Competitive equilibrium (excerpt from Economics in Two Lessons)

I’m now coming up to (what I hope will be) the most challenging part of my book-in-progress, Economics in Two Lessons. The core theoretical point the first part of the book (Lesson 1) is that, under a set of ideal assumptions, competitive equilibrium prices both reflect and determine the opportunity costs faced by consumers and produces. This means that there is no way to rearrange consumption to make someone better off unless someone else is made worse off. (I’ve already mentioned my reasons for avoiding the term “Pareto-optimal” in this context.

What I’m trying to do here is to spell out the logic underlying these results in a way that foreshadows the discussion of market failure and income distribution, in Lesson 2, but still shows the power of market mechanisms. I’ll probably need a few goes at this, and this is my first try. Critical comments on everything from the underlying theory to editorial nitpicks are welcome. Sincere praise is also welcome of course, but constructive criticism is best of all.

Competitive equilibrium

Let’s restate Lesson 1:

Market prices reflect and determine the opportunity costs faced by consumers and producers.

We’ve seen how market prices determine the opportunity costs we face in making economic decisions as consumers, workers and producers of goods and services. We can’t as individuals, change the market prices we face for goods and services in general, so we must take them as given in looking at the opportunity cost of different choices.

But Lesson 1 says something more, namely that market prices also reflect opportunity costs. That is, just as the opportunity costs of our choices are determined by market prices, those market prices are determined by our choices. Under ideal conditions, those choices, aggregated over all the members of a society, will reflect the opportunity costs for that society as a whole.

There is a large branch of economic theory devoted to proving results of this kind using formal mathematics. But the core of the idea may be approached using the idea of ‘no free lunches’ or, more precisely, ‘no benefits without equal opportunity costs’, discussed in the previous section.

As we saw then, this condition requires that all production be technologically efficient. If not, there is always a free lunch to be had by making production more efficient, producing more with the same inputs.

The second requirement ‘no free lunch’ requirement is that there should be no gains from mutually beneficial exchange remaining to be realised. It’s easy to see that this requirement is closely related to market prices.

Example 2: lets suppose that you own a new jacket that you would be willing to trade for tickets to tonight’s baseball game, while I have tickets and would be willing to trade them for your jacket.

Now lets look at market prices. If the market price of the jacket is greater than the price of the tickets, there is no need for you to trade with me. You can (assumption A) sell the jacket at the market price (which is unaffected by assumption C), use the proceeds to buy the tickets and have money left over. Since you make the best possible choices (assumption D) that’s what you will do. If I want to complete the trade, by selling my tickets and buying the jacket, I will have to make up the price difference. By assumption (E), no one else is affected.

On the other hand, if the market price of the jacket is less than that of the tickets, the fact that this price prevails indicates that there must be someone else willing to sell jackets, and buy tickets at those prices. So, I can sell my tickets and use the proceeds to buy a jacket, making an exchange that benefits both me and the other parties involved. You, on the other hand, am out of luck. At the prevailing prices, no one is willing to trade tickets for a jacket, and there are no remaining exchanges to be made.

This simple examples give a flavor of the argument that leads to Lesson 1. Intuitively, it suggests the conclusion that trade at market prices will capture all the potential gains from mutually beneficial exchanges, so that no free lunches will be left on the table. In other words, in market equilibrium, TANSTAAFL holds.

This is where casual presentations of Lesson 1 commonly stop. But the simple story above embodies a lot of assumptions about the way markets work:

The most important are:

(A) Everyone faces the same market-determined prices herefor all goods and services, including labor of any given quality, and everyone can buy or sell as much as they want to at the prevailing prices

(B) Everyone is fully aware of the prices they face for all goods and services, including how relevant uncertain events might affect those prices

(C) No one can influence the prices they face

(D) Everyone makes the best possible choices given their preferences and the technology available to them

(E) Sellers bear the full opportunity cost of producing the good, and buyers receive the full benefit of consuming it, no more and no less. That is, no one can shift costs associated with production or consumption to anyone else without compensation (for example, by dumping waste products into the environment) and no one else receives benefits for which they do not pay.

We can go back to the example to see where each of these conditions fits in

If the market price of the jacket is greater than the price of the tickets, there is no need for you to trade with me. You can (assumption A) sell the jacket at the market price (which is unaffected by assumption C), use the proceeds to buy the tickets and have money left over. Since you make the best possible choices (assumption D) that’s what you will do. If I want to complete the trade, by selling my tickets and buying the jacket, I will have to make up the price difference. By assumption (E), no one else is affected.

This more complicated version of the story can be formulated in mathematical terms to show that, under the stated conditions (and some additional technical requirements), a competitive equilibrium will arise in which there are no free lunches; that is, any potential benefit entails an opportunity cost that is at least as great.

In this ‘perfectly competitive equilibrium, the price of any particular good good is equal, for everyone who consumes that good, to the opportunity cost of a change in consumption, expressed in terms of the alternative possible expenditures. Similarly, firms can maximise profits only if the prices of the goods they produce are equal to the opportunity cost of the resources that could be saved by producing less of those goods.

This point is the core of Lesson 1. In a perfect competitive equilibrium prices exactly match opportunity cost. So, there are no ‘free lunches’ left. More precisely, any additional benefit that can be generated for anyone in the economy must be matched by an equal or greater opportunity cost, where opportunity cost is measured by the goods and services foregone, valued at the equilibrium prices. This opportunity cost may be borne by those who benefit from the change or by others.

Hazlitt, and many subsequent writers, implicitly assume something much stronger: that if prices reflect opportunity costs, there is no room for improvement in public policy. In particular, he assumes that any policy that benefits one group at the expense of others is undesirable. To put it more strongly, the distribution of income associated with competitive market equilibrium, based on existing private property rights, is assumed to be optimal.[^1]

This idea is false: as we will see there are a vast number (in the usual mathematical formulation, infinitely many) possible outcomes in which there are no free lunches, each corresponding to a different allocation of rights and a different market equilibrium.

We will discuss the issue of income distribution when we come to Lesson 2. Before doing this, we will consider a variety of examples to illustrate Lesson 1.

[^1]: Hazlitt’s reasoning is reinforced, in many economics texts, by the description of the competitive market equilibrium as “Pareto-optimal” or “efficient”. These misleading terms are discussed here.

fn1: Hazlitt’s reasoning is reinforced, in many economics texts, by the description of the competitive market equilibrium as “Pareto-optimal” or “efficient”. These misleading terms are discussed here.

45 thoughts on “Competitive equilibrium (excerpt from Economics in Two Lessons)

  1. @Newtownian

    Mathematicians prove theorems, that is, logical deductions from premises. There’s a whole body of maths called proof theory about what this means. What can’t be proved is that a particular set of premises actually applies to a real-world problem.

    Economic concepts of equilibrium have little if anything to do with chemical equilibrium and are much closer to physics (statics and dynamics).

  2. Didn’t Popper mention that there were conventional truths, logical or axiomatic truths and empirical or scientific “truths”? The last one has to be put in quotes as it really means something like “high probability of being true”.

    A conventional truth is that the man who runs this blog is named John Quiggin or that we drive on the left side of the road in Australia. These things are true by convention and common useage. I won’t give definitions for the other truths here.

    The interesting issue for Popper and many others was why is mathematics able to refer to reality successfully? Of course, it’s only a subset of maths that more or less refers to reality. Plenty of other maths deals with imaginary numbers, extra dimensions and so on. Yet these techniques too have their uses.

    To my thinking, I guess that a better description of economic general equilibrium maths (about which I actually know nothing) would be that it is an attempt to model the behaviour of certain real world systems (markets) or at least model certain idealised forms of these real world systems.

    Again, I believe (and can only believe without knowledge in this area) that these models could be useful for discovering certain possible or technical aspects (I am guessing) about markets. I don’t believe that these models are anywhere near being useful for managing full political economies, if they ever could be. But as I say these are just unsubstantiated beliefs or guesses on my part.

  3. John,

    Isn’t there a real problem with statements like:

    “This more complicated version of the story can be formulated in mathematical terms to show that, under the stated conditions (and some additional technical requirements), a competitive equilibrium will arise in which there are no free lunches; that is, any potential benefit entails an opportunity cost that is at least as great”?

    The sticking point for me is the word ‘arise’ which implies that there is a robust and general story to be told in theory about convergence to competitive equilibrium from an arbitrary starting point. But what exactly is that story? Walras recognised the problem and it isn’t clear to me that the neo-Walrasian program has yet provided the solution. Logically, statements about the *properties* of a competitive equilibrium are unconnected to the question of whether such an equilibrium can be *attained* in a given economy. Proving that under certain (immensely restrictive!) circumstances it can be shown that a price vector exists that would support trades that lead to allocations that have the ‘no free lunch’ property does not establish that such a vector could be realised through trade at non-equilibrium prices.

    Assuming that one follows from the other is question-begging on a grand scale (a point Frank Hahn made a lot in his fight against Lucas et al), and a vice of Hazlitt and his ilk. It certainly (and unfortunately) seems to undermine your argument in a serious way. Austrians, of course, are able to retain the rhetoric of market *processes* without the GE apparatus but I doubt that that’s a direction you want to go.

  4. I’ve been reading Stiglitz recently, and he seems to require two assumptions for market equilibrium that I don’t see in your text: That markets be complete, and that markets clear. I don’t pretend to be an economist, so these may be implicit in the OP, but I would be interested in understanding how these affect your reasoning?

  5. @Andrae

    These are both in (A). “Complete” means “for all goods and services” and “markets clear” means “everyone can buy or sell as much as they want to at the prevailing prices”. I’ve spelt out what Stiglitz says in economist shorthand.

    @Ikonoklast I’ve tried to say in the preface that I won’t be claiming micro (at least not the neoclassical micro underlying GE) as the foundation for macro

    @Wyile I am approaching this as a response to the Austrian approach which is implicit in Hazlitt. So, I’m not going to worry about neoclassical theory questions like existence, multiplicity, convergence etc. Rather, I’m going to respond to the Austrians on their own terms.

  6. This is probably off-topic. I read an online essay by some economist (forget his name already) and he was basically arguing the old “society doesn’t exist, only individuals exist” line.

    If I was in a room where anyone said that I would heckle: “Individuals don’t exist, only atoms exist.”

    The thing is, if you want to deny emergent phenomena, they have to go far more reductionist than simply denying that society exists. Heck, even atoms don’t make the cut of existing if society doesn’t make that cut.

  7. Ross Gittens knows what opportunity cost is.

    “Put at its simplest, the concept of opportunity cost says that if you’ve got a dollar, you can only spend it once. This truth might be glaringly apparent, but it’s surprising how often grown men (and, less commonly, grown women) forget it.”

    http://www.smh.com.au/comment/increasing-gst-a-fanciful-fix-for-strained-budgets-20150721-gigv1o.html#ixzz3gZLa5eCe

    Ikon, I read someone else say to those who still love the idea of the magnificent individual that there are no individuals; there is only society.

    How is it possible to be ‘an individual’ without other people? It’s the same thing as the tree in the forest making no noise if there is no person to hear it.

  8. @Ikonoclast

    The ‘no such thing as society’ view might be recast in terms of the problem of defining social welfare. Arrow’s General Possibility Theorem shows the intractable difficulties associated with defining social preferences via aggregation of individual preferences. Hence much blithe talk of social welfare on that basis is actually incoherent, there being no way to define ‘social welfare’, let alone measure its ups and downs. You could decide to try to define social welfare on a basis other than individual preference satisfaction, but that is still open to the Rylean question: once we have identified all individuals and the institutions with which they interact, where is the separate thing called ‘society’ that is an agent experiencing welfare fluctuations?

  9. The closest I ever got to economics was dating a economics student so this is likely stupid but if we have the conditions that Prof Quiggin sets up: Given TANSTAFL applies then presumably no one can make capital gains money on the stock market? Or it seems anywhere else.

  10. @Wylie Bradford

    Once we have identified all atoms and the chemical bonds they make when they they interact, where is the separate thing called a person that is an agent experiencing welfare fluctuations?

    Once you, in a theoretical or thought-experiment manner, pull a complex system apart into “component pieces” you no longer have the complex system you began with. This is axiomatically and trivially true. Such thought experiments prove precisely nothing.

  11. “The market is a radical experiment which violated fundamental human needs and capacities. You can see this in the violent struggles that were required to impose market conditions on people. In the United States, for example, about one sixth of the gross national product, over a trillion dollars per year, is devoted to marketing. Marketing is manipulation and deceit. It tries to turn people into something they aren’t — individuals focused solely on themselves, maximising their consumption of goods that they don’t need.” – Noam Chomsky.

  12. @Ikonoclast

    Let me first stress that I do not endorse the ideological overtones of the classic ‘there’s no such thing as society’ discourse, involving as it does a methodological reductionism that is untenable. I’m pretty sure we’re in agreement on that score.

    That being said, you might want to point out how you avoid the regress in your counter-argument – ‘atoms’ haven’t been a viable stopping point for a long time in physics terms. One might find oneself ultimately arguing that nothing exists. The line about complex-systems is also somewhat question-begging. The context in which statements are made is important. Even though we are both made up of the same stuff I presume you agree that while you and I can talk to each other (as we are now) there is no sense in which ‘Australia’ can talk to ‘France’ in the same way.

    I focused on welfare questions for a reason, a reason that renders your remarks about the person beside the point. Often there is an ascription of welfare to ‘society’ (social welfare) that proceeds from an analogy to individual welfare. That is what I identified as deeply problematic and since there is no analogy drawn between the relevant properties of the person and the properties of their constituent atoms (e.g. atoms aren’t sentient and don’t experience welfare changes) the comparison is invalid.

    “Society’ is a perfectly useful portmanteau term for ‘all individuals and the institutions with which they interact’ just like ‘team’ is for a collection of players and staff and administrative structures and orchestra for a collection of musicians and associated staff and administrative structures. Factual statements made on that basis are fine e.g. ‘the team toured Europe on a bus’, ‘the orchestra has widened its repertoire’ and ‘Australian society has become more ethnically diverse’. But faced with the statement ‘the orchestra is happier now compared to last year’ we’re entitled to ask exactly what is meant by that. Is it some statement about average happiness (measured somehow) of the musicians and other staff? What it can’t be is a statement about the happiness of the orchestra qua agent separate from the individuals that comprise it as in that sense (not every possible sense) there is no such thing. Ditto ‘there’s no such thing as society’ is an adequate response to claims that society is better or worse off that presuppose the existence of ‘society’ as a separate welfare-experiencing agent.

  13. @Wylie Bradford

    Overall I get your drift now and we seem to be on the same page. Our seemingly different positions might be a difference in emphasis.

    I agree that for reductionism purposes “‘atoms’ haven’t been a viable stopping point for a long time in physics terms”. I had typed some more text and then deleted it. I didn’t want to reduce matters further because I would have fallen foul of “Plasmaatron’s Law”. The commenter on this blog called plasmaatron (spelling?) justifiably accuses me of “theory dropping” if I mention quantum theory or worse, string theory, when I have no real scientific or mathematical grasp of either.

    You say “But faced with the statement ‘the orchestra is happier now compared to last year’ we’re entitled to ask exactly what is meant by that.”

    However, if there was a village with badly undernourished children and adults and a government or charity assisted with food aid as well as longer term water and farming projects then in one year we could very likely say accurately. “The village is better nourished now compared to last year.”

    Admittedly, we mean the people of the village not the entire village as such (as a collection of people and infrastructure etc.). I think the issue gets a bit semantic. When we use collective nouns like “village”, the context often enables us to determine whether we mean people or collections of things or both.

    “The village is better nourished.” is understandable though it might be better English to say “The villagers are better nourished.”

    “The village is less dilapidated”, would probably alert us we were talking about huts, houses, tracks, fences and so on.

    I use “nourished” as an example because good nourishment is a welfare goal more amenable to objective measures than happiness.

  14. It doesn’t take a market to create a free lunch. IDTAMTCAF.

    I think the effects of markets are over-emphasised and over-estimated in our system. To my mind, the market is a second order phenomenon at best. The first order phenomenon is production. Without production there can be no consumption and no market.

    I will make a needed detour and then come back to the point. I tend to think of “society” in sociological terms. We humans live in society with our fellows. This means we live in association and it specifically means what could be called the “four Cs”: closeness, communication, cooperation and competition.

    In some ways, “closeness” can just be “proximity” and proximity itself is now technologically mediated. Distant humans can be brought “close” in certain ways at certain times with technology.

    “Competition” also requires some comment. Most human competition in society (or in a city, a nation or the globe if you prefer) occurs within a rule-based system. Thus there is a cooperative level or phase which occurs first and which lays down the rules and the institutions of competition. This is true for games and business, for cricket or competitive tendering or general market place competition. Rule-less competition is very rare. Total war without any rules of war is the only situation I can think of where there would be completely rule-less competition between two groups. Each group nevertheless would have to obey cooperative rules internal to their own group in order to successfully prosecute total and rule-less war against another group.

    Coming back to IDTAMTCAF (It doesn’t take a market to create a free lunch).

    Have you ever painted house exteriors by yourself? If, like me, you have done so you will have realised things like this. Planks and trestles are very unwieldy objects even if they are not particularly heavy for the average man. Moving and re-setting trestles and planks by yourself in a crowded obstacle field of a house yard (trees, shrubs, carports, window awnings, gables, finistrations etc.) is an awkward, time-consuming business. So is running up and down trestles when you forget something or drop something.

    If two solo painters each paint a house alone (and even leaving aside the fact that they will need to buy or hire two plank/trestle kits, one set each) they will each have relatively slow, awkward time of it. If they work together, the jobs speed up. Each house takes less than half the time once two are painting it. Re-setting trestles and planks is quicker. Retrieving and passing up items is quicker. One painter can finish applying one pot while the other mixes the next batch and so on.

    When it comes to items being carried: Imagine a work site relying on human carrying ability. A certain item may be too heavy for one man to lift (even one end). Yet four men may successfully carry and place these items. Thus the increase in productivity is infinite in going from a one man work team to a four man work team. Here we have an infinite increase in productivity and nary a market in sight. By the way, these are Amish men so there is no market for their labour. 😉

    This will sort of illustrate why I think markets are a second order phenomenon.

  15. @jrkrideau

    Given TANSTAFL applies then presumably no one can make capital gains money on the stock market? Or it seems anywhere else.

    That’s pretty much what the standard version of the model says. I’m not aware of any version of the model that explains the massive returns to financial market operators.

  16. Capital gains should be made by decreasing inefficiencies – producingu more with the same inputs.

    Analysing inputs seems to be an almost impossible task; Benoit Mandelbroit said that financial markets are driven by “wild randomness”.

  17. A couple of quotes from John Ralston Saul:

    “[T]he free market may be a good, bad or insufficient idea, but, in any case, it is just a crude commercial code. Now it is regularly equated with or given credit for or even precedence over the freedom of man. But the freedom of man is a moral statement on the human condition, both in the practical and in the humanist sense. To equate it with a school of business is to betray a certain confusion. An unconscious unease.”

    “[Modern capitalism] is masterful at producing services people don’t need and in large part probably don’t want. It is brilliant at convincing people that they do need and want them. But it has difficulty turning itself to the production of those services which people really do need. Not only that, it often spends an enormous amount of time and effort convincing people that those services are either unrealistic, marginal or counterproductive.”

  18. I put this post below in the wrong thread. This is the right thread I think.

    Perhaps J.Q. or other supporters of “the market” can tell me how “Automobile Capitalism” was ever efficient in any sense. By “Automobile Capitalism” I simply mean the adaptation of our society, circa 1950 to the present, to entirely suit the automobile’s needs via cityscapes, roadscapes, landscapes, factories; indeed our whole built infrastructure, transport structure and production system. How was this “efficient” in any sense? (Except one trivial, worthless sense which I will come to.)

    1. Mass transit is more efficient economically and in energy/material terms.
    2. It (automobile culture) has contributed seriously to climate change.
    3. Injuries and fatalities were and are far higher than with other mass transit systems.
    4. Excessive amounts of land were and are devoted to automobile use.

    I could go on. There is no way that one can argue this was an efficient outcome unless one uses the flawed criteria that economic efficiency is building a lot of stuff with less resources than other methods whilst at the same time ignoring the needlessness, uselessness and even seriously damaging nature (to humans and the biosphere) of much of the stuff actually being built. Only by ignoring this huge flaw in its own logic can the “market economy” under really existing capitalism, claim efficiency for itself. Indeed, just about the only thing it has been efficient at is wrecking the planet and impoverishing third world people and others who suffered and suffer from imperialism and its successor systems.

  19. @John Quiggin
    Does “complete” include markets for capital goods and property rights? Because as I stated above your formulation seems to imply that inefficient owners of rights will not sell to more efficient potential owners of rights.

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