a function of prices.)

2. Data

This example economy consists of three individuals, each endowed with one unit of a different commodity (Table 1). The individuals also differ in tastes, as expressed by the utility functions in Table 2. Our problem is to determine equibrium prices for this simple economy and the price dynamics.

Table 1: Agent's Endowments

Mary: 1 Apple, 0 Bananas, 0 Cantaloupes

Nancy: 0 Apples, 1 Banana, 0 Cantaloupes

Olivia: 0 Apples, 0 Bananas, 1 Cantaloupe

Table 2: Agent's Preferents

Mary: Um = min( Xa, Xb )

Nancy: Un = min( Xb, Xc )

Olivia: Uo = min( Xa, Xc )

3. Demand Functions

Each agent maximizes their utility, subject to their budget constraint. Consider a single agent, for example, Mary. Mary chooses non-negative Xa, Xb, Xc to maximize

Um = min( Xa, Xb )

such that

Pa Xa + Pb Xb + Pc Xc ≤ Pa

Since Mary derives no utility from cantaloupes, she will not consume any of them. Thus, Mary's problem can be graphed in a two-dimensional quantity space for apples and bananas. Each isoquant, depicting a given level of utility is L-shaped, with the lower-left part of the L along a ray projecting to the northeast from the origin at a 45 degree angle.The budget constraint is a line sloping downward to the right.

The solution to this constrained utility-maximizing problem is a point along the ray at 45-degrees for the utility isoquant intersected there by the budget constraint.

Symbolically:

Xa* = Xb* = Pa/(Pa + Pb)

Xc* = 0

One can find Nancy and Olivia's demand functions by symmetrical arguments. Aggregate excess demand functions are the difference between aggregate demands and aggregate supplies. Aggregate demands are individual demand functions summed across the individuals. Aggregate supplies, in this pure exchange economy, are endowments summed across individuals. In fact, the aggregate supply of each commodity is one unit here. A bit of algebra yields:

Za = Pc/(Pa + Pc) - Pb/(Pa + Pb)

Zb = Pa/(Pa + Pb) - Pc/(Pb + Pc)

Zc = Pb/(Pa + Pc) - Pa/(Pa + Pc)

where Za, Zb, and Zc are the aggregate excess demand functions for apples, bananas, and cantelopes, respectively.

The numeraire is arbitrary. One can confine prices to lie on the unit sphere:

Pa^(2) + Pb^(2) + Pc^(2) = 1

4. Equilibrium

In equilibrium, aggregate excess demand functions are zero. The only equilibrium is one in which all prices are equal:

Pa* = Pb* = Pc* = (1/3)^(1/2)

5. Dynamics

I postulate that when the aggregate excess demand for a particular commodity is positive, the price of that commodity rises. Likewise, when aggregate excess demand is negative, the price falls. The simplest dynamical system with these properties is one in which the rate of change of prices with respect to time is equal to the aggregate excess demands:

d Pa/dt = Pc/(Pa + Pc) - Pb/(Pa + Pb)

d Pb/dt = Pa/(Pa + Pb) - Pc/(Pb + Pc)

d Pc/dt = Pb/(Pa + Pc) - Pa/(Pa + Pc)

Under these dynamics, the equilibrium is unstable. Solutions around the equilibrium spiral out on the unit sphere to a limit cycle. The equilibrium point will not be attained.

6. Conclusion

The failure of General Equilibrium Theory to limit dynamics, I gather, is intrinsic to methodological individualism, in which independent agents can have arbitrary preferences and endowments. Attempts to explain economies seem to need to postulate influences on tastes and income above the level of the individual, for example, by others in one's social class or through some sort of structuralist theory. In other words, there is too such a thing as society. I take Kirman (1989) to point in this direction.

I might as well mention that the arbitrary dynamics implied by orthodox economic theory undermines a certain political outlook. I refer to the idea that we ought to loosen restrictions on trade, but ensure some sort of redistribution so as to ensure that everybody participates in the supposedly enlarged pie. I take the second welfare theorem to be the basis for this view. But that redistribution doesn't necessarily lead to the economy converging to the original equilibrium, as altered by 'free' trade.

REFERENCE

Alan Kirman. 1989. The intrinsic limits of modern economic theory: the emperor has no clothes, Economic Journal, V. 99, N. 395: 126-139

Herbert Scarf. 1960. Some examples of global instability of the competitive equilibrium, International Economic Review, V. 1, N. 3 (September): 157-172

>"The purpose of studying economics is not to acquire a set of ready-made answers to economic questions, but to learn how to avoid being deceived by economists." -- Joan Robinson

Do you think the theory of supply and demand explains something about how markets work? If so, what do you mean by 'supply' and 'demand'? In the theory, what more basic ideas do these theories build on?

I have noticed that many pro-capitalists here are unwilling to answer these questions. Some have engaged in long back-and-forths where they refused to answer. I will provide one example, here. I could provide more. I often do not engage in the longer conversations.

And, for some reason, the pro-capitalists hardly ever try to publicly help others out.

It seems to me that if you want to discuss the subreddit's theme, it is helpful to have some understanding of academic economics over, say, the last century.

Even before the October revolution, Lenin advocated state capitalism. He stated he was opposing other socialists who wanted to jump directly to socialism. The idea that the Soviet Union was state capitalism is NOT something that socialists came up after the 1989 fall of the Berlin wall.

Lenin thought of imperialism as co-extensive with government-supported trusts. Mark Twain had his suspect financial transactions in The Gilded Age center around setting up a railroad with government-granted rights of way, for example. Lenin wanted the government to take over large corporations and these trusts, in order to promote economic development in Russia:

>"We are publishing in this issue the resolution on economic measures for combating dislocation, passed by the Conference of Factory Committees.

>The main idea of the resolution is to indicate the conditions for actual control over the capitalists and production in contrast to the empty phrases about control used by the bourgeoisie and the petty-bourgeois officials...

>...We Pravda people are said to be deviating from Marxism to syndicalism just because we defend the resolution... We suggest nothing like the ridiculous transfer of the railways to the railwaymen, or the tanneries to the tanners. What we do suggest is workers’ control, which should develop into complete regulation of production and distribution by the workers, into 'nation-wide organisation' of the exchange of grain for manufactured goods, etc. (with 'extensive use of urban and rural co-operatives'). What we suggest is 'the transfer of all state power to the Soviets of Workers', Soldiers' and Peasants’ Deputies'.

>Take the sugar syndicate or the state railways in Russia or the oil barons, etc. What is that but state capitalism? How can you 'skip' what already exists?

>The point is that people who have turned Marxism into a kind of stiffly bourgeois doctrine evade the specific issues posed by reality, which in Russia has in practice produced a combination of the syndicates in industry and the small-peasant farms in the countryside. They evade these specific issues by advancing pseudo-intellectual, and in fact utterly meaningless, arguments about a 'permanent revolution', about 'introducing' socialism, and other nonsense...

>...These arguments are ridiculously stupid, for what makes socialism objectively impossible is the small-scale economy which we by no means presume to expropriate, or even to regulate or control....

>...Not regulation of and control over the workers by the capitalist class, but vice versa. This is the point. Not confidence in the 'state', fit for a Louis Blanc, but demand for a state led by the proletarians and semi-proletarians - that is how we must combat economic dislocation. Any other solution is sheer bunkum and deception." -- Lenin, Economic Dislocation and the Proletariat's Struggle Against It. Pravda, 17 June 1917. In Collected Works, vol. 25.

In practice, state capitalism in the Soviet Union meant the supposed vanguard of the vanguard party substituting itself for the workers.